NAME

Math::GMPf - perl interface to the GMP library's floating point (mpf) functions.

DEPENDENCIES

This module needs the GMP C library - available from:
http://gmplib.org

DESCRIPTION

A bigfloat module utilising the Gnu MP (GMP) library.
Basically this module simply wraps all of the 'mpf'
floating point functions provided by that library.
The documentation below extensively plagiarises the
GMP documentation at http://gmplib.org .
See the Math::GMPf test suite for some examples
of usage.

SYNOPSIS

use Math::GMPf qw(:mpf);

my $string = '.123542@2'; # mantissa = (.)12345
                      # exponent = 2
# my $string = '12.354'; # alternative string format

my $base = 10;

# Set the default precision to at least 80 bits.
Rmpf_set_default_prec(80);

# Create the Math::GMPf object
my $bn1 = Rmpf_init_set_str($string, $base);

# Create another Math::GMPf object that holds
# an initial value of zero, but with at least
# 131 bits of precision.
my $bn2 = Rmpf_init2(131);

# Create another Math::GMPf object that holds
# an initial value of zero, with default precision.
my $bn3 = Rmpf_init();

# Or just use the new() function:
my $bn4 = Math::GMPf->new(116.8129);

# Perform some operations ... see 'FUNCTIONS' below.

.
.

# print out the value held by $bn1 (in octal):
print Rmpf_get_str($bn1, 8, 0), "\n"; 

# print out the value held by $bn1 (in decimal):
print Rmpf_get_str($bn1, 10, 0);

# print out the value held by $bn1 (in base 29)
# using the (alternative) TRmpf_out_str()
# function. (This function doesn't print a newline.)
TRmpf_out_str(*STDOUT, 29, 0, $bn1);

MEMORY MANAGEMENT

Objects created with Rmpf_init* functions have been
blessed into package Math::GMPf. They will
therefore be automatically cleaned up by the
DESTROY() function whenever they go out of scope.

For each Rmpf_init* fnction there is a corresponding
Rmpf_init*_nobless function. If you wish you can 
create unblessed objects using these functions.
It will then be up to you to clean up the memory
associated with these objects by calling
Rmpf_clear($op), for each object. Alternatively the objects
will be cleaned up when the script ends. I don't know
why you would want to create unblessed objects. The
point is that you can if you want to.  

FUNCTIONS

  See the GMP documentation at http://gmplib.org

  These next 3 functions are demonstrated above:
  $rop   = Rmpf_init_set_str($str, $base); # 1 < abs($base) < 63
  $rop   = Rmpf_init2($bits); # $bits > 0
  $str = Rmpf_get_str($r, $base, $digits); # 1 < abs($base) < 63 
  The third argument to Rmpf_get_str() specifies the number
  of digits required to be output. Up to $digits digits
  will be generated.  Trailing zeros are not returned.  No
  more digits than can be accurately represented by OP are
  ever generated.  If $digits is 0 then that accurate
  maximum number of digits are generated.

  The following functions are simply wrappers around a GMP
  function of the same name. eg. Rmpf_swap() is a wrapper around
  mpf_swap() which is fully documented in the GMP manual at
  http://gmplib.org.

  "$rop", "$op1", "$op2", etc. are simply Math::GMPf objects
  - the return value of one of the Rmpf_init* functions
  (or their '_nobless' counterpart).
  They are in fact references to GMP structures.
  The "$rop" argument(s) contain the result(s) of the calculation
  being done, the "$op" argument(s) being the input(s) into that 
  calculation.
  Generally, $rop, $op1, $op2, etc. can be the same perl variable,
  though usually they will be distinct perl variables referencing
  distinct GMP structures.
  Eg. something like Rmpf_add($r1, $r1, $r1),
  where $r1 *is* the same reference to the same GMP structure,
  would add $r1 to itself and store the result in $r1. Think of it
  as $r1 += $r1. Otoh, Rmpf_add($r1, $r2, $r3), where each of the
  arguments is a different reference to a different GMP structure
  would add $r2 to $r3 and store the result in $r1. Think of it as
  $r1 = $r2 + $r3. Mostly, the first argument is the argument that 
  stores the result and subsequent arguments provide the input values.
  Exceptions to this can be found in some of the functions that
  actually return a value. 
  Like I say, see the GMP manual for details. I hope it's 
  intuitively obvious or quickly becomes so. Also see the test
  suite that comes with the distro for some examples of usage.

