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Math::Float128

Module Version: 0.10
Math::Float128 - perl interface to C's (quadmath) __float128 operations

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")

The following operations are overloaded: + - * / ** += -= *= /= **= != == <= >= <=> < > ++ -- = abs bool ! int print sqrt log exp sin cos atan2 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 an NV (floating point value) then that value is used. The variable is considered to be an NV if the NOK flag is set. 4. If the variable is a string (ie the POK flag is set) then the value of that string is used. 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.

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.

$f = InfF128($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).

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.

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.

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.

$iv = Math::Float128::nnumflag(); # not exported Returns the value of the non-numeric flag. This flag is initialized to zero, but incemented by 1 whenever a function is handed a string containing non-numeric characters. The value of the flag therefore tells us how many times functions have been handed such a string. The flag can be reset to 0 by running Math::Float128::clear_nnum(). Math::Float128::set_nnum($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.

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.

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. Copyright 2013-16 Sisyphus

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

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