all

 SYNOPSIS
  Tests if all elements of an array are non-zero

 USAGE
  Char_Type all (Array_Type a [,Int_Type dim])

 DESCRIPTION
  The `all' function examines the elements of a numeric array and
  returns 1 if all elements are non-zero, otherwise it returns 0. If a
  second argument is given, then it specifies the dimension of the
  array over which the function is to be applied.  In this case, the
  result will be an array with the same shape as the input array minus
  the specified dimension.

 EXAMPLE
  Consider the 2-d array

      1       2       3       4        5
      6       7       8       9       10

  generated by

      a = _reshape ([1:10], [2, 5]);

  Then `all(a)' will return 1, and `all(a>3, 0)' will return
  a 1-d array

      [0, 0, 0, 1, 1]

  Similarly, `all(a>3, 1)' will return the 1-d array

      [0,1]


 SEE ALSO
  where, any

--------------------------------------------------------------

any

 SYNOPSIS
  Test if any element of an array is non-zero

 USAGE
  Char_Type any (Array_Type a [,Int_Type dim])

 DESCRIPTION
  The `any' function examines the elements of a numeric array and
  returns 1 if any element is both non-zero and not a NaN, otherwise
  it returns 0.  If a second argument is given, then it specifies
  the dimension of the array to be tested.

 EXAMPLE
  Consider the 2-d array

      1       2       3       4        5
      6       7       8       9       10

  generated by

      a = _reshape ([1:10], [2, 5]);

  Then `any(a==3)' will return 1, and `any(a==3, 0)'
  will return a 1-d array with elements:

      0        0       1       0       0


 SEE ALSO
  where, all

--------------------------------------------------------------

array_info

 SYNOPSIS
  Returns information about an array

 USAGE
  (Array_Type, Integer_Type, DataType_Type) array_info (Array_Type a)

 DESCRIPTION
  The `array_info' function returns information about the array `a'.
  It returns three values: an 1-d integer array specifying the
  size of each dimension of `a', the number of dimensions of
  `a', and the data type of `a'.

 EXAMPLE
  The `array_info' function may be used to find the number of rows
  of an array:

    define num_rows (a)
    {
       variable dims, num_dims, data_type;

       (dims, num_dims, data_type) = array_info (a);
       return dims [0];
    }


 SEE ALSO
  typeof, array_shape, length, reshape, _reshape

--------------------------------------------------------------

array_map

 SYNOPSIS
  Apply a function to each element of an array

 USAGE
  Array_Type array_map (type, func, arg0, ...)

    DataType_Type type;
    Ref_Type func;


 DESCRIPTION
  The `array_map' function may be used to apply a function to each
  element of an array and returns the resulting values as an array of
  the specified type.  The `type' parameter indicates what kind of
  array should be returned and generally corresponds to the return
  type of the function.  The `arg0' parameter should be an array
  and is used to determine the dimensions of the resulting array.  If
  any subsequent arguments correspond to an array of the same size,
  then those array elements will be passed in parallel with the first
  arrays arguments.

 EXAMPLE
  The first example illustrates how to apply the `strlen' function
  to an array of strings:

     S = ["", "Train", "Subway", "Car"];
     L = array_map (Integer_Type, &strlen, S);

  This is equivalent to:

     S = ["", "Train", "Subway", "Car"];
     L = Integer_Type [length (S)];
     for (i = 0; i < length (S); i++) L[i] = strlen (S[i]);


  Now consider an example involving the `strcat' function:

     files = ["slang", "slstring", "slarray"];

     exts = ".c";
     cfiles = array_map (String_Type, &strcat, files, exts);
     % ==> cfiles = ["slang.c", "slstring.c", "slarray.c"];

     exts =  [".a",".b",".c"];
     xfiles = array_map (String_Type, &strcat, files, exts);
     % ==> xfiles = ["slang.a", "slstring.b", "slarray.c"];


 NOTES
  Many mathematical functions already work transparantly on arrays.
  For example, the following two statements produce identical results:

     B = sin (A);
     B = array_map (Double_Type, &sin, A);


 SEE ALSO
  array_info, strlen, strcat, sin

--------------------------------------------------------------

array_reverse

 SYNOPSIS
  Reverse the elements of an array

 USAGE
  array_reverse (Array_Type a [,Int_Type i0, Int_Type i1] [,Int_Type dim])

 DESCRIPTION
  In its simplest form, the `array_reverse' function reverses the
  elements of an array.  If passed 2 or 4 arguments,
  `array_reverse' reverses the elements of the specified
  dimension of a multi-dimensional array.  If passed 3 or 4 arguments,
  the parameters `i0' and `i1' specify a range of elements
  to reverse.

 EXAMPLE
  If `a' is a one dimensional array, then

    array_reverse (a, i, j);
    a[[i:j]] = a[[j:i:-1]];

  are equivalent to one another.  However, the form using
  `array_reverse' is about 10 times faster than the version that
  uses explicit array indexing.

 SEE ALSO
  array_swap, transpose

--------------------------------------------------------------

array_shape

 SYNOPSIS
  Get the shape or dimensions of an array

 USAGE
  dims = array_shape (Array_Type a)

 DESCRIPTION
   This function returns an array representing the dimensionality or
   shape of a specified array.  The `array_info' function also
   returns this information but for many purposes the
   `array_shape' function is more convenient.

 SEE ALSO
  array_info, reshape

--------------------------------------------------------------

array_sort

 SYNOPSIS
  Sort an array

 USAGE
  Array_Type array_sort (Array_Type a [, String_Type or Ref_Type f])

 DESCRIPTION
  `array_sort' sorts the array `a' into ascending order and
  returns an integer array that represents the result of the sort. If
  the optional second parameter `f' is present, the function
  specified by `f' will be used to compare elements of `a';
  otherwise, a built-in sorting function will be used.

  If `f' is present, then it must be either a string representing
  the name of the comparison function, or a reference to the function.
  The sort function represented by `f' must be a S-Lang function
  that takes two arguments.  The function must return an integer that
  is less than zero if the first parameter is considered to be less
  than the second, zero if they are equal, and a value greater than
  zero if the first is greater than the second.

  If the comparison function is not specified, then a built-in comparison
  function appropriate for the data type will be used.  For example,
  if `a' is an array of character strings, then the sort will be
  performed using the `strcmp' function.

  The integer array returned by this function is simply an index array
  that indicates the order of the sorted array.  The input array
  `a' is not changed.

 EXAMPLE
  An array of strings may be sorted using the `strcmp' function
  since it fits the specification for the sorting function described
  above:

     A = ["gamma", "alpha", "beta"];
     I = array_sort (A, &strcmp);

  Alternatively, one may use

     variable I = array_sort (A);

  to use the built-in comparison function.

  After the `array_sort' has executed, the variable `I' will
  have the values `[2, 0, 1]'.  This array can be used to
  re-shuffle the elements of `A' into the sorted order via the
  array index expression `A = A[I]'.  This operation may also be
  written:

     A = A[array_sort(A)];


 EXAMPLE
  A homogeneous list may be sorted by first converting it to an array
  as follows:

    list = list[ array_sort( list_to_array(list) ) ];

  Alternatively one may use

    a = list_to_array (list);
    list[*] = a[array_sort(a)];

  to get the effect of an "in-place" sort.

 SEE ALSO
  strcmp, list_to_array

--------------------------------------------------------------

array_swap

 SYNOPSIS
  Swap elements of an array

 USAGE
  array_swap (Array_Type a, Int_Type i, Int_Type j)

 DESCRIPTION
  The `array_swap' function swaps the specified elements of an
  array.  It is equivalent to

    (a[i], a[j]) = (a[j], a[i]);

  except that it executes several times faster than the above construct.

 SEE ALSO
  array_reverse, transpose

--------------------------------------------------------------

cumsum

 SYNOPSIS
  Compute the cumulative sum of an array

 USAGE
  result = cumsum (Array_Type a [, Int_Type dim])

 DESCRIPTION
  The `cumsum' function performs a cumulative sum over the
  elements of a numeric array and returns the result.  If a second
  argument is given, then it specifies the dimension of the array to
  be summed over.  For example, the cumulative sum of
  `[1,2,3,4]', is the array `[1,1+2,1+2+3,1+2+3+4]', i.e.,
  `[1,3,6,10]'.

 SEE ALSO
  sum, sumsq

--------------------------------------------------------------

init_char_array

 SYNOPSIS
  Initialize an array of characters

 USAGE
  init_char_array (Array_Type a, String_Type s)

 DESCRIPTION
  The `init_char_array' function may be used to initialize a
  character array `a' by setting the elements of the array
  `a' to the corresponding characters of the string `s'.

 EXAMPLE
  The statements

     variable a = Char_Type [10];
     init_char_array (a, "HelloWorld");

   creates an character array and initializes its elements to the
   characters in the string `"HelloWorld"'.

 NOTES
   The character array must be large enough to hold all the characters
   of the initialization string.

 SEE ALSO
  bstring_to_array, strlen, strcat

--------------------------------------------------------------

_isnull

 SYNOPSIS
  Check an array for NULL elements

 USAGE
  Char_Type[] = _isnull (a[])

 DESCRIPTION
  This function may be used to test for the presence of NULL elements
  of an array.   Specifically, it returns a Char_Type array of
  with the same number of elements and dimensionality of the input
  array.  If an element of the input array is NULL, then the
  corresponding element of the output array will be set to 1,
  otherwise it will be set to 0.

 EXAMPLE
  Set all NULL elements of a string array `A' to the empty
  string `""':

     A[where(_isnull(A))] = "";


 NOTES
  It is important to understand the difference between `A==NULL'
  and `_isnull(A)'.  The latter tests all elements of `A'
  against NULL, whereas the former only tests `A' itself.

 SEE ALSO
  where, array_map

--------------------------------------------------------------

length

 SYNOPSIS
  Get the length of an object

 USAGE
  Integer_Type length (obj)

 DESCRIPTION
  The `length' function may be used to get information about the
  length of an object.  For simple scalar data-types, it returns 1.
  For arrays, it returns the total number of elements of the array.

 NOTES
  If `obj' is a string, `length' returns 1 because a
  String_Type object is considered to be a scalar.  To get the
  number of characters in a string, use the `strlen' function.

 SEE ALSO
  array_info, array_shape, typeof, strlen

--------------------------------------------------------------

max

 SYNOPSIS
  Get the maximum value of an array

 USAGE
  result = max (Array_Type a [,Int_Type dim])

 DESCRIPTION
  The `max' function examines the elements of a numeric array and
  returns the value of the largest element.  If a second argument is
  given, then it specifies the dimension of the array to be searched.
  In this case, an array of dimension one less than that of the input array
  will be returned with the corresponding elements in the specified
  dimension replaced by the maximum value in that dimension.

 EXAMPLE
  Consider the 2-d array

      1       2       3       4        5
      6       7       8       9       10

  generated by

      a = _reshape ([1:10], [2, 5]);

  Then `max(a)' will return `10', and `max(a,0)' will return
  a 1-d array with elements

      6       7       8       9       10


 NOTES
  This function ignores NaNs in the input array.

 SEE ALSO
  min, maxabs, sum, reshape

--------------------------------------------------------------

maxabs

 SYNOPSIS
  Get the maximum absolute value of an array

 USAGE
  result = maxabs (Array_Type a [,Int_Type dim])

 DESCRIPTION
  The `maxabs' function behaves like the `max' function
  except that it returns the maximum absolute value of the array. That
  is, `maxabs(x)' is equivalent to `max(abs(x)'. See the
  documentation for the `max' function for more information.

