1package bigfloat;
2require "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$rnd_mode = 'even';
32
33#   bigfloat routines
34#
35#   fadd(NSTR, NSTR) return NSTR            addition
36#   fsub(NSTR, NSTR) return NSTR            subtraction
37#   fmul(NSTR, NSTR) return NSTR            multiplication
38#   fdiv(NSTR, NSTR[,SCALE]) returns NSTR   division to SCALE places
39#   fneg(NSTR) return NSTR                  negation
40#   fabs(NSTR) return NSTR                  absolute value
41#   fcmp(NSTR,NSTR) return CODE             compare undef,<0,=0,>0
42#   fround(NSTR, SCALE) return NSTR         round to SCALE digits
43#   ffround(NSTR, SCALE) return NSTR        round at SCALEth place
44#   fnorm(NSTR) return (NSTR)               normalize
45#   fsqrt(NSTR[, SCALE]) return NSTR        sqrt to SCALE places
46
47# Convert a number to canonical string form.
48#   Takes something that looks like a number and converts it to
49#   the form /^[+-]\d+E[+-]\d+$/.
50sub 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) : $6));
57    } else {
58	'NaN';
59    }
60}
61
62# normalize number -- for internal use
63sub norm { #(mantissa, exponent) return fnum_str
64    local($_, $exp) = @_;
65    if ($_ 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", $_, $exp);
74	}
75    }
76}
77
78# negation
79sub main'fneg { #(fnum_str) return fnum_str
80    local($_) = &'fnorm($_[0]);
81    vec($_,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    $_;
89}
90
91# absolute value
92sub main'fabs { #(fnum_str) return fnum_str
93    local($_) = &'fnorm($_[0]);
94    s/^-/+/;		                       # mash sign
95    $_;
96}
97
98# multiplication
99sub main'fmul { #(fnum_str, fnum_str) return fnum_str
100    local($x,$y) = (&'fnorm($_[0]),&'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+$ye);
107    }
108}
109
110# addition
111sub main'fadd { #(fnum_str, fnum_str) return fnum_str
112    local($x,$y) = (&'fnorm($_[0]),&'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
124sub main'fsub { #(fnum_str, fnum_str) return fnum_str
125    &'fadd($_[0],&'fneg($_[1]));
126}
127
128# division
129#   args are dividend, divisor, scale (optional)
130#   result has at most max(scale, length(dividend), length(divisor)) digits
131sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
132{
133    local($x,$y,$scale) = (&'fnorm($_[0]),&'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
148# round int $q based on fraction $r/$base using $rnd_mode
149sub round { #(int_str, int_str, int_str) return int_str
150    local($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($q,0,1) eq '+')) ||
161		   ($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) ||
162		   ($rnd_mode eq 'even' && $q =~ /[24680]$/)        ||
163		   ($rnd_mode eq 'odd'  && $q =~ /[13579]$/)        )) ) {
164	    $q;                     # round down
165	} else {
166	    &'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
167				    # round up
168	}
169    }
170}
171
172# round the mantissa of $x to $scale digits
173sub main'fround { #(fnum_str, scale) return fnum_str
174    local($x,$scale) = (&'fnorm($_[0]),$_[1]);
175    if ($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,0,$scale+1),
183			 "+0".substr($xm,$scale+1,1),"+10"),
184		  $xe+length($xm)-$scale-1);
185	}
186    }
187}
188
189# round $x at the 10 to the $scale digit place
190sub main'ffround { #(fnum_str, scale) return fnum_str
191    local($x,$scale) = (&'fnorm($_[0]),$_[1]);
192    if ($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($xm,0,1).'0',
208		      "+0".substr($xm,1,1),"+10"), $scale);
209	    } else {
210		&norm(&round(substr($xm,0,$xe),
211		      "+0".substr($xm,$xe,1),"+10"), $scale);
212	    }
213	}
214    }
215}
216
217# compare 2 values returns one of undef, <0, =0, >0
218#   returns undef if either or both input value are not numbers
219sub main'fcmp #(fnum_str, fnum_str) return cond_code
220{
221    local($x, $y) = (&'fnorm($_[0]),&'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,0,1).'1')
229             || &bigint'cmp($xm,$ym))
230	);
231    }
232}
233
234# square root by Newtons method.
235sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
236    local($x, $scale) = (&'fnorm($_[0]), $_[1]);
237    if ($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
2541;
255