[p5sagit/p5-mst-13.2.git] / lib / bigfloat.pl

package bigfloat;
require "bigint.pl";

# Arbitrary length float math package
#
# number format
#   canonical strings have the form /[+-]\d+E[+-]\d+/
#   Input values can have inbedded 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
\f
# 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$4" ne '') {
	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $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($_) = &'fnorm($_[0]);
    substr($_,0,1) =~ tr/+-/-+/ if ($_ ne '+0E+0'); # flip sign
    $_;
}

# absolute value
sub main'fabs { #(fnum_str) return fnum_str
    local($_) = &'fnorm($_[0]);
    substr($_,0,1) = '+' unless $_ eq 'NaN';                       # mash sign
    $_;
}

# multiplication
sub main'fmul { #(fnum_str, fnum_str) return fnum_str
    local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[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+$ye);
    }
}
\f
# addition
sub main'fadd { #(fnum_str, fnum_str) return fnum_str
    local($x,$y) = (&'fnorm($_[0]),&'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($_[0],&'fneg($_[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,$scale) = (&'fnorm($_[0]),&'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),$ym),
	    $xe-$ye-$scale);
    }
}
\f
# 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($q,0,1) eq '+')) ||
		   ($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) ||
		   ($rnd_mode eq 'even' && $q =~ /[24680]$/)        ||
		   ($rnd_mode eq 'odd'  && $q =~ /[13579]$/)        )) ) {
	    $q;                     # round down
	} else {
	    &'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
				    # round up
	}
    }
}

