# Arbitrary length float math package
# canonical strings have the form /[+-]\d+E[+-]\d+/
# Input values can have inbedded whitespace
# 'NaN' An input parameter was "Not a Number" or
# divide by zero or sqrt of negative number
# Division is computed to
# max($div_scale,length(dividend).length(divisor))
# Also used for default sqrt scale
# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
# fadd(NSTR, NSTR) return NSTR addition
# fsub(NSTR, NSTR) return NSTR subtraction
# fmul(NSTR, NSTR) return NSTR multiplication
# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
# fneg(NSTR) return NSTR negation
# fabs(NSTR) return NSTR absolute value
# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
# fround(NSTR, SCALE) return NSTR round to SCALE digits
# ffround(NSTR, SCALE) return NSTR round at SCALEth place
# fnorm(NSTR) return (NSTR) normalize
# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
# Convert a number to canonical string form.
# Takes something that looks like a number and converts it to
# the form /^[+-]\d+E[+-]\d+$/.
sub main
'fnorm { #(string) return fnum_str
s/\s+//g; # strip white space
if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
# normalize number -- for internal use
sub norm { #(mantissa, exponent) return fnum_str
s/^([+-])0+/$1/; # strip leading zeros
$exp += length($1) if (s/(0+)$//); # strip trailing zeros
sprintf("%sE%+ld", $_, $exp);
sub main'fneg
{ #(fnum_str) return fnum_str
local($_) = &'fnorm($_[0]);
vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
sub main'fabs
{ #(fnum_str) return fnum_str
local($_) = &'fnorm($_[0]);
sub main'fmul
{ #(fnum_str, fnum_str) return fnum_str
local($x,$y) = (&'fnorm($_[0]),&'fnorm
($_[1]));
if ($x eq 'NaN' || $y eq 'NaN') {
local($xm,$xe) = split('E',$x);
local($ym,$ye) = split('E',$y);
&norm
(&'bmul($xm,$ym),$xe+$ye);
sub main'fadd
{ #(fnum_str, fnum_str) return fnum_str
local($x,$y) = (&'fnorm($_[0]),&'fnorm
($_[1]));
if ($x eq 'NaN' || $y eq 'NaN') {
local($xm,$xe) = split('E',$x);
local($ym,$ye) = split('E',$y);
($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
&norm
(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
sub main'fsub
{ #(fnum_str, fnum_str) return fnum_str
&'fadd($_[0],&'fneg
($_[1]));
# args are dividend, divisor, scale (optional)
# result has at most max(scale, length(dividend), length(divisor)) digits
sub main
'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
local($x,$y,$scale) = (&'fnorm
($_[0]),&'fnorm($_[1]),$_[2]);
if ($x eq 'NaN
' || $y eq 'NaN
' || $y eq '+0E+0') {
local($xm,$xe) = split('E
',$x);
local($ym,$ye) = split('E
',$y);
$scale = $div_scale if (!$scale);
$scale = length($xm)-1 if (length($xm)-1 > $scale);
$scale = length($ym)-1 if (length($ym)-1 > $scale);
$scale = $scale + length($ym) - length($xm);
&norm(&round(&'bdiv
($xm.('0' x
$scale),$ym),$ym),
# round int $q based on fraction $r/$base using $rnd_mode
sub round
{ #(int_str, int_str, int_str) return int_str
if ($q eq 'NaN' || $r eq 'NaN') {
} elsif ($rnd_mode eq 'trunc') {
local($cmp) = &'bcmp(&'bmul
($r,'+2'),$base);
($rnd_mode eq '-inf' && (substr($q,0,1) eq '+')) ||
($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) ||
($rnd_mode eq 'even' && $q =~ /[24680]$/) ||
($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
&'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
# round the mantissa of $x to $scale digits
sub main'fround
{ #(fnum_str, scale) return fnum_str
local($x,$scale) = (&'fnorm($_[0]),$_[1]);
if ($x eq 'NaN
' || $scale <= 0) {
local($xm,$xe) = split('E
',$x);
if (length($xm)-1 <= $scale) {
&norm(&round(substr($xm,0,$scale+1),
"+0".substr($xm,$scale+1,1),"+10"),
$xe+length($xm)-$scale-1);
# round $x at the 10 to the $scale digit place
sub main'ffround
{ #(fnum_str, scale) return fnum_str
local($x,$scale) = (&'fnorm($_[0]),$_[1]);
local($xm,$xe) = split('E
',$x);
$xe = length($xm)+$xe-$scale;
&norm(&round('+0',"+0".substr($xm,1,1),"+10"), $scale);
&norm(&round(substr($xm,0,$trunc),
"+0".substr($xm,$trunc,1),"+10"), $scale);
# compare 2 values returns one of undef, <0, =0, >0
# returns undef if either or both input value are not numbers
sub main'fcmp
#(fnum_str, fnum_str) return cond_code
local($x, $y) = (&'fnorm($_[0]),&'fnorm
($_[1]));
if ($x eq "NaN" || $y eq "NaN") {
( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
(($xe <=> $ye) * (substr($x,0,1).'1')
# square root by Newtons method.
sub main'fsqrt
{ #(fnum_str[, scale]) return fnum_str
local($x, $scale) = (&'fnorm($_[0]), $_[1]);
if ($x eq 'NaN
' || $x =~ /^-/) {
} elsif ($x eq '+0E+0') {
local($xm, $xe) = split('E
',$x);
$scale = $div_scale if (!$scale);
$scale = length($xm)-1 if ($scale < length($xm)-1);
local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
$guess = &'fmul
(&'fadd($guess,&'fdiv
($x,$guess,$gs*2)),".5");
&'fround($guess, $scale);