  "$ui" means any integer that will fit into a C 'unsigned long int'.

  "$si" means any integer that will fit into a C 'signed long int'.

  "$double" means any number (not necessarily integer) that will fit
  into a C 'double

  "$bool" means a value (usually a 'signed long int') in which
  the only interest is whether it's true or false.

  "$str" simply means a string of symbols that represent a number,
  eg "1234567890987654321234567@7" which might be a base 10 number,
  or "zsa34760sdfgq123r5@11" which would have to represent a base 36
  number (because "z" is a valid digit only in base 36). Valid
  bases for GMP numbers are 2 to 62 (inclusive).

  ########################

  INITIALIZATION FUNCTIONS

  Normally, a variable should be initialized once only or at least be
  cleared, using `Rmpf_clear', between initializations.
  'DESTROY' (which calls 'Rmpf_clear') is automatically called on 
  blessed objects whenever they go out of scope.

  First read the section 'MEMORY MANAGEMENT' (above).

  $bits = Rmpf_get_default_prec();
   Return the current default default precision.

  Rmpf_set_default_prec($bits); 
   Set the default precision to be *at least* $bits bits.  All
   subsequent calls to `Rmpf_init' will use this precision, but
   previously initialized variables are unaffected.

  $rop = Math::GMPf::new();
  $rop = Math::GMPf->new();
  $rop = new Math::GMPf();
  $rop = Rmpf_init();
  $rop = Rmpf_init_nobless();
   Initialize $rop to 0. The precision of $rop is undefined
   unless a default precision has already been established by
   a call to `Rmpf_set_default_prec'.

  $rop = Rmpf_init2($bits);
  $rop = Rmpf_init2_nobless($bits);
    Initialize $rop to 0 and set its precision to be
    *at least* $bits bits. 

  $bits = Rmpf_get_prec($op);
   Return the current precision of $op, in bits.

  Rmpf_set_prec($rop, $bits);
   Set the precision of $rop to be *at least* $bits bits.
   The value in $rop will be truncated to the new precision.
   This function requires internal reallocation of memory,
   and so should not be used in a tight loop.

  Rmpf_set_prec_raw($rop, $bits);
   Set the precision of $rop to be *at least* $bits bits, without
   changing the memory allocated. $bits must be no more than the 
   allocated precision for $rop, that being the precision when $rop
   was initialized, or in the most recent `Rmpf_set_prec'.
   The value in $rop is unchanged, and in particular if it had a
   higher precision than $bits it will retain that higher precision
   New values written to $rop will use the new value $bits.
   Before calling `Rmpf_clear' (which will happen when a blessed
   Math::GMPf object goes out of scope) or the full `Rmpf_set_prec',
   another `Rmpf_set_prec_raw' call must be made to restore $rop to
   its original allocated precision.  Failing to do so will have 
   unpredictable results.
   `Rmpf_get_prec' can be used before `Rmpf_set_prec_raw' to get the
   original allocated precision.  After `Rmpf_set_prec_raw' it
   reflects the $bits value set.
   `Rmpf_set_prec_raw' is an efficient way to use a Math::GMPf
   object at different precisions during a calculation, perhaps to
   gradually increase precision in an iteration, or just to use
   various different precisions for different purposes during a
   calculation.

  ####################

  ASSIGNMENT FUNCTIONS

  Rmpf_set($rop, $op); 
  Rmpf_set_ui($rop, $ui);
  Rmpf_set_si($rop, $si);
  Rmpf_set_d($rop, $double);
  Rmpf_set_z($rop, $z); # $z is a Math::GMPz object.
  Rmpf_set_q($rop, $q); # $q is a Math::GMPq object. 
   Set the value of $rop from the 2nd arg.

