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5303340c LW |
1 | package bigfloat; |
2 | require "bigint.pl"; | |
a6d71656 GS |
3 | # |
4 | # This library is no longer being maintained, and is included for backward | |
5 | # compatibility with Perl 4 programs which may require it. | |
8e1a0ca7 S |
6 | # This legacy library is deprecated and will be removed in a future |
7 | # release of perl. | |
a6d71656 GS |
8 | # |
9 | # In particular, this should not be used as an example of modern Perl | |
10 | # programming techniques. | |
11 | # | |
12 | # Suggested alternative: Math::BigFloat | |
8e1a0ca7 S |
13 | |
14 | warn( "The 'bigfloat.pl' legacy library is deprecated and will be" | |
15 | . " removed in the next major release of perl. Please use the" | |
16 | . " Math::BigFloat module instead." ); | |
17 | ||
5303340c LW |
18 | # Arbitrary length float math package |
19 | # | |
68decaef LW |
20 | # by Mark Biggar |
21 | # | |
5303340c LW |
22 | # number format |
23 | # canonical strings have the form /[+-]\d+E[+-]\d+/ | |
5d7098d5 | 24 | # Input values can have embedded whitespace |
5303340c LW |
25 | # Error returns |
26 | # 'NaN' An input parameter was "Not a Number" or | |
27 | # divide by zero or sqrt of negative number | |
28 | # Division is computed to | |
79072805 | 29 | # max($div_scale,length(dividend)+length(divisor)) |
5303340c LW |
30 | # digits by default. |
31 | # Also used for default sqrt scale | |
32 | ||
33 | $div_scale = 40; | |
34 | ||
35 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. | |
36 | ||
37 | $rnd_mode = 'even'; | |
38 | ||
39 | # bigfloat routines | |
40 | # | |
41 | # fadd(NSTR, NSTR) return NSTR addition | |
42 | # fsub(NSTR, NSTR) return NSTR subtraction | |
43 | # fmul(NSTR, NSTR) return NSTR multiplication | |
44 | # fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places | |
45 | # fneg(NSTR) return NSTR negation | |
46 | # fabs(NSTR) return NSTR absolute value | |
47 | # fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0 | |
48 | # fround(NSTR, SCALE) return NSTR round to SCALE digits | |
49 | # ffround(NSTR, SCALE) return NSTR round at SCALEth place | |
50 | # fnorm(NSTR) return (NSTR) normalize | |
51 | # fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places | |
52 | \f | |
53 | # Convert a number to canonical string form. | |
54 | # Takes something that looks like a number and converts it to | |
55 | # the form /^[+-]\d+E[+-]\d+$/. | |
56 | sub main'fnorm { #(string) return fnum_str | |
57 | local($_) = @_; | |
58 | s/\s+//g; # strip white space | |
afea815c CS |
59 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ |
60 | && ($2 ne '' || defined($4))) { | |
61 | my $x = defined($4) ? $4 : ''; | |
62 | &norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6)); | |
5303340c LW |
63 | } else { |
64 | 'NaN'; | |
65 | } | |
66 | } | |
67 | ||
68 | # normalize number -- for internal use | |
69 | sub norm { #(mantissa, exponent) return fnum_str | |
70 | local($_, $exp) = @_; | |
71 | if ($_ eq 'NaN') { | |
72 | 'NaN'; | |
73 | } else { | |
74 | s/^([+-])0+/$1/; # strip leading zeros | |
75 | if (length($_) == 1) { | |
76 | '+0E+0'; | |
77 | } else { | |
78 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros | |
79 | sprintf("%sE%+ld", $_, $exp); | |
80 | } | |
81 | } | |
82 | } | |
83 | ||
84 | # negation | |
85 | sub main'fneg { #(fnum_str) return fnum_str | |
79072805 | 86 | local($_) = &'fnorm($_[$[]); |
e334a159 | 87 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
f70c35af GS |
88 | if ( ord("\t") == 9 ) { # ascii |
89 | s/^H/N/; | |
90 | } | |
91 | else { # ebcdic character set | |
92 | s/\373/N/; | |
93 | } | |
5303340c LW |
94 | $_; |
95 | } | |
96 | ||
97 | # absolute value | |
98 | sub main'fabs { #(fnum_str) return fnum_str | |
79072805 | 99 | local($_) = &'fnorm($_[$[]); |
68decaef | 100 | s/^-/+/; # mash sign |
5303340c LW |
101 | $_; |
102 | } | |
103 | ||
104 | # multiplication | |
105 | sub main'fmul { #(fnum_str, fnum_str) return fnum_str | |
79072805 | 106 | local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1])); |
5303340c LW |
107 | if ($x eq 'NaN' || $y eq 'NaN') { |
108 | 'NaN'; | |
109 | } else { | |
110 | local($xm,$xe) = split('E',$x); | |
111 | local($ym,$ye) = split('E',$y); | |
112 | &norm(&'bmul($xm,$ym),$xe+$ye); | |
113 | } | |
114 | } | |
115 | \f | |
116 | # addition | |
117 | sub main'fadd { #(fnum_str, fnum_str) return fnum_str | |
79072805 | 118 | local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1])); |
5303340c LW |
119 | if ($x eq 'NaN' || $y eq 'NaN') { |
120 | 'NaN'; | |
121 | } else { | |
122 | local($xm,$xe) = split('E',$x); | |
123 | local($ym,$ye) = split('E',$y); | |
124 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); | |
125 | &norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye); | |
126 | } | |
127 | } | |
128 | ||
129 | # subtraction | |
130 | sub main'fsub { #(fnum_str, fnum_str) return fnum_str | |
79072805 | 131 | &'fadd($_[$[],&'fneg($_[$[+1])); |
