NAME

Math::Decimal128 - perl interface to C's _Decimal128 operations.

DEPENDENCIES

``````   In order to compile this module, a C compiler that provides
the _Decimal128 type is needed.``````

DESCRIPTION

``````   Math::Decimal128 supports up to 34 decimal digits of significand
(mantissa) and an exponent range of -6143 to +6144.
The smallest expressable value is
-9.999999999999999999999999999999999e6144 which is also
equivalent to
-9.999999999999999999999999999999999e6111.
The largest expressable value is
9.999999999999999999999999999999999e6144 which is also
equivalent to
9.999999999999999999999999999999999e6111.
The closest we can get to zero is (plus or minus) 1e-6176
(which is also equivalent to
1000000000000000000000000000000000e-6209).

This module allows decimal floating point arithmetic via

In the documentation that follows, "\$mantissa" is a perl scalar
holding a string of up to 34 decimal digits, optionally prefixed
with a '+' or '-' sign:
\$mantissa = '1234';
\$mantissa = '1234567890123456';``````

SYNOPSIS

``````   use Math::Decimal128 qw(:all);

my \$d128_1 = MEtoD128('9927', -2); # the decimal 99.27
my \$d128_2 = MEtoD128('3', 0);     # the decimal 3.0
\$d128_1 /= \$d128_2;
print \$d128_1; # prints 3309e-2 (33.09)``````

``````   The following operations are overloaded:
+ - * /
+= -= *= /=
!= == <= >= <=> < >
++ --
=
abs bool int print

Arguments to the overloaded operations must be Math::Decimal128
objects or integer (IV/UV) values or string (PV) values.
Strings can match /^(\-|\+)?(nan|inf)/i or be in floating point,
scientific notation or integer formats. Eg '113', '12.34', '12e-9',
'-12.34e+106', '-9E8', '-NaN', 'inf' are all valid strings.

\$d128_2 = \$d128_1 + \$d128_0; #ok
\$d128_2 = \$d128_1 + 15;      # ok

\$d128_2 = \$d128_1 + 3.1;     # Error.
If you really want to add the NV 3.1 you need to:
\$d128_2 = \$d128_1 + NVtoD128(3.1);

\$d128_2 = \$d128_1 + '3.1';

as that would make it very easy to inadvertently introduce a value
that was not intended.``````

CREATION & ASSIGNMENT FUNCTIONS

``````    The following create and assign a new Math::Decimal128 object.

##################################
# Create, and assign from a string
\$d128 = PVtoD128(\$string);

eg: \$d128 = PVtoD128('-9427199254740993');
\$d128 = PVtoD128('-930719925474.0993e-15');
\$d128 = Math::Decimal128->new('-978719925474.0993e-20');
\$d128 = Math::Decimal128->new('-9307199254740993e-23');

If the string arg contains characters that (according to perl's
looks_like_number API function) don't make sense in numeric
context, then a global non-numeric flag which was initialised to
0 is incremented - and the value assigned is in accordance with
perl's usual rules. If \$Math::Decimal128::NNW (0 by default)
is set to 1, then a non-numeric warning is also issued whenever
the non-numeric flag is incremented. The arg can be in either
integer format, scientific notation, float format or (+-)inf/nan.
Doing Math::Decimal128->new(\$string) will also create and assign
using PVtoD128().
The nnumflag function returns the current value of the global.
It can be cleared to 0 by running clear_nnum() and set to x with
set_nnum(x).
PVtoD128 is now a much improved way of creating and assigning - so
much so that I'm now recommending it as the preferred way of
creating a Math::Decimal128 object.
If you have a (\$mantissa, \$exponent) pair as your value and you
wish to create a Math::Decimal128 object using PVtoD128 you can do:
\$d128 = PVtoD128(MEtoPVl(\$mantissa, \$exponent));
or simply:
\$d128 = PVtoD128(\$mantissa . 'e' . \$exponent);

###############################################
# Create, and assign from mantissa and exponent
\$d128 = MEtoD128(\$mantissa, \$exponent);

eg: \$d128 = MEtoD128('12345', -3); # 12.345

It's a little kludgy, but this is a safe and sure way
of creating the Math::Decimal128 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.)
Doing Math::Decimal64->new(\$mantissa, \$exponent) will also
create and assign using MEtoD128(), and is equally acceptable.

###############################################
# Create, and assign from mantissa and exponent
\$d128 = DPDtoD128(\$mantissa, \$exponent);

eg: \$d128 = DPDtoD128('12345', -3); # 12.345

This is perhaps a quicker way of creating the Math::Decimal128
object with the intended value - but works only for DPD format
- ie only if d128_fmt() returns 'DPD'.
The mantissa string can be 'inf' or 'nan', optionally prefixed
with '-' or '+'. Otherwise, the mantissa string must
represent an integer value (with implied '.0' at the end) - ie
cannot contain a decimal point.

#################################################
# Create, and assign from a UV (unsigned integer)
\$d128 = UVtoD128(\$uv);

eg: \$d128 = UVtoD128(~0);

Doing Math::Decimal128->new(\$uv) will also create and assign
using UVtoD128().
Assigns the UV value to the Math::Decimal128 object.

################################################
# Create, and assign from an IV (signed integer)
\$d128 = IVtoD128(\$iv);

eg: \$d128 = IVtoD128(-15); # -15.0

Doing Math::Decimal128->new(\$iv) will also create and assign
using IVtoD128().
Assigns the UV value to the Math::Decimal128 object.

#############################################################
# Create, and assign from an existing Math::Decimal128 object
\$d128 = D128toD128(\$d128_0);
Also:
\$d128 = Math::Decimal128->new(\$d128_0);
\$d128 = \$d128_0; # uses overloaded '='

#######################################
# Create, and assign from an NV (real))
\$d128 = NVtoD128(\$nv);

eg: \$d128 = NVtoD128(-3.25);

Doing Math::Decimal128->new(\$nv) will also create and assign
using NVtoD128().
Might not always assign the value you think it does. (Eg,

################################
# Create, and assign using new()
\$d128 = Math::Decimal128->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::Decimal128 object
with a value of NaN is returned.
If 2 arguments are supplied it uses MEtoD128().
If one argument is provided, that arg's internal flags are
used to determine the appropriate function to call.
Dies if that argument is an NV - allowing an NV argument makes
it very easy to inadvertently assign an unintended value.

####################################
# Create, and assign using STRtoD128
\$d128 = STRtoD128(\$string);
If your C compiler provides the strtod128 function &&
function then you can use this function.
usage is is as for PVtoD128().

##############################``````

ASSIGN A NEW VALUE TO AN EXISTING OBJECT

