package Math::MPFR;
use strict;
use warnings;
use POSIX;
use Config;
use Math::MPFR::Prec;
use Math::MPFR::Random; # Needs to be loaded before Math::MPFR
use constant GMP_RNDN => 0;
use constant GMP_RNDZ => 1;
use constant GMP_RNDU => 2;
use constant GMP_RNDD => 3;
use constant MPFR_RNDN => 0;
use constant MPFR_RNDZ => 1;
use constant MPFR_RNDU => 2;
use constant MPFR_RNDD => 3;
use constant MPFR_RNDA => 4;
use constant MPFR_RNDF => 5;
use constant _UOK_T => 1;
use constant _IOK_T => 2;
use constant _NOK_T => 3;
use constant _POK_T => 4;
use constant _MATH_MPFR_T => 5;
use constant _MATH_GMPf_T => 6;
use constant _MATH_GMPq_T => 7;
use constant _MATH_GMPz_T => 8;
use constant _MATH_GMP_T => 9;
use constant _MATH_MPC_T => 10;
use constant MPFR_FLAGS_UNDERFLOW => 1;
use constant MPFR_FLAGS_OVERFLOW => 2;
use constant MPFR_FLAGS_NAN => 4;
use constant MPFR_FLAGS_INEXACT => 8;
use constant MPFR_FLAGS_ERANGE => 16;
use constant MPFR_FLAGS_DIVBY0 => 32;
use constant MPFR_FLAGS_ALL => 63;
use constant MPFR_FREE_LOCAL_CACHE => 1;
use constant MPFR_FREE_GLOBAL_CACHE => 2;
use constant LITTLE_ENDIAN => $Config{byteorder} =~ /^1/ ? 1 : 0;
use constant MM_HP => LITTLE_ENDIAN ? 'h*' : 'H*';
use constant MPFR_3_1_6_OR_LATER => Math::MPFR::Random::_MPFR_VERSION() > 196869 ? 1 : 0;
use constant MPFR_4_0_2_OR_LATER => Math::MPFR::Random::_MPFR_VERSION() >= 262146 ? 1 : 0;
use constant MPFR_PV_NV_BUG => Math::MPFR::Random::_has_pv_nv_bug();
use constant NV_IS_DOUBLEDOUBLE => 1 + (2 ** -200) > 1 ? 1 : 0;
# Inspired by https://github.com/Perl/perl5/issues/19550, which affects only perl-5.35.10:
use constant ISSUE_19550 => Math::MPFR::Random::_issue_19550();
use subs qw(MPFR_VERSION MPFR_VERSION_MAJOR MPFR_VERSION_MINOR
MPFR_VERSION_PATCHLEVEL MPFR_VERSION_STRING
RMPFR_PREC_MIN RMPFR_PREC_MAX
MPFR_DBL_DIG MPFR_LDBL_DIG MPFR_FLT128_DIG
GMP_LIMB_BITS GMP_NAIL_BITS
);
use overload
'++' => \&overload_inc,
'--' => \&overload_dec,
'+' => \&overload_add,
'-' => \&overload_sub,
'*' => \&overload_mul,
'/' => \&overload_div,
'+=' => \&overload_add_eq,
'-=' => \&overload_sub_eq,
'*=' => \&overload_mul_eq,
'/=' => \&overload_div_eq,
'""' => \&overload_string,
'>' => \&overload_gt,
'>=' => \&overload_gte,
'<' => \&overload_lt,
'<=' => \&overload_lte,
'<=>' => \&overload_spaceship,
'==' => \&overload_equiv,
'!=' => \&overload_not_equiv,
'!' => \&overload_not,
'bool' => \&overload_true,
'=' => \&overload_copy,
'abs' => \&overload_abs,
'**' => \&overload_pow,
'**=' => \&overload_pow_eq,
'<<' => \&overload_mul_2exp,
'<<=' => \&overload_mul_2exp_eq,
'>>' => \&overload_div_2exp,
'>>=' => \&overload_div_2exp_eq,
'atan2'=> \&overload_atan2,
'cos' => \&overload_cos,
'sin' => \&overload_sin,
'log' => \&overload_log,
'exp' => \&overload_exp,
'int' => \&overload_int,
'sqrt' => \&overload_sqrt;
require Exporter;
*import = \&Exporter::import;
require DynaLoader;
my @tags = qw(
GMP_RNDD GMP_RNDN GMP_RNDU GMP_RNDZ
IOK_flag NOK_flag POK_flag
MPFR_DBL_DIG MPFR_FLT128_DIG MPFR_LDBL_DIG
MPFR_FLAGS_ALL MPFR_FLAGS_DIVBY0 MPFR_FLAGS_ERANGE MPFR_FLAGS_INEXACT MPFR_FLAGS_NAN
MPFR_FLAGS_OVERFLOW MPFR_FLAGS_UNDERFLOW
MPFR_FREE_LOCAL_CACHE MPFR_FREE_GLOBAL_CACHE
MPFR_RNDA MPFR_RNDD MPFR_RNDF MPFR_RNDN MPFR_RNDU MPFR_RNDZ MPFR_PV_NV_BUG
MPFR_VERSION MPFR_VERSION_MAJOR MPFR_VERSION_MINOR MPFR_VERSION_PATCHLEVEL MPFR_VERSION_STRING
RMPFR_PREC_MAX RMPFR_PREC_MIN RMPFR_VERSION_NUM
Rmpfr_abs Rmpfr_acos Rmpfr_acosh Rmpfr_acospi Rmpfr_acosu
Rmpfr_add Rmpfr_add_d Rmpfr_add_q Rmpfr_add_si Rmpfr_add_ui Rmpfr_add_z
Rmpfr_agm Rmpfr_ai
Rmpfr_asin Rmpfr_asinh Rmpfr_asinpi Rmpfr_asinu
Rmpfr_atan Rmpfr_atan2 Rmpfr_atan2pi Rmpfr_atan2u Rmpfr_atanh Rmpfr_atanpi Rmpfr_atanu
Rmpfr_beta
Rmpfr_buildopt_decimal_p Rmpfr_buildopt_float128_p Rmpfr_buildopt_gmpinternals_p
Rmpfr_buildopt_sharedcache_p Rmpfr_buildopt_tls_p Rmpfr_buildopt_tune_case
Rmpfr_can_round Rmpfr_cbrt Rmpfr_ceil Rmpfr_check_range
Rmpfr_clear Rmpfr_clear_divby0 Rmpfr_clear_erangeflag Rmpfr_clear_flags Rmpfr_clear_inexflag
Rmpfr_clear_nanflag Rmpfr_clear_overflow Rmpfr_clear_underflow Rmpfr_clears
Rmpfr_cmp Rmpfr_cmp_IV Rmpfr_cmp_NV Rmpfr_cmp_d Rmpfr_cmp_f Rmpfr_cmp_float128 Rmpfr_cmp_ld
Rmpfr_cmp_q Rmpfr_cmp_si Rmpfr_cmp_si_2exp Rmpfr_cmp_sj Rmpfr_cmp_ui Rmpfr_cmp_ui_2exp
Rmpfr_cmp_uj Rmpfr_cmp_z Rmpfr_cmpabs Rmpfr_cmpabs_ui
Rmpfr_compound_si
Rmpfr_const_catalan Rmpfr_const_euler Rmpfr_const_log2 Rmpfr_const_pi
Rmpfr_copysign
Rmpfr_cos Rmpfr_cosh Rmpfr_cospi Rmpfr_cosu Rmpfr_cot Rmpfr_coth
Rmpfr_csc Rmpfr_csch
Rmpfr_d_div Rmpfr_d_sub Rmpfr_deref2 Rmpfr_digamma Rmpfr_dim
Rmpfr_div Rmpfr_div_2exp Rmpfr_div_2si Rmpfr_div_2ui Rmpfr_div_d Rmpfr_div_q Rmpfr_div_si
Rmpfr_div_ui Rmpfr_div_z Rmpfr_divby0_p
Rmpfr_dot Rmpfr_dump Rmpfr_eint Rmpfr_eq Rmpfr_equal_p Rmpfr_erandom Rmpfr_erangeflag_p
