NAME
Math::Float128 - perl interface to C's (quadmath) __float128 operations
DESCRIPTION
use Math::Float128 qw(:all);
$arg = ~0; # largest UV
$f1 = Math::Float128->new($arg); # Assign the UV ~0 to $f2.
$f2 = UVtoF128($arg); # Assign the UV ~0 to $f2.
$arg = -21;
$f1 = Math::Float128->new($arg); # Assign the IV -21 to $f2.
$f2 = IVtoF128($arg); # Assign the IV -21 to $f2.
$arg = 32.1;
$f1 = Math::Float128->new($arg); # Assign the NV 32.1 to $f2.
$f2 = NVtoF128($arg); # Assign the NV 32.1 to $f2.
$arg = "32.1";
$f1 = Math::Float128->new($arg); # Assign strtoflt128("32.1") to $f2.
$f2 = STRtoF128($arg); # Assign strtoflt128("32.1") to $f2.
$f3 = Math::Float128->new($f1); # Assign the value of $f1 to $f3.
$f4 = F128toF128($f1); # Assign the value of $f1 to $f4.
$f5 = $f1; # Assign the value of $f1 to $f5.
This behaviour has changed from 0.04 and earlier.
A number of the functions below accept string arguments. These arguments
are passed to strtoflt128() and checked for the presence of non-numeric
characters. If any such non-numeric characters are detected, then the
global non-numeric flag (which is initially set to 0) will be incremented.
Neither leading nor trailing whitespace is deemed non-numeric, but any
other (ie internal) whitespace *is* regarded as non-numeric.
You can query the value held by the global non-numeric flag by running
Math::Float128::nnumflag() and you can manually alter the value of this
global using Math::Float128::set_nnum and Math::Float128::clear_nnum.
These functions are documented below.
NOTE:
Math::Float128->new(32.1) != Math::Float128->new('32.1') unless
$Config{nvtype} reports __float128. The same holds for many (but not
all) numeric values. In general, it's not always true (and is often
untrue) that Math::Float128->new($n) == Math::Float128->new("$n")OVERLOADING
The following operations are overloaded:
+ - * / **
+= -= *= /= **=
!= == <= >= <=> < >
++ --
""
abs bool ! int neg
sqrt log exp
sin cos atan2
=
NOTE: Making use of the '=' overloading is not recommended unless
you understand its caveats. See 'perldoc overload' and
read it thoroughly, including the documentation regarding
'copy constructors'.
In those situations where the overload subroutine operates on 2
perl variables, then obviously one of those perl variables is
a Math::Float128 object. To determine the value of the other
variable the subroutine works through the following steps (in
order), using the first value it finds, or croaking if it gets
to step 6:
1. If the variable is a UV (unsigned integer value) then that
value is used. The variable is considered to be a UV if
(perl 5.8) the UOK flag is set or if (perl 5.6) SvIsUV()
returns true.
2. If the variable is an IV (signed integer value) then that
value is used. The variable is considered to be an IV if the
IOK flag is set.
3. If the variable is a string (ie the POK flag is set) then the
value of that string is used.
4. If the variable is an NV (floating point value) then that
value is used. The variable is considered to be an NV if the
NOK flag is set.
5. If the variable is a Math::Float128 object then the value
encapsulated in that object is used.
6. If none of the above is true, then the second variable is
deemed to be of an invalid type. The subroutine croaks with
an appropriate error message.ASSIGNMENT FUNCTIONS
The following functions return a Math::Float128 object ($f).
$f = Math::Float128->new($arg);
Returns a Math::Float128 object to which the numeric value of $arg
has been assigned.
If no arg is supplied then $f will be NaN.
$f = UVtoF128($arg);
Returns a Math::Float128 object to which the numeric (unsigned
integer) value of $arg has been assigned.
$f = IVtoF128($arg);
Returns a Math::Float128 object to which the numeric (signed
integer) value of $arg has been assigned.
$f = NVtoF128($arg);
Returns a Math::Float128 object to which the numeric (floating
point) value of $arg has been assigned.
