| 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 | $rnd_mode = 'even';
|
|---|
| 32 |
|
|---|
| 33 | # bigfloat routines
|
|---|
| 34 | #
|
|---|
| 35 | # fadd(NSTR, NSTR) return NSTR addition
|
|---|
| 36 | # fsub(NSTR, NSTR) return NSTR subtraction
|
|---|
| 37 | # fmul(NSTR, NSTR) return NSTR multiplication
|
|---|
| 38 | # fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
|
|---|
| 39 | # fneg(NSTR) return NSTR negation
|
|---|
| 40 | # fabs(NSTR) return NSTR absolute value
|
|---|
| 41 | # fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
|
|---|
| 42 | # fround(NSTR, SCALE) return NSTR round to SCALE digits
|
|---|
| 43 | # ffround(NSTR, SCALE) return NSTR round at SCALEth place
|
|---|
| 44 | # fnorm(NSTR) return (NSTR) normalize
|
|---|
| 45 | # fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
|
|---|
| 46 | |
|---|
| 47 |
|
|---|
| 48 | # Convert a number to canonical string form.
|
|---|
| 49 | # Takes something that looks like a number and converts it to
|
|---|
| 50 | # the form /^[+-]\d+E[+-]\d+$/.
|
|---|
| 51 | sub main'fnorm { #(string) return fnum_str
|
|---|
| 52 | local($_) = @_;
|
|---|
| 53 | s/\s+//g; # strip white space
|
|---|
| 54 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/
|
|---|
| 55 | && ($2 ne '' || defined($4))) {
|
|---|
| 56 | my $x = defined($4) ? $4 : '';
|
|---|
| 57 | &norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
|
|---|
| 58 | } else {
|
|---|
| 59 | 'NaN';
|
|---|
| 60 | }
|
|---|
| 61 | }
|
|---|
| 62 |
|
|---|
| 63 | # normalize number -- for internal use
|
|---|
| 64 | sub norm { #(mantissa, exponent) return fnum_str
|
|---|
| 65 | local($_, $exp) = @_;
|
|---|
| 66 | if ($_ eq 'NaN') {
|
|---|
| 67 | 'NaN';
|
|---|
| 68 | } else {
|
|---|
| 69 | s/^([+-])0+/$1/; # strip leading zeros
|
|---|
| 70 | if (length($_) == 1) {
|
|---|
| 71 | '+0E+0';
|
|---|
| 72 | } else {
|
|---|
| 73 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros
|
|---|
| 74 | sprintf("%sE%+ld", $_, $exp);
|
|---|
| 75 | }
|
|---|
| 76 | }
|
|---|
| 77 | }
|
|---|
| 78 |
|
|---|
| 79 | # negation
|
|---|
| 80 | sub main'fneg { #(fnum_str) return fnum_str
|
|---|
| 81 | local($_) = &'fnorm($_[$[]);
|
|---|
| 82 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
|
|---|
| 83 | if ( ord("\t") == 9 ) { # ascii
|
|---|
| 84 | s/^H/N/;
|
|---|
| 85 | }
|
|---|
| 86 | else { # ebcdic character set
|
|---|
| 87 | s/\373/N/;
|
|---|
| 88 | }
|
|---|
| 89 | $_;
|
|---|
| 90 | }
|
|---|
| 91 |
|
|---|
| 92 | # absolute value
|
|---|
| 93 | sub main'fabs { #(fnum_str) return fnum_str
|
|---|
| 94 | local($_) = &'fnorm($_[$[]);
|
|---|
| 95 | s/^-/+/; # mash sign
|
|---|
| 96 | $_;
|
|---|
| 97 | }
|
|---|
| 98 |
|
|---|
| 99 | # multiplication
|
|---|
| 100 | sub main'fmul { #(fnum_str, fnum_str) return fnum_str
|
|---|
| 101 | local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
|
|---|
| 102 | if ($x eq 'NaN' || $y eq 'NaN') {
|
|---|
| 103 | 'NaN';
|
|---|
| 104 | } else {
|
|---|
| 105 | local($xm,$xe) = split('E',$x);
|
|---|
| 106 | local($ym,$ye) = split('E',$y);
|
|---|
| 107 | &norm(&'bmul($xm,$ym),$xe+$ye);