Rmpfr_erf Rmpfr_erfc Rmpfr_exp Rmpfr_exp10 Rmpfr_exp10m1 Rmpfr_exp2 Rmpfr_exp2m1 Rmpfr_expm1
Rmpfr_fac_ui
Rmpfr_fits_IV_p Rmpfr_fits_intmax_p Rmpfr_fits_sint_p Rmpfr_fits_slong_p Rmpfr_fits_sshort_p
Rmpfr_fits_uint_p Rmpfr_fits_uintmax_p Rmpfr_fits_ulong_p Rmpfr_fits_ushort_p
Rmpfr_flags_clear Rmpfr_flags_restore Rmpfr_flags_save Rmpfr_flags_set Rmpfr_flags_test
Rmpfr_floor
Rmpfr_fma Rmpfr_fmma Rmpfr_fmms Rmpfr_fmod Rmpfr_fmod_ui Rmpfr_fmodquo Rmpfr_fms
Rmpfr_fpif_export Rmpfr_fpif_import Rmpfr_fprintf Rmpfr_frac
Rmpfr_free_cache Rmpfr_free_cache2 Rmpfr_free_pool Rmpfr_frexp Rmpfr_gamma Rmpfr_gamma_inc
Rmpfr_get_DECIMAL128 Rmpfr_get_DECIMAL64 Rmpfr_get_FLOAT128 Rmpfr_get_IV Rmpfr_get_LD Rmpfr_get_NV
Rmpfr_get_d Rmpfr_get_d1 Rmpfr_get_d_2exp Rmpfr_get_default_prec Rmpfr_get_default_rounding_mode
Rmpfr_get_emax Rmpfr_get_emax_max Rmpfr_get_emax_min Rmpfr_get_emin Rmpfr_get_emin_max
Rmpfr_get_emin_min Rmpfr_get_exp Rmpfr_get_f Rmpfr_get_float128 Rmpfr_get_flt Rmpfr_get_ld
Rmpfr_get_ld_2exp Rmpfr_get_patches Rmpfr_get_prec Rmpfr_get_q Rmpfr_get_si Rmpfr_get_sj
Rmpfr_get_str Rmpfr_get_str_ndigits Rmpfr_get_str_ndigits_alt Rmpfr_get_ui Rmpfr_get_uj
Rmpfr_get_version Rmpfr_get_z Rmpfr_get_z_2exp Rmpfr_get_z_exp
Rmpfr_grandom Rmpfr_greater_p Rmpfr_greaterequal_p Rmpfr_hypot Rmpfr_inexflag_p Rmpfr_inf_p
Rmpfr_init Rmpfr_init2 Rmpfr_init2_nobless Rmpfr_init_nobless Rmpfr_init_set Rmpfr_init_set_IV
Rmpfr_init_set_IV_nobless Rmpfr_init_set_NV Rmpfr_init_set_NV_nobless Rmpfr_init_set_d
Rmpfr_init_set_d_nobless Rmpfr_init_set_f Rmpfr_init_set_f_nobless Rmpfr_init_set_float128
Rmpfr_init_set_float128_nobless Rmpfr_init_set_ld Rmpfr_init_set_nobless Rmpfr_init_set_q
Rmpfr_init_set_q_nobless Rmpfr_init_set_si Rmpfr_init_set_si_nobless Rmpfr_init_set_str
Rmpfr_init_set_str_nobless Rmpfr_init_set_ui Rmpfr_init_set_ui_nobless Rmpfr_init_set_z
Rmpfr_init_set_z_nobless Rmpfr_inits Rmpfr_inits2 Rmpfr_inits2_nobless Rmpfr_inits_nobless
Rmpfr_inp_str Rmpfr_integer_p Rmpfr_integer_string Rmpfr_j0 Rmpfr_j1 Rmpfr_jn Rmpfr_less_p
Rmpfr_lessequal_p Rmpfr_lessgreater_p Rmpfr_lgamma Rmpfr_li2 Rmpfr_lngamma
Rmpfr_log Rmpfr_log10 Rmpfr_log10p1 Rmpfr_log1p Rmpfr_log2 Rmpfr_log2p1 Rmpfr_log_ui
Rmpfr_max Rmpfr_min Rmpfr_min_prec Rmpfr_modf
Rmpfr_mul Rmpfr_mul_2exp Rmpfr_mul_2si Rmpfr_mul_2ui Rmpfr_mul_d Rmpfr_mul_q Rmpfr_mul_si
Rmpfr_mul_ui Rmpfr_mul_z
Rmpfr_nan_p Rmpfr_nanflag_p Rmpfr_neg Rmpfr_nextabove Rmpfr_nextbelow Rmpfr_nexttoward
Rmpfr_nrandom Rmpfr_number_p Rmpfr_out_str Rmpfr_overflow_p
Rmpfr_pow Rmpfr_pow_IV Rmpfr_pow_si Rmpfr_pow_sj Rmpfr_pow_ui Rmpfr_pow_uj Rmpfr_pow_z
Rmpfr_pown Rmpfr_powr Rmpfr_prec_round Rmpfr_print_rnd_mode Rmpfr_printf Rmpfr_q_div
Rmpfr_randclear Rmpfr_randinit_default Rmpfr_randinit_lc_2exp Rmpfr_randinit_lc_2exp_size
Rmpfr_randinit_mt Rmpfr_random2 Rmpfr_randseed Rmpfr_randseed_ui Rmpfr_rec_root Rmpfr_rec_sqrt
Rmpfr_regular_p Rmpfr_reldiff Rmpfr_remainder Rmpfr_remquo
Rmpfr_rint Rmpfr_rint_ceil Rmpfr_rint_floor Rmpfr_rint_round Rmpfr_rint_roundeven Rmpfr_rint_trunc
Rmpfr_root Rmpfr_rootn_ui Rmpfr_round Rmpfr_round_nearest_away Rmpfr_roundeven
Rmpfr_sec Rmpfr_sech Rmpfr_set Rmpfr_set_DECIMAL128 Rmpfr_set_DECIMAL64 Rmpfr_set_FLOAT128
Rmpfr_set_IV Rmpfr_set_LD Rmpfr_set_NV Rmpfr_set_d Rmpfr_set_default_prec
Rmpfr_set_default_rounding_mode Rmpfr_set_divby0 Rmpfr_set_emax Rmpfr_set_emin Rmpfr_set_erangeflag
Rmpfr_set_exp Rmpfr_set_f Rmpfr_set_float128 Rmpfr_set_flt Rmpfr_set_inexflag Rmpfr_set_inf
Rmpfr_set_ld Rmpfr_set_nan Rmpfr_set_nanflag Rmpfr_set_overflow Rmpfr_set_prec Rmpfr_set_prec_raw
Rmpfr_set_q Rmpfr_set_si Rmpfr_set_si_2exp Rmpfr_set_sj Rmpfr_set_sj_2exp Rmpfr_set_str Rmpfr_set_ui
Rmpfr_set_ui_2exp Rmpfr_set_uj Rmpfr_set_uj_2exp Rmpfr_set_underflow Rmpfr_set_z Rmpfr_set_z_2exp
Rmpfr_set_zero Rmpfr_setsign Rmpfr_sgn Rmpfr_si_div Rmpfr_si_sub Rmpfr_signbit
Rmpfr_sin Rmpfr_sin_cos Rmpfr_sinh Rmpfr_sinh_cosh Rmpfr_sinpi Rmpfr_sinu
Rmpfr_snprintf Rmpfr_sprintf Rmpfr_sqr Rmpfr_sqrt Rmpfr_sqrt_ui Rmpfr_strtofr
Rmpfr_sub Rmpfr_sub_d Rmpfr_sub_q Rmpfr_sub_si Rmpfr_sub_ui Rmpfr_sub_z Rmpfr_subnormalize
Rmpfr_sum Rmpfr_swap
Rmpfr_tan Rmpfr_tanh Rmpfr_tanpi Rmpfr_tanu
Rmpfr_total_order_p Rmpfr_trunc
Rmpfr_ui_div Rmpfr_ui_pow Rmpfr_ui_pow_ui Rmpfr_ui_sub Rmpfr_underflow_p Rmpfr_unordered_p
Rmpfr_urandom Rmpfr_urandomb Rmpfr_y0 Rmpfr_y1 Rmpfr_yn
Rmpfr_z_div Rmpfr_z_sub Rmpfr_zero_p Rmpfr_zeta Rmpfr_zeta_ui
TRmpfr_inp_str TRmpfr_out_str
anytoa atodouble atonum atonv
check_exact_decimal decimalize doubletoa
fr_cmp_q_rounded mpfr_max_orig_len mpfr_min_inter_prec mpfrtoa numtoa nvtoa nvtoa_test
prec_cast q_add_fr q_cmp_fr q_div_fr q_mul_fr q_sub_fr rndna
);
@Math::MPFR::EXPORT_OK = (@tags, 'bytes');
our $VERSION = '4.28';
#$VERSION = eval $VERSION;
Math::MPFR->DynaLoader::bootstrap($VERSION);