$f2 = F128toF128($f1);
Returns a Math::Float128 object that is a copy of the
Math::Float128 object provided as the argument.
Courtesy of overloading, this is in effect no different to doing:
$f2 = $f1;
$f = STRtoF128($str);
Returns a Math::Float128 object that has the value of the string
$str.ASSIGNMENT OF A NEW VALUE TO AN EXISTING OBJECT
fromUV($rop, $arg);
Assigns the numeric (unsigned integer) value of $arg to the
Math:Float128 object $rop.
fromIV($rop, $arg);
Assigns the numeric (signed integer) value of $arg to the
Math:Float128 object $rop.
fromNV($rop, $arg);
Assigns the numeric (floating point) value of $arg to the
Math:Float128 object $rop.
fromSTR($rop, $str);
Assigns the value of $str to the Math:Float128 object $rop.
fromF128($rop, $op);
Assigns the value of the Math::Float128 object $op to the
Math:Float128 object $rop.ASSIGNMENT OF INF, NAN, UNITY and ZERO
$f = InfF128($sign);
If $sign < 0, returns a Math::Float128 object set to
negative infinity; else returns a Math::Float128 object set
to positive infinity.
$f = NaNF128();
Returns a Math::Float128 object set to NaN (Not a Number).
$f = ZeroF128($sign);
If $sign < 0, returns a Math::Float128 object set to
negative zero; else returns a Math::Float128 object set to
zero.
$f = UnityF128($sign);
If $sign < 0, returns a Math::Float128 object set to
negative one; else returns a Math::Float128 object set to
one.
flt128_set_prec($precision);
Sets the precision of stringified values to $precision decimal
digits.
$precision = flt128_get_prec();
Returns the precision (in decimal digits) that will be used
when stringifying values (by printing them, or calling
F128toSTR).ASSIGNMENT OF QUADMATH.H CONSTANTS
The following functions return their values as either normal
perl scalar integer values ($iv) or Math::Float128 objects
($f), as appropriate.
$iv = FLT128_DIG;
Returns FLT128_DIG or croaks if FLT128_DIG is not defined.
$f = FLT128_MAX;
Returns FLT128_MAX or croaks if FLT128_MAX is not defined.
$f = FLT128_MIN;
Returns FLT128_MIN or croaks if FLT128_MIN is not defined.
$f = FLT128_EPSILON;
Returns FLT128_EPSILON or croaks if FLT128_EPSILON is not
defined.
$f = FLT128_DENORM_MIN;
Returns FLT128_DENORM_MIN or croaks if FLT128_DENORM_MIN is
not defined.
$iv = FLT128_MANT_DIG;
Returns FLT128_MANT_DIG or croaks if FLT128_MANT_DIG is not
defined.
$iv = FLT128_MIN_EXP;
Returns FLT128_MIN_EXP or croaks if FLT128_MIN_EXP is not
defined.
$iv = FLT128_MAX_EXP;
Returns FLT128_MAX_EXP or croaks if FLT128_MAX_EXP is not
defined.
$iv = FLT128_MIN_10_EXP;
Returns FLT128_MIN_10_EXP or croaks if FLT128_MIN_10_EXP is
not defined.
$iv = FLT128_MAX_10_EXP;
Returns FLT128_MAX_10_EXP or croaks if FLT128_MAX_10_EXP is
not defined.
$f = M_Eq;
Returns M_Eq (e) or expq(1.0) if M_Eq is not defined.
$f = M_LOG2Eq;
Returns M_LOG2Eq or log2q(expq(1.0)) if M_LOG2Eq is not
defined.
$f = M_LOG10Eq;
Returns M_LOG10Eq or log10q(expq(1.0)) if M_LOG10Eq is not
defined.
$f = M_LN2q;
Returns M_LN2q or logq(2) if M_LN2q is not defined.
$f = M_LN10q;
Returns M_LN10q or logq(10) if M_LN10q is not defined.
$f = M_PIq;
Returns M_PIq (pi) or 2 * asinq(1) if M_PIq is not defined.
