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   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;