# The ':mpfr' tag (below) is the same as @EXPORT_OK,
# except that the ':mpfr' tag does not include 'bytes'.
%Math::MPFR::EXPORT_TAGS =(mpfr => [@tags]);
$Math::MPFR::NNW = 0; # Set to 1 to allow "non-numeric" warnings for operations involving
# strings that contain non-numeric characters.
$Math::MPFR::NOK_POK = 0; # Set to 1 to allow warnings in new() and overloaded operations when
# a scalar that has set both NOK (NV) and POK (PV) flags is encountered
$Math::MPFR::doubletoa_fallback = 0; # If FALLBACK_NOTIFY is defined, this scalar Will be automatically
# incremented whenever the grisu3 algorithm (used by doubletoa) fails
# to produce correct result, and thus falls back to its designated
# fallback routine. (See the doubletoa documentation for details.)
%Math::MPFR::NV_properties = _get_NV_properties();
my %bytes = (53 => \&_d_bytes,
64 => \&_ld_bytes,
2098 => \&_dd_bytes,
113 => \&_f128_bytes,
);
my %fmt = (53 => 'a8',
64 => 'a10',
2098 => 'a16',
113 => 'a16',
);
sub dl_load_flags {0} # Prevent DynaLoader from complaining and croaking
sub Rmpfr_out_str {
if(@_ == 4) {
die "Inappropriate 1st arg supplied to Rmpfr_out_str" if _itsa($_[0]) != _MATH_MPFR_T;
return _Rmpfr_out_str($_[0], $_[1], $_[2], $_[3]);
}
if(@_ == 5) {
if(_itsa($_[0]) == _MATH_MPFR_T) {return _Rmpfr_out_strS($_[0], $_[1], $_[2], $_[3], $_[4])}
die "Incorrect args supplied to Rmpfr_out_str" if _itsa($_[1]) != _MATH_MPFR_T;
return _Rmpfr_out_strP($_[0], $_[1], $_[2], $_[3], $_[4]);
}
if(@_ == 6) {
die "Inappropriate 2nd arg supplied to Rmpfr_out_str" if _itsa($_[1]) != _MATH_MPFR_T;
return _Rmpfr_out_strPS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5]);
}
die "Wrong number of arguments supplied to Rmpfr_out_str()";
}
sub TRmpfr_out_str {
if(@_ == 5) {
die "Inappropriate 4th arg supplied to TRmpfr_out_str"
if _itsa($_[3]) != _MATH_MPFR_T;
return _TRmpfr_out_str($_[0], $_[1], $_[2], $_[3], $_[4]);
}
if(@_ == 6) {
if(_itsa($_[3]) == _MATH_MPFR_T) {return _TRmpfr_out_strS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5])}
die "Incorrect args supplied to TRmpfr_out_str"
if _itsa($_[4]) != _MATH_MPFR_T;
return _TRmpfr_out_strP($_[0], $_[1], $_[2], $_[3], $_[4], $_[5]);
}
if(@_ == 7) {
die "Inappropriate 5th arg supplied to TRmpfr_out_str"
if _itsa($_[4]) != _MATH_MPFR_T;
return _TRmpfr_out_strPS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5], $_[6]);
}
die "Wrong number of arguments supplied to TRmpfr_out_str()";
}
sub Rmpfr_get_str {
my ($mantissa, $exponent) = Rmpfr_deref2($_[0], $_[1], $_[2], $_[3]);
if($mantissa =~ s/@//g) { return $mantissa }
if($mantissa =~ /\-/ && $mantissa !~ /[^0,\-]/) {return '-0'}
if($mantissa !~ /[^0]/ ) {return '0'}
my $len = substr($mantissa, 0, 1) eq '-' ? 2 : 1;
if(!$_[2]) {
while(length($mantissa) > $len && substr($mantissa, -1, 1) eq '0') {
substr($mantissa, -1, 1, '');
}
}
$exponent--;
my $sep = $_[1] <= 10 ? 'e' : '@';
if(length($mantissa) == $len) {
if($exponent) {return $mantissa . $sep . $exponent}
return $mantissa;
}
substr($mantissa, $len, 0, '.');
if($exponent) {return $mantissa . $sep . $exponent}
return $mantissa;
}
sub overload_string {
return Rmpfr_get_str($_[0], 10, 0, Rmpfr_get_default_rounding_mode());
}
sub Rmpfr_integer_string {
if($_[1] < 2 || $_[1] > 36) {die("Second argument supplied to Rmpfr_integer_string() is not in acceptable range")}
my($mantissa, $exponent) = Rmpfr_deref2($_[0], $_[1], 0, $_[2]);
if($mantissa =~ s/@//g) { return $mantissa }
if($mantissa =~ /\-/ && $mantissa !~ /[^0,\-]/) {return '-0'}
return 0 if $exponent < 1;
my $sign = substr($mantissa, 0, 1) eq '-' ? 1 : 0;
$mantissa = substr($mantissa, 0, $exponent + $sign);
return $mantissa;
}
sub new {
# This function caters for 2 possibilities:
# 1) that 'new' has been called OOP style - in which
# case there will be a maximum of 3 args
# 2) that 'new' has been called as a function - in
# which case there will be a maximum of 2 args.
# If there are no args, then we just want to return an
# initialized Math::MPFR object
if(!@_) {return Rmpfr_init()}
if(@_ > 3) {die "Too many arguments supplied to new()"}
# If 'new' has been called OOP style, the first arg is the string
# "Math::MPFR" which we don't need - so let's remove it. However,
# if the first arg is a Math::MPFR object (which is a possibility),
# then we'll get a fatal error when we check it for equivalence to
# the string "Math::MPFR". So we first need to check that it's not
# an object - which we'll do by using the ref() function:
if(!ref($_[0]) && $_[0] eq "Math::MPFR") {
shift;
if(!@_) {return Rmpfr_init()}
}
# @_ can now contain a maximum of 2 args - the value, and if the value is
# a string, (optionally) the base of the numeric string.
if(@_ > 2) {die "Too many arguments supplied to new() - expected no more than two"}
my ($arg1, $type, $base);