5303340c LW |
132 | } |
133 | ||
134 | # division | |
135 | # args are dividend, divisor, scale (optional) | |
136 | # result has at most max(scale, length(dividend), length(divisor)) digits | |
137 | sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str | |
138 | { | |
79072805 | 139 | local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]); |
5303340c LW |
140 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
141 | 'NaN'; | |
142 | } else { | |
143 | local($xm,$xe) = split('E',$x); | |
144 | local($ym,$ye) = split('E',$y); | |
145 | $scale = $div_scale if (!$scale); | |
146 | $scale = length($xm)-1 if (length($xm)-1 > $scale); | |
147 | $scale = length($ym)-1 if (length($ym)-1 > $scale); | |
148 | $scale = $scale + length($ym) - length($xm); | |
5d7098d5 | 149 | &norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)), |
5303340c LW |
150 | $xe-$ye-$scale); |
151 | } | |
152 | } | |
153 | \f | |
154 | # round int $q based on fraction $r/$base using $rnd_mode | |
155 | sub round { #(int_str, int_str, int_str) return int_str | |
156 | local($q,$r,$base) = @_; | |
157 | if ($q eq 'NaN' || $r eq 'NaN') { | |
158 | 'NaN'; | |
159 | } elsif ($rnd_mode eq 'trunc') { | |
160 | $q; # just truncate | |
161 | } else { | |
162 | local($cmp) = &'bcmp(&'bmul($r,'+2'),$base); | |
163 | if ( $cmp < 0 || | |
164 | ($cmp == 0 && | |
165 | ( $rnd_mode eq 'zero' || | |
79072805 LW |
166 | ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || |
167 | ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || | |
5303340c LW |
168 | ($rnd_mode eq 'even' && $q =~ /[24680]$/) || |
169 | ($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) { | |
170 | $q; # round down | |
171 | } else { | |
79072805 | 172 | &'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); |
5303340c LW |
173 | # round up |
174 | } | |
175 | } | |
176 | } | |
177 | ||
178 | # round the mantissa of $x to $scale digits | |
179 | sub main'fround { #(fnum_str, scale) return fnum_str | |
79072805 | 180 | local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]); |
5303340c LW |
181 | if ($x eq 'NaN' || $scale <= 0) { |
182 | $x; | |
183 | } else { | |
184 | local($xm,$xe) = split('E',$x); | |
185 | if (length($xm)-1 <= $scale) { | |
186 | $x; | |
187 | } else { | |
79072805 LW |
188 | &norm(&round(substr($xm,$[,$scale+1), |
189 | "+0".substr($xm,$[+$scale+1,1),"+10"), | |
5303340c LW |
190 | $xe+length($xm)-$scale-1); |
191 | } | |
192 | } | |
193 | } | |
194 | \f | |
195 | # round $x at the 10 to the $scale digit place | |
196 | sub main'ffround { #(fnum_str, scale) return fnum_str | |
79072805 | 197 | local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]); |
5303340c LW |
198 | if ($x eq 'NaN') { |
199 | 'NaN'; | |
200 | } else { | |
201 | local($xm,$xe) = split('E',$x); | |
202 | if ($xe >= $scale) { | |
203 | $x; | |
204 | } else { | |
205 | $xe = length($xm)+$xe-$scale; | |
206 | if ($xe < 1) { | |
207 | '+0E+0'; | |
208 | } elsif ($xe == 1) { | |
5d7098d5 SK |
209 | # The first substr preserves the sign, which means that |
210 | # we'll pass a non-normalized "-0" to &round when rounding | |
211 | # -0.006 (for example), purely so that &round won't lose | |
212 | # the sign. | |
213 | &norm(&round(substr($xm,$[,1).'0', | |
214 | "+0".substr($xm,$[+1,1),"+10"), $scale); | |
5303340c | 215 | } else { |
79072805 LW |
216 | &norm(&round(substr($xm,$[,$xe), |
217 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); | |
5303340c LW |
218 | } |
219 | } | |
220 | } | |
221 | } | |
222 | ||
223 | # compare 2 values returns one of undef, <0, =0, >0 | |
224 | # returns undef if either or both input value are not numbers | |
225 | sub main'fcmp #(fnum_str, fnum_str) return cond_code | |
226 | { | |
79072805 | 227 | local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1])); |
5303340c LW |
228 | if ($x eq "NaN" || $y eq "NaN") { |
229 | undef; | |
5303340c | 230 | } else { |
68decaef LW |
231 | ord($y) <=> ord($x) |
232 | || | |
233 | ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), | |
79072805 | 234 | (($xe <=> $ye) * (substr($x,$[,1).'1') |
68decaef LW |
235 | || &bigint'cmp($xm,$ym)) |
236 | ); | |
5303340c LW |
237 | } |
238 | } | |
239 | \f | |
240 | # square root by Newtons method. | |
241 | sub main'fsqrt { #(fnum_str[, scale]) return fnum_str | |
79072805 | 242 | local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]); |
5303340c LW |
243 | if ($x eq 'NaN' || $x =~ /^-/) { |
244 | 'NaN'; | |
245 | } elsif ($x eq '+0E+0') { | |
246 | '+0E+0'; | |
247 | } else { | |
248 | local($xm, $xe) = split('E',$x); | |
249 | $scale = $div_scale if (!$scale); | |
250 | $scale = length($xm)-1 if ($scale < length($xm)-1); | |
251 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); | |
252 | while ($gs < 2*$scale) { | |
253 | $guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5"); | |
254 | $gs *= 2; | |
255 | } | |
256 | &'fround($guess, $scale); | |
257 | } | |
258 | } | |
259 | ||
260 | 1; |