# NAME

Math::Decimal64 - perl interface to C's _Decimal64 operations.

# DEPENDENCIES

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

# DESCRIPTION

``````   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

In the documentation that follows, "\$mantissa" is a perl scalar
holding a string of up to 16 decimal digits, optionally prefixed
with a '+' or '-' sign:
\$mantissa = '1234';
\$mantissa = '1234567890123456';``````

# SYNOPSIS

``````   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 neg

Arguments to the overloaded operations must be Math::Decimal64
objects, 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.

\$d64_2 = \$d64_1 + \$d128_0; #ok
\$d64_2 = \$d64_1 + 15;      #ok

\$d64_2 = \$d64_1 + 3.1;     # Error
If you really want to add the NV 3.1 you need to:
\$d64_2 = \$d64_1 + NVtoD64(3.1);

If you instead wish to add the decimal value 3.1:
\$d64_2 = \$d64_1 + '3.1';

Overloading of floats (NV values) will probably never be enabled
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::Decimal64 object.

##################################
# Create, and assign from a string
\$d64 = PVtoD64(\$string);

eg: \$d64 = PVtoD64('-9427199254740993');
\$d64 = PVtoD64('-9307199254740993e-15');
\$d64 = Math::Decimal64->new('-9787199254740.993e-20');
\$d64 = Math::Decimal64->new('-9307199254740993e-23');
\$d64 = Math::Decimal64->new('-inf');
\$d64 = Math::Decimal64->new('nan');
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::Decimal64::NNW (set to 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::Decimal64->new(\$string) will also create and assign
using PVtoD64().
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).
PVtoD64 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::Decimal64 object.
If you have a (\$mantissa, \$exponent) pair as your value and you
wish to create a Math::Decimal64 object using PVtoD64 you can do:
\$d64 = PVtoD64(MEtoPV(\$mantissa, \$exponent));
or simply:
\$d64 = PVtoD64(\$mantissa . 'e' . \$exponent);

###############################################
# Create, and assign from mantissa and exponent
\$d64 = MEtoD64(\$mantissa, \$exponent);

eg: \$d64 = MEtoD64('12345', -3); # 12.345

It's a little kludgy, but this is a safe and sure 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.)
Doing Math::Decimal64->new(\$mantissa, \$exponent) will also
create and assign using MEtoD64(), and is equally acceptable.

###############################################
# Create, and assign from mantissa and exponent
\$d64 = DPDtoD64(\$mantissa, \$exponent);

eg: \$d64 = DPDtoD64('12345', -3); # 12.345

This is perhaps a quicker way of creating the Math::Decimal64
object with the intended value - but works only for DPD format
- ie only if d64_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)
\$d64 = UVtoD64(\$uv);

eg: \$d64 = UVtoD64(~0);

Doing Math::Decimal64->new(\$uv) will also create and assign
using UVtoD64().
Assigns the designated UV value to the Math::Decimal64 object
(but loses precision if the _Decimal64 type has insufficient
precision to accommodate the precision of the IV).

################################################
# Create, and 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().
Assigns the designated IV value to the Math::Decimal64 object
(but loses precision if the _Decimal64 type has insufficient
precision to accommodate the precision of the IV).

############################################################
# Create, and assign from an existing Math::Decimal64 object
\$d64 = D64toD64(\$d64_0);
Also:
\$d64 = Math::Decimal64->new(\$d64_0);
\$d64 = \$d64_0; # uses overloaded '='

#######################################
# Create, and assign from an NV (real))
\$d64 = NVtoD64(\$nv);

eg: \$d64 = NVtoD64(-3.25);

Doing Math::Decimal64->new(\$nv) is now a fatal error. NV's can
now be assigned using only either NVtoD64() or assignNV().
Might not always assign the value you think it does, but should
be fine for assigning decimal values that have en exact base 2
representation. (Eg, see test 5 in t/overload_cmp.t.)

################################
# Create, and 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.
Dies if that argument is an NV - allowing an NV argument makes
it very easy to inadvertently assign an unintended value, and
is therefore now disallowed.

###################################
# Create, and 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().

