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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;
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