Commit | Line | Data |
5303340c |
1 | package bigfloat; |
2 | require "bigint.pl"; |
3 | |
4 | # Arbitrary length float math package |
5 | # |
6 | # number format |
7 | # canonical strings have the form /[+-]\d+E[+-]\d+/ |
8 | # Input values can have inbedded whitespace |
9 | # Error returns |
10 | # 'NaN' An input parameter was "Not a Number" or |
11 | # divide by zero or sqrt of negative number |
12 | # Division is computed to |
13 | # max($div_scale,length(dividend).length(divisor)) |
14 | # digits by default. |
15 | # Also used for default sqrt scale |
16 | |
17 | $div_scale = 40; |
18 | |
19 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
20 | |
21 | $rnd_mode = 'even'; |
22 | |
23 | # bigfloat routines |
24 | # |
25 | # fadd(NSTR, NSTR) return NSTR addition |
26 | # fsub(NSTR, NSTR) return NSTR subtraction |
27 | # fmul(NSTR, NSTR) return NSTR multiplication |
28 | # fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places |
29 | # fneg(NSTR) return NSTR negation |
30 | # fabs(NSTR) return NSTR absolute value |
31 | # fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0 |
32 | # fround(NSTR, SCALE) return NSTR round to SCALE digits |
33 | # ffround(NSTR, SCALE) return NSTR round at SCALEth place |
34 | # fnorm(NSTR) return (NSTR) normalize |
35 | # fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places |
36 | \f |
37 | # Convert a number to canonical string form. |
38 | # Takes something that looks like a number and converts it to |
39 | # the form /^[+-]\d+E[+-]\d+$/. |
40 | sub main'fnorm { #(string) return fnum_str |
41 | local($_) = @_; |
42 | s/\s+//g; # strip white space |
43 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { |
44 | &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); |
45 | } else { |
46 | 'NaN'; |
47 | } |
48 | } |
49 | |
50 | # normalize number -- for internal use |
51 | sub norm { #(mantissa, exponent) return fnum_str |
52 | local($_, $exp) = @_; |
53 | if ($_ eq 'NaN') { |
54 | 'NaN'; |
55 | } else { |
56 | s/^([+-])0+/$1/; # strip leading zeros |
57 | if (length($_) == 1) { |
58 | '+0E+0'; |
59 | } else { |
60 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros |
61 | sprintf("%sE%+ld", $_, $exp); |
62 | } |
63 | } |
64 | } |
65 | |
66 | # negation |
67 | sub main'fneg { #(fnum_str) return fnum_str |
68 | local($_) = &'fnorm($_[0]); |
69 | substr($_,0,1) =~ tr/+-/-+/ if ($_ ne '+0E+0'); # flip sign |
70 | $_; |
71 | } |
72 | |
73 | # absolute value |
74 | sub main'fabs { #(fnum_str) return fnum_str |
75 | local($_) = &'fnorm($_[0]); |
fe14fcc3 |
76 | substr($_,0,1) = '+' unless $_ eq 'NaN'; # mash sign |
5303340c |
77 | $_; |
78 | } |
79 | |
80 | # multiplication |
81 | sub main'fmul { #(fnum_str, fnum_str) return fnum_str |
82 | local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1])); |
83 | if ($x eq 'NaN' || $y eq 'NaN') { |
84 | 'NaN'; |
85 | } else { |
86 | local($xm,$xe) = split('E',$x); |
87 | local($ym,$ye) = split('E',$y); |
88 | &norm(&'bmul($xm,$ym),$xe+$ye); |
89 | } |
90 | } |
91 | \f |
92 | # addition |
93 | sub main'fadd { #(fnum_str, fnum_str) return fnum_str |
94 | local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1])); |
95 | if ($x eq 'NaN' || $y eq 'NaN') { |
96 | 'NaN'; |
97 | } else { |
98 | local($xm,$xe) = split('E',$x); |
99 | local($ym,$ye) = split('E',$y); |
100 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
101 | &norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
102 | } |
103 | } |
104 | |
105 | # subtraction |
106 | sub main'fsub { #(fnum_str, fnum_str) return fnum_str |
107 | &'fadd($_[0],&'fneg($_[1])); |
108 | } |
109 | |
110 | # division |
111 | # args are dividend, divisor, scale (optional) |
112 | # result has at most max(scale, length(dividend), length(divisor)) digits |
113 | sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
114 | { |
115 | local($x,$y,$scale) = (&'fnorm($_[0]),&'fnorm($_[1]),$_[2]); |
