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