$f = M_PI_2q;
Returns M_PI_2q (pi/2) or asinq(1) if M_PI_2q is not defined.
$f = M_PI_4q;
Returns M_PI_4q (pi/4) or asinq(1)/2 if M_PI_4q is not defined.
$f = M_1_PIq;
Returns M_1_PIq (1/pi) or 0.5/asinq(1) if M_1_PIq is not
defined.
$f = M_2_PIq;
Returns M_2_PIq (2/pi) or 1/asinq(1) if M_2_PIq is not defined.
$f = M_2_SQRTPIq;
Returns M_2_SQRTPIq (2/sqrt(pi)) or 2/sqrtq(pi) if M_2_SQRTPIq
is not defined.
$f = M_SQRT2q;
Returns M_SQRT2q or sqrtq(2)) if M_SQRT2q is not defined.
$f = M_SQRT1_2q;
Returns M_SQRT1_2q or 1/sqrtq(2)) if M_SQRT1_2q is not defined.RETRIEVAL FUNCTIONS
The following functions provide ways of seeing the value of
Math::Float128 objects.
$string = F128toSTR($f);
Returns the value of the Math::Float128 object as a string.
The returned string will contain the same as is displayed by
"print $f", except that print() will strip the trailing zeroes
in the mantissa (significand) whereas F128toSTR won't.
By default, provides 36 decimal digits of precision. This can be
altered by specifying the desired precision (in decimal digits)
in a call to flt128_set_prec.
$string = F128toSTRP(f, $precision);
Same as F128toSTR, but takes an additional arg that specifies the
precision (in decimal digits) of the stringified return value.
$nv = F128toNV($f);
This function returns the value of the Math::Float128 object to
a perl scalar (NV). It may not translate the value accurately,
depending, of course, upon both the value that the object holds
and the precision of the NV's mantissa.MATH LIBRARY FUNCTIONS
With the following functions, "$rop" and "$op" are Math::Float128
objects, and "$iv" is just a normal perl scalar that either
holds a signed integer value (rhs), or to which a signed integer value
will be returned (lhs).
These are just interfaces to the quadmath equivalents to the (fairly
standard) math library functions. I'm assuming you already have
access to the documentation of those math library functions.
These functions do not check their argument types - if you get
a segfault, check that you've supplied the correct argument type(s).
acos_F128($rop, $op);
acos($op) is assigned to $rop.
acosh_F128($rop, $op);
acosh($op) is assigned to $rop.
asin_F128($rop, $op);
asin($op) is assigned to $rop.
asinh_F128($rop, $op);
asinh($op) is assigned to $rop.
atan_F128($rop, $op);
atan($op) is assigned to $rop.
atanh_F128($rop, $op);
atanh($op) is assigned to $rop.
atan2_F128($rop, $op1, $op2);
atan2($op1, $op2) is assigned to $rop.
cbrt_F128($rop, $op);
cbrt($op) is assigned to $rop.
ceil_F128($rop, $op);
ceil($op) is assigned to $rop.
copysign_F128($rop, $op1, $op2);
copysign($op1, $op2) is assigned to $rop.
cosh_F128($rop, $op);
cosh($op) is assigned to $rop.
On mingw-w64 compilers, coshq() crashes, so for those compilers
we assign sqrt((sinh($op) ** 2) + 1) to $rop.
cos_F128($rop, $op);
cos($op) is assigned to $rop.
erf_F128($rop, $op);
erf($op) is assigned to $rop.
erfc_F128($rop, $op);
erfc($op) is assigned to $rop.
exp_F128($rop, $op);
exp($op) is assigned to $rop.
On mingw-w64 compilers, expq() crashes, so for those compilers
we assign pow(M_Eq, $op), ie e**$op, to $rop.
expm1_F128($rop, $op);
expm1($op) is assigned to $rop.
fabs_F128($rop, $op);
fabs($op) is assigned to $rop.
fdim_F128($rop, $op1, $op2);
fdim($op1, $op2) is assigned to $rop.
