nant's projects / dragonfly.git / blame
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|---|---|---|
| 6ff43c94 PA |
1 | |
| 2 | /* @(#)k_cos.c 1.3 95/01/18 */ | |
| 3 | /* $FreeBSD: head/lib/msun/src/k_cos.c 176408 2008-02-19 12:54:14Z bde $ */ | |
| b34b60bc JS |
4 | /* |
| 5 | * ==================================================== | |
| 6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
| 7 | * | |
| 6ff43c94 | 8 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| b34b60bc | 9 | * Permission to use, copy, modify, and distribute this |
| 6ff43c94 | 10 | * software is freely granted, provided that this notice |
| b34b60bc JS |
11 | * is preserved. |
| 12 | * ==================================================== | |
| b34b60bc JS |
13 | */ |
| 14 | ||
| 15 | /* | |
| 16 | * __kernel_cos( x, y ) | |
| 17 | * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 | |
| 18 | * Input x is assumed to be bounded by ~pi/4 in magnitude. | |
| 6ff43c94 | 19 | * Input y is the tail of x. |
| b34b60bc JS |
20 | * |
| 21 | * Algorithm | |
| 22 | * 1. Since cos(-x) = cos(x), we need only to consider positive x. | |
| 23 | * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. | |
| 24 | * 3. cos(x) is approximated by a polynomial of degree 14 on | |
| 25 | * [0,pi/4] | |
| 26 | * 4 14 | |
| 27 | * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x | |
| 28 | * where the remez error is | |
| 6ff43c94 | 29 | * |
| b34b60bc JS |
30 | * | 2 4 6 8 10 12 14 | -58 |
| 31 | * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 | |
| 6ff43c94 PA |
32 | * | | |
| 33 | * | |
| 34 | * 4 6 8 10 12 14 | |
| b34b60bc | 35 | * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
| 6ff43c94 PA |
36 | * cos(x) ~ 1 - x*x/2 + r |
| 37 | * since cos(x+y) ~ cos(x) - sin(x)*y | |
| b34b60bc JS |
38 | * ~ cos(x) - x*y, |
| 39 | * a correction term is necessary in cos(x) and hence | |
| 40 | * cos(x+y) = 1 - (x*x/2 - (r - x*y)) | |
| 6ff43c94 PA |
41 | * For better accuracy, rearrange to |
| 42 | * cos(x+y) ~ w + (tmp + (r-x*y)) | |
| 43 | * where w = 1 - x*x/2 and tmp is a tiny correction term | |
| 44 | * (1 - x*x/2 == w + tmp exactly in infinite precision). | |
| 45 | * The exactness of w + tmp in infinite precision depends on w | |
| 46 | * and tmp having the same precision as x. If they have extra | |
| 47 | * precision due to compiler bugs, then the extra precision is | |
| 48 | * only good provided it is retained in all terms of the final | |
| 49 | * expression for cos(). Retention happens in all cases tested | |
| 50 | * under FreeBSD, so don't pessimize things by forcibly clipping | |
| 51 | * any extra precision in w. | |
| b34b60bc JS |
52 | */ |
| 53 | ||
| 6ff43c94 | 54 | #include "math.h" |
| b34b60bc JS |
55 | #include "math_private.h" |
| 56 | ||
| 57 | static const double | |
| 58 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ | |
| 59 | C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ | |
| 60 | C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ | |
| 61 | C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ | |
| 62 | C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ | |
| 63 | C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ | |
| 64 | C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ | |
| 65 | ||
| 66 | double | |
| 67 | __kernel_cos(double x, double y) | |
| 68 | { | |
| 6ff43c94 PA |
69 | double hz,z,r,w; |
| 70 | ||
| b34b60bc | 71 | z = x*x; |
| 6ff43c94 PA |
72 | w = z*z; |
| 73 | r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); | |
| 74 | hz = 0.5*z; | |
| 75 | w = one-hz; | |
| 76 | return w + (((one-w)-hz) + (z*r-x*y)); | |
| b34b60bc | 77 | } |