# $_[0] is the value, $_[1] (if supplied) is the base of the number
# in the string $[_0].
$arg1 = shift; # At this point, an infnan might acquire a POK flag - thus
# assigning to $type a value of 4, instead of 3. Such behaviour also
# turns $arg into a PV and NV dualvar. It's a fairly inconsequential
# bug - https://github.com/Perl/perl5/issues/19550.
# I could workaround this by simply not shifting and re-assigning, but
# I'll leave it as it is - otherwise there's nothing to mark that this
# minor issue (which might also show up in user code) ever existed.
$base = 0;
$type = _itsa($arg1);
if(!$type) {die "Inappropriate argument supplied to new()"}
my @ret;
# Create a Math::MPFR object that has $arg1 as its value.
# Die if there are any additional args (unless $type == 4)
if($type == _UOK_T) {
if(@_ ) {die "Too many arguments supplied to new() - expected only one"}
if(Math::MPFR::_has_longlong()) {
my $ret = Rmpfr_init();
Rmpfr_set_uj($ret, $arg1, Rmpfr_get_default_rounding_mode());
return $ret;
}
else {
@ret = Rmpfr_init_set_ui($arg1, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
}
if($type == _IOK_T) {
if(@_ ) {die "Too many arguments supplied to new() - expected only one"}
if(Math::MPFR::_has_longlong()) {
my $ret = Rmpfr_init();
Rmpfr_set_sj($ret, $arg1, Rmpfr_get_default_rounding_mode());
return $ret;
}
else {
@ret = Rmpfr_init_set_si($arg1, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
}
if($type == _NOK_T) {
if(@_ ) {die "Too many arguments supplied to new() - expected only one"}
if(MPFR_PV_NV_BUG) {
if(_SvPOK($arg1)) {
set_nok_pok(nok_pokflag() + 1);
if($Math::MPFR::NOK_POK) {
warn "Scalar passed to new() is both NV and PV. Using NV (numeric) value";
}
}
}
my $ret = Rmpfr_init();
Rmpfr_set_NV($ret, $arg1, Rmpfr_get_default_rounding_mode());
return $ret;
}
if($type == _POK_T) {
if(@_ > 1) {die "Too many arguments supplied to new() - expected no more than two"}
if(_SvNOK($arg1)) {
set_nok_pok(nok_pokflag() + 1);
if($Math::MPFR::NOK_POK) {
warn "Scalar passed to new() is both NV and PV. Using PV (string) value";
}
}
$base = shift if @_;
@ret = Rmpfr_init_set_str($arg1, $base, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
if($type == _MATH_MPFR_T) {
if(@_) {die "Too many arguments supplied to new() - expected only one"}
@ret = Rmpfr_init_set($arg1, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
if($type == _MATH_GMPf_T) {
if(@_) {die "Too many arguments supplied to new() - expected only one"}
@ret = Rmpfr_init_set_f($arg1, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
if($type == _MATH_GMPq_T) {
if(@_) {die "Too many arguments supplied to new() - expected only one"}
@ret = Rmpfr_init_set_q($arg1, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
if($type == _MATH_GMPz_T || $type == _MATH_GMP_T) {
if(@_) {die "Too many arguments supplied to new() - expected only one"}
@ret = Rmpfr_init_set_z($arg1, Rmpfr_get_default_rounding_mode());
return $ret[0];
}
}
sub Rmpfr_printf {
if(@_ == 3){
if(_itsa($_[1]) == 2) {wrap_mpfr_printf_rnd(@_)}
else {die "The second (of 3) arguments given to Rmpfr_printf() is not a valid rounding argument"}
}
else {die "Rmpfr_printf must take 2 or 3 arguments: format string, [rounding,], and variable" if @_ != 2;
wrap_mpfr_printf(@_)}
}
sub Rmpfr_fprintf {
if(@_ == 4){
if(_itsa($_[2]) == 2) {wrap_mpfr_fprintf_rnd(@_)}
else {die "The third (of 4) arguments given to Rmpfr_fprintf() is not a valid rounding argument"}
}
else {die "Rmpfr_fprintf must take 3 or 4 arguments: filehandle, format string, [rounding,], and variable" if @_ != 3;
wrap_mpfr_fprintf(@_)}
}
sub Rmpfr_sprintf {
my $len;
if(@_ == 5){
if(_itsa($_[2]) == 2) {
$len = wrap_mpfr_sprintf_rnd(@_);
return $len;
}
else {die "The third (of 5) arguments given to Rmpfr_sprintf() is not a valid rounding argument"}
}
die "Rmpfr_sprintf must take 4 or 5 arguments: buffer, format string, [rounding,], variable and buffer size" if @_ != 4;
$len = wrap_mpfr_sprintf(@_);
return $len;
}
sub Rmpfr_snprintf {
my $len;
if(@_ == 6){
if(_itsa($_[3]) == 2) {
$len = wrap_mpfr_snprintf_rnd(@_);
return $len;
}
else {die "The fourth (of 6) arguments given to Rmpfr_snprintf() is not a valid rounding argument"}
}
die "Rmpfr_snprintf must take 5 or 6 arguments: buffer, bytes written, format string, [rounding,], variable and buffer size" if @_ != 5;
$len = wrap_mpfr_snprintf(@_);
return $len;
}
sub Rmpfr_inits {
my @ret;
for(1 .. $_[0]) {
$ret[$_ - 1] = Rmpfr_init();
}
return @ret;
}
sub Rmpfr_inits2 {
my @ret;
for(1 .. $_[1]) {
$ret[$_ - 1] = Rmpfr_init2($_[0]);
}
return @ret;
}
sub Rmpfr_inits_nobless {
my @ret;
for(1 .. $_[0]) {
$ret[$_ - 1] = Rmpfr_init_nobless();
}
return @ret;
}
sub Rmpfr_inits2_nobless {
my @ret;
for(1 .. $_[1]) {
$ret[$_ - 1] = Rmpfr_init2_nobless($_[0]);
}
return @ret;
}
sub MPFR_VERSION () {return _MPFR_VERSION()}
sub MPFR_VERSION_MAJOR () {return _MPFR_VERSION_MAJOR()}
sub MPFR_VERSION_MINOR () {return _MPFR_VERSION_MINOR()}
sub MPFR_VERSION_PATCHLEVEL () {return _MPFR_VERSION_PATCHLEVEL()}
sub MPFR_VERSION_STRING () {return _MPFR_VERSION_STRING()}
sub MPFR_DBL_DIG () {return _DBL_DIG()}
sub MPFR_LDBL_DIG () {return _LDBL_DIG()}
sub MPFR_FLT128_DIG () {return _FLT128_DIG()}
sub GMP_LIMB_BITS () {return _GMP_LIMB_BITS()}
sub GMP_NAIL_BITS () {return _GMP_NAIL_BITS()}
sub atonum {
if(MPFR_3_1_6_OR_LATER) {
return atonv($_[0])
if $_[0] =~ /^[\-\+]?inf|^[\-\+]?nan/i; # buggy perls can numify infnan strings to 0.
my $copy = $_[0]; # Don't mess with $_[0] flags
my $ret = "$copy" + 0;
return $ret if _itsa($ret) < 3; # IV
return atonv($_[0]); # NV
}
die("atonum needs atonv, but atonv is not available with this version (", MPFR_VERSION_STRING, ") of the mpfr library");
}
sub check_exact_decimal {
unless( MPFR_3_1_6_OR_LATER ) {
warn "check_exact_decimal() requires mpfr-3.1.6 or later\n";
die "Math::MPFR was built against mpfr-", MPFR_VERSION_STRING;
}
my($str, $op) = (shift, shift);
if( !Rmpfr_regular_p($op) ) { # $op is either zero, inf, or nan.
