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Math::LongDouble

Module Version: 0.18
Math::LongDouble - perl interface to C's long double operations

use Math::LongDouble qw(:all); $arg = ~0; # largest UV $d1 = Math::LongDouble->new($arg); # Assign the UV ~0 to $d2. $d2 = UVtoLD($arg); # Assign the UV ~0 to $d2. $arg = -21; $d1 = Math::LongDouble->new($arg); # Assign the IV -21 to $d2. $d2 = IVtoLD($arg); # Assign the IV -21 to $d2. $arg = 32.1; $d1 = Math::LongDouble->new($arg); # Assign the NV 32.1 to $d2. $d2 = NVtoLD($arg); # Assign the NV 32.1 to $d2. $arg = "32.1"; $d1 = Math::LongDouble->new($arg); # Assign strtold("32.1") to $d2. $d2 = STRtoLD($arg); # Assign strtold("32.1") to $d2. $d3 = Math::LongDouble->new($d1); # Assign the value of $d1 to $d3. $d4 = LDtoLD($d1); # Assign the value of $d1 to $d4. $d5 = $d1; # Assign the value of $d1 to $d5. This behaviour has changed from 0.06 and earlier. A number of the functions below accept string arguments. These arguments having been handed to strtold() will be 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::LongDouble->new(32.1) != Math::LongDouble->new('32.1') unless $Config{nvtype} reports 'long double'. The same holds for many (but not all) numeric values. In general, it's not always true (and is often untrue) that Math::LongDouble->new($n) == Math::LongDouble->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::LongDouble 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::LongDouble 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 create and assign a new Math::LongDouble. $ld = Math::LongDouble->new($arg); Returns a Math::LongDouble object to which the numeric value of $arg has been assigned. If $arg is not provided then the value of $ld will be NaN. $ld = UVtoLD($arg); Returns a Math::LongDouble object to which the numeric (unsigned integer) value of $arg has been assigned. $ld = IVtoLD($arg); Returns a Math::LongDouble object to which the numeric (signed integer) value of $arg has been assigned. $ld = NVtoLD($arg); Returns a Math::LongDouble object to which the numeric (floating point) value of $arg has been assigned. $ld2 = LDtoLD($ld1); Returns a Math::LongDouble object that is a copy of the Math::LongDouble object provided as the argument. Courtesy of overloading, this is in effect no different to doing: $ld2 = $ld1; $ld = STRtoLD($str); Returns a Math::LongDouble object that has the value of the string $str.

$ld = InfLD($sign); If $sign < 0, returns a Math::LongDouble object set to negative infinity; else returns a Math::LongDouble object set to positive infinity. $ld = NaNLD(); If $sign < 0, returns a Math::longDouble object set to NaN. $ld = ZeroLD($sign); If $sign < 0, returns a Math::LongDouble object set to negative zero; else returns a Math::LongDouble object set to zero. $ld = UnityLD($sign); If $sign < 0, returns a Math::LongDouble object set to negative one; else returns a Math::LongDouble object set to one. ld_set_prec($precision); Sets the precision of stringified values to $precision decimal digits. Default precision is set in the XS global _DIGITS to 1 + ceil(MANT_PREC * log(2) / log(10) where MANT_PREC is LDBL_MANT_DIG if float.h defines that symbol. Else MANT_PREC is DBL_MANT_DIG if float.h defines that symbol. Else MANT_PREC is 21 (which is the correct value for a 64-bit precision mantissa). $precision = ld_get_prec(); Returns the precision (in decimal digits) that will be used when stringifying values (by printing them, or calling LDtoSTR).

