NAME
Math::LongDouble - perl interface to C's long double operations (for perls that don't already have that capability)
BUGS
This module has bugs on perls built with a Microsoft compiler (eg
ActivePerl) - even if the binaries installed onto the MSVC-built
perl were built using MinGW on a MinGW-built perl such as Strawberry
Perl (where no such problem exists).
By some means that is still unclear, the 'long double' precision
can apparently be reduced to 'double' precision whenever a
Math::LongDouble object is raised to a power (or a square root taken)
on MSVC-built perls.
This bug manifests itself in causing some test failures in t/cmp.t
and t/pow.t.DESCRIPTION
If your perl's NV is a 'long double', then there's no point in using this
module. But if your perl's NV is a 'double', then this module provides
you with a way of performing arithmetic operations with long double
precision.
use Math::LongDouble qw(:all);
my $arg = 32.1;
my $ld1 = Math::LongDouble->new($arg);# Stringify $arg, then assign
# using C's strtold()
my $ld2 = NVtoLD($arg); # Assign the NV 32.1 to $ld2.OVERLOADING
The following operations are overloaded:
+ - * / **
+= -= *= /= **=
!= == <= >= <=> < >
++ --
=
abs bool ! int print
sqrt log exp
sin cos atan2
Arguments to the overloaded operations must be Math::LongDouble
objects.
$ld = $ld + 3.1; # currently an error. Do instead:
$ld = $ld + Math::LongDouble->new('3.1');ASSIGNMENT FUNCTIONS
The following create and assign a new Math::LongDouble.
$ld = Math::LongDouble->new($arg);
Returns a Math::LongDouble object to which the numeric value of $arg
has been assigned.
If no arg is supplied then $ld will be NaN.
$ld = UVtoLD($arg);
Returns a Math::LongDouble object to which the numeric (unsigned
integer) value of $arg has been assigned.
$ld = IVtoLD($arg);
Returns a Math::LongDouble object to which the numeric (signed
integer) value of $arg has been assigned.
$ld = NVtoLD($arg);
Returns a Math::LongDouble object to which the numeric (floating
point) value of $arg has been assigned.
$ld2 = LDtoLD($ld1);
Returns a Math::LongDouble object that is a copy of the
Math::LongDouble object provided as the argument.
Courtesy of overloading, this is in effect no different to doing:
$ld2 = $ld1;
$ld = STRtoLD($str);
Returns a Math::LongDouble object that has the value of the string
$str.ASSIGNMENT OF INF, NAN, UNITY and ZERO
$ld = InfLD($sign);
If $sign < 0, returns a Math::LongDouble object set to
negative infinity; else returns a Math::LongDouble object set
to positive infinity.
$ld = NaNLD($sign);
If $sign < 0, returns a Math::longDouble object set to
negative NaN; else returns a Math::LongDouble object set to
positive NaN. It may be problematical as to whether a NaN
with the correct sign has been returned ... but, either way,
it should return a NaN.
$ld = ZeroLD($sign);
If $sign < 0, returns a Math::LongDouble object set to
negative zero; else returns a Math::LongDouble object set to
zero.
$ld = UnityLD($sign);
If $sign < 0, returns a Math::LongDouble object set to
negative one; else returns a Math::LongDouble object set to
one.
ld_set_prec($precision);
Sets the precision of stringified values to $precision decimal
digits.
$precision = ld_get_prec();
Returns the precision (in decimal digits) that will be used
when stringifying values (by printing them, or calling
LDtoSTR).RETRIEVAL FUNCTIONS
The following functions provide ways of seeing the value of
Math::LongDouble objects.
$nv = LDtoNV($ld);
This function returns the value of the Math::LongDouble object to
a perl scalar (NV). It may not translate the value accurately.
$string = LDtoSTR($ld);
Returns the value of the Math::LongDouble object as a string.
The returned string will contain the same as is displayed by
"print $ld", except that print() will strip the trailing zeroes
in the mantissa (significand) whereas LDtoSTR won't.
By default, provides 18 decimal digits of precision. This can be
altered by specifying the desired precision (in decimal digits)
in a call to ld_set_prec.