if( Rmpfr_nan_p($op) && $str =~ /^nan$/i ) { return 1 }
if( Rmpfr_signbit($op) ) {
if( Rmpfr_zero_p($op) && $str eq '-0' ) { return 1 }
if( Rmpfr_inf_p($op) && $str =~ /^\-inf$/i ) { return 1 }
}
else {
if( Rmpfr_zero_p($op) && $str eq '0' ) { return 1 }
if( Rmpfr_inf_p($op) && $str =~ '^inf$/i' ) { return 1 }
}
return 0;
}
my $check = Rmpfr_init2(Rmpfr_get_prec($op));
my $inex = Rmpfr_strtofr($check, $str, 10, MPFR_RNDN);
if($inex == 0 && $op == $check) { return 1 }
return 0;
}
sub mpfr_min_inter_prec {
die "Wrong number of args to mpfr_min_inter_prec()" unless @_ == 3;
my $ob = shift; # base of original representation
my $op = shift; # precision (no. of base $ob digits in mantissa) of original representation
my $nb = shift; # base of new representation
my $np; # min required precision (no. of base $nb digits in mantissa) of new representation
my %h = (2 => 1, 4 => 2, 8 => 3, 16 => 4, 32 => 5, 64 => 6,
3 => 1, 9 => 2, 27 => 3,
5 => 1, 25 => 2,
6 => 1, 36 => 2,
7 => 1, 49 => 2);
return $op
if $ob == $nb;
if(_bases_are_power_of_same_integer($ob, $nb)) {
$np = POSIX::ceil($op * $h{$ob} / $h{$nb});
return $np;
}
$np = POSIX::ceil(1 + ($op * log($ob) / log($nb)));
return $np;
}
sub mpfr_max_orig_len {
die "Wrong number of args to maximum_orig_length()" if @_ != 3;
my $ob = shift; # base of original representation
my $nb = shift; # base of new representation
my $np = shift; # precision (no. of base $nb digits in mantissa) of new representation
my $op; # max precision (no. of base $ob digits in mantissa) of original representation
my %h = (2 => 1, 4 => 2, 8 => 3, 16 => 4, 32 => 5, 64 => 6,
3 => 1, 9 => 2, 27 => 3,
5 => 1, 25 => 2,
6 => 1, 36 => 2,
7 => 1, 49 => 2);
return $np
if $ob == $nb;
if(_bases_are_power_of_same_integer($ob, $nb)) {
$op = POSIX::floor($np * $h{$nb} / $h{$ob});
return $op;
}
$op = POSIX::floor(($np - 1) * log($nb) / log($ob));
return $op;
}
sub _bases_are_power_of_same_integer {
# This function currently doesn't get called if $_[0] == $_[1]
# Return true if:
# 1) Both $_[0] and $_[1] are in the range 2..64 (inclusive)
# &&
# 2) Both $_[0] and $_[1] are powers of the same integer - eg 8 & 32, or 9 & 27, or 7 & 49, ....
# Else return false.
return 1
if( ($_[0] == 2 || $_[0] == 16 || $_[0] == 8 || $_[0] == 64 || $_[0] == 32 || $_[0] == 4)
&&
($_[1] == 2 || $_[1] == 16 || $_[1] == 8 || $_[1] == 64 || $_[1] == 32 || $_[1] == 4) );
return 1
if( ($_[0] == 3 || $_[0] == 9 || $_[0] == 27)
&&
($_[1] == 3 || $_[1] == 9 || $_[1] == 27) );
return 1
if( ($_[0] == 5 || $_[0] == 25)
&&
($_[1] == 5 || $_[1] == 25) );
return 1
if( ($_[0] == 6 || $_[0] == 36)
&&
($_[1] == 6 || $_[1] == 36) );
return 1
if( ($_[0] == 7 || $_[0] == 49)
&&
($_[1] == 7 || $_[1] == 49) );
return 0;
}
sub bytes {
my($val, $bits, $ret) = (shift, shift);
my $itsa = _itsa($val);
# $itsa == 4 implies that $val's POK flag is set && IOK flag is unset.
# $itsa == 5 implies that $val is a Math::MPFR::object.
# We now croak if neither of those cases is satisfied.
die "1st arg to Math::MPFR::bytes must be either a string or a Math::MPFR object"
if($itsa != 4 && $itsa != 5);
die "2nd argument given to Math::MPFR::bytes is neither 53 nor 64 nor 2098 nor 113"
unless($bits == 53 || $bits == 64 || $bits == 2098 || $bits == 113);
$ret = $itsa == 4 ? unpack MM_HP, pack $fmt{$bits}, $bytes {$bits} -> ($val)
: unpack MM_HP, pack $fmt{$bits}, _bytes_fr($val, $bits);
return scalar reverse $ret if LITTLE_ENDIAN;
return $ret;
}
sub rndna {
my $coderef = shift;
my $rop = shift;
my $big_prec = Rmpfr_get_prec($rop) + 1;
my $ret;
if($coderef == \&Rmpfr_prec_round) {
my $temp = Rmpfr_init2($big_prec); # need a temp object
Rmpfr_set($temp, $rop, MPFR_RNDN);
$ret = Rmpfr_prec_round($temp, $_[0] + 1, MPFR_RNDN);
if(!$ret) {return Rmpfr_prec_round($rop, $_[0], MPFR_RNDA)}
return Rmpfr_prec_round($rop, $_[0], MPFR_RNDN);
}
Rmpfr_prec_round($rop, $big_prec, MPFR_RNDN);
$ret = $coderef->($rop, @_, MPFR_RNDN);
if($ret) { # not a midpoint value
Rmpfr_prec_round($rop, $big_prec - 1, $ret < 0 ? MPFR_RNDA : MPFR_RNDZ);
return $ret;
}
if(_lsb($rop) == 0) {
Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDZ);
return 0;
}
return Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDA);
}
sub Rmpfr_round_nearest_away {
my $coderef = shift;
my $rop = shift;
my $big_prec = Rmpfr_get_prec($rop) + 1;
my $ret;
my $emin = Rmpfr_get_emin();
if($emin <= Rmpfr_get_emin_min()) {
warn "\n Rmpfr_round_nearest_away requires that emin ($emin)\n",
" be greater than or equal to emin_min (", Rmpfr_get_emin_min(), ")\n";
die " You need to set emin (using Rmpfr_set_emin()) accordingly";
}
Rmpfr_set_emin($emin - 1);
if($coderef == \&Rmpfr_prec_round) {
my $temp = Rmpfr_init2($big_prec); # need a temp object
Rmpfr_set($temp, $rop, MPFR_RNDN);
$ret = Rmpfr_prec_round($temp, $_[0] + 1, MPFR_RNDN);
if(!$ret) {
$ret = Rmpfr_prec_round($rop, $_[0], MPFR_RNDA);
Rmpfr_set_emin($emin);
return $ret;
}
$ret = Rmpfr_prec_round($rop, $_[0], MPFR_RNDN);
Rmpfr_set_emin($emin);
return $ret;
}
Rmpfr_prec_round($rop, $big_prec, MPFR_RNDN);
$ret = $coderef->($rop, @_, MPFR_RNDN);
if($ret) { # not a midpoint value