 SEE ALSO
  min, max, minabs

--------------------------------------------------------------

min

 SYNOPSIS
  Get the minimum value of an array

 USAGE
  result = min (Array_Type a [,Int_Type dim])

 DESCRIPTION
  The `min' function examines the elements of a numeric array and
  returns the value of the smallest element.  If a second argument is
  given, then it specifies the dimension of the array to be searched.
  In this case, an array of dimension one less than that of the input array
  will be returned with the corresponding elements in the specified
  dimension replaced by the minimum value in that dimension.

 EXAMPLE
  Consider the 2-d array

      1       2       3       4       5
      6       7       8       9       10

  generated by

      a = _reshape ([1:10], [2, 5]);

  Then `min(a)' will return `1', and `min(a,0)' will return
  a 1-d array with elements

      1        2       3       4       5


 NOTES
  This function ignores NaNs in the input array.

 SEE ALSO
  max, sum, reshape

--------------------------------------------------------------

minabs

 SYNOPSIS
  Get the minimum absolute value of an array

 USAGE
  result = minabs (Array_Type a [,Int_Type dim])

 DESCRIPTION
  The `minabs' function behaves like the `min' function
  except that it returns the minimum absolute value of the array. That
  is, `minabs(x)' is equivalent to `min(abs(x)'. See the
  documentation for the `min' function for more information.

 SEE ALSO
  min, max, maxabs

--------------------------------------------------------------

_reshape

 SYNOPSIS
  Copy an array to a new shape

 USAGE
  Array_Type _reshape (Array_Type A, Array_Type I)

 DESCRIPTION
  The `_reshape' function creates a copy of an array `A',
  reshapes it to the form specified by `I' and returns the result.
  The elements of `I' specify the new dimensions of the copy of
  `A' and must be consistent with the number of elements `A'.

 EXAMPLE
  If `A' is a `100' element 1-d array, a new 2-d array of
  size `20' by `5' may be created from the elements of `A'
  by

      B = _reshape (A, [20, 5]);


 NOTES
  The `reshape' function performs a similar function to
  `_reshape'.  In fact, the `_reshape' function could have been
  implemented via:

     define _reshape (a, i)
     {
        a = @a;     % Make a new copy
        reshape (a, i);
        return a;
     }


 SEE ALSO
  reshape, array_shape, array_info

--------------------------------------------------------------

reshape

 SYNOPSIS
  Reshape an array

 USAGE
  reshape (Array_Type A, Array_Type I)

 DESCRIPTION
  The `reshape' function changes the shape of `A' to have the
  shape specified by the 1-d integer array `I'.  The elements of `I'
  specify the new dimensions of `A' and must be consistent with
  the number of elements `A'.

 EXAMPLE
  If `A' is a `100' element 1-d array, it can be changed to a
  2-d `20' by `5' array via

      reshape (A, [20, 5]);

  However, `reshape(A, [11,5])' will result in an error because
  the `[11,5]' array specifies `55' elements.

 NOTES
  Since `reshape' modifies the shape of an array, and arrays are
  treated as references, then all references to the array will
  reference the new shape.  If this effect is unwanted, then use the
  `_reshape' function instead.

 SEE ALSO
  _reshape, array_info, array_shape

--------------------------------------------------------------

sum

 SYNOPSIS
  Sum over the elements of an array

 USAGE
  result = sum (Array_Type a [, Int_Type dim])

 DESCRIPTION
  The `sum' function sums over the elements of a numeric array and
  returns its result.  If a second argument is given, then it
  specifies the dimension of the array to be summed over.  In this
  case, an array of dimension one less than that of the input array
  will be returned.

  If the input array is an integer type, then the resulting value will
  be a Double_Type.  If the input array is a Float_Type,
  then the result will be a Float_Type.

 EXAMPLE
  The mean of an array `a' of numbers is

    sum(a)/length(a)


 SEE ALSO
  cumsum, sumsq, transpose, reshape

--------------------------------------------------------------

sumsq

 SYNOPSIS
  Sum over the squares of the elements of an array

 USAGE
  result = sumsq (Array_Type a [, Int_Type dim])

 DESCRIPTION
  The `sumsq' function sums over the squares of the elements of a
  numeric array and returns its result.  If a second argument is
  given, then it specifies the dimension of the array to be summed
  over.  In this case, an array of dimension one less than that of the
  input array will be returned.

  If the input array is an integer type, then the resulting value will
  be a Double_Type.  If the input array is a Float_Type,
  then the result will be a Float_Type.

  For complex arrays, the sum will be over the squares of the moduli of
  the complex elements.

 SEE ALSO
  cumsum, sumsq, hypot, transpose, reshape

--------------------------------------------------------------

transpose

 SYNOPSIS
  Transpose an array

 USAGE
  Array_Type transpose (Array_Type a)

 DESCRIPTION
  The `transpose' function returns the transpose of a specified
  array.  By definition, the transpose of an array, say one with
  elements `a[i,j,...k]' is an array whose elements are
  `a[k,...,j,i]'.

 SEE ALSO
  _reshape, reshape, sum, array_info, array_shape

--------------------------------------------------------------

where

 USAGE
  Array_Type where (Array_Type a [, Ref_Type jp])

 DESCRIPTION
  The `where' function examines a numeric array `a' and
  returns an integer array giving the indices of `a'
  where the corresponding element of `a' is non-zero.  The
  function accepts an optional Ref_Type argument that will be
  set to complement set of indices, that is, the indices where
  `a' is zero.  In fact

     i = where (a);
     j = where (not a);

  and

     i = where (a, &j);

  are equivalent, but the latter form is prefered since it executes
  about twice as fast as the former.

  Although this function may appear to be simple or even trivial, it
  is arguably one of the most important and powerful functions for
  manipulating arrays.

 EXAMPLE
  Consider the following:

    variable X = [0.0:10.0:0.01];
    variable A = sin (X);
    variable I = where (A < 0.0);
    A[I] = cos (X) [I];

  Here the variable `X' has been assigned an array of doubles
  whose elements range from `0.0' through `10.0' in
  increments of `0.01'.  The second statement assigns `A' to
  an array whose elements are the `sin' of the elements of `X'.
  The third statement uses the `where' function to get the indices of
  the elements of `A' that are less than 0.  Finally, the
  last statement replaces those elements of `A' by the cosine of the
  corresponding elements of `X'.

 NOTES
  Support for the optional argument was added to version 2.1.0.

 SEE ALSO
  wherefirst, wherelast, wherenot, array_info, array_shape, _isnull

--------------------------------------------------------------

wherenot

 SYNOPSIS
  Get indices where a numeric array is 0

 USAGE
  Array_Type wherenot (Array_Type)

 DESCRIPTION
  This function is equivalent to `where(not a)'.  See the
  documentation for `where' for more information.

 SEE ALSO
  where, wherefirst, wherelast

--------------------------------------------------------------

wherefirst

 SYNOPSIS
  Get the index of the first non-zero array element

 USAGE
  Int_Type wherefirst (Array_Type a [,start_index])

 DESCRIPTION
  The `wherefirst' function returns the index of the first
  non-zero element of a specified array.  If the optional parameter
  `start_index' is given, the search will take place starting
  from that index.  If a non-zero element is not found, the function
  will return NULL.

 NOTES
  The single parameter version of this function is equivalent to

     define wherefirst (a)
     {
        variable i = where (a);
        if (length(i))
          return i[0];
        else
          return NULL;
     }


 SEE ALSO
  where, wherelast

--------------------------------------------------------------

wherelast

 SYNOPSIS
  Get the index of the last non-zero array element

 USAGE
  Int_Type wherelast (Array_Type a [,start_index])

 DESCRIPTION
  The `wherelast' function returns the index of the last
  non-zero element of a specified array.  If the optional parameter
  `start_index' is given, the backward search will take place starting
  from that index.  If a non-zero element is not found, the function
  will return NULL.

 NOTES
  The single parameter version of this function is equivalent to

     define wherefirst (a)
     {
        variable i = where (a);
        if (length(i))
          return i[-1];
        else
          return NULL;
     }


 SEE ALSO
  where, wherefirst

--------------------------------------------------------------

assoc_delete_key

 SYNOPSIS
  Delete a key from an Associative Array

 USAGE
  assoc_delete_key (Assoc_Type a, String_Type k)

 DESCRIPTION
  The `assoc_delete_key' function deletes a key given by `k'
  from the associative array `a'.  If the specified key does not
  exist in `a', then this function has no effect.

 SEE ALSO
  assoc_key_exists, assoc_get_keys

--------------------------------------------------------------

assoc_get_keys

 SYNOPSIS
  Return all the key names of an Associative Array

 USAGE
  String_Type[] assoc_get_keys (Assoc_Type a)

 DESCRIPTION
  This function returns all the key names of an associative array
  `a' as an ordinary one dimensional array of strings.  If the
  associative array contains no keys, an empty array will be returned.

 SEE ALSO
  assoc_get_values, assoc_key_exists, assoc_delete_key, length

--------------------------------------------------------------

assoc_get_values

 SYNOPSIS
  Return all the values of an Associative Array

 USAGE
  Array_Type assoc_get_keys (Assoc_Type a)

 DESCRIPTION
  This function returns all the values in the associative array
  `a' as an array of proper type.  If the associative array
  contains no keys, an empty array will be returned.

 EXAMPLE
  Suppose that `a' is an associative array of type
  Integer_Type, i.e., it was created via

      variable a = Assoc_Type[Integer_Type];

  The the following may be used to print the values of the array in
  ascending order:

      static define int_sort_fun (x, y)
      {
         return sign (x - y);
      }
      define sort_and_print_values (a)
      {
         variable v = assoc_get_values (a);
         variable i = array_sort (v, &int_sort_fun);
         v = v[i];
         foreach (v)
           {
              variable vi = ();
              () = fprintf (stdout, "%d\n", vi);
           }
      }


 SEE ALSO
  assoc_get_values, assoc_key_exists, assoc_delete_key, array_sort

--------------------------------------------------------------

assoc_key_exists

 SYNOPSIS
  Check to see whether a key exists in an Associative Array

 USAGE
  Integer_Type assoc_key_exists (Assoc_Type a, String_Type k)

 DESCRIPTION
  The `assoc_key_exists' function may be used to determine whether
  or not a specified key `k' exists in an associative array `a'.
  It returns 1 if the key exists, or 0 if it does not.

 SEE ALSO
  assoc_get_keys, assoc_get_values, assoc_delete_key

--------------------------------------------------------------

array_to_bstring

 SYNOPSIS
  Convert an array to a binary string

 USAGE
  BString_Type array_to_bstring (Array_Type a)

 DESCRIPTION
   The `array_to_bstring' function returns the elements of an
   array `a' as a binary string.

 SEE ALSO
  bstring_to_array, init_char_array

--------------------------------------------------------------

bstring_to_array

 SYNOPSIS
  Convert a binary string to an array of characters

 USAGE
  UChar_Type[] bstring_to_array (BString_Type b)

 DESCRIPTION
   The `bstring_to_array' function returns an array of unsigned
   characters whose elements correspond to the bytes in the
   binary string.