``````     #######################################
assignMEl(\$d128, \$mantissa, \$exponent);
Assigns the value represented by (\$mantissa, \$exponent)
to the Math::Decimal128 object, \$d128.

eg: assignMEl(\$d128, '123459', -6); # 0.123459

########################################
assignDPDl(\$d128, \$mantissa, \$exponent);
Assigns the value represented by (\$mantissa, \$exponent)
to the Math::Decimal128 object, \$d128. This works more
efficiently than assignMEl(), but works only when the
_Decimal128 type is DPD-formatted. (\$Math::Decimal128::fmt
and the d128_fmt() function  will tell you whether the
_Decimal128 is DPD-formatted or BID-formatted.)

eg: assignDPDl(\$d128, '123459', -6); # 0.123459

##########################
assignIVl (\$d128, \$iv);
assignUVl (\$d128, \$uv);
assignNVl (\$d128, \$nv);
assignPVl (\$d128, \$string); # see PVtoD128 docs (above)
assignD128(\$d128, \$d128_0);
Assigns the value represented by the second arg (resp. the
IV,UV, NV,PV, Math::Decimal128 object) to the
Math::Decimal128 object, \$d128.

eg: assignPVl(\$d128, '123459e-6'); # 0.123459

##################
assignNaNl(\$d128);
Assigns a NaN to the Math::Decimal128 object, \$d128.

#########################
assignInfl(\$d128, \$sign);
Assigns an Inf to the Math::Decimal128 object, \$d128.
If \$sign is negative, assigns -Inf; otherwise +Inf.

#########################``````

INF, NAN and ZERO OBJECTS

``````     #######################
\$d128 = InfD128(\$sign);
If \$sign < 0, creates a new Math::Decimal128 object set to
negative infinity; else creates a Math::Decimal128 object set
to positive infinity.

##################
\$d128 = NaND128();
Creates a new Math::Decimal128 object set to NaN.
Same as "\$d128 = Math::Decimal128->new();"

########################
\$d128 = ZeroD128(\$sign);
If \$sign < 0, creates a new Math::Decimal128 object set to
negative zero; else creates a Math::Decimal128 object set to
zero.

########################``````

RETRIEVAL FUNCTIONS

``````    The following functions provide ways of seeing the value of
Math::Decimal128 objects.

#############################
\$string = decode_d128(\$d128);
This function calls either decode_dpd() or decode_bid(),
depending upon the formatting used to encode the
_Decimal128 value (as determined by the d128_fmt() sub).
It returns the value as a string of the form (-)ME, where:
"M" is the mantissa, containing up to 34 base 10 digits;
"E" is the letter "e" followed by the exponent;
A minus sign is prefixed to any -ve number (incl -0), but no
sign at all is prefixed for +ve numbers (incl +0).
Returns the strings '+inf', '-inf', 'nan' for (respectively)
+infinity, -infinity, NaN.
The value will be decoded correctly.

###################################
\$string = decode_dpd(\$d128_binary);
\$string = decode_bid(\$d128_binary);

As for decode_d128(), except it takes the 128-bit binary
representation of the _Decimal128 value as its argument. This
argument is derived from the Math::Decimal128 object (\$d128)
by doing:
\$binary = hex2bin(d128_bytes(\$d128));
DPD and BID formats will return different strings - so you
need to know which encoding (DPD or BID) was used, and then
call the appropriate decode_*() function for that encoding.
\$Math::Decimal128::fmt and the d128_fmt() sub will tell you
which encoding is in use.

