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Math::Decimal64

Module Version: 0.06
Math::Decimal64 - (alpha) perl interface to C's _Decimal64 operations.

In order to compile this module, a C compiler that provides the _Decimal64 type is needed.

Note that this module is alpha software. It seems to work ok for me on Windows 7 (Intel processor,compiling with gcc-4.6.3, gcc-4.7.0) and Ubuntu-12.04LTS (Amd64 processor, gcc-4.6.3). It also works for me on Debian wheezy (PowerpC processor, gcc-4.6.3) apart from caveats mentioned in the docs below. Math::Decimal64 supports up to 16 decimal digits of significand (mantissa) and an exponent range of -383 to +384. The smallest expressable value is -9.999999999999999e384 (which is also equivalent to -9999999999999999e369). The largest expressable value is 9.999999999999999e384 (which also equivalent to 9999999999999999e369). The closest we can get to zero is (plus or minus) 1e-384 (which is also equivalent to 1000000000000000e-399). This module allows decimal floating point arithmetic via operator overloading - see "OVERLOADING". In the documentation that follows, "$mantissa" is a perl scalar holding a string of up to 16 decimal digits: $mantissa = '1234'; $mantissa = '1234567890123456'; For many values, it normally shouldn't matter if $mantissa is assigned as a number: $mantissa = 1234; # should work ok. But on some perls there are values that *need* to be assigned as a string. For example, on perls where nvtype is an 8 byte 'double': $mantissa = '-9307199254740993'; # works fine $mantissa = -9307199254740993; # will assign wrong value So ... where you see "$mantissa" in the following docs, think *string* of up to 16 decimal digits".

use Math::Decimal64 qw(:all); my $d64_1 = MEtoD64('9927', -2); # the decimal 99.27 my $d64_2 = MEtoD64('3', 0); # the decimal 3.0 $d64_1 /= $d64_2; print $d64_1; # prints 3309e-2 (33.09)

The following operations are overloaded: + - * / += -= *= /= != == <= >= <=> < > ++ -- = abs bool int print Arguments to the overloaded operations must be Math::Decimal64 objects or integer (IV/UV) values. If your perl has 8-byte (or larger) IV/UV, then you may get unexpected results if you pass an IV/UV to the overloaded operators (because the precision of the IV/UV exceeds the precision of the _Decimal64 type) - it depends upon just how big the absolute value of the IV/UV is. $d64_2 = $d64_1 + 15; # ok $d64_2 = $d64_1 + 3.1; # Error. Best to either: $d64_2 = $d64_1 + MEtoD64('31',-1); # or (equivalentally): $d64_2 = $d64_1 + Math::Decimal64->new('31',-1);

The following create and assign a new Math::Decimal64 object. ################################### # Assign from mantissa and exponent $d64 = MEtoD64($mantissa, $exponent); eg: $d64 = MEtoD64('12345', -3); # 12.345 It's a little kludgy, but this is the safest and surest way of creating the Math::Decimal64 object with the intended value. Checks are conducted to ensure that the arguments are suitable. The mantissa string must represent an integer. (There's an implicit '.0' at the end of the string.) Only known caveat is that, since this function does a strtold() on the mantissa, the 'long double' needs to have at least 55 bits of precision. Doing Math::Decimal64->new($mantissa, $exponent) will also create and assign using MEtoD64(), and is equally acceptable. ###################### # Assign from a string $d64 = PVtoD64($string); eg: $d64 = PVtoD64('-9427199254740993'); $d64 = PVtoD64('-9307199254740993e-15'); $d64 = Math::Decimal64->new('-9787199254740993'); $d64 = Math::Decimal64->new('-9307199254740993e-23'); Does no checks on its arg. The arg can be in either integer format or scientific notation or float format. Doing Math::Decimal64->new($string) will also create and assign using PVtoD64(). This assigns using the C standard library function strtold(), and then casting to a _Decimal64. It is significantly faster than MEtoD64 for exponents outside the range (-10 .. 10) and I think it is reliable so long as: 1) the 'long double' type has precision of 55 bits or more; 2) the 'long double' type accommodates the _Decimal64 type's exponent range; 3) Any (and all) digits after the mantissa's 16th digit are '0'. ##################################### # Assign from a UV (unsigned integer) $d64 = UVtoD64($uv); eg: $d64 = UVtoD64(~0); Doing Math::Decimal64->new($uv) will also create and assign using UVtoD64(). On perls where the UV is 8 bytes or larger, the precision of the UV exceeds the precision of the _Decimal64 - and this function is not therefore recommended on such perls (unless you're sure the UV value won't be subject to rounding). Check the size of the UV by running perl -V:ivsize #################################### # Assign from an IV (signed integer) $d64 = IVtoD64($iv); eg: $d64 = IVtoD64(-15); # -15.0 Doing Math::Decimal64->new($iv) will also create and assign using IVtoD64(). On perls where the IV is 8 bytes or larger, the precision of the UV exceeds the precision of the _Decimal64 - and this function is not therefore recommended on such perls (unless you're sure the IV value won't be subject to rounding). Check the size of the IV by running perl -V:ivsize ################################################ # Assign from an existing Math::Decimal64 object $d64 = D64toD64($d64_0); Also: $d64 = Math::Decimal64->new($d64_0); $d64 = $d64_0; # uses overloaded '=' ########################### # Assign from an NV (real)) $d64 = NVtoD64($nv); eg: $d64 = NVtoD64(-3.25); Doing Math::Decimal64->new($nv) will also create and assign using NVtoD64(). Might not always assign the value you think it does. (Eg, see test 5 in t/overload_cmp.t.) #################### # Assign using new() $d64 = Math::Decimal64->new([$arg1, [$arg2]]); This function calls one of the above functions. It determines the appropriate function to call by examining the argument(s) provided. If no argument is provided, a Math::Decimal64 object with a value of NaN is returned. If 2 arguments are supplied it uses MEtoD64(). If one argument is provided, that arg's internal flags are used to determine the appropriate function to call. ####################### # Assign using STRtoD64 $d64 = STRtoD64($string); If your C compiler provides the strtod64 function, and you configured the Makefile.PL to enable access to that function then you can use this function. usage is is as for PVtoD64(). ##############################