The following functions return their values as either normal perl scalar integer values ($iv) or Math::LongDouble objects ($ld), as appropriate. Those LD_DBL_* functions that return 'double' values could have been structured to return an NV, but they *do* return Math::LongDouble objects - mainly for consistency with their LD_LDBL_* counterparts. $iv = LD_DBL_DIG; $iv = LD_LDBL_DIG; Returns DBL_DIG/LDBL_DIG or croaks if DBL_DIG/LDBL_DIG is not defined. $ld = LD_DBL_MAX; $ld = LD_LDBL_MAX; Returns DBL_MAX/LDBL_MAX or croaks if DBL_MAX/LDBL_MAX is not defined. $ld = LD_DBL_MIN; $ld = LD_LDBL_MIN; Returns DBL_MIN/LDBL_MIN or croaks if DBL_MIN/LDBL_MIN is not defined. $ld = LD_DBL_EPSILON; $ld = LD_LDBL_EPSILON; Returns DBL_EPSILON/LDBL_EPSILON or croaks if DBL_EPSILON/LDBL_EPSILON is not defined. $ld = LD_DBL_DENORM_MIN; $ld = LD_LDBL_DENORM_MIN; Returns DBL_DENORM_MIN/LDBL_DENORM_MIN or croaks if DBL_DENORM_MIN/LDBL_DENORM_MIN is not defined. $iv = LD_DBL_MANT_DIG; $iv = LD_LDBL_MANT_DIG; Returns DBL_MANT_DIG/LDBL_MANT_DIG or croaks if DBL_MANT_DIG/LDBL_MANT_DIG is not defined. $iv = LD_DBL_MIN_EXP; $iv = LD_LDBL_MIN_EXP; Returns DBL_MIN_EXP/LDBL_MIN_EXP or croaks if DBL_MIN_EXP/LDBL_MIN_EXP is not defined. $iv = LD_DBL_MAX_EXP; $iv = LD_LDBL_MAX_EXP; Returns DBL_MAX_EXP/LDBL_MAX_EXP or croaks if DBL_MAX_EXP/LDBL_MAX_EXP is not defined. $iv = LD_DBL_MIN_10_EXP; $iv = LD_LDBL_MIN_10_EXP; Returns DBL_MIN_10_EXP/LDBL_MIN_10_EXP or croaks if DBL_MIN_10_EXP/LDBL_MIN_10_EXP is not defined. $iv = LD_DBL_MAX_10_EXP; $iv = LD_LDBL_MAX_10_EXP; Returns DBL_MAX_10_EXP/LDBL_MAX_10_EXP or croaks if DBL_MAX_10_EXP/LDBL_MAX_10_EXP is not defined. $ld = M_El; Returns M_El (e) or expl(1.0) if M_El is not defined. $ld = M_LOG2El; Returns M_LOG2El or log2l(expl(1.0)) if M_LOG2El is not defined. $ld = M_LOG10El; Returns M_LOG10El or log10l(expl(1.0)) if M_LOG10El is not defined. $ld = M_LN2l; Returns M_LN2l or logl(2) if M_LN2l is not defined. $ld = M_LN10l; Returns M_LN10l or logl(10) if M_LN10l is not defined. $ld = M_PIl; Returns M_PIl (pi) or 2 * asinl(1) if M_PIl is not defined. $ld = M_PI_2l; Returns M_PI_2l (pi/2) or asinl(1) if M_PI_2l is not defined. $ld = M_PI_4l; Returns M_PI_4l (pi/4) or asinl(1)/2 if M_PI_4l is not defined. $ld = M_1_PIl; Returns M_1_PIl (1/pi) or 0.5/asinl(1) if M_1_PIl is not defined. $ld = M_2_PIl; Returns M_2_PIl (2/pi) or 1/asinl(1) if M_2_PIl is not defined. $ld = M_2_SQRTPIl; Returns M_2_SQRTPIl (2/sqrt(pi)) or 2/sqrtl(pi) if M_2_SQRTPIl is not defined. $ld = M_SQRT2l; Returns M_SQRT2l or sqrtl(2)) if M_SQRT2l is not defined. $ld = M_SQRT1_2l; Returns M_SQRT1_2l or 1/sqrtl(2)) if M_SQRT1_2l is not defined.

The following functions provide ways of seeing the value of Math::LongDouble objects. $nv = LDtoNV($ld); This function returns the value of the Math::LongDouble object to a perl scalar (NV). It may not translate the value accurately. $string = LDtoSTR($ld); Returns the value of the Math::LongDouble object as a string. The returned string will contain the same as is displayed by "print $ld", except that print() will strip the trailing zeroes in the mantissa (significand) whereas LDtoSTR won't. By default, provides 21 decimal digits of precision for the typical 80-bit long double or 17 decimal digits if the long double is a double. The number of digits dispalayed can be altered by specifying the desired precision (in decimal digits) in a call to ld_set_prec. $string = LDtoSTRP($ld, $precision); Same as LDtoSTR, but takes an additional arg that specifies the precision (in decimal digits) of the stringified return value.