  Rmpf_set_str($rop, $str, $base);
   Set the value of $rop from the string in $str. The string is of
   the form `M@N' or, if the base is 10 or less, alternatively
   `MeN'. `M' is the mantissa and `N' is the exponent. The mantissa
   is always in the specified base. The exponent is either in the
   specified base or, if base is negative, in decimal. 
   The argument $base may be in the ranges 2 to 62, or -62 to -2.
   Negative values are used to specify that the exponent is in
   decimal. For bases up to 36, case is ignored; upper-case and
   lower-case letters have the same value; for bases 37 to 62,
   upper-case letter represent the usual 10..35 while lower-case
   letter represent 36..61. 
   Unlike the corresponding mpz function, the base will not be 
   determined from the leading characters of the string if base is 0.
   This is so that numbers like `0.23' are not interpreted as octal. 
   This function croaks if the entire string is not a valid number
   in base $base. 

  Rmpf_swap($rop1, $rop2);
   Swap $rop1 and $rop2. Both the values and the
   precisions of the two variables are swapped.

  ######################################

  COMBINED INITIALIZATION AND ASSIGNMENT

  NOTE: Do NOT use these functions if $rop has already
  been initialised. Instead use the Rmpz_set* functions 
  in 'Assignment Functions' (above)

  First read the section 'MEMORY MANAGEMENT' (above).

  $rop = Math::GMPf->new($arg);
  $rop = Math::GMPf::new($arg);
  $rop = new Math::GMPf($arg);
   Returns a Math::GMPf object with the value of $arg, with default
   precision. $arg can be either a number (signed integer, unsigned
   integer, signed fraction or unsigned fraction) or a string that 
   represents a numeric value. If $arg is a string, an optional
   additional argument that specifies the base of the number can
   be supplied to new(). If $arg is a string and no additional
   argument is supplied, base 10 is assumed.

  $rop = Rmpf_init_set($op);
  $rop = Rmpf_init_set_nobless($op);
  $rop = Rmpf_init_set_ui($ui);
  $rop = Rmpf_init_set_ui_nobless($ui);
  $rop = Rmpf_init_set_si($si);
  $rop = Rmpf_init_set_si_nobless($si);
  $rop = Rmpf_init_set_d($double);
  $rop = Rmpf_init_set_d_nobless($double);
   Initialise $rop and assign to it the value held by
   the functions argument. See the 'Rmpf_set*'
   functions above.

  $rop = Rmpf_init_set_str($str, $base);
  $rop = Rmpf_init_set_str_nobless($str, $base);
   Initialise $rop and assign to it the base $base
   value represented by $str. See the 'Rmpf_set_str'
   documentation above for details.

  ####################

  CONVERSION FUNCTIONS

  $double = Rmpf_get_d($op);
   Convert $op to a 'double'.

  $si = Rmpf_get_si($op);
  $ui = Rmpf_get_ui($op);
   Convert $op to a `signed long' or `unsigned long',
   truncating any fraction part.  If $op is too big for
   the return type, the result is undefined.

  ($double, $exp) = Rmpf_get_d_2exp($op);
   Find $double and $exp such that $double * (2 ** $exp),
   with 0.5<=abs($double)<1, is a good approximation to $op.
   This is similar to the standard C function `frexp'.

  $str = Rmpf_get_str($op, $base, $digits);
   Convert $op to a string of digits in base $base. $base can
   be 2 to 62.  Up to $digits digits will be generated. 
   Trailing zeros are not returned.  No more digits than can be
   accurately represented by $op are ever generated.  If $digits
   is 0 then that accurate maximum number of digits are generated.