|
|---|
| 108 | }
|
|---|
| 109 | }
|
|---|
| 110 | |
|---|
| 111 |
|
|---|
| 112 | # addition
|
|---|
| 113 | sub main'fadd { #(fnum_str, fnum_str) return fnum_str
|
|---|
| 114 | local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
|
|---|
| 115 | if ($x eq 'NaN' || $y eq 'NaN') {
|
|---|
| 116 | 'NaN';
|
|---|
| 117 | } else {
|
|---|
| 118 | local($xm,$xe) = split('E',$x);
|
|---|
| 119 | local($ym,$ye) = split('E',$y);
|
|---|
| 120 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
|
|---|
| 121 | &norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
|
|---|
| 122 | }
|
|---|
| 123 | }
|
|---|
| 124 |
|
|---|
| 125 | # subtraction
|
|---|
| 126 | sub main'fsub { #(fnum_str, fnum_str) return fnum_str
|
|---|
| 127 | &'fadd($_[$[],&'fneg($_[$[+1]));
|
|---|
| 128 | }
|
|---|
| 129 |
|
|---|
| 130 | # division
|
|---|
| 131 | # args are dividend, divisor, scale (optional)
|
|---|
| 132 | # result has at most max(scale, length(dividend), length(divisor)) digits
|
|---|
| 133 | sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
|
|---|
| 134 | {
|
|---|
| 135 | local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]);
|
|---|
| 136 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') {
|
|---|
| 137 | 'NaN';
|
|---|
| 138 | } else {
|
|---|
| 139 | local($xm,$xe) = split('E',$x);
|
|---|
| 140 | local($ym,$ye) = split('E',$y);
|
|---|
| 141 | $scale = $div_scale if (!$scale);
|
|---|
| 142 | $scale = length($xm)-1 if (length($xm)-1 > $scale);
|
|---|
| 143 | $scale = length($ym)-1 if (length($ym)-1 > $scale);
|
|---|
| 144 | $scale = $scale + length($ym) - length($xm);
|
|---|
| 145 | &norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
|
|---|
| 146 | $xe-$ye-$scale);
|
|---|
| 147 | }
|
|---|
| 148 | }
|
|---|
| 149 | |
|---|
| 150 |
|
|---|
| 151 | # round int $q based on fraction $r/$base using $rnd_mode
|
|---|
| 152 | sub round { #(int_str, int_str, int_str) return int_str
|
|---|
| 153 | local($q,$r,$base) = @_;
|
|---|
| 154 | if ($q eq 'NaN' || $r eq 'NaN') {
|
|---|
| 155 | 'NaN';
|
|---|
| 156 | } elsif ($rnd_mode eq 'trunc') {
|
|---|
| 157 | $q; # just truncate
|
|---|
| 158 | } else {
|
|---|
| 159 | local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
|
|---|
| 160 | if ( $cmp < 0 ||
|
|---|
| 161 | ($cmp == 0 &&
|
|---|
| 162 | ( $rnd_mode eq 'zero' ||
|
|---|
| 163 | ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) ||
|
|---|
| 164 | ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) ||
|
|---|
| 165 | ($rnd_mode eq 'even' && $q =~ /[24680]$/) ||
|
|---|
| 166 | ($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
|
|---|
| 167 | $q; # round down
|
|---|
| 168 | } else {
|
|---|
| 169 | &'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
|
|---|
| 170 | # round up
|
|---|
| 171 | }
|
|---|
| 172 | }
|
|---|
| 173 | }
|
|---|
| 174 |
|
|---|
| 175 | # round the mantissa of $x to $scale digits
|
|---|
| 176 | sub main'fround { #(fnum_str, scale) return fnum_str
|
|---|
| 177 | local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
|
|---|
| 178 | if ($x eq 'NaN' || $scale <= 0) {
|
|---|
| 179 | $x;