 SEE ALSO
  array_to_bstring, init_char_array

--------------------------------------------------------------

bstrlen

 SYNOPSIS
  Get the length of a binary string

 USAGE
  UInt_Type bstrlen (BString_Type s)

 DESCRIPTION
  The `bstrlen' function may be used to obtain the length of a
  binary string.  A binary string differs from an ordinary string (a C
  string) in that a binary string may include null chracters.

 EXAMPLE

    s = "hello\0";
    len = bstrlen (s);      % ==> len = 6
    len = strlen (s);       % ==> len = 5


 SEE ALSO
  strlen, length

--------------------------------------------------------------

count_byte_occurances

 SYNOPSIS
  Count the number of occurances of a byte in a binary string

 USAGE
  UInt_Type count_byte_occurances (bstring, byte)

 DESCRIPTION
  This function returns the number of times the specified byte
  occurs in the binary string `bstr'.

 NOTES
  This function uses byte-semanics.  If character semantics are
  desired, use the `count_char_occurances' function.

 SEE ALSO
  count_char_occurances

--------------------------------------------------------------

pack

 SYNOPSIS
  Pack objects into a binary string

 USAGE
  BString_Type pack (String_Type fmt, ...)

 DESCRIPTION
  The `pack' function combines zero or more objects (represented
  by the ellipses above) into a binary string according to the format
  string `fmt'.

  The format string consists of one or more data-type specification
  characters defined by the following table:

     c     signed byte
     C     unsigned byte
     h     short
     H     unsigned short
     i     int
     I     unsigned int
     l     long
     L     unsigned long
     m     long long
     M     unsigned long long
     j     16 bit int
     J     16 bit unsigned int
     k     32 bit int
     K     32 bit unsigned int
     q     64 bit int
     Q     64 bit unsigned int
     f     float
     d     double
     F     32 bit float
     D     64 bit float
     s     character string, null padded
     S     character string, space padded
     z     character string, null padded
     x     a null pad character

  A decimal length specifier may follow the data-type specifier.  With
  the exception of the `s' and `S' specifiers, the length
  specifier indicates how many objects of that data type are to be
  packed or unpacked from the string.  When used with the `s',
  `S', or `z' specifiers, it indicates the field width to be
  used.  If the length specifier is not present, the length defaults
  to one.

  When packing, unlike the `s' specifier, the `z' specifier
  guarantees that at least one null byte will be written even if the
  field has to be truncated to do so.

  With the exception of `c', `C', `s', `S', and
  `x', each of these may be prefixed by a character that indicates
  the byte-order of the object:

     >    big-endian order (network order)
     <    little-endian order
     =    native byte-order

  The default is to use native byte order.

  When unpacking via the `unpack' function, if the length
  specifier is greater than one, then an array of that length will be
  returned.  In addition, trailing whitespace and null characters are
  stripped when unpacking an object given by the `S' specifier.
  Trailing null characters will be stripped from an object represented
  by the `z' specifier.  No such stripping is performed by the `s'
  specifier.

 EXAMPLE

     a = pack ("cc", 'A', 'B');         % ==> a = "AB";
     a = pack ("c2", 'A', 'B');         % ==> a = "AB";
     a = pack ("xxcxxc", 'A', 'B');     % ==> a = "\0\0A\0\0B";
     a = pack ("h2", 'A', 'B');         % ==> a = "\0A\0B" or "\0B\0A"
     a = pack (">h2", 'A', 'B');        % ==> a = "\0\xA\0\xB"
     a = pack ("<h2", 'A', 'B');        % ==> a = "\0B\0A"
     a = pack ("s4", "AB", "CD");       % ==> a = "AB\0\0"
     a = pack ("s4s2", "AB", "CD");     % ==> a = "AB\0\0CD"
     a = pack ("S4", "AB", "CD");       % ==> a = "AB  "
     a = pack ("S4S2", "AB", "CD");     % ==> a = "AB  CD"
     a = pack ("z4", "AB");             % ==> a = "AB\0\0"
     a = pack ("s4", "ABCDEFG");        % ==> a = "ABCD"
     a = pack ("z4", "ABCDEFG");        % ==> a = "ABC\0"


 SEE ALSO
  unpack, sizeof_pack, pad_pack_format, sprintf

--------------------------------------------------------------

pad_pack_format

 SYNOPSIS
  Add padding to a pack format

 USAGE
  BString_Type pad_pack_format (String_Type fmt)

 DESCRIPTION
  The `pad_pack_format' function may be used to add the
  appropriate padding characters to the format `fmt' such that the
  data types specified by the format will be properly aligned on word
  boundaries.  This is especially important when reading or writing files
  that assume the native alignment.

 SEE ALSO
  pack, unpack, sizeof_pack

--------------------------------------------------------------

sizeof_pack

 SYNOPSIS
  Compute the size implied by a pack format string

 USAGE
  UInt_Type sizeof_pack (String_Type fmt)

 DESCRIPTION
  The `sizeof_pack' function returns the size of the binary string
  represented by the format string `fmt'.  This information may be
  needed when reading a structure from a file.

 SEE ALSO
  pack, unpack, pad_pack_format

--------------------------------------------------------------

unpack

 SYNOPSIS
  Unpack Objects from a Binary String

 USAGE
  (...) = unpack (String_Type fmt, BString_Type s)

 DESCRIPTION
  The `unpack' function unpacks objects from a binary string
  `s' according to the format `fmt' and returns the objects to
  the stack in the order in which they were unpacked.  See the
  documentation of the `pack' function for details about the
  format string.

 EXAMPLE

    (x,y) = unpack ("cc", "AB");          % ==> x = 'A', y = 'B'
    x = unpack ("c2", "AB");              % ==> x = ['A', 'B']
    x = unpack ("x<H", "\0\xAB\xCD");     % ==> x = 0xCDABuh
    x = unpack ("xxs4", "a b c\0d e f");  % ==> x = "b c\0"
    x = unpack ("xxS4", "a b c\0d e f");  % ==> x = "b c"


 SEE ALSO
  pack, sizeof_pack, pad_pack_format

--------------------------------------------------------------

Assoc_Type

 SYNOPSIS
  An associative array or hash type

 DESCRIPTION
  An Assoc_Type object is like an array except that it is
  indexed using strings and not integers.  Unlike an Array_Type
  object, the size of an associative array is not fixed, but grows as
  objects are added to the array.  Another difference is that ordinary
  arrays represent ordered object; however, the ordering of the
  elements of an `Assoc_Type' object is unspecified.

  An Assoc_Type object whose elements are of some data-type
  `d' may be created using using

    A = Assoc_Type[d];

  For example,

    A = Assoc_Type[Int_Type];

  will create an associative array of integers.  To create an
  associative array capable of storing an arbitrary type, use the form

    A = Assoc_Type[];


  An optional parameter may be used to specify a default value for
  array elements.  For example,

   A = Assoc_Type[Int_Type, -1];

  creates an integer-valued associative array with a default element
  value of -1.  Then `A["foo"]' will return -1 if the key
  `"foo"' does not exist in the array.  Default values are
  available only if the type was specified when the associative array
  was created.

  The following functions may be used with associative arrays:

    assoc_get_keys
    assoc_get_values
    assoc_key_exists
    assoc_delete_key

  The `length' function may be used to obtain the number of
  elements in the array.

  The `foreach' construct may be used with associative arrays via
  one of the following forms:

      foreach k,v (A) {...}
      foreach k (A) using ("keys") { ... }
      foreach v (A) using ("values") { ... }
      foreach k,v (A) using ("keys", "values") { ... }

  In all the above forms, the loop is over all elements of the array
  such that `v=A[k]'.

 SEE ALSO
  List_Type, Array_Type, Struct_Type

--------------------------------------------------------------

List_Type

 SYNOPSIS
  A list object

 DESCRIPTION
  An object of type `List_Type' represents a list, which is
  defined as an ordered heterogeneous collection of objects.
  A list may be created using, e.g.,

    empty_list = {};
    list_with_4_items = {[1:10], "three", 9, {1,2,3}};

  Note that the last item of the list in the last example is also a
  list.  A List_Type object may be manipulated by the following
  functions:

    list_new
    list_insert
    list_append
    list_delete
    list_reverse
    list_pop

  A `List_Type' object may be indexed using an array syntax with
  the first item on the list given by an index of 0.  The
  `length' function may be used to obtain the number of elements
  in the list.

  A copy of the list may be created using the @ operator, e.g.,
  `copy = @list'.

  The `foreach' statement may be used with a List_Type
  object to loop over its elements:

    foreach elem (list) {....}


 SEE ALSO
  Array_Type, Assoc_Type, Struct_Type

--------------------------------------------------------------

String_Type

 SYNOPSIS
  A string object

 DESCRIPTION
  An object of type `String_Type' represents a string of bytes or
  characters, which in general have different semantics depending upon
  the UTF-8 mode.

  The string obeys byte-semantics when indexed as an
  array.  That is, `S[0]' will return the first byte of the
  string `S'.  For character semantics, the nth character in the
  string may be obtained using `substr' function.

  The `foreach' statement may be used with a String_Type
  object `S' to loop over its bytes:

    foreach b (S) {....}
    foreach b (S) using ("bytes") {....}

  To loop over its characters, the following form may be used:

    foreach c (S) using ("chars") {...}

  When UTF-8 mode is not in effect, the byte and character forms will
  produce the same sequence.  Otherwise, the string will be decoded
  to generate the (wide) character sequence.  If the string contains
  an invalid UTF-8 encoded character, sucessive bytes of the invalid
  sequence will be returned as negative integers.  For example,
  `"a\xAB\x{AB}"' specifies a string composed of the character
  `a', a byte `0xAB', and the character `0xAB'.  In
  this case,

     foreach c ("a\xAB\x{AB}") {...}

  will produce the integer-valued sequence `'a', -0xAB, 0xAB'.

 SEE ALSO
  Array_Type, _slang_utf8_ok

--------------------------------------------------------------

Struct_Type

 SYNOPSIS
  A structure datatype

 DESCRIPTION
  A Struct_Type object with fields `f1', `f2',...,
  `fN' may be created using

    s = struct { f1, f2, ..., fN };

  The fields may be accessed via the "dot" operator, e.g.,

     s.f1 = 3;
     if (s12.f1 == 4) s.f1++;

  By default, all fields will be initialized to NULL.

  A structure may also be created using the dereference operator (@):

    s = @Struct_Type ("f1", "f2", ..., "fN");
    s = @Struct_Type ( ["f1", "f2", ..., "fN"] );

  Functions for manipulating structure fields include:

     _push_struct_field_values
     get_struct_field
     get_struct_field_names
     set_struct_field
     set_struct_fields


  The `foreach' loop may be used to loop over elements of a linked
  list.  Suppose that first structure in the list is called
  `root', and that the `child' field is used to form the
  chain.  Then one may walk the list using:

     foreach s (root) using ("child")
      {
         % s will take on successive values in the list
          .
          .
      }

  The loop will terminate when the last elements `child' field is
  NULL.  If no ``linking'' field is specified, the field name will
  default to `next'.

