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