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
|
/* $Xorg: cmsMath.c,v 1.4 2001/02/09 02:03:39 xorgcvs Exp $ */
/*
Copyright 1990, 1998 The Open Group
Permission to use, copy, modify, distribute, and sell this software and its
documentation for any purpose is hereby granted without fee, provided that
the above copyright notice appear in all copies and that both that
copyright notice and this permission notice appear in supporting
documentation.
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
OPEN GROUP BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Except as contained in this notice, the name of The Open Group shall not be
used in advertising or otherwise to promote the sale, use or other dealings
in this Software without prior written authorization from The Open Group.
*/
/* $XFree86: xc/lib/X11/cmsMath.c,v 3.5 2001/12/14 19:54:10 dawes Exp $ */
/*
* Stephen Gildea, MIT X Consortium, January 1991
*/
#include "Xlibint.h"
#include "Xcmsint.h"
#include <float.h>
#ifndef DBL_EPSILON
#define DBL_EPSILON 1e-6
#endif
#ifdef _X_ROOT_STATS
int cbrt_loopcount;
int sqrt_loopcount;
#endif
/* Newton's Method: x_n+1 = x_n - ( f(x_n) / f'(x_n) ) */
/* for cube roots, x^3 - a = 0, x_new = x - 1/3 (x - a/x^2) */
double
_XcmsCubeRoot(a)
double a;
{
register double abs_a, cur_guess, delta;
#ifdef DEBUG
printf("_XcmsCubeRoot passed in %g\n", a);
#endif
#ifdef _X_ROOT_STATS
cbrt_loopcount = 0;
#endif
if (a == 0.)
return 0.;
abs_a = a<0. ? -a : a; /* convert to positive to speed loop tests */
/* arbitrary first guess */
if (abs_a > 1.)
cur_guess = abs_a/8.;
else
cur_guess = abs_a*8.;
do {
#ifdef _X_ROOT_STATS
cbrt_loopcount++;
#endif
delta = (cur_guess - abs_a/(cur_guess*cur_guess))/3.;
cur_guess -= delta;
if (delta < 0.) delta = -delta;
} while (delta >= cur_guess*DBL_EPSILON);
if (a < 0.)
cur_guess = -cur_guess;
#ifdef DEBUG
printf("_XcmsCubeRoot returning %g\n", cur_guess);
#endif
return cur_guess;
}
/* for square roots, x^2 - a = 0, x_new = x - 1/2 (x - a/x) */
double
_XcmsSquareRoot(a)
double a;
{
register double cur_guess, delta;
#ifdef DEBUG
printf("_XcmsSquareRoot passed in %g\n", a);
#endif
#ifdef _X_ROOT_STATS
sqrt_loopcount = 0;
#endif
if (a == 0.)
return 0.;
if (a < 0.) {
/* errno = EDOM; */
return 0.;
}
/* arbitrary first guess */
if (a > 1.)
cur_guess = a/4.;
else
cur_guess = a*4.;
do {
#ifdef _X_ROOT_STATS
sqrt_loopcount++;
#endif
delta = (cur_guess - a/cur_guess)/2.;
cur_guess -= delta;
if (delta < 0.) delta = -delta;
} while (delta >= cur_guess*DBL_EPSILON);
#ifdef DEBUG
printf("_XcmsSquareRoot returning %g\n", cur_guess);
#endif
return cur_guess;
}
|
