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Diffstat (limited to 'libm/src/k_cos.c')
| -rw-r--r-- | libm/src/k_cos.c | 79 |
1 files changed, 0 insertions, 79 deletions
diff --git a/libm/src/k_cos.c b/libm/src/k_cos.c deleted file mode 100644 index 00916d7..0000000 --- a/libm/src/k_cos.c +++ /dev/null @@ -1,79 +0,0 @@ - -/* @(#)k_cos.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#ifndef lint -static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_cos.c,v 1.10 2005/10/26 12:36:18 bde Exp $"; -#endif - -/* - * __kernel_cos( x, y ) - * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * - * Algorithm - * 1. Since cos(-x) = cos(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. - * 3. cos(x) is approximated by a polynomial of degree 14 on - * [0,pi/4] - * 4 14 - * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x - * where the remez error is - * - * | 2 4 6 8 10 12 14 | -58 - * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 - * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then - * cos(x) ~ 1 - x*x/2 + r - * since cos(x+y) ~ cos(x) - sin(x)*y - * ~ cos(x) - x*y, - * a correction term is necessary in cos(x) and hence - * cos(x+y) = 1 - (x*x/2 - (r - x*y)) - * For better accuracy, rearrange to - * cos(x+y) ~ w + (tmp + (r-x*y)) - * where w = 1 - x*x/2 and tmp is a tiny correction term - * (1 - x*x/2 == w + tmp exactly in infinite precision). - * The exactness of w + tmp in infinite precision depends on w - * and tmp having the same precision as x. If they have extra - * precision due to compiler bugs, then the extra precision is - * only good provided it is retained in all terms of the final - * expression for cos(). Retention happens in all cases tested - * under FreeBSD, so don't pessimize things by forcibly clipping - * any extra precision in w. - */ - -#include "math.h" -#include "math_private.h" - -static const double -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ -C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ -C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ -C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ -C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ -C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ - -double -__kernel_cos(double x, double y) -{ - double hz,z,r,w; - - z = x*x; - r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); - hz = (float)0.5*z; - w = one-hz; - return w + (((one-w)-hz) + (z*r-x*y)); -} |