  User-defined data types are similar to the `Struct_Type'.  A
  type, e.g., `Vector_Type' may be created using:

    typedef struct { x, y, z } Vector_Type;

  Objects of this type may be created via the @ operator, e.g.,

    v = @Vector_Type;

  It is recommended that this be used in a function for creating such
  types, e.g.,

    define vector (x, y, z)
    {
       variable v = @Vector_Type;
       v.x = x;
       v.y = y;
       v.z = z;
       return v;
    }

  The action of the binary and unary operators may be defined for such
  types.  Consider the "+" operator.  First define a function for
  adding two `Vector_Type' objects:

    static define vector_add (v1, v2)
    {
       return vector (v1.x+v2.x, v1.y+v2.y, v1.z, v2.z);
    }

  Then use

    __add_binary ("+", Vector_Type, &vector_add, Vector_Type, Vector_Type);

  to indicate that the function is to be called whenever the "+"
  binary operation between two `Vector_Type' objects takes place,
  e.g.,

    V1 = vector (1, 2, 3);
    V2 = vector (8, 9, 1);
    V3 = V1 + V2;

  will assigned the vector (9, 11, 4) to `V3'.  Similarly, the
  `"*"' operator between scalars and vectors may be defined using:

    static define vector_scalar_mul (v, a)
    {
       return vector (a*v.x, a*v.y, a*v.z);
    }
    static define scalar_vector_mul (a, v)
    {
       return vector_scalar_mul (v, a);
    }
    __add_binary ("*", Vector_Type, &scalar_vector_mul, Any_Type, Vector_Type);
    __add_binary ("*", Vector_Type, &vector_scalar_mul, Vector_Type, Any_Type);

  Related functions include:

    __add_unary
    __add_string
    __add_destroy


 SEE ALSO
  List_Type, Assoc_Type

--------------------------------------------------------------

File_Type

 SYNOPSIS
  A type representing a C stdio object

 DESCRIPTION
  An File_Type is the interpreter's representation of a C
  stdio FILE object and is usually created using the `fopen'
  function, i.e.,

    fp = fopen ("file.dat", "r");

  Functions that utilize the File_Type include:

    fopen
    fclose
    fgets
    fputs
    ferror
    feof
    fflush
    fprintf
    fseek
    ftell
    fread
    fwrite
    fread_bytes

  The `foreach' construct may be used with File_Type
  objects via one of the following forms:

   foreach line (fp) {...}
   foreach byte (A) using ("char") { ... }   % read bytes
   foreach line (A) using ("line") { ... }   % read lines (default)
   foreach line (A) using ("wsline") { ... } % whitespace stripped from lines


 SEE ALSO
  List_Type, Array_Type, Struct_Type

--------------------------------------------------------------

_bofeof_info

 SYNOPSIS
  Control the generation of function callback code

 USAGE
  Int_Type _bofeof_info

 DESCRIPTION
 This value of this variable dictates whether or not the S-Lang
 interpeter will generate code to call the beginning and end of
 function callback handlers.  The value of this variable is local to
 the compilation unit, but is inherited by other units loaded by the
 current unit.

 If the value of this variable is 1 when a function is defined, then
 when the function is executed, the callback handlers defined via
 `_set_bof_handler' and `_set_eof_handler' will be called.

 SEE ALSO
  _set_bof_handler, _set_eof_handler, _boseos_info

--------------------------------------------------------------

_boseos_info

 SYNOPSIS
  Control the generation of BOS/EOS callback code

 USAGE
  Int_Type _boseos_info

 DESCRIPTION
 This value of this variable dictates whether or not the S-Lang
 interpeter will generate code to call the beginning and end of
 statement callback handlers.  The value of this variable is local to
 the compilation unit, but is inherited by other units loaded by the
 current unit.

 The value of `_boseos_info' controls the generation of code for
 callbacks as follows:

   Value      Description
   -----------------------------------------------------------------
     0        No code for making callbacks will be produced.
     1        Callback generation will take place for all non-branching
              and looping statements.
     2        Same as for 1 with the addition that code will also be
              generated for branching statements (if, !if, loop, ...)
     3        Same as 2, but also including break and continue
              statements.

 A non-branching statement is one that does not effect chain of
 execution.  Branching statements include all looping statements,
 conditional statement, `break', `continue', and `return'.

 EXAMPLE
 Consider the following:

   _boseos_info = 1;
   define foo ()
   {
      if (some_expression)
        some_statement;
   }
   _boseos_info = 2;
   define bar ()
   {
      if (some_expression)
        some_statement;
   }

 The function `foo' will be compiled with code generated to call the
 BOS and EOS handlers when `some_statement' is executed.  The
 function `bar' will be compiled with code to call the handlers
 for both `some_expression' and `some_statement'.

 NOTES
 The `sldb' debugger and `slsh''s `stkcheck.sl' make use of this
 facility.

 SEE ALSO
  _set_bos_handler, _set_eos_handler, _bofeof_info

--------------------------------------------------------------

_clear_error

 SYNOPSIS
  Clear an error condition (deprecated)

 USAGE
  _clear_error ()

 DESCRIPTION
  This function has been deprecated.  New code should make use of
  try-catch exception handling.

  This function may be used in error-blocks to clear the error that
  triggered execution of the error block.  Execution resumes following
  the statement, in the scope of the error-block, that triggered the
  error.

 EXAMPLE
  Consider the following wrapper around the `putenv' function:

    define try_putenv (name, value)
    {
       variable status;
       ERROR_BLOCK
        {
          _clear_error ();
          status = -1;
        }
       status = 0;
       putenv (sprintf ("%s=%s", name, value);
       return status;
    }

  If `putenv' fails, it generates an error condition, which the
  `try_putenv' function catches and clears.  Thus `try_putenv'
  is a function that returns -1 upon failure and 0 upon
  success.

 SEE ALSO
  _trace_function, _slangtrace, _traceback

--------------------------------------------------------------

_set_bof_handler

 SYNOPSIS
  Set the beginning of function callback handler

 USAGE
  _set_bof_handler (Ref_Type func)

 DESCRIPTION
 This function is used to set the function to be called prior to the
 execution of the body S-Lang function but after its arguments have
 been evaluated, provided that function was defined
 with `_bofeof_info' set appropriately.  The callback function
 must be defined to take a single parameter representing the name of
 the function and must return nothing.

 EXAMPLE

    private define bof_handler (fun)
    {
      () = fputs ("About to execute $fun"$, stdout);
    }
    _set_bos_handler (&bof_handler);


 NOTES

 SEE ALSO
  _set_eof_handler, _boseos_info, _set_bos_handler

--------------------------------------------------------------

_set_bos_handler

 SYNOPSIS
  Set the beginning of statement callback handler

 USAGE
  _set_bos_handler (Ref_Type func)

 DESCRIPTION
 This function is used to set the function to be called prior to the
 beginning of a statement.  The function will be passed two
 parameters: the name of the file and the line number of the statement
 to be executed.  It should return nothing.

 EXAMPLE

    private define bos_handler (file, line)
    {
      () = fputs ("About to execute $file:$line\n"$, stdout);
    }
    _set_bos_handler (&bos_handler);


 NOTES
 The beginning and end of statement handlers will be called for
 statements in a file only if that file was compiled with the variable
 `_boseos_info' set to a non-zero value.

 SEE ALSO
  _set_eos_handler, _boseos_info, _bofeof_info

--------------------------------------------------------------

_set_eof_handler

 SYNOPSIS
  Set the beginning of function callback handler

 USAGE
  _set_eof_handler (Ref_Type func)

 DESCRIPTION
 This function is used to set the function to be called at the end of
 execution of a S-Lang function, provided that function was compiled with
 `_bofeof_info' set accordingly.

 The callback function will be passed no parameters and it must return
 nothing.

 EXAMPLE

   private define eof_handler ()
   {
     () = fputs ("Done executing the function\n", stdout);
   }
   _set_eof_handler (&eof_handler);


 SEE ALSO
  _set_bof_handler, _bofeof_info, _boseos_info

--------------------------------------------------------------

_set_eos_handler

 SYNOPSIS
  Set the end of statement callback handler

 USAGE
  _set_eos_handler (Ref_Type func)

 DESCRIPTION
 This function is used to set the function to be called at the end of
 a statement.  The function will be passed no parameters and it should
 return nothing.

 EXAMPLE

   private define eos_handler ()
   {
     () = fputs ("Done executing the statement\n", stdout);
   }
   _set_eos_handler (&eos_handler);


 NOTES
 The beginning and end of statement handlers will be called for
 statements in a file only if that file was compiled with the variable
 `_boseos_info' set to a non-zero value.

 SEE ALSO
  _set_bos_handler, _boseos_info, _bofeof_info

--------------------------------------------------------------

_slangtrace

 SYNOPSIS
  Turn function tracing on or off

 USAGE
  Integer_Type _slangtrace

 DESCRIPTION
  The `_slangtrace' variable is a debugging aid that when set to a
  non-zero value enables tracing when function declared by
  `_trace_function' is entered.  If the value is greater than
  zero, both intrinsic and user defined functions will get traced.
  However, if set to a value less than zero, intrinsic functions will
  not get traced.

 SEE ALSO
  _trace_function, _traceback, _print_stack

--------------------------------------------------------------

_traceback

 SYNOPSIS
  Generate a traceback upon error

 USAGE
  Integer_Type _traceback

 DESCRIPTION
  `_traceback' is an intrinsic integer variable whose bitmapped value
  controls the generation of the call-stack traceback upon error.
  When set to 0, no traceback will be generated.  Otherwise its value
  is the bitwise-or of the following integers:

       1        Create a full traceback
       2        Omit local variable information
       4        Generate just one line of traceback

  The default value of this variable is 4.

 NOTES
  Running `slsh' with the `-g' option causes this variable to be
  set to 1.

 SEE ALSO
  _boseos_info

--------------------------------------------------------------

_trace_function

 SYNOPSIS
  Set the function to trace

 USAGE
  _trace_function (String_Type f)

 DESCRIPTION
  `_trace_function' declares that the S-Lang function with name
  `f' is to be traced when it is called.  Calling
  `_trace_function' does not in itself turn tracing on.  Tracing
  is turned on only when the variable `_slangtrace' is non-zero.

 SEE ALSO
  _slangtrace, _traceback

--------------------------------------------------------------

_get_frame_info

 SYNOPSIS
  Get information about a stack frame

 USAGE
  Struct_Type _get_frame_info (Integer_Type depth)

 DESCRIPTION
  `_get_frame_info' returns a structure with information about
  the function call stack from of depth `depth'. The structure
  contains the following fields:

    file: The file that contains the code of the stack frame.
    line: The line number the file the stack frame is in.
    function: the name of the function containing the code of the stack
      frame; it might be NULL if the code isn't inside a function.
    locals: Array of String_Type containing the names of variables local
      to the stack frame; it might be NULL if the stack frame doesn't
      belong to a function.
    namespace: The namespace the code of this stack frame is in.


 SEE ALSO
  _get_frame_variable, _use_frame_namespace

--------------------------------------------------------------

_get_frame_variable

 SYNOPSIS
  Get the value of a variable local to a stack frame

 USAGE
  Any_Type _get_frame_variable (Integer_Type depth, String_Type name)

 DESCRIPTION
  This function returns value of the variable `name' in the stack
  frame at depth `depth'.  This might not only be a local variable but
  also variables from outer scopes, e.g., a variable private to the
  namespace.

  If no variable with this name is found an `UndefinedNameError'
  will be thrown.  An `VariableUninitializedError' will be
  generated if the variable has no value.