With the following functions, "$rop" and "$op" are Math::LongDouble objects, and "$iv" is just a normal perl scalar that either holds a signed integer value, or to which a signed integer value will be returned. These are just interfaces to the standard math library functions. I'm assuming you already have access to their documentation. These functions do not check their argument types - if you get a segfault, check that you've supplied the correct argument type(s). acos_LD($rop, $op); acosl($op) is assigned to $rop. acosh_LD($rop, $op); acoshl($op) is assigned to $rop. asin_LD($rop, $op); asinl($op) is assigned to $rop. asinh_LD($rop, $op); asinhl($op) is assigned to $rop. atan_LD($rop, $op); atanl($op) is assigned to $rop. atanh_LD($rop, $op); atanhl($op) is assigned to $rop. atan2_LD($rop, $op1, $op2); atan2l($op1, $op2) is assigned to $rop. cbrt_LD($rop, $op); cbrtl($op) is assigned to $rop. ceil_LD($rop, $op); ceill($op) is assigned to $rop. copysign_LD($rop, $op1, $op2); copysignl($op1, $op2) is assigned to $rop. cosh_LD($rop, $op); coshl($op) is assigned to $rop. cos_LD($rop, $op); cosl($op) is assigned to $rop. erf_LD($rop, $op); erfl($op) is assigned to $rop. erfc_LD($rop, $op); erfcl($op) is assigned to $rop. exp_LD($rop, $op); expl($op) is assigned to $rop. expm1_LD($rop, $op); expm1l($op) is assigned to $rop. fabs_LD($rop, $op); fabsl($op) is assigned to $rop. fdim_LD($rop, $op1, $op2); fdiml($op1, $op2) is assigned to $rop. $iv = finite_LD($op); finite($op) is assigned to $iv. floor_LD($rop, $op); floorl($op) is assigned to $rop. fma_LD($rop, $op1, $op2, $op3); fmal($op1, $op2, $op3) is assigned to $rop. On mingw-w64 compilers, fmaq() crashes, so for those compilers we assign ($op1 * $op2)+$op3 to $rop. fmax_LD($rop, $op1, $op2); fmaxl($op1, $op2) is assigned to $rop. fmin_LD($rop, $op1, $op2); fmin($op1, $op2) is assigned to $rop. fmod_LD($rop, $op1, $op2); fmodl($op1, $op2) is assigned to $rop. frexp_LD($rop, $iv, $op); frexpl($op) is assigned to ($rop, $iv) hypot_LD($rop, $op1, $op2); hypotl($op1, $op2) is assigned to $rop. $iv = isinf_LD($op); isinf($op) is assigned to $iv. $iv = ilogb_LD($op); ilogbl($op) is assigned to $iv. $iv = isnan_LD($op); isnanl($op) is assigned to $iv. If Math::LOngDouble::_have_isnanl returns false, uses custom (_is_nan) XSub instead. ldexp_LD($rop, $op, $iv); ldexpl($op, $iv) is assigned to $rop. $iv should not contain a value that won't fit into a signed int lgamma_LD($rop, $op); lgammal($op) is assigned to $rop. $iv = llrint_LD($op); llrintl($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. $iv = llround_LD($op); llroundl($op) is assigned to $rop. This requires that perl's IV is large enough to hold a longlong int. Otherwise attempts to use this function will result in a fatal error, accompanied by a message stating that the function is unimplemented. log_LD($rop, $op); logl($op) is assigned to $rop. # base e log10_LD($rop, $op); log10l($op) is assigned to $rop. # base 10 log2_LD($rop, $op); log2l($op) is assigned to $rop. # base 2 log1p_LD($rop, $op); log1pl($op) is assigned to $rop. # base e $iv = lrint_LD($op); lrintl($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. $iv = lround_LD($op); lroundl($op) is assigned to $iv This requires that perl's IV is large enough to hold a long int. Otherwise attempts to use this function will result in a fatal error, accompanied by a message stating that the function is unimplemented. modf_LD($rop1, $rop2, $op); modfl($op) is assigned to ($rop1, $rop2). nan_LD($rop, $op); nanl($op) is assigned to $rop. If Math::LongDouble::_have_nanl returns false, uses custom (_get_nan) XSub instead. nearbyint_LD($rop, $op); nearbyintl($op) is assigned to $rop. nextafter_LD($rop, $op1, $op2); nextafterl($op1, $op2) is assigned to $rop. pow_LD($rop, $op1, $op2); pow($op1, $op2) is assigned to $rop. remainder_LD($rop, $op1, $op2); remainderl($op1, $op2) is assigned to $rop. remquo_LD($rop1, $rop2, $op1, $op2); remquol($op1, $op2) is assigned to ($rop1, $rop2). I find this function can return unexpected results with some compilers. Therefore, this function is not tested in the test suite. Use it at your own risk. $iv = rint_LD($op); rintl($op) is assigned to $rop. $iv = round_LD($op); roundl($op) is assigned to $iv. scalbln_LD($rop, $op, $iv); scalblnl($op, $iv) is assigned to $rop. $iv should not contain a value that won't fit into a signed long int. scalbn_LD($rop, $op, $iv); scalbnl($op, $iv) is assigned to $rop. $iv should not contain a value that won't fir into a signed int. $iv = signbit_LD($op); signbitl($op) is assigned to $iv. If Math::LongDouble::_have_signbitl returns false signbit() is used instead. sincos_LD($rop1, $rop2, $op); sinl($op) is assigned to $rop1. cosl($op) is assigned to $rop2. sinh_LD($rop, $op); sinhl($op) is assigned to $rop. sin_LD($rop, $op); sin($op) is assigned to $rop. sqrt_LD($rop, $op); sqrtl($op) is assigned to $rop. tan_LD($rop, $op); tanl($op) is assigned to $rop. tanh_LD($rop, $op); tanhl($op) is assigned to $rop. tgamma_LD($rop, $op); gammal($op) is assigned to $rop. trunc_LD($rop, $op); truncl($op) is assigned to $rop.

