| 1 |
package bigfloat; |
| 2 |
require "bigint.pl"; |
| 3 |
# |
| 4 |
# This library is no longer being maintained, and is included for backward |
| 5 |
# compatibility with Perl 4 programs which may require it. |
| 6 |
# |
| 7 |
# In particular, this should not be used as an example of modern Perl |
| 8 |
# programming techniques. |
| 9 |
# |
| 10 |
# Suggested alternative: Math::BigFloat |
| 11 |
# |
| 12 |
# Arbitrary length float math package |
| 13 |
# |
| 14 |
# by Mark Biggar |
| 15 |
# |
| 16 |
# number format |
| 17 |
# canonical strings have the form /[+-]\d+E[+-]\d+/ |
| 18 |
# Input values can have embedded whitespace |
| 19 |
# Error returns |
| 20 |
# 'NaN' An input parameter was "Not a Number" or |
| 21 |
# divide by zero or sqrt of negative number |
| 22 |
# Division is computed to |
| 23 |
# max($div_scale,length(dividend)+length(divisor)) |
| 24 |
# digits by default. |
| 25 |
# Also used for default sqrt scale |
| 26 |
|
| 27 |
$div_scale = 40; |
| 28 |
|
| 29 |
# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
| 30 |
|
| 31 |
$rnd_mode = 'even'; |
| 32 |
|
| 33 |
# bigfloat routines |
| 34 |
# |
| 35 |
# fadd(NSTR, NSTR) return NSTR addition |
| 36 |
# fsub(NSTR, NSTR) return NSTR subtraction |
| 37 |
# fmul(NSTR, NSTR) return NSTR multiplication |
| 38 |
# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places |
| 39 |
# fneg(NSTR) return NSTR negation |
| 40 |
# fabs(NSTR) return NSTR absolute value |
| 41 |
# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0 |
| 42 |
# fround(NSTR, SCALE) return NSTR round to SCALE digits |
| 43 |
# ffround(NSTR, SCALE) return NSTR round at SCALEth place |
| 44 |
# fnorm(NSTR) return (NSTR) normalize |
| 45 |
# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places |
| 46 |
|
| 47 |
# Convert a number to canonical string form. |
| 48 |
# Takes something that looks like a number and converts it to |
| 49 |
# the form /^[+-]\d+E[+-]\d+$/. |
| 50 |
sub main'fnorm { #(string) return fnum_str |
| 51 |
local($_) = @_; |
| 52 |
s/\s+//g; # strip white space |
| 53 |
if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ |
| 54 |
&& ($2 ne '' || defined($4))) { |
| 55 |
my $x = defined($4) ? $4 : ''; |
| 56 |
&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6)); |
| 57 |
} else { |
| 58 |
'NaN'; |
| 59 |
} |
| 60 |
} |
| 61 |
|
| 62 |
# normalize number -- for internal use |
| 63 |
sub norm { #(mantissa, exponent) return fnum_str |
| 64 |
local($_, $exp) = @_; |
| 65 |
if ($_ eq 'NaN') { |
| 66 |
'NaN'; |
| 67 |
} else { |
| 68 |
s/^([+-])0+/$1/; # strip leading zeros |
| 69 |
if (length($_) == 1) { |
| 70 |
'+0E+0'; |
| 71 |
} else { |
| 72 |
$exp += length($1) if (s/(0+)$//); # strip trailing zeros |
| 73 |
sprintf("%sE%+ld", $_, $exp); |
| 74 |
} |
| 75 |
} |
| 76 |
} |
| 77 |
|
| 78 |
# negation |
| 79 |
sub main'fneg { #(fnum_str) return fnum_str |
| 80 |
local($_) = &'fnorm($_[$[]); |
| 81 |
vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
| 82 |
if ( ord("\t") == 9 ) { # ascii |
| 83 |
s/^H/N/; |
| 84 |
} |
| 85 |
else { # ebcdic character set |
| 86 |
s/\373/N/; |
| 87 |
} |
| 88 |
$_; |
| 89 |
} |
| 90 |
|
| 91 |
# absolute value |
| 92 |
sub main'fabs { #(fnum_str) return fnum_str |
| 93 |
local($_) = &'fnorm($_[$[]); |
| 94 |
s/^-/+/; # mash sign |
| 95 |
$_; |
| 96 |
} |
| 97 |
|
| 98 |
# multiplication |
| 99 |
sub main'fmul { #(fnum_str, fnum_str) return fnum_str |
| 100 |
local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1])); |
| 101 |
if ($x eq 'NaN' || $y eq 'NaN') { |
| 102 |
'NaN'; |
| 103 |
} else { |
| 104 |
local($xm,$xe) = split('E',$x); |
| 105 |
local($ym,$ye) = split('E',$y); |
| 106 |
&norm(&'bmul($xm,$ym),$xe+$ye); |
| 107 |
} |
| 108 |
} |
| 109 |
|
| 110 |
# addition |
| 111 |
sub main'fadd { #(fnum_str, fnum_str) return fnum_str |
| 112 |
local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1])); |
| 113 |
if ($x eq 'NaN' || $y eq 'NaN') { |
| 114 |
'NaN'; |
| 115 |
} else { |
| 116 |
local($xm,$xe) = split('E',$x); |
| 117 |
local($ym,$ye) = split('E',$y); |
| 118 |
($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
| 119 |
&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
| 120 |
} |
| 121 |
} |
| 122 |
|
| 123 |
# subtraction |
| 124 |
sub main'fsub { #(fnum_str, fnum_str) return fnum_str |
| 125 |
&'fadd($_[$[],&'fneg($_[$[+1])); |
| 126 |
} |
| 127 |
|
| 128 |
# division |
| 129 |
# args are dividend, divisor, scale (optional) |
| 130 |
# result has at most max(scale, length(dividend), length(divisor)) digits |
| 131 |
sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
| 132 |
{ |
| 133 |
local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]); |
| 134 |
if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
| 135 |
'NaN'; |
| 136 |
} else { |
| 137 |
local($xm,$xe) = split('E',$x); |
| 138 |
local($ym,$ye) = split('E',$y); |
| 139 |
$scale = $div_scale if (!$scale); |
| 140 |
$scale = length($xm)-1 if (length($xm)-1 > $scale); |
| 141 |
$scale = length($ym)-1 if (length($ym)-1 > $scale); |
| 142 |
$scale = $scale + length($ym) - length($xm); |
| 143 |
&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)), |
| 144 |
$xe-$ye-$scale); |
| 145 |
} |
| 146 |
} |
| 147 |
|
| 148 |
# round int $q based on fraction $r/$base using $rnd_mode |
| 149 |
sub round { #(int_str, int_str, int_str) return int_str |
| 150 |
local($q,$r,$base) = @_; |
| 151 |
if ($q eq 'NaN' || $r eq 'NaN') { |
| 152 |
'NaN'; |
| 153 |
} elsif ($rnd_mode eq 'trunc') { |
| 154 |
$q; # just truncate |
| 155 |
} else { |
| 156 |
local($cmp) = &'bcmp(&'bmul($r,'+2'),$base); |
| 157 |
if ( $cmp < 0 || |
| 158 |
($cmp == 0 && |
| 159 |
( $rnd_mode eq 'zero' || |
| 160 |
($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || |
| 161 |
($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || |
| 162 |
($rnd_mode eq 'even' && $q =~ /[24680]$/) || |
| 163 |
($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) { |
| 164 |
$q; # round down |
| 165 |
} else { |
| 166 |
&'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); |
| 167 |
# round up |
| 168 |
} |
| 169 |
} |
| 170 |
} |
| 171 |
|
| 172 |
# round the mantissa of $x to $scale digits |
| 173 |
sub main'fround { #(fnum_str, scale) return fnum_str |
| 174 |
local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]); |
| 175 |
if ($x eq 'NaN' || $scale <= 0) { |
| 176 |
$x; |
| 177 |
} else { |
| 178 |
local($xm,$xe) = split('E',$x); |
| 179 |
if (length($xm)-1 <= $scale) { |
| 180 |
$x; |
| 181 |
} else { |
| 182 |
&norm(&round(substr($xm,$[,$scale+1), |
| 183 |
"+0".substr($xm,$[+$scale+1,1),"+10"), |
| 184 |
$xe+length($xm)-$scale-1); |
| 185 |
} |
| 186 |
} |
| 187 |
} |
| 188 |
|
| 189 |
# round $x at the 10 to the $scale digit place |
| 190 |
sub main'ffround { #(fnum_str, scale) return fnum_str |
| 191 |
local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]); |
| 192 |
if ($x eq 'NaN') { |
| 193 |
'NaN'; |
| 194 |
} else { |
| 195 |
local($xm,$xe) = split('E',$x); |
| 196 |
if ($xe >= $scale) { |
| 197 |
$x; |
| 198 |
} else { |
| 199 |
$xe = length($xm)+$xe-$scale; |
| 200 |
if ($xe < 1) { |
| 201 |
'+0E+0'; |
| 202 |
} elsif ($xe == 1) { |
| 203 |
# The first substr preserves the sign, which means that |
| 204 |
# we'll pass a non-normalized "-0" to &round when rounding |
| 205 |
# -0.006 (for example), purely so that &round won't lose |
| 206 |
# the sign. |
| 207 |
&norm(&round(substr($xm,$[,1).'0', |
| 208 |
"+0".substr($xm,$[+1,1),"+10"), $scale); |
| 209 |
} else { |
| 210 |
&norm(&round(substr($xm,$[,$xe), |
| 211 |
"+0".substr($xm,$[+$xe,1),"+10"), $scale); |
| 212 |
} |
| 213 |
} |
| 214 |
} |
| 215 |
} |
| 216 |
|
| 217 |
# compare 2 values returns one of undef, <0, =0, >0 |
| 218 |
# returns undef if either or both input value are not numbers |
| 219 |
sub main'fcmp #(fnum_str, fnum_str) return cond_code |
| 220 |
{ |
| 221 |
local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1])); |
| 222 |
if ($x eq "NaN" || $y eq "NaN") { |
| 223 |
undef; |
| 224 |
} else { |
| 225 |
ord($y) <=> ord($x) |
| 226 |
|| |
| 227 |
( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), |
| 228 |
(($xe <=> $ye) * (substr($x,$[,1).'1') |
| 229 |
|| &bigint'cmp($xm,$ym)) |
| 230 |
); |
| 231 |
} |
| 232 |
} |
| 233 |
|
| 234 |
# square root by Newtons method. |
| 235 |
sub main'fsqrt { #(fnum_str[, scale]) return fnum_str |
| 236 |
local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]); |
| 237 |
if ($x eq 'NaN' || $x =~ /^-/) { |
| 238 |
'NaN'; |
| 239 |
} elsif ($x eq '+0E+0') { |
| 240 |
'+0E+0'; |
| 241 |
} else { |
| 242 |
local($xm, $xe) = split('E',$x); |
| 243 |
$scale = $div_scale if (!$scale); |
| 244 |
$scale = length($xm)-1 if ($scale < length($xm)-1); |
| 245 |
local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
| 246 |
while ($gs < 2*$scale) { |
| 247 |
$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5"); |
| 248 |
$gs *= 2; |
| 249 |
} |
| 250 |
&'fround($guess, $scale); |
| 251 |
} |
| 252 |
} |
| 253 |
|
| 254 |
1; |