 SEE ALSO
  _get_frame_info, _use_frame_namespace

--------------------------------------------------------------

_use_frame_namespace

 SYNOPSIS
  Selects the namespace of a stack frame

 USAGE
  _use_frame_namespace (Integer_Type depth)

 DESCRIPTION
  This function sets the current namespace to the one belonging to the
  call stack frame at depth `depth'.

 SEE ALSO
  _get_frame_info, _get_frame_variable

--------------------------------------------------------------

access

 SYNOPSIS
  Check to see if a file is accessable

 USAGE
  Int_Type access (String_Type pathname, Int_Type mode)

 DESCRIPTION
 This functions checks to see if the current process has access to the
 specified pathname.  The `mode' parameter determines the type of
 desired access.  Its value is given by the bitwise-or of one or more
 of the following constants:

    R_OK   Check for read permission
    W_OK   Check for write permission
    X_OK   Check for execute permission
    F_OK   Check for existence


 The function will return 0 if process has the requested access
 permissions to the file, otherwise it will return -1 and set
 `errno' accordingly.

 Access to a file depend not only upon the file itself, but also upon
 the permissions of each of the directories in the pathname.  The
 checks are done using the real user and group ids of the process, and
 not using the effective ids.

 SEE ALSO
  stat_file

--------------------------------------------------------------

chdir

 SYNOPSIS
  Change the current working directory

 USAGE
  Int_Type chdir (String_Type dir)

 DESCRIPTION
  The `chdir' function may be used to change the current working
  directory to the directory specified by `dir'.  Upon success it
  returns zero.  Upon failure it returns `-1' and sets
  `errno' accordingly.

 SEE ALSO
  mkdir, stat_file

--------------------------------------------------------------

chmod

 SYNOPSIS
  Change the mode of a file

 USAGE
  Int_Type chmod (String_Type file, Int_Type mode)

 DESCRIPTION
  The `chmod' function changes the permissions of the specified
  file to those given by `mode'.  It returns `0' upon
  success, or `-1' upon failure setting `errno' accordingly.

  See the system specific documentation for the C library
  function `chmod' for a discussion of the `mode' parameter.

 SEE ALSO
  chown, stat_file

--------------------------------------------------------------

chown

 SYNOPSIS
  Change the owner of a file

 USAGE
  Int_Type chown (String_Type file, Int_Type uid, Int_Type gid)

 DESCRIPTION
  The `chown' function is used to change the user-id and group-id of
  `file' to `uid' and `gid', respectively.  It returns
  0 upon success and -1 upon failure, with `errno'
  set accordingly.

 NOTES
  On most systems, only the superuser can change the ownership of a
  file.

  Some systems do not support this function.

 SEE ALSO
  chmod, stat_file

--------------------------------------------------------------

getcwd

 SYNOPSIS
  Get the current working directory

 USAGE
  String_Type getcwd ()

 DESCRIPTION
  The `getcwd' function returns the absolute pathname of the
  current working directory.  If an error occurs or it cannot
  determine the working directory, it returns NULL and sets
  `errno' accordingly.

 NOTES
  Under Unix, OS/2, and MSDOS, the pathname returned by this function
  includes the trailing slash character.  It may also include
  the drive specifier for systems where that is meaningful.

 SEE ALSO
  mkdir, chdir, errno

--------------------------------------------------------------

hardlink

 SYNOPSIS
  Create a hard-link

 USAGE
  Int_Type hardlink (String_Type oldpath, String_Type newpath)

 DESCRIPTION
  The `hardlink' function creates a hard-link called
  `newpath' to the existing file `oldpath'.  If the link was
  sucessfully created, the function will return 0.  Upon error, the
  function returns -1 and sets `errno' accordingly.

 NOTES
  Not all systems support the concept of a hard-link.

 SEE ALSO
  symlink

--------------------------------------------------------------

listdir

 SYNOPSIS
  Get a list of the files in a directory

 USAGE
  String_Type[] listdir (String_Type dir)

 DESCRIPTION
  The `listdir' function returns the directory listing of all the
  files in the specified directory `dir' as an array of strings.
  It does not return the special files `".."' and `"."' as
  part of the list.

 SEE ALSO
  stat_file, stat_is, length

--------------------------------------------------------------

lstat_file

 SYNOPSIS
  Get information about a symbolic link

 USAGE
  Struct_Type lstat_file (String_Type file)

 DESCRIPTION
  The `lstat_file' function behaves identically to `stat_file'
  but if `file' is a symbolic link, `lstat_file' returns
  information about the link itself, and not the file that it
  references.

  See the documentation for `stat_file' for more information.

 NOTES
  On systems that do not support symbolic links, there is no
  difference between this function and the `stat_file' function.

 SEE ALSO
  stat_file, readlink

--------------------------------------------------------------

mkdir

 SYNOPSIS
  Create a new directory

 USAGE
  Int_Type mkdir (String_Type dir [,Int_Type mode])

 DESCRIPTION
  The `mkdir' function creates a directory whose name is specified
  by the `dir' parameter with permissions given by the optional
  `mode' parameter.  Upon success `mkdir' returns 0, or it
  returns `-1' upon failure setting `errno' accordingly.  In
  particular, if the directory already exists, the function will fail
  and set errno to EEXIST.

 EXAMPLE

     define my_mkdir (dir)
     {
        if (0 == mkdir (dir)) return;
        if (errno == EEXIST) return;
        throw IOError,
           sprintf ("mkdir %s failed: %s", dir, errno_string (errno));
     }


 NOTES
  The `mode' parameter may not be meaningful on all systems.  On
  systems where it is meaningful, the actual permissions on the newly
  created directory are modified by the process's umask.

 SEE ALSO
  rmdir, getcwd, chdir, fopen, errno

--------------------------------------------------------------

readlink

 SYNOPSIS
  String_Type readlink (String_Type path)

 USAGE
  Get the value of a symbolic link

 DESCRIPTION
  The `readlink' function returns the value of a symbolic link.
  Upon failure, NULL is returned and `errno' set accordingly.

 NOTES
  Not all systems support this function.

 SEE ALSO
  symlink, lstat_file, stat_file, stat_is

--------------------------------------------------------------

remove

 SYNOPSIS
  Delete a file

 USAGE
  Int_Type remove (String_Type file)

 DESCRIPTION
  The `remove' function deletes a file.  It returns 0 upon
  success, or -1 upon error and sets `errno' accordingly.

 SEE ALSO
  rename, rmdir

--------------------------------------------------------------

rename

 SYNOPSIS
  Rename a file

 USAGE
  Int_Type rename (String_Type old, String_Type new)

 DESCRIPTION
  The `rename' function renames a file from `old' to `new'
  moving it between directories if necessary.  This function may fail
  if the directories are not on the same file system.  It returns
  0 upon success, or -1 upon error and sets `errno' accordingly.

 SEE ALSO
  remove, errno

--------------------------------------------------------------

rmdir

 SYNOPSIS
  Remove a directory

 USAGE
  Int_Type rmdir (String_Type dir)

 DESCRIPTION
  The `rmdir' function deletes the specified directory.  It returns
  0 upon success or -1 upon error and sets `errno' accordingly.

 NOTES
  The directory must be empty before it can be removed.

 SEE ALSO
  rename, remove, mkdir

--------------------------------------------------------------

stat_file

 SYNOPSIS
  Get information about a file

 USAGE
  Struct_Type stat_file (String_Type file)

 DESCRIPTION
  The `stat_file' function returns information about `file'
  through the use of the system `stat' call.  If the stat call
  fails, the function returns NULL and sets errno accordingly.
  If it is successful, it returns a stat structure with the following
  integer-value fields:

    st_dev
    st_ino
    st_mode
    st_nlink
    st_uid
    st_gid
    st_rdev
    st_size
    st_atime
    st_mtime
    st_ctime

  See the C library documentation of `stat' for a discussion of the
  meanings of these fields.

 EXAMPLE
  The following example shows how the `stat_file' function may be
  used to get the size of a file:

     define file_size (file)
     {
        variable st;
        st = stat_file(file);
        if (st == NULL)
          throw IOError, "Unable to stat $file"$;
        return st.st_size;
     }


 SEE ALSO
  lstat_file, stat_is

--------------------------------------------------------------

stat_is

 SYNOPSIS
  Parse the st_mode field of a stat structure

 USAGE
  Char_Type stat_is (String_Type type, Int_Type st_mode)

 DESCRIPTION
  The `stat_is' function returns a boolean value according to
  whether or not the `st_mode' parameter is of the specified type.
  Specifically, `type' must be one of the strings:

     "sock"     (socket)
     "fifo"     (fifo)
     "blk"      (block device)
     "chr"      (character device)
     "reg"      (regular file)
     "lnk"      (link)
     "dir"      (dir)

  It returns a non-zero value if `st_mode' corresponds to
  `type'.

 EXAMPLE
  The following example illustrates how to use the `stat_is'
  function to determine whether or not a file is a directory:

     define is_directory (file)
     {
        variable st;

        st = stat_file (file);
        if (st == NULL) return 0;
        return stat_is ("dir", st.st_mode);
     }


 SEE ALSO
  stat_file, lstat_file

--------------------------------------------------------------

symlink

 SYNOPSIS
  Create a symbolic link

 USAGE
  status = symlink (String_Type oldpath, String_Type new_path)

 DESCRIPTION
  The `symlink' function may be used to create a symbolic link
  named `new_path' for  `oldpath'.  If successful, the function
  returns 0, otherwise it returns -1 and sets `errno' appropriately.

 NOTES
  This function is not supported on all systems and even if supported,
  not all file systems support the concept of a symbolic link.

 SEE ALSO
  readlink, hardlink

--------------------------------------------------------------

_$

 SYNOPSIS
  Expand the dollar-escaped variables in a string

 USAGE
  String_Type _$(String_Type s)

 DESCRIPTION
 This function expands the dollar-escaped variables in a string and
 returns the resulting string.

 EXAMPLE
 Consider the following code fragment:

     private variable Format = "/tmp/foo-$time.$pid";
     define make_filename ()
     {
        variable pid = getpid ();
        variable time = _time ();
        return _$(Format);
     }

 Note that the variable `Format' contains dollar-escaped
 variables, but because the `$' suffix was omitted from the
 string literal, the variables are not expanded.  Instead expansion is
 deferred until execution of the `make_filename' function through
 the use of the `_$' function.

 SEE ALSO
  eval, getenv

--------------------------------------------------------------

autoload

 SYNOPSIS
  Load a function from a file

 USAGE
  autoload (String_Type funct, String_Type file)

 DESCRIPTION
  The `autoload' function is used to declare `funct' to the
  interpreter and indicate that it should be loaded from `file'
  when it is actually used.  If `func' contains a namespace
  prefix, then the file will be loaded into the corresponding
  namespace.  Otherwise, if the `autoload' function is called
  from an execution namespace that is not the Global namespace nor an
  anonymous namespace, then the file will be loaded into the execution
  namespace.

 EXAMPLE
    Suppose `bessel_j0' is a function defined in the file
    `bessel.sl'.  Then the statement

      autoload ("bessel_j0", "bessel.sl");

    will cause `bessel.sl' to be loaded prior to the execution of
    `bessel_j0'.

 SEE ALSO
  evalfile, import

--------------------------------------------------------------

byte_compile_file

 SYNOPSIS
  Compile a file to byte-code for faster loading.

