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