perl/lib/bigfloat.pl

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.
#
# 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;
Revision:	1.1
Committed:	Thu Jun 30 14:27:08 2005 UTC (21 years, 3 months ago) by root
Content type:	text/plain
Branch:	MAIN
CVS Tags:	PERL-5-8-7, HEAD
Branch point for:	PERL
Log Message:	* empty log message *
#	User	Rev	Content
1	root	1.1	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			$rnd_mode = 'even';
32
33			# bigfloat routines
34			#
35			# fadd(NSTR, NSTR) return NSTR addition
36			# fsub(NSTR, NSTR) return NSTR subtraction
37			# fmul(NSTR, NSTR) return NSTR multiplication
38			# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
39			# fneg(NSTR) return NSTR negation
40			# fabs(NSTR) return NSTR absolute value
41			# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
42			# fround(NSTR, SCALE) return NSTR round to SCALE digits
43			# ffround(NSTR, SCALE) return NSTR round at SCALEth place
44			# fnorm(NSTR) return (NSTR) normalize
45			# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
46
47			# Convert a number to canonical string form.
48			# Takes something that looks like a number and converts it to
49			# the form /^[+-]\d+E[+-]\d+$/.
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+$ye);
107			}
108			}
109
110			# addition
111			sub main'fadd { #(fnum_str, fnum_str) return fnum_str
112			local($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
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
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,$ym))
230			);
231			}
232			}
233
234			# square root by Newtons method.
235			sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
236			local($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;