 USAGE
  byte_compile_file (String_Type file, Int_Type method)

 DESCRIPTION
  The `byte_compile_file' function byte-compiles `file'
  producing a new file with the same name except a `'c'' is added
  to the output file name.  For example, `file' is
  `"site.sl"', then this function produces a new file named
  `site.slc'.

 NOTES
  The `method' parameter is not used in the current
  implementation, but may be in the future.  For now, set
  it to `0'.

 SEE ALSO
  evalfile

--------------------------------------------------------------

eval

 SYNOPSIS
  Interpret a string as S-Lang code

 USAGE
  eval (String_Type expression [,String_Type namespace])

 DESCRIPTION
  The `eval' function parses a string as S-Lang code and executes the
  result.  If called with the optional namespace argument, then the
  string will be evaluated in the specified namespace.  If that
  namespace does not exist it will be created first.

  This is a useful function in many contexts including those where
  it is necessary to dynamically generate function definitions.

 EXAMPLE

    if (0 == is_defined ("my_function"))
      eval ("define my_function () { message (\"my_function\"); }");


 SEE ALSO
  is_defined, autoload, evalfile

--------------------------------------------------------------

evalfile

 SYNOPSIS
  Interpret a file containing S-Lang code

 USAGE
  Int_Type evalfile (String_Type file [,String_Type namespace])

 DESCRIPTION
  The `evalfile' function loads `file' into the interpreter
  and executes it.  If called with the optional namespace argument,
  the file will be loaded into the specified namespace, which will be
  created if necessary.  If given no namespace argument and the file
  has already been loaded, then it will be loaded again into an
  anonymous namespace.  A namespace argument given by the empty string
  will also cause the file to be loaded into a new anonymous namespace.

  If no errors were encountered, 1 will be returned; otherwise,
  a S-Lang exception will be thrown and the function will return zero.

 EXAMPLE

    define load_file (file)
    {
       try
       {
         () = evalfile (file);
       }
       catch AnyError;
    }


 NOTES
  For historical reasons, the return value of this function is not
  really useful.

  The file is searched along an application-defined load-path.  The
  `get_slang_load_path' and `set_slang_load_path' functions
  may be used to set and query the path.

 SEE ALSO
  eval, autoload, set_slang_load_path, get_slang_load_path

--------------------------------------------------------------

get_slang_load_path

 SYNOPSIS
  Get the value of the interpreter's load-path

 USAGE
  String_Type get_slang_load_path ()

 DESCRIPTION
  This function retrieves the value of the delimiter-separated search
  path used for loading files.  The delimiter is OS-specific and may
  be queried using the `path_get_delimiter' function.

 NOTES
  Some applications may not support the built-in load-path searching
  facility provided by the underlying library.

 SEE ALSO
  set_slang_load_path, path_get_delimiter

--------------------------------------------------------------

set_slang_load_path

 SYNOPSIS
  Set the value of the interpreter's load-path

 USAGE
  set_slang_load_path (String_Type path)

 DESCRIPTION
  This function may be used to set the value of the
  delimiter-separated search path used by the `evalfile' and
  `autoload' functions for locating files.  The delimiter is
  OS-specific and may be queried using the `path_get_delimiter'
  function.

 EXAMPLE

    public define prepend_to_slang_load_path (p)
    {
       variable s = stat_file (p);
       if (s == NULL) return;
       if (0 == stat_is ("dir", s.st_mode))
         return;

       p = sprintf ("%s%c%s", p, path_get_delimiter (), get_slang_load_path ());
       set_slang_load_path (p);
    }


 NOTES
  Some applications may not support the built-in load-path searching
  facility provided by the underlying library.

 SEE ALSO
  get_slang_load_path, path_get_delimiter, evalfile, autoload

--------------------------------------------------------------

get_import_module_path

 SYNOPSIS
  Get the search path for dynamically loadable objects

 USAGE
  String_Type get_import_module_path ()

 DESCRIPTION
  The `get_import_module_path' may be used to get the search path
  for dynamically shared objects.  Such objects may be made accessible
  to the application via the `import' function.

 SEE ALSO
  import, set_import_module_path

--------------------------------------------------------------

import

 SYNOPSIS
  Dynamically link to a specified module

 USAGE
  import (String_Type module [, String_Type namespace])

 DESCRIPTION
  The `import' function causes the run-time linker to dynamically
  link to the shared object specified by the `module' parameter.
  It searches for the shared object as follows: First a search is
  performed along all module paths specified by the application.  Then
  a search is made along the paths defined via the
  `set_import_module_path' function.  If not found, a search is
  performed along the paths given by the `SLANG_MODULE_PATH'
  environment variable.  Finally, a system dependent search is
  performed (e.g., using the `LD_LIBRARY_PATH' environment
  variable).

  The optional second parameter may be used to specify a namespace
  for the intrinsic functions and variables of the module.  If this
  parameter is not present, the intrinsic objects will be placed into
  the active namespace, or global namespace if the active namespace is
  anonymous.

  This function throws an `ImportError' if the specified module is
  not found.

 NOTES
  The `import' function is not available on all systems.

 SEE ALSO
  set_import_module_path, use_namespace, current_namespace, getenv, evalfile

--------------------------------------------------------------

set_import_module_path

 SYNOPSIS
  Set the search path for dynamically loadable objects

 USAGE
  set_import_module_path (String_Type path_list)

 DESCRIPTION
  The `set_import_module_path' may be used to set the search path
  for dynamically shared objects.  Such objects may be made accessible
  to the application via the `import' function.

  The actual syntax for the specification of the set of paths will
  vary according to the operating system.  Under Unix, a colon
  character is used to separate paths in `path_list'.  For win32
  systems a semi-colon is used.  The `path_get_delimiter'
  function may be used to get the value of the delimiter.

 SEE ALSO
  import, get_import_module_path, path_get_delimiter

--------------------------------------------------------------

add_doc_file

 SYNOPSIS
  Make a documentation file known to the help system

 USAGE
  add_doc_file (String_Type file)

 DESCRIPTION
  The `add_doc_file' is used to add a documentation file to the
  system.  Such files are searched by the
  `get_doc_string_from_file' function.  The `file' must be
  specified using the full path.

 SEE ALSO
  set_doc_files, get_doc_files, get_doc_string_from_file

--------------------------------------------------------------

_apropos

 SYNOPSIS
  Generate a list of functions and variables

 USAGE
  Array_Type _apropos (String_Type ns, String_Type s, Integer_Type flags)

 DESCRIPTION
  The `_apropos' function may be used to get a list of all defined
  objects in the namespace `ns' whose name matches the regular
  expression `s' and whose type matches those specified by
  `flags'.  It returns an array of strings containing the names
  matched.

  The second parameter `flags' is a bit mapped value whose bits
  are defined according to the following table

     1          Intrinsic Function
     2          User-defined Function
     4          Intrinsic Variable
     8          User-defined Variable


 EXAMPLE

    define apropos (s)
    {
      variable n, name, a;
      a = _apropos ("Global", s, 0xF);

      vmessage ("Found %d matches:", length (a));
      foreach name (a)
        message (name);
    }

  prints a list of all matches.

 NOTES
  If the namespace specifier `ns' is the empty string `""',
  then the namespace will default to the static namespace of the
  current compilation unit.

 SEE ALSO
  is_defined, sprintf, _get_namespaces

--------------------------------------------------------------

_function_name

 SYNOPSIS
  Returns the name of the currently executing function

 USAGE
  String_Type _function_name ()

 DESCRIPTION
  This function returns the name of the currently executing function.
  If called from top-level, it returns the empty string.

 SEE ALSO
  _trace_function, is_defined

--------------------------------------------------------------

__get_defined_symbols

 SYNOPSIS
  Get the symbols defined by the preprocessor

 USAGE
  Int_Type __get_defined_symbols ()

 DESCRIPTION
  The `__get_defined_symbols' functions is used to get the list of
  all the symbols defined by the S-Lang preprocessor.  It pushes each
  of the symbols on the stack followed by the number of items pushed.

 SEE ALSO
  is_defined, _apropos, _get_namespaces

--------------------------------------------------------------

get_doc_files

 SYNOPSIS
  Get the list of documentation files

 USAGE
  String_Type[] = get_doc_files ()

 DESCRIPTION
  The `get_doc_files' function returns the internal list of
  documentation files as an array of strings.

 SEE ALSO
  set_doc_files, add_doc_file, get_doc_string_from_file

--------------------------------------------------------------

get_doc_string_from_file

 SYNOPSIS
  Read documentation from a file

 USAGE
  String_Type get_doc_string_from_file ([String_Type f,] String_Type t)

 DESCRIPTION
  If called with two arguments, `get_doc_string_from_file' opens
  the documentation file `f' and searches it for topic `t'.
  Otherwise, it will search an internal list of documentation files
  looking for the documentation associated with the topic `t'.  If
  found, the documentation for `t' will be returned, otherwise the
  function will return NULL.

  Files may be added to the internal list via the `add_doc_file'
  or `set_doc_files' functions.

 SEE ALSO
  add_doc_file, set_doc_files, get_doc_files, _slang_doc_dir

--------------------------------------------------------------

_get_namespaces

 SYNOPSIS
  Returns a list of namespace names

 USAGE
  String_Type[] _get_namespaces ()

 DESCRIPTION
  This function returns a string array containing the names of the
  currently defined namespaces.

 SEE ALSO
  _apropos, use_namespace, implements, __get_defined_symbols

--------------------------------------------------------------

is_defined

 SYNOPSIS
  Determine if a variable or function is defined

 USAGE
  Integer_Type is_defined (String_Type name)

 DESCRIPTION
   This function is used to determine whether or not a function or
   variable of the given name has been defined.  If the specified name
   has not been defined, the function returns 0.  Otherwise, it
   returns a non-zero value that depends on the type of object
   attached to the name. Specifically, it returns one of the following
   values:

     +1     intrinsic function
     +2     slang function
     -1     intrinsic variable
     -2     slang variable
      0     undefined


 EXAMPLE
    Consider the function:

    define runhooks (hook)
    {
       if (2 == is_defined(hook)) eval(hook);
    }

    This function could be called from another S-Lang function to
    allow customization of that function, e.g., if the function
    represents a mode, the hook could be called to setup keybindings
    for the mode.

 SEE ALSO
  typeof, eval, autoload, __get_reference, __is_initialized

--------------------------------------------------------------

__is_initialized

 SYNOPSIS
  Determine whether or not a variable has a value

 USAGE
  Integer_Type __is_initialized (Ref_Type r)

 DESCRIPTION
   This function returns non-zero of the object referenced by `r'
   is initialized, i.e., whether it has a value.  It returns 0 if the
   referenced object has not been initialized.

 EXAMPLE
   The function:

    define zero ()
    {
       variable f;
       return __is_initialized (&f);
    }

  will always return zero, but

    define one ()
    {
       variable f = 0;
       return __is_initialized (&f);
    }

  will return one.

 SEE ALSO
  __get_reference, __uninitialize, is_defined, typeof, eval

--------------------------------------------------------------

_NARGS

 SYNOPSIS
  The number of parameters passed to a function

 USAGE
  Integer_Type _NARGS
   The value of the `_NARGS' variable represents the number of
   arguments passed to the function.  This variable is local to each
   function.