|
|---|
| 180 | } else {
|
|---|
| 181 | local($xm,$xe) = split('E',$x);
|
|---|
| 182 | if (length($xm)-1 <= $scale) {
|
|---|
| 183 | $x;
|
|---|
| 184 | } else {
|
|---|
| 185 | &norm(&round(substr($xm,$[,$scale+1),
|
|---|
| 186 | "+0".substr($xm,$[+$scale+1,1),"+10"),
|
|---|
| 187 | $xe+length($xm)-$scale-1);
|
|---|
| 188 | }
|
|---|
| 189 | }
|
|---|
| 190 | }
|
|---|
| 191 | |
|---|
| 192 |
|
|---|
| 193 | # round $x at the 10 to the $scale digit place
|
|---|
| 194 | sub main'ffround { #(fnum_str, scale) return fnum_str
|
|---|
| 195 | local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
|
|---|
| 196 | if ($x eq 'NaN') {
|
|---|
| 197 | 'NaN';
|
|---|
| 198 | } else {
|
|---|
| 199 | local($xm,$xe) = split('E',$x);
|
|---|
| 200 | if ($xe >= $scale) {
|
|---|
| 201 | $x;
|
|---|
| 202 | } else {
|
|---|
| 203 | $xe = length($xm)+$xe-$scale;
|
|---|
| 204 | if ($xe < 1) {
|
|---|
| 205 | '+0E+0';
|
|---|
| 206 | } elsif ($xe == 1) {
|
|---|
| 207 | # The first substr preserves the sign, which means that
|
|---|
| 208 | # we'll pass a non-normalized "-0" to &round when rounding
|
|---|
| 209 | # -0.006 (for example), purely so that &round won't lose
|
|---|
| 210 | # the sign.
|
|---|
| 211 | &norm(&round(substr($xm,$[,1).'0',
|
|---|
| 212 | "+0".substr($xm,$[+1,1),"+10"), $scale);
|
|---|
| 213 | } else {
|
|---|
| 214 | &norm(&round(substr($xm,$[,$xe),
|
|---|
| 215 | "+0".substr($xm,$[+$xe,1),"+10"), $scale);
|
|---|
| 216 | }
|
|---|
| 217 | }
|
|---|
| 218 | }
|
|---|
| 219 | }
|
|---|
| 220 |
|
|---|
| 221 | # compare 2 values returns one of undef, <0, =0, >0
|
|---|
| 222 | # returns undef if either or both input value are not numbers
|
|---|
| 223 | sub main'fcmp #(fnum_str, fnum_str) return cond_code
|
|---|
| 224 | {
|
|---|
| 225 | local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
|
|---|
| 226 | if ($x eq "NaN" || $y eq "NaN") {
|
|---|
| 227 | undef;
|
|---|
| 228 | } else {
|
|---|
| 229 | ord($y) <=> ord($x)
|
|---|
| 230 | ||
|
|---|
| 231 | ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
|
|---|
| 232 | (($xe <=> $ye) * (substr($x,$[,1).'1')
|
|---|
| 233 | || &bigint'cmp($xm,$ym))
|
|---|
| 234 | );
|
|---|
| 235 | }
|
|---|
| 236 | }
|
|---|
| 237 | |
|---|
| 238 |
|
|---|
| 239 | # square root by Newtons method.
|
|---|
| 240 | sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
|
|---|
| 241 | local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]);
|
|---|
| 242 | if ($x eq 'NaN' || $x =~ /^-/) {
|
|---|
| 243 | 'NaN';
|
|---|
| 244 | } elsif ($x eq '+0E+0') {
|
|---|
| 245 | '+0E+0';
|
|---|
| 246 | } else {
|
|---|
| 247 | local($xm, $xe) = split('E',$x);
|
|---|
| 248 | $scale = $div_scale if (!$scale);
|
|---|
| 249 | $scale = length($xm)-1 if ($scale < length($xm)-1);
|
|---|
| 250 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
|
|---|
| 251 | while ($gs < 2*$scale) {
|
|---|
| 252 | $guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
|
|---|
| 253 | $gs *= 2;
|
|---|
| 254 | }
|
|---|
| 255 | &'fround($guess, $scale);
|
|---|
| 256 | }
|
|---|
| 257 | }
|
|---|
| 258 |
|
|---|
| 259 | 1;
|
|---|