#############################
\$fstring = D128toFSTR(\$d128);

Returns a string in floating point format (as distinct from
scientific notation) - ie as 0.123 instead of 123e-3.
And, yes, (eg) the _Decimal128 value 123e201 will be returned
as a string consisting of '123' followed by 201 zeroes.

######################################
\$rstring = D128toRSTR(\$d128, \$places);
Same as D128toFSTR() but the returned string has been rounded
(to nearest, ties to even) to the number of decimal places
specified by \$places.
Croaks with appropriate error message if \$places < 0.

#########################################
(\$mantissa, \$exponent) = D128toME(\$d128);
Returns the value of the Math::Decimal128 object as a
mantissa (string of up to 34 decimal digits) and exponent.
You can then manipulate those values to output the

######################
\$nv = D128toNV(\$d128);
This function returns the value of the Math::Decimal128
object to a perl scalar (NV). It will not translate the value
accurately if the precision required to express the value
precisely as a _Decimal128 value is greater than the precision
provided by the NV.

############
print \$d128;
Will print the value in the format (eg) -12345e-2, which
equates to the decimal -123.45. Uses D128toME().``````

OTHER FUNCTIONS

``````     #################
\$iv = Math::Decimal128::nnumflag(); # not exported
Returns the value of the non-numeric flag. This flag is
initialized to zero, but incemented by 1 whenever the
_atodecimal function (used internally by assignPV and
PVtoD128) is handed a string containing non-numeric
characters. The value of the flag therefore tells us how
many times _atodecimal() was handed such a string. The flag
can be reset to 0 by running clear_nnum().

##############
Math::Decimal128::set_nnum(\$iv); # not exported
Resets the global non-numeric flag to the value specified by
\$iv.

#############
Math::Decimal128::clear_nnum(); # not exported
Resets the global non-numeric flag to 0.(Essentially the same
as running set_nnum(0).)

################################
(\$man, \$exp) = PVtoMEl(\$string);
\$string is a string representing a floating-point value - eg
'inf', '+nan', '123.456', '-1234.56e-1', or '12345.6E-2'.
The function returns an array of (mantissa, exponent), where
the mantissa is a string of base 10 digits (prefixed with a
'-' for -ve values) with an implied decimal point at the
end of the string. For strings such as 'inf' and 'nan', the
mantissa will be set to \$string, and the exponent to 0.
For the example strings given above, the returned arrays
would be ('inf', 0), ('+nan', 0), ('123456', -3), ('-123456',
-3) and ('123456', -3) respectively.

########################################
\$string = MEtoPVl(\$mantissa, \$exponent);
If \$mantissa =~ /inf|nan/i returns \$mantissa.
Else returns \$mantissa . 'e' . \$exponent.

##################
\$fmt = d128_fmt();
Returns either 'DPD' or 'BID', depending upon whether the
(internal) _Decimal128 values are encoded using the 'Densely
Packed Decimal' format or the 'Binary Integer Decimal'
format.

#########################
\$hex = d128_bytes(\$d128);
Returns the hex representation of the _Decimal128 value
as a string of 32 hex characters.

#############################
\$binary = hex2bin(\$d128_hex);
Takes the string returned by d128_bytes (above) and
rewrites it in binary form - ie as a string of 128 base 2
digits.

###################
\$d128 = DEC128_MAX; # 9999999999999999999999999999999999e6111
\$d128 = DEC128_MIN; # 1e-6176
DEC128_MAX is the largest positive finite representable
_Decimal128 value.
DEC128_MIN is the smallest positive non-zero representable
_Decimal128 value.
Multiply these by -1 to get their negative counterparts.

#####################
\$d128 = Exp10l(\$pow);
Returns a Math::Decimal128 object with a value of
10 ** \$pow.

#########################
\$bool = have_strtod128();
Returns true if, when building Math::Decimal128,
the Makefile.PL was configured to make the STRtoD128()
function available for your build of Math::Decimal128. Else
returns false.
(No use making this function available if your compiler's
C library doesn't provide the strtod128 function.)

###########################
\$test = is_ZeroD128(\$d128);
Returns:
-1 if \$d128 is negative zero;
1 if \$d128 is a positive zero;
0 if \$d128 is not zero.

##########################
\$test = is_InfD128(\$d128);
Returns:
-1 if \$d128 is negative infinity;
1 if \$d128 is positive infinity;
0 if \$d128 is not infinity.

##########################
\$bool = is_NaND128(\$d128);
Returns:
1 if \$d128 is a NaN;
0 if \$d128 is not a NaN.

#########################
\$sign = get_signl(\$d128);
Returns the sign ('+' or '-') of \$d128.

#######################
\$exp = get_expl(\$d128);
Returns the exponent of \$d128. This is the value that's
stored internally within the encapsulated _Decimal128 value;
it may differ from the value that you assigned. For example,
if you've assigned the value MEtoD128('100', 0) it will
probably be held internally as '1e2', not '100e0'.

#######################``````

``````    This program is free software; you may redistribute it and/or
``    Sisyphus <sisyphus at(@) cpan dot (.) org>``