# round the mantissa of $x to $scale digits
sub main'fround { #(fnum_str, scale) return fnum_str
    local($x,$scale) = (&'fnorm($_[0]),$_[1]);
    if ($x eq 'NaN' || $scale <= 0) {
	$x;
    } else {
	local($xm,$xe) = split('E',$x);
	if (length($xm)-1 <= $scale) {
	    $x;
	} else {
	    &norm(&round(substr($xm,0,$scale+1),
			 "+0".substr($xm,$scale+1,1),"+10"),
		  $xe+length($xm)-$scale-1);
	}
    }
}
\f
# round $x at the 10 to the $scale digit place
sub main'ffround { #(fnum_str, scale) return fnum_str
    local($x,$scale) = (&'fnorm($_[0]),$_[1]);
    if ($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) {
		&norm(&round('+0',"+0".substr($xm,1,1),"+10"), $scale);
	    } else {
		&norm(&round(substr($xm,0,$trunc),
		      "+0".substr($xm,$trunc,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, $y) = (&'fnorm($_[0]),&'fnorm($_[1]));
    if ($x eq "NaN" || $y eq "NaN") {
	undef;
    } elsif ($x eq $y) {
	0;
    } elsif (ord($x) != ord($y)) {
	(ord($y) - ord($x));                # based on signs
    } else {
	local($xm,$xe) = split('E',$x);
	local($ym,$ye) = split('E',$y);
	if ($xe ne $ye) {
	    ($xe - $ye) * (substr($x,0,1).'1');
	} else {
	    &bigint'cmp($xm,$ym);           # based on value
	}
    }
}
\f
# square root by Newtons method.
sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
    local($x, $scale) = (&'fnorm($_[0]), $_[1]);
    if ($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;
Commit	Line	Data
5303340c	1	package bigfloat;
	2	require "bigint.pl";
	3
	4	# Arbitrary length float math package
	5	#
	6	# number format
	7	# canonical strings have the form /[+-]\d+E[+-]\d+/
	8	# Input values can have inbedded whitespace
	9	# Error returns
	10	# 'NaN' An input parameter was "Not a Number" or
	11	# divide by zero or sqrt of negative number
	12	# Division is computed to
	13	# max($div_scale,length(dividend).length(divisor))
	14	# digits by default.
	15	# Also used for default sqrt scale
	16
	17	$div_scale = 40;
	18
	19	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	20
	21	$rnd_mode = 'even';
	22
	23	# bigfloat routines
	24	#
	25	# fadd(NSTR, NSTR) return NSTR addition
	26	# fsub(NSTR, NSTR) return NSTR subtraction
	27	# fmul(NSTR, NSTR) return NSTR multiplication
	28	# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
	29	# fneg(NSTR) return NSTR negation
	30	# fabs(NSTR) return NSTR absolute value
	31	# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
	32	# fround(NSTR, SCALE) return NSTR round to SCALE digits
	33	# ffround(NSTR, SCALE) return NSTR round at SCALEth place
	34	# fnorm(NSTR) return (NSTR) normalize
	35	# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
	36	\f
	37	# Convert a number to canonical string form.
	38	# Takes something that looks like a number and converts it to
	39	# the form /^[+-]\d+E[+-]\d+$/.
	40	sub main'fnorm { #(string) return fnum_str
	41	local($_) = @_;
	42	s/\s+//g; # strip white space
	43	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
	44	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
	45	} else {
	46	'NaN';
	47	}
	48	}
	49
	50	# normalize number -- for internal use
	51	sub norm { #(mantissa, exponent) return fnum_str
	52	local($_, $exp) = @_;
	53	if ($_ eq 'NaN') {
	54	'NaN';
	55	} else {
	56	s/^([+-])0+/$1/; # strip leading zeros
	57	if (length($_) == 1) {
	58	'+0E+0';
	59	} else {
	60	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	61	sprintf("%sE%+ld", $_, $exp);
	62	}
	63	}
	64	}
65
66	# negation
67	sub main'fneg { #(fnum_str) return fnum_str
68	local($_) = &'fnorm($_[0]);
69	substr($_,0,1) =~ tr/+-/-+/ if ($_ ne '+0E+0'); # flip sign
70	$_;
71	}
72
73	# absolute value
74	sub main'fabs { #(fnum_str) return fnum_str
75	local($_) = &'fnorm($_[0]);
fe14fcc3	76	substr($_,0,1) = '+' unless $_ eq 'NaN'; # mash sign
5303340c	77	$_;
	78	}
	79
	80	# multiplication
	81	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
	82	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
	83	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	84	'NaN';
	85	} else {
	86	local($xm,$xe) = split('E',$x);
	87	local($ym,$ye) = split('E',$y);
	88	&norm(&'bmul($xm,$ym),$xe+$ye);
	89	}
	90	}
	91	\f
	92	# addition
	93	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
	94	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
	95	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	96	'NaN';
	97	} else {
	98	local($xm,$xe) = split('E',$x);
	99	local($ym,$ye) = split('E',$y);
	100	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	101	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	102	}
	103	}
	104
	105	# subtraction
	106	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
	107	&'fadd($_[0],&'fneg($_[1]));
	108	}
	109
	110	# division
	111	# args are dividend, divisor, scale (optional)
	112	# result has at most max(scale, length(dividend), length(divisor)) digits
	113	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	114	{
	115	local($x,$y,$scale) = (&'fnorm($_[0]),&'fnorm($_[1]),$_[2]);
	116	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	117	'NaN';
	118	} else {
	119	local($xm,$xe) = split('E',$x);
	120	local($ym,$ye) = split('E',$y);
	121	$scale = $div_scale if (!$scale);
	122	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	123	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	124	$scale = $scale + length($ym) - length($xm);
	125	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),$ym),
	126	$xe-$ye-$scale);
	127	}
	128	}
	129	\f
	130	# round int $q based on fraction $r/$base using $rnd_mode
	131	sub round { #(int_str, int_str, int_str) return int_str
	132	local($q,$r,$base) = @_;
	133	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	134	'NaN';
	135	} elsif ($rnd_mode eq 'trunc') {
	136	$q; # just truncate
	137	} else {
	138	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	139	if ( $cmp < 0 \|\|
	140	($cmp == 0 &&
141	( $rnd_mode eq 'zero' \|\|
142	($rnd_mode eq '-inf' && (substr($q,0,1) eq '+')) \|\|
143	($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) \|\|
144	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
145	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
146	$q; # round down
147	} else {
148	&'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
149	# round up
150	}
151	}
152	}
153
154	# round the mantissa of $x to $scale digits
155	sub main'fround { #(fnum_str, scale) return fnum_str
156	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
157	if ($x eq 'NaN' \|\| $scale <= 0) {
158	$x;
159	} else {
160	local($xm,$xe) = split('E',$x);
161	if (length($xm)-1 <= $scale) {
162	$x;
163	} else {
164	&norm(&round(substr($xm,0,$scale+1),
165	"+0".substr($xm,$scale+1,1),"+10"),
166	$xe+length($xm)-$scale-1);
167	}
168	}
169	}
170	\f
171	# round $x at the 10 to the $scale digit place
172	sub main'ffround { #(fnum_str, scale) return fnum_str
173	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
174	if ($x eq 'NaN') {
175	'NaN';
176	} else {
177	local($xm,$xe) = split('E',$x);
178	if ($xe >= $scale) {
179	$x;
180	} else {
181	$xe = length($xm)+$xe-$scale;
182	if ($xe < 1) {
183	'+0E+0';
184	} elsif ($xe == 1) {
185	&norm(&round('+0',"+0".substr($xm,1,1),"+10"), $scale);
186	} else {
187	&norm(&round(substr($xm,0,$trunc),
188	"+0".substr($xm,$trunc,1),"+10"), $scale);
189	}
190	}
191	}
192	}
193
194	# compare 2 values returns one of undef, <0, =0, >0
195	# returns undef if either or both input value are not numbers
196	sub main'fcmp #(fnum_str, fnum_str) return cond_code
197	{
198	local($x, $y) = (&'fnorm($_[0]),&'fnorm($_[1]));
199	if ($x eq "NaN" \|\| $y eq "NaN") {
200	undef;
201	} elsif ($x eq $y) {
202	0;
203	} elsif (ord($x) != ord($y)) {
204	(ord($y) - ord($x)); # based on signs
205	} else {
206	local($xm,$xe) = split('E',$x);
207	local($ym,$ye) = split('E',$y);
208	if ($xe ne $ye) {
209	($xe - $ye) * (substr($x,0,1).'1');
210	} else {
211	&bigint'cmp($xm,$ym); # based on value
212	}
213	}
214	}
215	\f
216	# square root by Newtons method.
217	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
218	local($x, $scale) = (&'fnorm($_[0]), $_[1]);
219	if ($x eq 'NaN' \|\| $x =~ /^-/) {
220	'NaN';
221	} elsif ($x eq '+0E+0') {
222	'+0E+0';
223	} else {
224	local($xm, $xe) = split('E',$x);
225	$scale = $div_scale if (!$scale);
226	$scale = length($xm)-1 if ($scale < length($xm)-1);
227	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
228	while ($gs < 2*$scale) {
229	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
230	$gs *= 2;
231	}
232	&'fround($guess, $scale);
233	}
234	}
235
236	1;