$iv = Math::LongDouble::nnumflag(); # not exported Returns the value of the non-numeric flag. This flag is initialized to zero, but incemented by 1 whenever a function is handed a string containing non-numeric characters. The value of the flag therefore tells us how many times functions have been handed such a string. The flag can be reset to 0 by running Math::LongDouble::clear_nnum(). Math::LongDouble::set_nnum($iv); # not exported Resets the global non-numeric flag to the value specified by $iv. Math::LongDouble::clear_nnum(); # not exported Resets the global non-numeric flag to 0.(Essentially the same as running Math::LongDouble::set_nnum(0).) $bool = is_NaNLD($ld); Returns 1 if $ld is a Math::LongDouble NaN. Else returns 0 $int = is_InfLD($ld) If the Math::LongDouble object $ld is -inf, returns -1. If it is +inf, returns 1. Otherwise returns 0. $int = is_ZeroLD($ld); If the Math::LongDouble object $ld is -0, returns -1. If it is zero, returns 1. Otherwise returns 0. $int = cmp_NV($ld, $nv); $nv can be any perl number - ie NV, UV or IV. If the Math::LongDouble object $ld < $nv returns -1. If it is > $nv, returns 1. Otherwise returns 0. $hex = ld_bytes($ld); Returns the hex representation of the value held by $ld as a string of X hex characters, where X == the size of the long double (in bytes) multiplied by 2.

$min_prec = ld_min_inter_prec($orig_base, $orig_length, $to_base); $max_len = ld_max_orig_len($orig_base, $to_base, $to_prec); $min_base = ld_min_inter_base($orig_base, $orig_length, $to_prec); $max_base = ld_max_orig_base($orig_length, $to_base, $to_prec); The last 4 of the above functions establish the relationship between $orig_base, $orig_length, $to_base and $to_prec. Given any 3 of those 4, there's a function there to determine the value of the 4th. Let's say we have some base 10 floating point numbers comprising 16 significant digits, and we want to convert those numbers to a base 2 data type (say, 'long double'). If we then convert the value of that long double to a 16-digit base 10 float are we guaranteed of getting the original value back ? It all depends upon the precision of the 'long double' type, and the min_inter_prec() subroutine will tell you what the minimum required precision is (in order to be sure of getting the original value back). We have: $min_prec = ld_min_inter_prec($orig_base, $orig_length, $to_base); In our example case that becomes: $min_prec = ld_min_inter_prec(10, 16, 2); which will set $min_prec to 55. That is, so long as the long double type has a precision of at least 55 bits, you can pass 16-digit, base 10, floating point values to it and back again, and be assured of retrieving the original value. (Naturally, this is assuming absence of buggy behaviour, and correct rounding practice.) Similarly, you might like to know the maximum significant number of base 10 digits that can be specified, when assigning to (say) a 53-bit double. We have: $max_len = ld_max_orig_len($orig_base, $to_base, $to_prec); For this second example that becomes: $max_len = ld_max_orig_len(10, 2, 53); which will set $max_len to 15. That is, so long as your base 10 float consists of no more than 15 siginificant digits, you can pass it to a 53-bit double and back again, and be assured of retrieving the original value. (Again, we assume absence of bugs and correct rounding practice.) It is to be expected that ld_max_orig_len(10, 2, $double_prec) and ld_max_orig_len(10, 2, $long_double_prec) will (resp.) return the same values as LD_DBL_DIG and LD_LDBL_DIG. ($double_prec is the precision, in bits, of the C 'double' type, and $long_double_prec is the precision, in bits, of the C 'long double' type.) The last 2 of the above subroutines (ie ld_min_inter_base and ld_max_orig_base) are provided mainly for completeness. Normally, there wouldn't be a need to use these last 2 forms ... but who knows ... The above examples demonstrate usage in relation to conversion between bases 2 and 10. The functions apply just as well to conversions between bases of any values. The Math::MPFR module provides 4 identical functions, prefixed with 'mpfr_' instead of 'ld_' (to avoid name clashes). Similarly, it provides constants (prefixed with 'MPFR_' instead of 'LD_') that reflect the values of float.h's DBL_DIG and LDBL_DIG.

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. Copyright 2012-16, Sisyphus

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

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