lib/perl5/5.6.1/bigfloat.pl

   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 $rnd_mode = 'even';
  32
  33 #   bigfloat routines
  34 #
  35 #   fadd(NSTR, NSTR) return NSTR            addition
  36 #   fsub(NSTR, NSTR) return NSTR            subtraction
  37 #   fmul(NSTR, NSTR) return NSTR            multiplication
  38 #   fdiv(NSTR, NSTR[,SCALE]) returns NSTR   division to SCALE places
  39 #   fneg(NSTR) return NSTR                  negation
  40 #   fabs(NSTR) return NSTR                  absolute value
  41 #   fcmp(NSTR,NSTR) return CODE             compare undef,<0,=0,>0
  42 #   fround(NSTR, SCALE) return NSTR         round to SCALE digits
  43 #   ffround(NSTR, SCALE) return NSTR        round at SCALEth place
  44 #   fnorm(NSTR) return (NSTR)               normalize
  45 #   fsqrt(NSTR[, SCALE]) return NSTR        sqrt to SCALE places
  46 \f
  47 # Convert a number to canonical string form.
  48 #   Takes something that looks like a number and converts it to
  49 #   the form /^[+-]\d+E[+-]\d+$/.
  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+$ye);
 107     }
 108 }
 109 \f
 110 # addition
 111 sub main'fadd { #(fnum_str, fnum_str) return fnum_str
 112     local($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 \f
 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 \f
 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,$ym))
 230         );
 231     }
 232 }
 233 \f
 234 # square root by Newtons method.
 235 sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
 236     local($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;