  ($man, $exp) = Rmpf_deref2($op, $base, $digits);
   Returns the mantissa to $man (as a string of digits, prefixed with
   a minus sign if $op is negative), and returns the exponent to $exp.
   There's an implicit decimal point to the left of the first digit in
   $man. The third argument to Rmpf_deref2() specifies the number of
   digits required to be output in the mantissa. No more digits than
   can be accurately represented by $op are ever generated. If $digits
   is 0 then that accurate maximum number of digits are generated

  ####################

  ARITHMETIC FUNCTIONS

  Rmpf_add($rop, $op1, $op2);
  Rmpf_add_ui($rop, $op, $ui);
   $rop = 2nd arg + 3rd arg.

  Rmpf_sub($rop, $op1, $op2);
  Rmpf_sub_ui($rop, $op, $ui);
  Rmpf_ui_sub($rop, $ui, $op);
   $rop = 2nd arg - 3rd arg.

  Rmpf_mul($rop, $op1, $op2);
  Rmpf_mul_ui($rop, $op, $ui);
   $rop = 2nd arg * 3rd arg.

  Rmpf_div($rop, $op1, $op2); 
  Rmpf_ui_div($rop, $ui, $op);
  Rmpf_div_ui($rop, $op, $ui);
   $rop = 2nd arg / 3rd arg.

  Rmpf_sqrt($rop, $op);
  Rmpf_sqrt_ui($rop, $ui);
   $rop = 2nd arg ** 0.5.

  Rmpf_pow_ui($rop, $op, $ui);
   $ROP = $OP ** $ui.

  Rmpf_neg($rop, $op); 
   $rop = -$op.

  Rmpf_abs($rop, $op);
   $rop = abs($op).

  Rmpf_mul_2exp($rop, $op, $ui);
   $rop = $op * (2 ** $ui).

  Rmpf_div_2exp($rop, $op, $ui);
   $rop = $op / (2 ** $ui).

  #################### 

  COMPARISON FUNCTIONS

  $si = Rmpf_cmp($op1, $op2); 
  $si = Rmpf_cmp_ui($op, $ui);
  $si = Rmpf_cmp_si($op, $si);
  $si = Rmpf_cmp_d($op, $double);
   Compare 1st arg and 2nd arg.  Return a positive value if 
   1st arg >  2nd arg, zero if 1st arg = 2nd arg, and a 
   negative value if 1st arg < 2nd arg.

  Rmpf_eq($op1, $op2, $bits);
   Return non-zero if the first $bits bits of $op1 and $op2
   are equal, zero otherwise.  I.e., test if $op1 and $op2
   are approximately equal.
   Caution: Currently only whole limbs are compared, and only in an
   exact fashion.

  Rmpf_reldiff($rop, $op1, $op2);
   $rop = abs($op1 - $op2) / $op1.

  $si = Rmpf_sgn($op);
   Returns either +1 or -1 (or 0 if $op is zero).

  ##########################

  INPUT AND OUTPUT FUNCTIONS

  $bytes_read = Rmpf_inp_str($rop, $base);
   BEST TO USE TRmpf_inp_str INSTEAD.
   Read a string in base $base from STDIN, and put the read
   float in $rop. The string is of the form `M@N' or, if 
   $base is 10 or less, alternatively `MeN'.  `M' is the
   mantissa and `N' is the exponent.  The mantissa is always
   in the specified base. The exponent is either in the
   specified base or, if $base is negative,in decimal. The
   decimal point expected is taken from the current locale,
   on systems providing `localeconv'. The argument $base may
   be in the ranges 2 to 36, or -36 to -2. Negative values
   are used to specify that the exponent is in decimal.
   Unlike the corresponding `Math::GMPz' function, the
   base will not be determined from the leading characters
   of the string if $base is 0. This is so that numbers
   like `0.23' are not interpreted as octal.