$iv = finite_F128($op);
finite($op) is assigned to $iv.
floor_F128($rop, $op);
floor($op) is assigned to $rop.
fma_F128($rop, $op1, $op2, $op3);
fma($op1, $op2, $op3) is assigned to $rop.
On mingw-w64 compilers, fmaq() crashes, so for those compilers
we assign ($op1 * $op2)+$op3 to $rop.
fmax_F128($rop, $op1, $op2);
fmax($op1, $op2) is assigned to $rop.
fmin_F128($rop, $op1, $op2);
fmin($op1, $op2) is assigned to $rop.
fmod_F128($rop, $op1, $op2);
fmod($op1, $op2) is assigned to $rop.
frexp_F128($rop, $iv, $op);
frexp($op) is assigned to ($rop, $iv)
hypot_F128($rop, $op1, $op2);
hypot($op1, $op2) is assigned to $rop.
$iv = isinf_F128($op);
isinf($op) is assigned to $iv.
$iv = ilogb_F128($op);
ilogb($op) is assigned to $iv.
$iv = isnan_F128($op);
isnan($op) is assigned to $iv.
j0_F128($rop, $op);
j0($op) is assigned to $rop.
j1_F128($rop, $op);
j1($op) is assigned to $rop.
jn_F128($rop, $iv, $op);
jn($iv, $op) is assigned to $rop.
$iv should not contain a value that won't fit into a signed int.
ldexp_F128($rop, $op, $iv);
ldexp($op, $iv) is assigned to $rop.
$iv should not contain a value that won't fit into a signed int
lgamma_F128($rop, $op);
lgamma($op) is assigned to $rop.
$iv = llrint_F128($op);
llrint($op) is assigned to $iv.
This requires that perl's IV is large enough to hold a longlong
int. Otherwise attempts to use this function will result in a fatal
error, accompanied by a message stating that the function is
unimplemented.
$iv = llround_F128($op);
llround($op) is assigned to $rop.
This requires that perl's IV is large enough to hold a longlong
int. Otherwise attempts to use this function will result in a fatal
error, accompanied by a message stating that the function is
unimplemented.
log_F128($rop, $op);
log($op) is assigned to $rop. # base e
log10_F128($rop, $op);
log($op) is assigned to $rop. # base 10
log2_F128($rop, $op);
log($op) is assigned to $rop. # base 2
log1p_F128($rop, $op);
log1p($op) is assigned to $rop. # base e
$iv = lrint_F128($op);
lrint($op) is assigned to $iv.
This requires that perl's IV is large enough to hold a long int.
Otherwise attempts to use this function will result in a fatal
error, accompanied by a message stating that the function is
unimplemented.
$iv = lround_F128($op);
lround($op) is assigned to $iv
This requires that perl's IV is large enough to hold a long int.
Otherwise attempts to use this function will result in a fatal
error, accompanied by a message stating that the function is
unimplemented.
modf_F128($rop1, $rop2, $op);
modf($op) is assigned to ($rop1, $rop2).
nan_F128($rop, $op);
nan($op) is assigned to $rop.
nearbyint_F128($rop, $op);
nearbyint($op) is assigned to $rop.
On mingw-w64 compilers, nearbyintq() crashes, so for those compilers
we manually go through the procedure of assigning the correct value
(for the current rounding mode) to $rop.
nextafter_F128($rop, $op1, $op2);
nextafter($op1, $op2) is assigned to $rop.
pow_F128($rop, $op1, $op2);
pow($op1, $op2) is assigned to $rop.
remainder_F128($rop, $op1, $op2);
remainder($op1, $op2) is assigned to $rop.
remquo_F128($rop1, $rop2, $op1, $op2);
remquo($op1, $op2) is assigned to ($rop1, $rop2).
$iv = rint_F128($op);
rint($op) is assigned to $rop.
$iv = round_F128($op);
round($op) is assigned to $iv.
scalbln_F128($rop, $op, $iv);
scalbln($op, $iv) is assigned to $rop.
