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920dae64 AT |
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 | $rnd_mode = 'even'; | |
32 | ||
33 | # bigfloat routines | |
34 | # | |
35 | # fadd(NSTR, NSTR) return NSTR addition | |
36 | # fsub(NSTR, NSTR) return NSTR subtraction | |
37 | # fmul(NSTR, NSTR) return NSTR multiplication | |
38 | # fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places | |
39 | # fneg(NSTR) return NSTR negation | |
40 | # fabs(NSTR) return NSTR absolute value | |
41 | # fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0 | |
42 | # fround(NSTR, SCALE) return NSTR round to SCALE digits | |
43 | # ffround(NSTR, SCALE) return NSTR round at SCALEth place | |
44 | # fnorm(NSTR) return (NSTR) normalize | |
45 | # fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places | |
46 | \f | |
47 | # Convert a number to canonical string form. | |
48 | # Takes something that looks like a number and converts it to | |
49 | # the form /^[+-]\d+E[+-]\d+$/. | |
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+$ye); | |
107 | } | |
108 | } | |
109 | \f | |
110 | # addition | |
111 | sub main'fadd { #(fnum_str, fnum_str) return fnum_str | |
112 | local($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 | \f | |
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 | \f | |
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,$ym)) | |
230 | ); | |
231 | } | |
232 | } | |
233 | \f | |
234 | # square root by Newtons method. | |
235 | sub main'fsqrt { #(fnum_str[, scale]) return fnum_str | |
236 | local($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; |