 EXAMPLE
   This example uses the `_NARGS' variable to print the list of
   values passed to the function:

     define print_values ()
     {
        variable arg;

        if (_NARGS == 0)
          {
             message ("Nothing to print");
             return;
          }
        foreach arg (__pop_args (_NARGS))
          vmessage ("Argument value is: %S", arg.value);
     }


 SEE ALSO
  __pop_args, __push_args, typeof

--------------------------------------------------------------

set_doc_files

 SYNOPSIS
  Set the internal list of documentation files

 USAGE
  set_doc_files (String_Type[] list)

 DESCRIPTION
  The `set_doc_files' function may be used to set the internal
  list of documentation files.  It takes a single parameter, which is
  required to be an array of strings.  The internal file list is set
  to the files specified by the elements of the array.

 EXAMPLE
  The following example shows how to add all the files in a specified
  directory to the internal list.  It makes use of the `glob'
  function that is distributed as part of `slsh'.

     files = glob ("/path/to/doc/files/*.sld");
     set_doc_files ([files, get_doc_files ()]);


 SEE ALSO
  get_doc_files, add_doc_file, get_doc_string_from_file

--------------------------------------------------------------

_slang_doc_dir

 SYNOPSIS
  Installed documentation directory

 USAGE
  String_Type _slang_doc_dir

 DESCRIPTION
   The `_slang_doc_dir' variable is a read-only variable that
   specifies the compile-time installation location of the S-Lang
   documentation.

 SEE ALSO
  get_doc_string_from_file

--------------------------------------------------------------

_slang_version

 SYNOPSIS
  The S-Lang library version number

 USAGE
  Integer_Type _slang_version

 DESCRIPTION
   `_slang_version' is a read-only variable that gives the version
   number of the S-Lang library.

 SEE ALSO
  _slang_version_string

--------------------------------------------------------------

_slang_version_string

 SYNOPSIS
  The S-Lang library version number as a string

 USAGE
  String_Type _slang_version_string

 DESCRIPTION
  `_slang_version_string' is a read-only variable that gives a
  string representation of the version number of the S-Lang library.

 SEE ALSO
  _slang_version

--------------------------------------------------------------

list_append

 SYNOPSIS
  Append an object to a list

 USAGE
  list_append (List_Type list, object [,Int_Type nth])

 DESCRIPTION
  The `list_append' function is like `list_insert' except
  this function appends the object to the the list.  The optional
  argument `nth' may be used to specify where the object is to be
  appended.  See the documentation on `list_insert' for more details.

 SEE ALSO
  list_insert, list_delete, list_pop, list_new, list_reverse

--------------------------------------------------------------

list_delete

 SYNOPSIS
  Remove an item from a list

 USAGE
  list_delete (List_Type list, Int_Type nth)

 DESCRIPTION
  This function removes the `nth' item in the specified list.
  The first item in the list corresponds to a value of `nth'
  equal to zero.  If `nth' is negative, then the indexing is with
  respect to the end of the list with the last item corresponding to
  `nth' equal to -1.

 SEE ALSO
  list_insert, list_append, list_pop, list_new, list_reverse

--------------------------------------------------------------

list_insert

 SYNOPSIS
  Insert an item into a list

 USAGE
  list_insert (List_Type list, object [,Int_Type nth])

 DESCRIPTION
  This function may be used to insert an object into the specified
  list.  With just two arguments, the object will be inserted at the
  beginning of the list.  The optional third argument, `nth', may
  be used to specify the insertion point.  The first item in the list
  corresponds to a value of `nth' equal to zero.  If `nth'
  is negative, then the indexing is with respect to the end of the
  list with the last item given by a value of `nth' equal to -1.

 NOTES
  It is important to note that

    list_insert (list, object, 0);

  is not the same as

    list = {object, list}

  since the latter creates a new list with two items, `object'
  and the old list.

 SEE ALSO
  list_append, list_pop, list_delete, list_new, list_reverse

--------------------------------------------------------------

list_new

 SYNOPSIS
  Create a new list

 USAGE
  List_Type list_new ()

 DESCRIPTION
  This function creates a new empty List_Type object.  Such a
  list may also be created using the syntax

     list = {};


 SEE ALSO
  list_delete, list_insert, list_append, list_reverse, list_pop

--------------------------------------------------------------

list_pop

 SYNOPSIS
  Extract an item from a list

 USAGE
  object = list_pop (List_Type list [, Int_Type nth])

 DESCRIPTION
  The `list_pop' function returns a object from a list deleting
  the item from the list in the process.  If the second argument is
  present, then it may be used to specify the position in the list
  where the item is to be obtained.  If called with a single argument,
  the first item in the list will be used.

 SEE ALSO
  list_delete, list_insert, list_append, list_reverse, list_new

--------------------------------------------------------------

list_reverse

 SYNOPSIS
  Reverse a list

 USAGE
  list_reverse (List_Type list)

 DESCRIPTION
  This function may be used to reverse the items in list.

 NOTES
  This function does not create a new list.  The list passed to the
  function will be reversed upon return from the function.  If it is
  desired to create a separate reversed list, then a separate copy
  should be made, e.g.,

     rev_list = @list;
     list_reverse (rev_list);


 SEE ALSO
  list_new, list_insert, list_append, list_delete, list_pop

--------------------------------------------------------------

list_to_array

 SYNOPSIS
  Convert a list into an array

 USAGE
  Array_Type list_to_array (List_Type list [,DataType_Type type])

 DESCRIPTION
 The `list_to_array' function converts a list of objects into an
 array of the same length and returns the result.  The optional
 argument may be used to specify the array's data type.  If no
 `type' is given, `list_to_array' tries to find the common
 data type of all list elements. This function will generate an
 exception if the list is empty and no type has been specified, or the
 objects in the list cannot be converted to a common type.

 NOTES
 A future version of this function may produce an Any_Type
 array for an empty or heterogeneous list.

 SEE ALSO
  length, typecast, __pop_list, typeof, array_sort

--------------------------------------------------------------

abs

 SYNOPSIS
  Compute the absolute value of a number

 USAGE
  y = abs(x)

 DESCRIPTION
  The `abs' function returns the absolute value of an arithmetic
  type.  If its argument is a complex number (Complex_Type),
  then it returns the modulus.  If the argument is an array, a new
  array will be created whose elements are obtained from the original
  array by using the `abs' function.

 SEE ALSO
  sign, sqr

--------------------------------------------------------------

acos

 SYNOPSIS
  Compute the arc-cosine of a number

 USAGE
  y = acos (x)

 DESCRIPTION
  The `acos' function computes the arc-cosine of a number and
  returns the result.  If its argument is an array, the
  `acos' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

acosh

 SYNOPSIS
  Compute the inverse cosh of a number

 USAGE
  y = acosh (x)

 DESCRIPTION
  The `acosh' function computes the inverse hyperbolic cosine of a number and
  returns the result.  If its argument is an array, the
  `acosh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

asin

 SYNOPSIS
  Compute the arc-sine of a number

 USAGE
  y = asin (x)

 DESCRIPTION
  The `asin' function computes the arc-sine of a number and
  returns the result.  If its argument is an array, the
  `asin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

asinh

 SYNOPSIS
  Compute the inverse-sinh of a number

 USAGE
  y = asinh (x)

 DESCRIPTION
  The `asinh' function computes the inverse hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `asinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

atan

 SYNOPSIS
  Compute the arc-tangent of a number

 USAGE
  y = atan (x)

 DESCRIPTION
  The `atan' function computes the arc-tangent of a number and
  returns the result.  If its argument is an array, the
  `atan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  atan2, cos, acosh, cosh

--------------------------------------------------------------

atan2

 SYNOPSIS
  Compute the arc-tangent of the ratio of two variables

 USAGE
  z = atan2 (y, x)

 DESCRIPTION
  The `atan2' function computes the arc-tangent of the ratio
  `y/x' and returns the result as a value that has the
  proper sign for the quadrant where the point (x,y) is located.  The
  returned value `z' will satisfy (-PI < z <= PI).  If either of the
  arguments is an array, an array of the corresponding values will be returned.

 SEE ALSO
  hypot, cos, atan, acosh, cosh

--------------------------------------------------------------

atanh

 SYNOPSIS
  Compute the inverse-tanh of a number

 USAGE
  y = atanh (x)

 DESCRIPTION
  The `atanh' function computes the inverse hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `atanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

ceil

 SYNOPSIS
  Round x up to the nearest integral value

 USAGE
  y = ceil (x)

 DESCRIPTION
  This function rounds its numeric argument up to the nearest integral
  value. If the argument is an array, the corresponding array will be
  returned.

 SEE ALSO
  floor, round

--------------------------------------------------------------

Conj

 SYNOPSIS
  Compute the complex conjugate of a number

 USAGE
  z1 = Conj (z)

 DESCRIPTION
  The `Conj' function returns the complex conjugate of a number.
  If its argument is an array, the `Conj' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Imag, abs

--------------------------------------------------------------

cos

 SYNOPSIS
  Compute the cosine of a number

 USAGE
  y = cos (x)

 DESCRIPTION
  The `cos' function computes the cosine of a number and
  returns the result.  If its argument is an array, the
  `cos' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

cosh

 SYNOPSIS
  Compute the hyperbolic cosine of a number

 USAGE
  y = cosh (x)

 DESCRIPTION
  The `cosh' function computes the hyperbolic cosine of a number and
  returns the result.  If its argument is an array, the
  `cosh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

--------------------------------------------------------------

feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

--------------------------------------------------------------

fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

--------------------------------------------------------------

floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

--------------------------------------------------------------

flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

--------------------------------------------------------------

fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

--------------------------------------------------------------

get_float_format

 SYNOPSIS
  Get the format for printing floating point values.

 USAGE
  String_Type get_float_format ()

 DESCRIPTION
 The `get_float_format' retrieves the format string used for
 printing single and double precision floating point numbers.  See the
 documentation for the `set_float_format' function for more
 information about the format.

 SEE ALSO
  set_float_format

--------------------------------------------------------------

hypot

 SYNOPSIS
  Compute sqrt(x^2+y^2)

 USAGE
  r = hypot (x [,y])

 DESCRIPTION
  If given two arguments, `hypot' function computes the quantity
  `sqrt(x^2+y^2)' except that it employs an algorithm that tries
  to avoid arithmetic overflow when `x' or `y' are large.
  If either argument is an array, an array of the corresponding values
  will be returned.

  If given a single array argument `x', the `hypot' function will
  compute `sqrt(sumsq(x))', where `sumsq(x)' computes the sum
  of the squares of the elements of `x'.

 SEE ALSO
  atan2, cos, atan, acosh, cosh, sum, sumsq

--------------------------------------------------------------

Imag

 SYNOPSIS
  Compute the imaginary part of a number

 USAGE
  i = Imag (z)

 DESCRIPTION
  The `Imag' function returns the imaginary part of a number.
  If its argument is an array, the `Imag' function will be applied to each
  element and the result returned as an array.

 SEE ALSO
  Real, Conj, abs

--------------------------------------------------------------

isinf

 SYNOPSIS
  Test for infinity

 USAGE
  y = isinf (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE infinity, or 0
  otherwise. If the argument is an array, an array of the
  corresponding values will be returned.

 SEE ALSO
  isnan, _Inf

--------------------------------------------------------------

isnan

 SYNOPSIS
  isnan

 USAGE
  y = isnan (x)

 DESCRIPTION
  This function returns 1 if x corresponds to an IEEE NaN (Not a Number),
  or 0 otherwise.  If the argument is an array, an array of
  the corresponding values will be returned.

