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