  $bytes_read = TRmpf_inp_str($rop, $stream, $base);
   As for Rmpf_inp_str, except that there's the capability to read
   from somewhere other than STDIN.
   To read from STDIN:
      TRmpf_inp_str($rop, *stdin, $base);
   To read from an open filehandle (let's call it FH):
      TRmpf_inp_str($rop, \*FH, $base);

  $bytes_written = Rmpf_out_str([$prefix,] $op, $base, $digits  [, $suffix]);
   BEST TO USE TRmpf_out_str INSTEAD.
   Print $op to stream, as a string of digits. Return the number of
   bytes written, or if an error occurred, return 0. The mantissa is
   prefixed with an `0.' and is in the given base, which may vary 
   from 2 to 62 or from -2 to -36. An exponent is then printed,
   separated by an `e', or if the base is greater than 10 then by an
   `@'. The exponent is always in decimal. The decimal point follows
   the current locale, on systems providing localeconv. For bases in
   the range 2..36, digits and lower-case letters are used; for
   -2..-36, digits and upper-case letters are used; for 37..62, digits,
   upper-case letters, and lower-case letters (in that significance
   order) are used. Up to $digits will be printed from the mantissa,
   except that no more digits than are accurately representable by $op 
   will be printed. $digits can be 0 to select that accurate maximum. 
   The optional last argument ($suffix) is a string (eg "\n") that
   will be appended to the output. The optional first argument 
   ($prefix) is a string that will be prepended to the output. Note
   that either none, one, or both, of $prefix and $suffix may be
   supplied. ($bytes_written does not include the number of bytes in
   $suffix and $prefix.)

  $bytes_written = TRmpf_out_str([$prefix,] $stream, $base, $digits, $op, [, $suffix]);
   As for Rmpf_out_str, except that there's the capability to print
   to somewhere other than STDOUT. Note that the order of the args
   is different (to match the order of the mpf_out_str args).
   To print to STDERR:
      TRmpf_out_str(*stderr, $base, $digits, $op);
   To print to an open filehandle (let's call it FH):
      TRmpf_out_str(\*FH, $base, $digits, $op);

  #######################

  MISCELLANEOUS FUNCTIONS

  Rmpf_ceil($rop, $op); 
  Rmpf_floor($rop, $op); 
  Rmpf_trunc($rop, $op);
   Set $rop to $op rounded to an integer.  `Rmpf_ceil' rounds to the
   next higher integer, `mpf_floor' to the next lower, and
   `Rmpf_trunc' to the integer towards zero.

  $bool = Rmpf_integer_p($op);
   Return non-zero if $op is an integer.

  $bool = Rmpf_fits_ulong_p($op); 
  $bool = Rmpf_fits_slong_p($op);
  $bool = Rmpf_fits_uint_p($op); 
  $bool = Rmpf_fits_sint_p($op);
  $bool = Rmpf_fits_ushort_p($op);
  $bool = Rmpf_fits_sshort_p($op);
   Return non-zero if OP would fit in the respective C data
   type, when truncated to an integer.

  #######################

  RANDOM NUMBER FUNCTIONS 

  In the random number functions, @r is an array of 
  Math::GMPf objects (one for each random number that is
  required). $how_many is the number of random numbers you 
  want and must be equal to scalar(@r). $bits is simply the
  number of random bits required. Before calling the random
  number functions, $state must be initialised and seeded.

  $state = Math::GMPz::rand_init($op); # $op is the seed.
   Without Math::GMPz, you can't use this function. (There are
   better alternatives listed immediately below, anyway.)
   Initialises and seeds $state, ready for use with the random
   number functions. However, $state has not been blessed into
   any package, and therefore does not get cleaned up when it 
   goes out of scope. To avoid memory leaks you therefore need
   to call 'Math::GMPz::rand_clear($state);' once you have
   finished with it and before it goes out of scope. Also, it
   uses the default algorithm. Consider using the following
   initialisation and seeding routines - they provide a choice of
   algorithm, and there's no need to call rand_clear() when
   you've finished with them.

  $state = fgmp_randinit_default();
   This is the Math::GMPf interface to the gmp library function
  'gmp_randinit_default'.
   $state is blessed into package Math::GMPf::Random and will be
   automatically cleaned up when it goes out of scope.
   Initialize $state with a default algorithm. This will be a
   compromise between speed and randomness, and is recommended for
   applications with no special requirements. Currently this is
   the gmp_randinit_mt function (Mersenne Twister algorithm).