 SEE ALSO
  isinf, _NaN

--------------------------------------------------------------

log

 SYNOPSIS
  Compute the logarithm of a number

 USAGE
  y = log (x)

 DESCRIPTION
  The `log' function computes the natural logarithm of a number and
  returns the result.  If its argument is an array, the
  `log' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh, log1p

--------------------------------------------------------------

log10

 SYNOPSIS
  Compute the base-10 logarithm of a number

 USAGE
  y = log10 (x)

 DESCRIPTION
  The `log10' function computes the base-10 logarithm of a number and
  returns the result.  If its argument is an array, the
  `log10' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

log1p

 SYNOPSIS
  Compute the logarithm of 1 plus a number

 USAGE
  y = log1p (x)

 DESCRIPTION
  The `log1p' function computes the natural logarithm of 1.0 plus
  `x' returns the result.  If its argument is an array, the
  `log1p' function will be applied to each element and the results
  returned as an array.

  This function should be used instead of `log(1+x)' to avoid
  numerical errors whenever `x' is close to 0.

 SEE ALSO
  log, expm1, cos, atan, acosh, cosh

--------------------------------------------------------------

_max

 SYNOPSIS
  Compute the maximum of two values

 USAGE
  z = _max (x,y)

 DESCRIPTION
  The `_max' function returns a floating point number equal to the
  maximum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  max, _min, min

--------------------------------------------------------------

_min

 SYNOPSIS
  Compute the minimum of two values

 USAGE
  z = _min (x,y)

 DESCRIPTION
  The `_min' function returns a floating point number equal to the
  minimum value of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 NOTES
  This function returns a floating point result even when both
  arguments are integers.

 SEE ALSO
  min, _max, max

--------------------------------------------------------------

mul2

 SYNOPSIS
  Multiply a number by 2

 USAGE
  y = mul2(x)

 DESCRIPTION
  The `mul2' function multiplies an arithmetic type by two and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array by
  using the `mul2' function.

 SEE ALSO
  sqr, abs

--------------------------------------------------------------

nint

 SYNOPSIS
  Round to the nearest integer

 USAGE
  i = nint(x)

 DESCRIPTION
  The `nint' rounds its argument to the nearest integer and
  returns the result.  If its argument is an array, a new array will
  be created whose elements are obtained from the original array
  elements by using the `nint' function.

 SEE ALSO
  round, floor, ceil

--------------------------------------------------------------

polynom

 SYNOPSIS
  Evaluate a polynomial

 USAGE
  Double_Type polynom([a0,a1,...aN], x [,use_factorial])

 DESCRIPTION
 The `polynom' function returns the value of the polynomial expression

     a0 + a1*x + a2*x^2 + ... + aN*x^N

 where the coefficients are given by an array of values
 `[a0,...,aN]'.  If `x' is an array, the function will
 return a corresponding array.  If the value of the optional
 `use_factorial' parameter is non-zero, then each term in the sum
 will be normalized by the corresponding factorial, i.e.,

     a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!


 NOTES
  Prior to version 2.2, this function had a different calling syntax
  and and was less useful.

  The `polynom' function does not yet support complex-valued
  coefficients.

  For the case of a scalar value of `x' and a small degree
  polynomial, it is more efficient to use an explicit expression.

 SEE ALSO
  exp

--------------------------------------------------------------

Real

 SYNOPSIS
  Compute the real part of a number

 USAGE
  r = Real (z)

 DESCRIPTION
  The `Real' function returns the real part of a number. If its
  argument is an array, the `Real' function will be applied to
  each element and the result returned as an array.

 SEE ALSO
  Imag, Conj, abs

--------------------------------------------------------------

round

 SYNOPSIS
  Round to the nearest integral value

 USAGE
  y = round (x)

 DESCRIPTION
  This function rounds its argument to the nearest integral value and
  returns it as a floating point result. If the argument is an array,
  an array of the corresponding values will be returned.

 SEE ALSO
  floor, ceil, nint

--------------------------------------------------------------

set_float_format

 SYNOPSIS
  Set the format for printing floating point values.

 USAGE
  set_float_format (String_Type fmt)

 DESCRIPTION
  The `set_float_format' function is used to set the floating
  point format to be used when floating point numbers are printed.
  The routines that use this are the traceback routines and the
  `string' function, any anything based upon the `string'
  function. The default value is `"%S"', which causes the number
  to be displayed with enough significant digits such that
  `x==atof(string(x))'.

 EXAMPLE

     set_float_format ("%S");        % default
     s = string (PI);                %  --> s = "3.141592653589793"
     set_float_format ("%16.10f");
     s = string (PI);                %  --> s = "3.1415926536"
     set_float_format ("%10.6e");
     s = string (PI);                %  --> s = "3.141593e+00"


 SEE ALSO
  get_float_format, string, sprintf, atof, double

--------------------------------------------------------------

sign

 SYNOPSIS
  Compute the sign of a number

 USAGE
  y = sign(x)

 DESCRIPTION
  The `sign' function returns the sign of an arithmetic type.  If
  its argument is a complex number (Complex_Type), the
  `sign' will be applied to the imaginary part of the number.  If
  the argument is an array, a new array will be created whose elements
  are obtained from the original array by using the `sign'
  function.

  When applied to a real number or an integer, the `sign' function
  returns -1, 0, or `+1' according to whether the number is
  less than zero, equal to zero, or greater than zero, respectively.

 SEE ALSO
  abs

--------------------------------------------------------------

sin

 SYNOPSIS
  Compute the sine of a number

 USAGE
  y = sin (x)

 DESCRIPTION
  The `sin' function computes the sine of a number and
  returns the result.  If its argument is an array, the
  `sin' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sinh

 SYNOPSIS
  Compute the hyperbolic sine of a number

 USAGE
  y = sinh (x)

 DESCRIPTION
  The `sinh' function computes the hyperbolic sine of a number and
  returns the result.  If its argument is an array, the
  `sinh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

sqr

 SYNOPSIS
  Compute the square of a number

 USAGE
  y = sqr(x)

 DESCRIPTION
  The `sqr' function returns the square of an arithmetic type.  If its
  argument is a complex number (Complex_Type), then it returns
  the square of the modulus.  If the argument is an array, a new array
  will be created whose elements are obtained from the original array
  by using the `sqr' function.

 NOTES
  For real scalar numbers, using `x*x' instead of `sqr(x)'
  will result in faster executing code.  However, if `x' is an
  array, then `sqr(x)' will execute faster.

 SEE ALSO
  abs, mul2

--------------------------------------------------------------

sqrt

 SYNOPSIS
  Compute the square root of a number

 USAGE
  y = sqrt (x)

 DESCRIPTION
  The `sqrt' function computes the square root of a number and
  returns the result.  If its argument is an array, the
  `sqrt' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  sqr, cos, atan, acosh, cosh

--------------------------------------------------------------

tan

 SYNOPSIS
  Compute the tangent of a number

 USAGE
  y = tan (x)

 DESCRIPTION
  The `tan' function computes the tangent of a number and
  returns the result.  If its argument is an array, the
  `tan' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

tanh

 SYNOPSIS
  Compute the hyperbolic tangent of a number

 USAGE
  y = tanh (x)

 DESCRIPTION
  The `tanh' function computes the hyperbolic tangent of a number and
  returns the result.  If its argument is an array, the
  `tanh' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  cos, atan, acosh, cosh

--------------------------------------------------------------

_ispos

 SYNOPSIS
  Test if a number is greater than 0

 USAGE
  Char_Type _ispos(x)

 DESCRIPTION
  This function returns 1 if a number is greater than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

_isneg

 SYNOPSIS
  Test if a number is less than 0

 USAGE
  Char_Type _isneg(x)

 DESCRIPTION
  This function returns 1 if a number is less than 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _ispos, _isnonneg

--------------------------------------------------------------

_isnonneg

 SYNOPSIS
  Test if a number is greater than or equal to 0

 USAGE
  Char_Type _isnonneg(x)

 DESCRIPTION
  This function returns 1 if a number is greater or equal to 0, and zero
  otherwise.  If the argument is an array, then the corresponding
  array of boolean (Char_Type) values will be returned.

 SEE ALSO
  _isneg, _isnonneg

--------------------------------------------------------------

errno

 SYNOPSIS
  Error code set by system functions

 USAGE
  Int_Type errno

 DESCRIPTION
  A---------------------------------------------

_diff

 SYNOPSIS
  Compute the absolute difference of two values

 USAGE
  y = _diff (x, y)

 DESCRIPTION
  The `_diff' function returns a floating point number equal to
  the absolute value of the difference of its two arguments.
  If either argument is an array, an array of the corresponding values
  will be returned.

 SEE ALSO
  abs

--------------------------------------------------------------

exp

 SYNOPSIS
  Compute the exponential of a number

 USAGE
  y = exp (x)

 DESCRIPTION
  The `exp' function computes the exponential of a number and
  returns the result.  If its argument is an array, the
  `exp' function will be applied to each element and the result returned
  as an array.

 SEE ALSO
  expm1, cos, atan, acosh, cosh

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expm1

 SYNOPSIS
  Compute exp(x)-1

 USAGE
  y = expm1(x)

 DESCRIPTION
  The `expm1' function computes `exp(x)-1' and returns the
  result.  If its argument is an array, the `expm1' function will
  be applied to each element and the results returned as an array.

  This function should be called whenever `x' is close to 0 to
  avoid the numerical error that would arise in a naive computation of
  `exp(x)-1'.

 SEE ALSO
  expm1, log1p, cos, atan, acosh, cosh

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feqs

 SYNOPSIS
  Test the approximate equality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
 This function compares two floating point numbers `a' and
 `b', and returns a non-zero value if they are equal to within a
 specified tolerance; otherwise 0 will be returned.  If either is an
 array, a corresponding boolean array will be returned.

 The tolerances are specified as relative and absolute differences via
 the optional third and fourth arguments.  If no optional arguments
 are present, the tolerances default to `reldiff=0.01' and
 `absdiff=1e-6'.  If only the relative difference has been
 specified, the absolute difference (`absdiff') will be taken to
 be 0.0.

 For the case when `|b|>=|a|', `a' and `b' are
 considered to be equal to within the specified tolerances if either
 `|b-a|<=absdiff' or `|b-a|/|b|<=reldiff' is true.

 SEE ALSO
  fneqs, fgteqs, flteqs

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fgteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a >= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, flteqs

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floor

 SYNOPSIS
  Round x down to the nearest integer

 USAGE
  y = floor (x)

 DESCRIPTION
  This function rounds its numeric argument down to the nearest
  integral value. If the argument is an array, the corresponding array
  will be returned.

 SEE ALSO
  ceil, round, nint

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flteqs

 SYNOPSIS
  Compare two numbers using specified tolerances
.

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

     (a <= b) or feqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fneqs, fgteqs

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fneqs

 SYNOPSIS
  Test the approximate inequality of two numbers

 USAGE
  Char_Type feqs (a, b [,reldiff [,absdiff]]

 DESCRIPTION
  This function is functionally equivalent to:

    not fneqs(a,b,...)

  See the documentation of `feqs' for more information.

 SEE ALSO
  feqs, fgteqs, flteqs

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get_float_format

 SYNOPSIS
  Get the form