diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/k_cos.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/k_cos.c | 108 |
1 files changed, 1 insertions, 107 deletions
diff --git a/sysdeps/ieee754/dbl-64/k_cos.c b/sysdeps/ieee754/dbl-64/k_cos.c index 7e38ef7915..cc5c205a5f 100644 --- a/sysdeps/ieee754/dbl-64/k_cos.c +++ b/sysdeps/ieee754/dbl-64/k_cos.c @@ -1,107 +1 @@ -/* @(#)k_cos.c 5.1 93/09/24 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, - for performance improvement on pipelined processors. -*/ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc 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 when x > 0.3, let qx = |x|/4 with - * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. - * Then - * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). - * Note that 1-qx and (x*x/2-qx) is EXACT here, and the - * magnitude of the latter is at least a quarter of x*x/2, - * thus, reducing the rounding error in the subtraction. - */ - -#include "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -C[] = { - 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ - 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ - -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ - 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ - -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ - 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ - -1.13596475577881948265e-11}; /* 0xBDA8FAE9, 0xBE8838D4 */ - -#ifdef __STDC__ - double __kernel_cos(double x, double y) -#else - double __kernel_cos(x, y) - double x,y; -#endif -{ - double a,hz,z,r,qx,r1,r2,r3,z1,z2,z3; - int32_t ix; - z = x*x; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; /* ix = |x|'s high word*/ - if(ix<0x3e400000) { /* if x < 2**27 */ - if(((int)x)==0) return C[0]; /* generate inexact */ - } -#ifdef DO_NOT_USE_THIS - r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); -#else - r1=z*C[6];r1=r1+C[5];z1=z*z; - r2=z*C[4];r2=r2+C[3];z2=z1*z; - r3=z*C[2];r3=r3+C[1];z3=z2*z1; - r=z3*r1+z2*r2+z*r3; -#endif - if(ix < 0x3FD33333) /* if |x| < 0.3 */ - return C[0] - (0.5*z - (z*r - x*y)); - else { - if(ix > 0x3fe90000) { /* x > 0.78125 */ - qx = 0.28125; - } else { - INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ - } - hz = 0.5*z-qx; - a = C[0]-qx; - return a - (hz - (z*r-x*y)); - } -} +/* Not needed anymore. */ |