  $state = fgmp_randinit_mt();
   This is the Math::GMPf interface to the gmp library function
  'gmp_randinit_mt'.
   Currently identical to fgmp_randinit_default().

  $state = fgmp_randinit_lc_2exp($mpz, $ui, $m2exp);
   This is the Math::GMPf interface to the gmp library function
   'gmp_randinit_lc_2exp'. $mpz is a Math::GMP or Math::GMPz object,
   so one of those modules is required in order to make use of this
   function.
   $state is blessed into package Math::GMPf::Random and will be
   automatically cleaned up when it goes out of scope.
   Initialize $state with a linear congruential algorithm
   X = ($mpz*X + $ui) mod (2 ** $m2exp). The low bits of X in this
   algorithm are not very random. The least significant bit will have a
   period no more than 2, and the second bit no more than 4, etc. For
   this reason only the high half of each X is actually used. 
   When a random number of more than m2exp/2 bits is to be generated,
   multiple iterations of the recurrence are used and the results
   concatenated. 

  $state = fgmp_randinit_lc_2exp_size($ui);
   This is the Math::GMPf interface to the gmp library function
  'gmp_randinit_lc_2exp_size'.
   $state is blessed into package Math::GMPf::Random and will be
   automatically cleaned up when it goes out of scope.
   Initialize state for a linear congruential algorithm as per
   gmp_randinit_lc_2exp. a, c and m2exp are selected from a table,
   chosen so that $ui bits (or more) of each X will be used,
   ie. m2exp/2 >= $ui. 
   If $ui is bigger than the table data provides then the function fails
   and dies with an appropriate error message. The maximum value for $ui
   currently supported is 128. 

  $state2 = fgmp_randinit_set($state1);
   This is the Math::GMPf interface to the gmp library function
  'gmp_randinit_set'.
   $state2 is blessed into package Math::GMPf::Random and will be
   automatically cleaned up when it goes out of scope.
   Initialize $state2 with a copy of the algorithm and state from
   $state1.

  $state = fgmp_randinit_default_nobless();
  $state = fgmp_randinit_mt_nobless();
  $state = fgmp_randinit_lc_2exp_nobless($mpz, $ui, $m2exp);
  $state2 = fgmp_randinit_set_nobless($state1);
   As for the above comparable function, but $state is not blessed into
   any package. (Generally not useful - but they're available if you
   want them.)

  fgmp_randseed($state, $mpz); # $mpz is a Math::GMPz or Math::GMP object
  fgmp_randseed_ui($state, $ui);
   These are the Math::GMPz interfaces to the gmp library functions
   'gmp_randseed' and 'gmp_randseed_ui'.
   Seed an initialised (but not yet seeded) $state with $mpz/$ui.
   Either Math::GMP or Math::GMPz is required for 'gmp_randseed'.   

  Rmpf_urandomb(@r, $state, $bits, $how_many);
    Generate uniformly distributed random floats, all
    between 0 and 1, with $bits significant bits in the mantissa.

  Rmpf_random2(@r, $limbs, $exp, $how_many);
   Generate random floats of at most $limbs limbs, with long
   strings of zeros and ones in the binary representation.
   The exponent of the number is in the interval -$exp to $exp.
   This function is useful for testing functions and algorithms,
   since this kind of random numbers have proven to be more
   likely to trigger corner-case bugs.  Negative random 
   numbers are generated when $limbs is negative.

  $ui = fgmp_urandomb_ui($state, $bits);
   This is the Math::GMPf interface to the gmp library function
   'gmp_urandomb_ui'.
   Return a uniformly distributed random number of $bits bits, ie. in
   the range 0 to 2 ** ($bits - 1) inclusive. $bits must be less than or
   equal to the number of bits in an unsigned long. 