116 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
117 | 'NaN'; |
118 | } else { |
119 | local($xm,$xe) = split('E',$x); |
120 | local($ym,$ye) = split('E',$y); |
121 | $scale = $div_scale if (!$scale); |
122 | $scale = length($xm)-1 if (length($xm)-1 > $scale); |
123 | $scale = length($ym)-1 if (length($ym)-1 > $scale); |
124 | $scale = $scale + length($ym) - length($xm); |
125 | &norm(&round(&'bdiv($xm.('0' x $scale),$ym),$ym), |
126 | $xe-$ye-$scale); |
127 | } |
128 | } |
129 | \f |
130 | # round int $q based on fraction $r/$base using $rnd_mode |
131 | sub round { #(int_str, int_str, int_str) return int_str |
132 | local($q,$r,$base) = @_; |
133 | if ($q eq 'NaN' || $r eq 'NaN') { |
134 | 'NaN'; |
135 | } elsif ($rnd_mode eq 'trunc') { |
136 | $q; # just truncate |
137 | } else { |
138 | local($cmp) = &'bcmp(&'bmul($r,'+2'),$base); |
139 | if ( $cmp < 0 || |
140 | ($cmp == 0 && |
141 | ( $rnd_mode eq 'zero' || |
142 | ($rnd_mode eq '-inf' && (substr($q,0,1) eq '+')) || |
143 | ($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) || |
144 | ($rnd_mode eq 'even' && $q =~ /[24680]$/) || |
145 | ($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) { |
146 | $q; # round down |
147 | } else { |
148 | &'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1')); |
149 | # round up |
150 | } |
151 | } |
152 | } |
153 | |
154 | # round the mantissa of $x to $scale digits |
155 | sub main'fround { #(fnum_str, scale) return fnum_str |
156 | local($x,$scale) = (&'fnorm($_[0]),$_[1]); |
157 | if ($x eq 'NaN' || $scale <= 0) { |
158 | $x; |
159 | } else { |
160 | local($xm,$xe) = split('E',$x); |
161 | if (length($xm)-1 <= $scale) { |
162 | $x; |
163 | } else { |
164 | &norm(&round(substr($xm,0,$scale+1), |
165 | "+0".substr($xm,$scale+1,1),"+10"), |
166 | $xe+length($xm)-$scale-1); |
167 | } |
168 | } |
169 | } |
170 | \f |
171 | # round $x at the 10 to the $scale digit place |
172 | sub main'ffround { #(fnum_str, scale) return fnum_str |
173 | local($x,$scale) = (&'fnorm($_[0]),$_[1]); |
174 | if ($x eq 'NaN') { |
175 | 'NaN'; |
176 | } else { |
177 | local($xm,$xe) = split('E',$x); |
178 | if ($xe >= $scale) { |
179 | $x; |
180 | } else { |
181 | $xe = length($xm)+$xe-$scale; |
182 | if ($xe < 1) { |
183 | '+0E+0'; |
184 | } elsif ($xe == 1) { |
185 | &norm(&round('+0',"+0".substr($xm,1,1),"+10"), $scale); |
186 | } else { |
187 | &norm(&round(substr($xm,0,$trunc), |
188 | "+0".substr($xm,$trunc,1),"+10"), $scale); |
189 | } |
190 | } |
191 | } |
192 | } |
193 | |
194 | # compare 2 values returns one of undef, <0, =0, >0 |
195 | # returns undef if either or both input value are not numbers |
196 | sub main'fcmp #(fnum_str, fnum_str) return cond_code |
197 | { |
198 | local($x, $y) = (&'fnorm($_[0]),&'fnorm($_[1])); |
199 | if ($x eq "NaN" || $y eq "NaN") { |
200 | undef; |
201 | } elsif ($x eq $y) { |
202 | 0; |
203 | } elsif (ord($x) != ord($y)) { |
204 | (ord($y) - ord($x)); # based on signs |
205 | } else { |
206 | local($xm,$xe) = split('E',$x); |
207 | local($ym,$ye) = split('E',$y); |
208 | if ($xe ne $ye) { |
209 | ($xe - $ye) * (substr($x,0,1).'1'); |
210 | } else { |
211 | &bigint'cmp($xm,$ym); # based on value |
212 | } |
213 | } |
214 | } |
215 | \f |
216 | # square root by Newtons method. |
217 | sub main'fsqrt { #(fnum_str[, scale]) return fnum_str |
218 | local($x, $scale) = (&'fnorm($_[0]), $_[1]); |
219 | if ($x eq 'NaN' || $x =~ /^-/) { |
220 | 'NaN'; |
221 | } elsif ($x eq '+0E+0') { |
222 | '+0E+0'; |
223 | } else { |
224 | local($xm, $xe) = split('E',$x); |
225 | $scale = $div_scale if (!$scale); |
226 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
227 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
228 | while ($gs < 2*$scale) { |
229 | $guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5"); |
230 | $gs *= 2; |
231 | } |
232 | &'fround($guess, $scale); |
233 | } |
234 | } |
235 | |
236 | 1; |