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

# ASSIGN A NEW VALUE TO AN EXISTING OBJECT

``````     #####################################
assignME(\$d64, \$mantissa, \$exponent);
Assigns the value represented by (\$mantissa, \$exponent)
to the Math::Decimal64 object, \$d64.
Performs same argument checking as MEtoD64.

eg: assignME(\$d64, '123459', -6); # 0.123459

######################################
assignDPD(\$d64, \$mantissa, \$exponent);
Assigns the value represented by (\$mantissa, \$exponent)
to the Math::Decimal64 object, \$d64. This might work
more efficiently than assignME(), but works only when the
_Decimal64type is DPD-formatted. (The d64_fmt function
will tell you whether the _Decimal64 is DPD-formatted or
BID-formatted.)

eg: assignDPD(\$d64, '123459', -6); # 0.123459

########################
assignIV (\$d64, \$iv);
assignUV (\$d64, \$uv);
assignNV (\$d64, \$nv);
assignPV (\$d64, \$string); # See PVtoD64 doc (above)
assignD64(\$d64, \$d64_0);
Assigns the value represented by the second arg (resp. the
IV,UV,NV,PV, Math::Decimal64 object) to the
Math::Decimal64 object, \$d64.

eg: assignPV(\$d64, '12.3459e-6'); # 0.0000123459

################
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.

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

# INF, NAN and ZERO OBJECTS

``````     #####################
\$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.

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

# RETRIEVAL FUNCTIONS

``````    The following functions provide ways of seeing the value of
Math::Decimal64 objects.

###########################
\$string = decode_d64(\$d64);
This function calls either decode_dpd() or decode_bid(),
depending upon the formatting used to encode the
_Decimal64 value (as determined by the d64_fmt() sub).
It returns the value as a string of the form (-)ME, where:
"M" is the mantissa, containing up to 16 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(\$d64_binary);
\$string = decode_bid(\$d64_binary);

As for decode_d64(), except it takes the 64-bit binary
representation of the _Decimal64 value as its argument. This
argument is derived from the Math::Decimal64 object (\$d64)
by doing:
\$binary = hex2bin(d64_bytes(\$d64));
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::Decimal64::fmt will tell you which encoding is in use,
as also will the d64_fmt() subroutine.

###########################
\$fstring = D64toFSTR(\$d64);

Returns a string in floating point format (as distinct from
scientific notation) - ie as 0.123 instead of 123e-3.
And, yes, (eg) the _Decimal64 value 123e201 will be returned
as a string consisting of '123' followed by 201 zeroes.

####################################
\$rstring = D64toRSTR(\$d64, \$places);
Same as D64toFSTR() 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) = D64toME(\$d64);
Returns the value of the Math::Decimal64 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
decoded 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 decoded 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.

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

# OTHER FUNCTIONS

``````     ##################################
\$iv = Math::Decimal64::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
PVtoD64) 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::Decimal64::set_nnum(\$iv); # not exported
Resets the global non-numeric flag to the value specified by
\$iv.

##############################
Math::Decimal64::clear_nnum(); # not exported
Resets the global non-numeric flag to 0.(Essentially the same
as running set_nnum(0).)

################################
(\$man, \$exp) = PVtoME(\$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 = MEtoPV(\$mantissa, \$exponent);
If \$mantissa =~ /inf|nan/i returns \$mantissa.
Else returns \$mantissa . 'e' . \$exponent.

#################
\$fmt = d64_fmt();
Returns either 'DPD' or 'BID', depending upon whether the
(internal) _Decimal64 values are encoded using the 'Densely
Packed Decimal' format or the 'Binary Integer Decimal'
format.

#######################
\$hex = d64_bytes(\$d64);
Returns the hex representation of the _Decimal64 value
as a string of 16 hex characters.

############################
\$binary = hex2bin(\$d64_hex);
Takes the string returned by d64_bytes (above) and
rewrites it in binary form - ie as a string of 64 base 2
digits.

#################
\$d64 = DEC64_MAX; # 9999999999999999e369
\$d64 = DEC64_MIN; # 1e-398
DEC64_MAX is the largest positive finite representable
_Decimal64 value.
DEC64_MIN is the smallest positive non-zero representable
_Decimal64 value.
Multiply these by -1 to get their negative counterparts.

###################
\$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 zero, but not negative 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.

#######################
\$sign = get_sign(\$d64);
Returns the sign ('+' or '-') of \$d64.

#####################
\$exp = get_exp(\$d64);
Returns the exponent of \$d64. This is the exponent value
that's stored internally within the encapsulated _Decimal64
value; it may differ from the value that you assigned.
For example, if you've assigned the value MEtoD64('100', 0)
it will probably be held internally as '1e2', not '100e0',
in which case get_exp() would return 2, not 0.

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

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