$string = LDtoSTRP($ld, $precision);
Same as LDtoSTR, but takes an additional arg that specifies the
precision (in decimal digits) of the stringified return value.OTHER FUNCTIONS
$bool = is_NaNLD($ld);
Returns 1 if $ld is a Math::LongDouble NaN.
Else returns 0
$int = is_InfLD($ld)
If the Math::LongDouble object $ld is -inf, returns -1.
If it is +inf, returns 1.
Otherwise returns 0.
$int = is_ZeroLD($ld);
If the Math::LongDouble object $ld is -0, returns -1.
If it is zero, returns 1.
Otherwise returns 0.
$int = cmp_NV($ld, $nv);
$nv can be any perl number - ie NV, UV or IV.
If the Math::LongDouble object $ld < $nv returns -1.
If it is > $nv, returns 1.
Otherwise returns 0.BASE CONVERSIONS
$DBL_DIG = LD_DBL_DIG; # The value specified by float.h's DBL_DIG.
# Will be set to 0 if float.h doesn't define
# DBL_DIG.
$LDBL_DIG = LD_LDBL_DIG; # The value specified by float.h's LDBL_DIG.
# Will be set to 0 if float.h doesn't define
# LDBL_DIG.
$min_prec = ld_min_inter_prec($orig_base, $orig_length, $to_base);
$max_len = ld_max_orig_len($orig_base, $to_base, $to_prec);
$min_base = ld_min_inter_base($orig_base, $orig_length, $to_prec);
$max_base = ld_max_orig_base($orig_length, $to_base, $to_prec);
The last 4 of the above functions establish the relationship between
$orig_base, $orig_length, $to_base and $to_prec.
Given any 3 of those 4, there's a function there to determine the
value of the 4th.
Let's say we have some base 10 floating point numbers comprising 16
significant digits, and we want to convert those numbers to a base 2
data type (say, 'long double').
If we then convert the value of that long double to a 16-digit base 10
float are we guaranteed of getting the original value back ?
It all depends upon the precision of the 'long double' type, and the
min_inter_prec() subroutine will tell you what the minimum
required precision is (in order to be sure of getting the original
value back). We have:
$min_prec = ld_min_inter_prec($orig_base, $orig_length, $to_base);
In our example case that becomes:
$min_prec = ld_min_inter_prec(10, 16, 2);
which will set $min_prec to 55.
That is, so long as the long double type has a precision of at least 55
bits, you can pass 16-digit, base 10, floating point values to it and
back again, and be assured of retrieving the original value.
(Naturally, this is assuming absence of buggy behaviour, and correct
rounding practice.)
Similarly, you might like to know the maximum significant number of
base 10 digits that can be specified, when assigning to (say) a
53-bit double. We have:
$max_len = ld_max_orig_len($orig_base, $to_base, $to_prec);
For this second example that becomes:
$max_len = ld_max_orig_len(10, 2, 53);
which will set $max_len to 15.
That is, so long as your base 10 float consists of no more than 15
siginificant digits, you can pass it to a 53-bit double and back again,
and be assured of retrieving the original value.
(Again, we assume absence of bugs and correct rounding practice.)
It is to be expected that
ld_max_orig_len(10, 2, $double_prec)
and
ld_max_orig_len(10, 2, $long_double_prec)
will (resp.) return the same values as LD_DBL_DIG and LD_LDBL_DIG.
($double_prec is the precision, in bits, of the C 'double' type,
and $long_double_prec is the precision, in bits, of the C 'long double'
type.)
The last 2 of the above subroutines (ie ld_min_inter_base and
ld_max_orig_base) are provided mainly for completeness.
Normally, there wouldn't be a need to use these last 2 forms ... but
who knows ...
The above examples demonstrate usage in relation to conversion between
bases 2 and 10. The functions apply just as well to conversions between
bases of any values.
The Math::MPFR module provides 4 identical functions, prefixed with
'mpfr_' instead of 'ld_' (to avoid name clashes).
Similarly, it provides constants (prefixed with 'MPFR_' instead of
'LD_') that reflect the values of float.h's DBL_DIG and LDBL_DIG.LICENSE
This program is free software; you may redistribute it and/or modify
it under the same terms as Perl itself.
Copyright 2012, 2013 SisyphusAUTHOR
Sisyphus <sisyphus at(@) cpan dot (.) org>