  $ui2 = fgmp_urandomm_ui($state, $ui1);
   This is the Math::GMPf interface to the gmp library function
   'gmp_urandomm_ui'.
   Return a uniformly distributed random number in the range 0 to
   $ui1 - 1, inclusive.  

  fgmp_randclear($state);
  Math::GMPz::rand_clear($state);
   Destroys $state, as also does Math::GMPf::Random::DESTROY - three
   identical functions.
   Use only if $state is an unblessed object - ie if it was initialised
   using Math::GMPz::rand_init() or one of the fgmp_randinit*_nobless
   functions. 

   ####################

   OPERATOR OVERLOADING

   Overloading works with numbers, strings (base 10 only)
   and Math::GMPf objects. Strings are coerced into
   Math::GMPf objects (with default precision).

   The following operators are overloaded:
    + - * / ** sqrt (Return values have default precision)
    += -= *= /= **= (Precision remains unchanged)
    < <= > >= == != <=>
    ! not
    abs (Return value has default precision)
    int (on perl 5.8 only, NA on perl 5.6.
         Return value has default precision.)
    = (The copy that gets modified will have default precision.
      The other copy retains the precision of the original)
    "" 

   Atempting to use the overloaded operators with objects that
   have been blessed into some package other than 'Math::GMPf'
   will not work.

   In those situations where the overload subroutine operates on 2
   perl variables, then obviously one of those perl variables is
   a Math::GMPf object. To determine the value of the other variable
   the subroutine works through the following steps (in order),
   using the first value it finds, or croaking if it gets
   to step 6:

   1. If the variable is an unsigned long then that value is used.
      The variable is considered to be an unsigned long if 
      (perl 5.8) the UOK flag is set or if (perl 5.6) SvIsUV() 
      returns true.

   2. If the variable is a signed long int, then that value is used.
      The variable is considered to be a signed long int if the
      IOK flag is set. (In the case of perls built with
      -Duse64bitint, the variable is treated as a signed long long
      int if the IOK flag is set.)

   3. If the variable is a double, then that value is used. The
      variable is considered to be a double if the NOK flag is set.

   4. If the variable is a string (ie the POK flag is set) then the
      base 10 value of that string is used. If the POK flag is set,
      but the string is not a valid base 10 number, the subroutine
      croaks with an appropriate error message.

   5. If the variable is a Math::GMPf object then the value of that
      object is used.

   6. If none of the above is true, then the second variable is
      deemed to be of an invalid type. The subroutine croaks with
      an appropriate error message.

  #####

  OTHER

  $GMP_version = Math::GMPf::gmp_v;
   Returns the version of the GMP library (eg 4.1.3). The function
   is not exportable.

  $GMP_cc = Math::GMPf::__GMP_CC;
  $GMP_cflags = Math::GMPf::__GMP_CFLAGS;
   These functions are not exportable.
   If Math::GMPf has been built against gmp-4.2.3 or later,
   returns respectively the CC and CFLAGS settings that were used
   to compile the gmp library.
   Returns undef if Math::GMPf has been built against an earlier
   version of the gmp library.

  $major = Math::GMPf::__GNU_MP_VERSION;
  $minor = Math::GMPf::__GNU_MP_VERSION_MINOR;
  $patchlevel = Math::GMPf::__GNU_MP_VERSION_PATCHLEVEL;
   Returns respectively the major, minor, and patchlevel numbers
   for the GMP library version used by Math::GMPf. (These 
   functions are in @EXPORT_OK and are therefore exportable by
   request.) 

