/* @(#)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. | |
* ==================================================== | |
*/ | |
#include <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
#if defined(LIBM_SCCS) && !defined(lint) | |
__RCSID("$NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz 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" | |
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 a,hz,z,r,qx; | |
int32_t ix; | |
GET_HIGH_WORD(ix,x); | |
ix &= 0x7fffffff; /* ix = |x|'s high word*/ | |
if(ix<0x3e400000) { /* if x < 2**27 */ | |
if(((int)x)==0) return one; /* generate inexact */ | |
} | |
z = x*x; | |
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); | |
if(ix < 0x3FD33333) /* if |x| < 0.3 */ | |
return one - (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 = one-qx; | |
return a - (hz - (z*r-x*y)); | |
} | |
} |