$iv should not contain a value that won't fit into a signed
long int.
scalbn_F128($rop, $op, $iv);
scalbn($op, $iv) is assigned to $rop.
$iv should not contain a value that won't fir into a signed int.
$iv = signbit_F128($op);
signbit($op) is assigned to $iv.
sincos_F128($rop1, $rop2, $op);
sin($op) is assigned to $rop1.
cos($op) is assigned to $rop2.
sinh_F128($rop, $op);
sinh($op) is assigned to $rop.
sin_F128($rop, $op);
sin($op) is assigned to $rop.
sqrt_F128($rop, $op);
sqrt($op) is assigned to $rop.
tan_F128($rop, $op);
tan($op) is assigned to $rop.
tanh_F128($rop, $op);
tanh($op) is assigned to $rop.
tgamma_F128($rop, $op);
gamma($op) is assigned to $rop.
On mingw-w64 compilers, tgammaq() crashes, so for those compilers
we assign pow(M_Eq, lgamma($op)), ie e**lgamma($op), to $rop.
trunc_F128($rop, $op);
trunc($op) is assigned to $rop.
y0_F128($rop, $op);
y0($op) is assigned to $rop.
y1_F128($rop, $op);
y1($op) is assigned to $rop.
yn_F128 ($rop, $iv, $op);
yn($iv, $op) is assigned to $rop.
$iv should not contain a value that won't fit into a signed int.OTHER FUNCTIONS
$iv = Math::Float128::nnumflag(); # not exported
Returns the value of the non-numeric flag. This flag is
initialized to zero, but incemented by 1 whenever a function
is handed a string containing non-numeric characters. The
value of the flag therefore tells us how many times functions
have been handed such a string. The flag can be reset to 0 by
running Math::Float128::clear_nnum().
Math::Float128::set_nnum($iv); # not exported
Resets the global non-numeric flag to the value specified by
$iv.
Math::Float128::clear_nnum(); # not exported
Resets the global non-numeric flag to 0.(Essentially the same
as running Math::Float128::set_nnum(0).)
$bool = is_NaNF128($f);
Returns 1 if $f is a Math::Float128 NaN.
Else returns 0
$int = is_InfF128($f)
If the Math::Float128 object $f is -inf, returns -1.
If it is +inf, returns 1.
Otherwise returns 0.
$int = is_ZeroF128($f);
If the Math::Float128 object $f is -0, returns -1.
If it is zero, returns 1.
Otherwise returns 0.
$int = cmp2NV($f, $nv);
$nv can be any perl number - ie NV, UV or IV.
If the Math::Float128 object $f < $nv returns -1.
If it is > $nv, returns 1.
Otherwise returns 0.
$hex = f128_bytes($f);
Returns the hex representation of the _float128 value
as a string of 32 hex characters.
$iv = Math::Float128::nok_pokflag(); # not exported
Returns the value of the nok_pok flag. This flag is
initialized to zero, but incemented by 1 whenever a
scalar that is both a float (NOK) and string (POK) is passed
to new() or to an overloaded operator. The value of the flag
therefore tells us how many times such events occurred . The
flag can be reset to 0 by running clear_nok_pok().
Math::Float128::set_nok_pok($iv); # not exported
Resets the nok_pok flag to the value specified by $iv.
Math::Float128::clear_nok_pok(); # not exported
Resets the nok_pok flag to 0.(Essentially the same
as running set_nok_pok(0).)BUGS
The mingw64 compilers have buggy coshq(), expq(), fmaq(), tgammaq()
and nearbyintq() functions that crash when called. When a mingw64
compiler is detected, this module uses workarounds for those problem
functions. See the documentation (above) for cosh_F128(), exp_F128(),
fma_F128(), nearbyint_F128() and tgamma_F128() for an outline of the
workarounds involved.LICENSE
This program is free software; you may redistribute it and/or modify
it under the same terms as Perl itself.
Copyright 2013-18, 2020 SisyphusAUTHOR
Sisyphus <sisyphus at(@) cpan dot (.) org>