assignME($d64, $mantissa, $exponent); Assigns the value represented by ($mantissa, $exponent) to the Math::Decimal64 object, $d64. Performs same argument checking as MEtoD64. Same caveats apply here as to MEtoD64 - see the MEtoD64 documentation. eg: assignME($d64, '123459', -6); # 0.123459 assignPV($d64, $string); Assigns the value represented by $string to the Math::Decimal64 object, $d64. Doesn't check to see what $string contains. Same caveats apply here as to PVtoD64() - see the PVtoD64 documentation (above). eg: assignPV($d64, '123459e-6'); # 0.123459 assignNaN($d64); Assigns a NaN to the Math::Decimal64 object, $d64. assignInf($d64, $sign); Assigns an Inf to the Math::Decimal64 object, $d64. If $sign is negative, assigns -Inf; otherwise +Inf.

$d64 = InfD64($sign); If $sign < 0, creates a new Math::Decimal64 object set to negative infinity; else creates a Math::Decimal64 object set to positive infinity. $d64 = NaND64(); Creates a new Math::Decimal64 object set to NaN. Same as "$d64 = Math::Decimal64->new();" $d64 = ZeroD64($sign); If $sign < 0, creates a new Math::Decimal64 object set to negative zero; else creates a Math::Decimal64 object set to zero.

The following functions provide ways of seeing the value of Math::Decimal64 objects. ($mantissa, $exponent) = D64toME($d64); Returns the value of the Math::Decimal object as a mantissa (string of up to 16 decimal digits) and exponent. You can then manipulate those values to output the value in your preferred format. Afaik, the value will be translated accurately. ($mantissa, $exponent) = FR64toME($d64); Requires that Math::MPFR version 3.18 or later has been loaded. It also requires that Math:MPFR has been built with support for the mpfr library's Decimal64 conversion functions - in which case Math::MPFR::_WANT_DECIMAL_FLOATS() will return true. (Otherwise it returns false.) Afaik, the value will be translated accurately. $nv = D64toNV($d64); This function returns the value of the Math::Decimal64 object to a perl scalar (NV). Under certain conditions it may not translate the value accurately. print $d64; Will print the value in the format (eg) -12345e-2, which equates to the decimal -123.45. Uses D64toME(). pFR $d64; Will print the value in the format (eg) -12345e-2, which equates to the decimal -123.45. Uses FR64toME() - which should always print the value accurately, but requires that Math::MPFR: 1) has been loaded; 2) supports the Decimal64 mpfr conversion functions.

$d64 = Exp10($pow); Returns a Math::Decimal64 object with a value of 10 ** $pow, for $pow in the range (-398 .. 384). Croaks with appropriate message if $pow is not within that range. $bool = have_strtod64(); Returns true if, when building Math::Decimal64, the Makefile.PL was configured to make the STRtoD64() function available for your build of Math::Decimal64. Else returns false. (No use making this function available if your compiler's C library doesn't provide the strtod64 function.) $test = is_ZeroD64($d64); Returns: -1 if $d64 is negative zero; 1 if $d64 is a positive zero; 0 if $d64 is not zero. $test = is_InfD64($d64); Returns: -1 if $d64 is negative infinity; 1 if $d64 is positive infinity; 0 if $d64 is not infinity. $bool = is_NaND64($d64); Returns: 1 if $d64 is a NaN; 0 if $d64 is not a NaN. LDtoD64($d64, $ld); # $ld is a Math::LongDouble object D64toLD($ld, $d64); # $ld is a Math::LongDouble object Conversions between Math::LongDouble and Math::Decimal64 objects - done by simply casting the long double value to a _Decimal64 value, or (resp.) vice-versa. Requires that Math::LongDouble has been loaded.

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. Copyright 2012-13 Sisyphus

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

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