  ################

  FORMATTED OUTPUT

  NOTE: The format specification can be found at:
  http://gmplib.org/manual/Formatted-Output-Strings.html#Formatted-Output-Strings
  However, the use of '*' to take an extra variable for width and
  precision is not allowed in this implementation. Instead, it is
  necessary to interpolate the variable into the format string - ie,
  instead of:
    Rmpf_printf("%*Zd\n", $width, $mpz);
  we need:
    Rmpf_printf("%${width}Zd\n", $mpz);

  $si = Rmpf_printf($format_string, $var);

   This function changed with the release of Math-GMPz-0.27.
   Now (unlike the GMP counterpart), it is limited to taking 2
   arguments - the format string, and the variable to be formatted.
   That is, you can format only one variable at a time.
   If there is no variable to be formatted, then the final arg
   can be omitted - a suitable dummy arg will be passed to the XS
   code for you. ie the following will work:
    Rmpf_printf("hello world\n");
   Returns the number of characters written, or -1 if an error
   occurred.

  $si = Rmpf_fprintf($fh, $format_string, $var);

   This function (unlike the GMP counterpart) is limited to taking
   3 arguments - the filehandle, the format string, and the variable
   to be formatted. That is, you can format only one variable at a time.
   If there is no variable to be formatted, then the final arg
   can be omitted - a suitable dummy arg will be passed to the XS
   code for you. ie the following will work:
    Rmpf_fprintf($fh, "hello world\n");
   Other than that, the rules outlined above wrt Rmpf_printf apply.
   Returns the number of characters written, or -1 if an error
   occurred.

  $si = Rmpf_sprintf($buffer, $format_string, $var);

   This function (unlike the GMP counterpart) is limited to taking
   3 arguments - the buffer, the format string, and the variable
   to be formatted. If there is no variable to be formatted, then the
   final arg can be omitted - a suitable dummy arg will be passed to
   the XS code for you. ie the following will work:
    Rmpf_sprintf($buffer, "hello world\n");
   $buffer must be large enough to accommodate the formatted string,
   and is truncated to the length of that formatted string.
   If you prefer to have the resultant string returned (rather
   than stored in $buffer), use Rmpf_sprintf_ret instead - which will
   also leave the length of $buffer unaltered.
   Returns the number of characters written, or -1 if an error
   occurred.

  $string = Rmpf_sprintf_ret($buffer, $format_string, $var);

   As for Rmpf_sprintf, but returns the formatted string, as well as
   storing it in $buffer. $buffer needs to be large enough to 
   accommodate the formatted string. The length of $buffer will be
   unaltered.

  $si = Rmpf_snprintf($buffer, $bytes, $format_string, $var);

   Form a null-terminated string in $buffer. No more than $bytes 
   bytes will be written. To get the full output, $bytes must be
   enough for the string and null-terminator. $buffer must be large
   enough to accommodate the string and null-terminator, and is
   truncated to the length of that string (and null-terminator).
   The return value is the total number of characters which ought
   to have been produced, excluding the terminating null.
   If $si >= $bytes then the actual output has been truncated to
   the first $bytes-1 characters, and a null appended.
   This function (unlike the GMP counterpart) is limited to taking
   4 arguments - the buffer, the maximum number of bytes to be
   returned, the format string, and the variable to be formatted.
   If there is no variable to be formatted, then the final arg can
   be omitted - a suitable dummy arg will be passed to the XS code
   for you. ie the following will work:
    Rmpf_snprintf($buffer, 12, "hello world");
   If you prefer to have the resultant string returned (rather
   than stored in $buffer), use Rmpf_snprintf_ret instead - which will
   also leave the length of $buffer unaltered.

  $string = Rmpf_snprintf_ret($buffer, $bytes, $format_string, $var);

   As for Rmpf_snprintf, but returns the formatted string, as well as
   storing it in $buffer. $buffer needs to be large enough to 
   accommodate the formatted string. The length of $buffer will be
   unaltered. The length of $string (as reported by perl's length
   function) will be no greater than $bytes.

  ###############################
  ###############################

BUGS

You can get segfaults if you pass the wrong type of
argument to the functions - so if you get a segfault, the
first thing to do is to check that the argument types 
you have supplied are appropriate.

LICENSE

This program is free software; you may redistribute it and/or 
modify it under the same terms as Perl itself.
Copyright 2006-2008, 2009, 2010, Sisyphus

AUTHOR

Sisyphus <sisyphus at(@) cpan dot (.) org>