Rmpfr_prec_round($rop, $big_prec - 1, $ret < 0 ? MPFR_RNDA : MPFR_RNDZ);
Rmpfr_set_emin($emin);
return $ret;
}
my $nuisance = Rmpfr_init();
Rmpfr_set_ui ($nuisance, 2, MPFR_RNDD);
Rmpfr_pow_si ($nuisance, $nuisance, Rmpfr_get_emin(), MPFR_RNDD);
Rmpfr_div_2ui($nuisance, $nuisance, 1, MPFR_RNDD);
if(abs($rop) == $nuisance) {
Rmpfr_mul_ui($rop, $rop, 2, MPFR_RNDD);
Rmpfr_set_emin($emin);
return (Rmpfr_signbit($rop) ? -1 : 1);
}
if(_lsb($rop) == 0) {
Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDZ);
Rmpfr_set_emin($emin);
return 0;
}
$ret = Rmpfr_prec_round($rop, $big_prec - 1, MPFR_RNDA);
Rmpfr_set_emin($emin);
return $ret;
}
sub _get_NV_properties {
my($bits, $PREC, $max_dig, $min_pow, $normal_min, $NV_MAX, $nvtype, $emax, $emin);
if ($Config{nvtype} eq 'double') {
$bits = 53; $PREC = 64; $max_dig = 17; $min_pow = -1074;
$normal_min = 2 ** -1022; $NV_MAX = POSIX::DBL_MAX; $emin = -1073; $emax = 1024;
}
elsif($Config{nvtype} eq '__float128') {
$bits = 113; $PREC = 128; $max_dig = 36; $min_pow = -16494; $normal_min = 2 ** -16382;
$NV_MAX = 1.18973149535723176508575932662800702e+4932; $emin = -16493; $emax = 16384;
}
elsif($Config{nvtype} eq 'long double') {
if(_required_ldbl_mant_dig() == 53) {
$bits = 53; $PREC = 64; $max_dig = 17; $min_pow = -1074;
$normal_min = 2 ** -1022; $NV_MAX = POSIX::DBL_MAX; $emin = -1073; $emax = 1024;
}
elsif(_required_ldbl_mant_dig() == 113) {
$bits = 113; $PREC = 128; $max_dig = 36; $min_pow = -16494;
$normal_min = 2 ** -16382; $NV_MAX = POSIX::LDBL_MAX; $emin = -16493; $emax = 16384;
}
elsif(_required_ldbl_mant_dig() == 64) {
$bits = 64; $PREC = 80; $max_dig = 21; $min_pow = -16445;
$normal_min = 2 ** -16382; $NV_MAX = POSIX::LDBL_MAX; $emin = -16444; $emax = 16384;
}
elsif(_required_ldbl_mant_dig() == 2098) {
$bits = 2098; $PREC = 2104; $max_dig = 33; $min_pow = -1074;
$normal_min = 2 ** -1022; $NV_MAX = POSIX::LDBL_MAX; $emin = -1073; $emax = 1024;
}
else {
my %properties = ('type' => 'unknown long double type');
return %properties;
}
}
else {
my %properties = ('type' => 'unknown nv type');
return %properties;
}
my %properties = (
'bits' => $bits,
'PREC' => $PREC,
'max_dig' => $max_dig,
'min_pow' => $min_pow,
'normal_min' => $normal_min,
'NV_MAX' => $NV_MAX,
'emin' => $emin,
'emax' => $emax,
);
return %properties;
}
sub perl_set_fallback_flag {
$Math::MPFR::doubletoa_fallback++;
}
sub mpfrtoa {
die "1st arg to mpfrtoa() must be a Math::MPFR object"
unless ref($_[0]) eq 'Math::MPFR';
my $obj = shift;
my $min_normal_prec = defined($_[0]) ? shift : 0;
return _mpfrtoa($obj, $min_normal_prec);
}
sub anytoa {
die "1st argument given to anytoa() must be a Math::MPFR object"
unless Math::MPFR::_itsa($_[0]) == 5;
my $v = shift;
my $bits;
if($_[0]) {
$bits = shift;
die "2nd argument given to anytoa() must be 0 or 53 or 64 or 113 or 2098"
unless ($bits == 53 || $bits == 64 || $bits == 113 || $bits == 2098);
}
else {
$bits = Rmpfr_get_prec($v);
die "Precision of arg given to anytoa() must be 53 or 64 or 113 or 2098"
unless ($bits == 53 || $bits == 64 || $bits == 113 || $bits == 2098);
}
my $emax = Rmpfr_get_emax(); # Save original value
my $emin = Rmpfr_get_emin(); # Save original value
my $f_init = Rmpfr_init2($bits);
my %emax_emin = (53 => [1024, -1073, -1022 ],
64 => [16384, -16444, -16382],
2098 => [1024, -1073, -1022 ],
113 => [16384, -16493, -16382],
);
Rmpfr_set_emax($emax_emin{$bits}->[0]);
Rmpfr_set_emin($emax_emin{$bits}->[1]);
# DoubleDouble
if($bits == 2098) {
Rmpfr_strtofr($f_init, "$v", 0, MPFR_RNDN);
if(!Rmpfr_regular_p($f_init)) {
Rmpfr_set_emax($emax); # Revert to original value
Rmpfr_set_emin($emin); # Revert to original value
return mpfrtoa($f_init);
}
# Obtain the pair of doubles pertinent to $f_init.
# $msd is the "more siginificant double" and $lsd
# is the "less significant double".
my($msd, $lsd) = _mpfr2dd($f_init);
if($lsd == 0 ) {
my $f = Rmpfr_init2(53);
Rmpfr_set_d($f, $msd, MPFR_RNDN);
Rmpfr_set_emax($emax); # Revert to original value
Rmpfr_set_emin($emin); # Revert to original value
return anytoa($f, 53);
}
# Determine the no. of implied (intermediate)
# bits that lie between the end of $msd and
# and the start of $lsd
my $intermediates = _intermediate_bits($msd, $lsd);
my $f_final = Rmpfr_init2(106 + $intermediates);
Rmpfr_set_d($f_final, $msd, MPFR_RNDN);
Rmpfr_add_d($f_final, $f_final, $lsd, MPFR_RNDN);
Rmpfr_set_emax($emax); # Revert to original value
Rmpfr_set_emin($emin); # Revert to original value
return mpfrtoa($f_final);
} # End DoubleDouble
# The next 4 lines cater for the possibility that
# the value is either subnormal or infinite or
# zero for the floating point type specified by
# the value of $bits.
my $inex = Rmpfr_strtofr($f_init, "$v", 0, MPFR_RNDN);
if(Rmpfr_regular_p($f_init) && Rmpfr_get_exp($f_init) < $emax_emin{$bits}->[2]) {
# The value is subnormal, and therefore requires further treatment.
Rmpfr_subnormalize($f_init, $inex, MPFR_RNDN);
my ($significand, $exponent) = Rmpfr_deref2($f_init, 2, 0, MPFR_RNDN);
my $f_final = Rmpfr_init2(1 + $exponent - $emax_emin{$bits}->[1]);
if($significand =~ s/^\-/-0./) { # The value is -ve.
Rmpfr_strtofr($f_final, "${significand}p$exponent", 2, MPFR_RNDN);
}
else { # The value is positive
Rmpfr_strtofr($f_final, "0.${significand}p$exponent", 2, MPFR_RNDN);
}
Rmpfr_set_emax($emax); # Revert to original value
Rmpfr_set_emin($emin); # Revert to original value
return mpfrtoa($f_final);
}
Rmpfr_set_emax($emax); # Revert to original value
Rmpfr_set_emin($emin); # Revert to original value
return mpfrtoa($f_init);
}
###########################
###########################
sub nvtoa_test {
# 1st arg must be a string (POK);
# 2nd arg must be either an NV (NOK) or a Math::MPFR object
die "nvtoa_test() requires at least version 3.1.6 of the MPFR library"
if 196870 > MPFR_VERSION;
my ($s, $n, $is_nv, $ret) = (shift, shift, 0, 0);
my ($check, $debug);
$debug = defined($_[0]) ? $_[0] : 0;
print "ARG1: $s\nARG2: $n\n"
if $debug;
die "First arg to nvtoa_test() must be a string"
unless _SvPOK($s);
if(ref($n) eq 'Math::MPFR') {
$check = Rmpfr_init2(Rmpfr_get_prec($n));
Rmpfr_set($check, abs($n), MPFR_RNDN);
}
else {
die "2nd arg to nvtoa_test() must be either an NV or a Math::MPFR object"
unless _SvNOK($n);
$is_nv = 1;
$check = abs(atonv("$s"));
}
# Check that signs match:
if($s =~ s/^\-//) {
die "In nvtoa_test(): signs do not match"
if $n > 0;
}
else {
die "In nvtoa_test():mismatch of signs"
if($n < 0);
}
$n = abs($n); # deal only with the +ve form
# for simplicity.
# Handle inf, nan and zero - test that both $n and $check
# are the same. No further testing required.
if($check == 0) {
return 15 if $n == 0;
return 0;
}
return 0 if $n == 0;
my $new = Math::MPFR->new($check);
if(Rmpfr_nan_p($new)) {
return 15 if $n != $n;
return 0;
}
return 0 if $n != $n;
if(Rmpfr_inf_p($new)) {
return 15 if $new == $n;
return 0;
}
return 0 if $n/$n != $n/$n;
$ret++ if $check == $n; # round trip successful
my @r = split /e/i, $s;
if($debug) {
print "SPLIT:\n$r[0]";
if(defined($r[1])) { print " $r[1]\n" }
else { print " no exponent\n" }
}
# Increment $ret by 8 if and only if there are no errant trailing
# zeroes in $r[0] .
if(!defined($r[1])) {
$ret += 8 if ($r[0] =~ /\.0$/ || $r[0] !~ /0$/);
$r[1] = 0; # define $r[1] by setting it to zero.
}
else {
$ret += 8 unless $r[0] =~ /0$/;
}
# We remove from $s any trailing mantissa zeroes, and then
# replace the least significant digit with zero.
# IOW, we effectively chop off the least siginificant digit, thereby
# rounding it down to the next lowest decimal precision.)
# This altered string should assign to a value less than $n.
chop($r[0]) while $r[0] =~ /0$/;
$r[0] =~ s/\.$//;
while($r[0] =~ /0$/) {
chop $r[0];
$r[1]++;
}
return $ret + 6 if length($r[0]) < 2; # chop test and increment test inapplicable.
substr($r[0], -1, 1, '0');
my $chopped = $r[1] ? $r[0] . 'e' . $r[1]
: $r[0];
print "CHOPPED:\n$chopped\n\n" if $debug;
if($is_nv) {
$ret += 2 if atonv($chopped) < $n; # chop test ok.
}
else {
Rmpfr_set_str($check, $chopped, 10, MPFR_RNDN);
$ret += 2 if $check < $n; # chop test ok.
}
# Now we derive a value that is $s rounded up to the next lowest
# decimal representation.
# This new string should assign to a value that is greater
# than the given $n.
if($r[0] =~ /\./) {
# We must remove the '.', do the string increment,
# and then reinsert the '.' in the appropriate place.
my @mantissa = split /\./, $r[0];
my $point_pos = -(length($mantissa[1]));
my $t = $mantissa[0] . $mantissa[1];
print "Man (if):\n$t\n" if $debug == 2;
$t++ for 1..10;
print "Man++ (if):\n$t\n" if $debug == 2;
substr($t, $point_pos, 0, '.');
$r[0] = $t;
}
else {
print "R0 (else):\n$r[0]\n" if $debug == 2;
$r[0]++ for 1..10;
print "R0++ (else):\n$r[0]\n" if $debug == 2;
}
my $incremented = defined($r[1]) ? $r[0] . 'e' . $r[1]
: $r[0];
print "INCREMENTED:\n$incremented\n" if $debug;
if($is_nv) {
$ret += 4 if atonv($incremented) > $n; # increment test ok.
}
else {
Rmpfr_set_str($check, $incremented, 10, MPFR_RNDN);
$ret += 4 if $check > $n; # chop test ok.
}
return $ret;
}
#############################
#############################
sub _mpfr2dd {
# Can be called from anytoa()
my $obj = shift;
my $msd = Rmpfr_get_d($obj, MPFR_RNDN);
$obj -= $msd;
return ($msd, Rmpfr_get_d($obj, MPFR_RNDN));
}
sub _intermediate_bits {
# Can be called from anytoa()
my($exp1, $exp2) = (_get_exp(shift), _get_exp(shift));
return $exp1 - 53 - $exp2;
}
sub _get_exp {
# Can be called from anytoa(), via _intermediate_bits().
# For as long as we support perl-5.8, we cannot use
# the "d<" and "d>" templates.
my $hex;
if(LITTLE_ENDIAN) {
$hex = scalar reverse unpack "h*", pack "d", $_[0];
}
else {
$hex = unpack "H*", pack "d", $_[0];
}
my $exp = hex(substr($hex, 0, 3));
$exp -= 2048 if $exp > 2047; # Remove sign bit
$exp++ unless $exp; # increment if 0
return ($exp - 1023);
}
*Rmpfr_get_z_exp = \&Rmpfr_get_z_2exp;
*prec_cast = \&Math::MPFR::Prec::prec_cast;
*Rmpfr_randinit_default = \&Math::MPFR::Random::Rmpfr_randinit_default;
*Rmpfr_randinit_mt = \&Math::MPFR::Random::Rmpfr_randinit_mt;
*Rmpfr_randinit_lc_2exp = \&Math::MPFR::Random::Rmpfr_randinit_lc_2exp;
*Rmpfr_randinit_lc_2exp_size = \&Math::MPFR::Random::Rmpfr_randinit_lc_2exp_size;
sub nvtoa {
# Special handling required for DoubleDouble
# Unable to get the _nvtoa XSub to work flawlessly with DoubleDoubles,
# I've switched to using the _mpfrtoa XSub, as I did with Math::FakeDD
# It's an emabrrassingly awful hack, but will have to do until something
# better comes along.
if(NV_IS_DOUBLEDOUBLE) {
my $nv = shift;
my $unpacked = unpack "H*", pack "D>", $nv;
my $msd = unpack "d>", pack "H*", substr($unpacked, 0, 16); # more significant double
my $lsd = unpack "d>", pack "H*", substr($unpacked, 16, 16); # less significant double
my $mpfr = Rmpfr_init2(2098);
Rmpfr_set_ld($mpfr, $nv, MPFR_RNDN);
my($neg, $prec, $different_signs) = (Rmpfr_signbit($mpfr), 0, 0);
unless(Rmpfr_regular_p($mpfr)) {
if(Rmpfr_zero_p($mpfr)) {
return "-0.0" if $neg;
return "0.0";
}
return "NaN" if Rmpfr_nan_p($mpfr);
# Must be Inf
return "-Inf" if $neg;
return "Inf";
}
# set $mpfr to abs($mpfr)
# $nv remains unaltered
if($mpfr < 0) {
Rmpfr_neg($mpfr, $mpfr, MPFR_RNDN);
$neg = 1;
}
my $exp = Rmpfr_get_exp($mpfr);
if($lsd == 0) {
my $addon = 1074;
unless( MPFR_4_0_2_OR_LATER ) { # 4.0.1 or earlier
# Prior to mpfr-4.0.2, there are issues with precision < 2,
# but DBL_DENORM_MIN calls for a precision of one bit.
# We therefore return the hard coded value for this case.
if($exp == -1073) {
# $mpfr is 2 ** -1074
my $ret = $neg ? '-5e-324' : '5e-324';
return $ret;
}
}
$prec = $addon + $exp;
Rmpfr_prec_round($mpfr, $prec, MPFR_RNDN);
# Provide 2nd arg of 728 to mpfrtoa().
# 2 ** -348 (prec = 727) needs this.
return '-' . mpfrtoa($mpfr, 728) if $neg;
return mpfrtoa($mpfr, 728);
} # close $lsd == 0
my $m_msd = Rmpfr_init2(53);
my $m_lsd = Rmpfr_init2(53);
Rmpfr_set_d($m_msd, $msd, MPFR_RNDN);
Rmpfr_set_d($m_lsd, $lsd, MPFR_RNDN);
if(abs($lsd) >= 2 ** -1022) {
# lsd is not subnormal.
$prec = Rmpfr_get_exp($m_msd) - Rmpfr_get_exp($m_lsd) + 53;
if( ($lsd < 0 && $msd > 0) || ($msd < 0 && $lsd > 0) ) {
$prec--;
$different_signs = 1; # one double < 0, the other > 0
}
my $mpfr_copy = Rmpfr_init2(2098);
Rmpfr_set($mpfr_copy, $mpfr, MPFR_RNDN);
Rmpfr_prec_round($mpfr_copy, $prec, MPFR_RNDN);
my $trial_repro = mpfrtoa($mpfr_copy);
my $trial_dd = atonv($trial_repro);
if($trial_dd == $nv || ($neg == 1 && $trial_dd == abs($nv)) ) {
return '-' . $trial_repro if $neg;
return $trial_repro;
}
$prec++;
# Might need to be incremented again if the 2 doubles have different sign.
}
else {
$prec = Rmpfr_get_exp($m_msd) + 1073; # $prec should be > 0
$prec++ if $prec == 0;
my $mpfr_copy = Rmpfr_init2(2098);
Rmpfr_set($mpfr_copy, $mpfr, MPFR_RNDN);
Rmpfr_prec_round($mpfr_copy, $prec, MPFR_RNDN);
my $trial_repro = mpfrtoa($mpfr_copy);
my $trial_dd = atonv($trial_repro);
if($trial_dd == $nv || ($neg == 1 && $trial_dd == abs($nv)) ) {
return '-' . $trial_repro if $neg;
return $trial_repro;
}
$prec++;
}
my $mpfr_orig = Rmpfr_init2(2098);
Rmpfr_set($mpfr_orig, $mpfr, MPFR_RNDN); # copy $mpfr to $mpfr_orig
Rmpfr_prec_round($mpfr, $prec, MPFR_RNDN);
if($different_signs) {
my $candidate = mpfrtoa($mpfr, 53);
# Might fail either the "chop" test or
# the "round trip" test, but not both.
if(abs($nv) != atonv($candidate)) {
# First check whether decrementing the mantissa
# allows the round trip to succeed.
my $ret = _decrement($candidate);
if(abs($nv) == atonv($ret)) {
return '-' . $ret if $neg;
return $ret;
}
# Fails round trip - so we increment $prec. We then
# can't use $mpfr again as its precision has already
# been altered, so we use $mpfr_orig.
$prec++;
Rmpfr_prec_round($mpfr_orig, $prec, MPFR_RNDN);
return '-' . mpfrtoa($mpfr_orig, 53) if $neg;
return mpfrtoa($mpfr_orig, 53);
}
my $ret = _chop_test($candidate, $nv, 0);
if($ret eq 'ok') {
return '-' . $candidate if $neg;
return $candidate;
}
# The value we now return is the value calculated
# for precision $prec, but with the least significant
# mantissa digit removed.
return '-' . $ret if $neg;
return $ret;
} # close different signs
else {
# We need to detect the (rare) case that a chopped and
# then incremented mantissa passes the round trip.
my $can = mpfrtoa($mpfr, 53);
my $ret = _chop_test($can, $nv, 1);
if($ret eq 'ok') {
return '-' . $can if $neg;
return $can;
}
return '-' . $ret if $neg;
return $ret;
} # close same signs
}
else {
# Not a doubledouble - simply use the _nvtoa XSub
return _nvtoa(shift);
}
}
sub numtoa { # Special handling required for DoubleDouble
if(NV_IS_DOUBLEDOUBLE) {
my $arg = shift;
return nvtoa($arg) if _SvNOK($arg);
return _numtoa($arg);
}
else {
return _numtoa(shift);
}
}
sub _chop_test {
my @r = split /e/i, shift;
my $op = shift;
# If $do_increment is set, then all we are not interested
# in the result of the chop test. We are interested in the
# result of the incrmentation - which we requires that we
# first perform the chop.
my $do_increment = defined($_[0]) ? shift
: 0;
# We remove from $r[0] any trailing mantissa zeroes, and then
# replace the least significant digit with zero.
# IOW, we effectively chop off the least siginificant digit, thereby
# rounding it down to the next lowest decimal precision.)
# This altered string should assign to a DoubleDouble value that is
# less than the given $op.
chop($r[0]) while $r[0] =~ /0$/;
$r[0] =~ s/\.$//;
$r[1] = defined $r[1] ? $r[1] : 0;
while($r[0] =~ /0$/) {
chop $r[0];
$r[1]++;
}
return 'ok' if length($r[0]) < 2; # chop test inapplicable.
substr($r[0], -1, 1, '');
$r[1]++ unless $r[0] =~ /\./;
$r[0] =~ s/\.$/.0/
unless $r[1];
$r[0] =~ s/\.$//;
if(!$do_increment) {
# We are interested only in the chop test
my $chopped = $r[1] ? $r[0] . 'e' . $r[1]
: $r[0];
return 'ok' if atonv($chopped) < abs($op); # chop test ok.
return $chopped;
}
# We are not interested in the chop test - the "chop" was
# done only as the first step in the incrementation, and
# it's the result of the following incrementation that
# interests us. Now we want, in effect, to do:
# ++$r[0];
# This value should then assign to a DoubleDouble value
# that is greater than the given $op.
if($r[0] =~ /\./) {
# We must remove the '.', do the string increment,
# and then reinsert the '.' in the appropriate place.
my @mantissa = split /\./, $r[0];
my $point_pos = -(length($mantissa[1]));
my $t = $mantissa[0] . $mantissa[1];
$t++;
substr($t, $point_pos, 0, '.');
$r[0] = $t;
}
else {
$r[0]++;
$r[1]++ while $r[0] =~ s/0$//;
}
my $incremented = $r[1] ? $r[0] . 'e' . $r[1]
: $r[0];
return $incremented if atonv($incremented) == abs($op);
return 'ok';
}
sub _decrement {
my $shift = shift;
my @r = split /e/i, $shift;
# Remove all trailing zeroes from $r[0];
if($r[0] =~ /\./) {
chop($r[0]) while $r[0] =~ /0$/;
}
$r[0] =~ s/\.$//;
$r[1] = defined $r[1] ? $r[1] : 0;
while($r[0] =~ /0$/) {
chop $r[0];
$r[1]++;
}
return $shift if length($r[0]) < 2;
my $substitute = substr($r[0], -1, 1) - 1;
substr($r[0], -1, 1, "$substitute");
my $ret = $r[1] ? $r[0] . 'e' . $r[1]
: $r[0];
return $ret;
}
#sub tz_test {
# # Detect any unwanted trailing zeroes
# # in values returned by nvtoa().
#
# my $s = shift;
# my @r = split /e/i, $s;
#
# if(!defined($r[1])) {
# return 1 if $r[0] =~ /\.0$/; # pass
# return 0 if $r[0] =~ /0$/; # fail
# }
#
# return 0 if $r[0] =~ /0$/; # fail (for our formatting convention)
# return 1; # pass
#}
1;
__END__