| | 1 | /* @(#)k_cos.c 5.1 93/09/24 */ |
| | 2 | /* |
| | 3 | * ==================================================== |
| | 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| | 5 | * |
| | 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| | 7 | * Permission to use, copy, modify, and distribute this |
| | 8 | * software is freely granted, provided that this notice |
| | 9 | * is preserved. |
| | 10 | * ==================================================== |
| | 11 | */ |
| | 12 | |
| | 13 | #if defined(LIBM_SCCS) && !defined(lint) |
| | 14 | static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; |
| | 15 | #endif |
| | 16 | |
| | 17 | /* |
| | 18 | * __kernel_cos( x, y ) |
| | 19 | * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 |
| | 20 | * Input x is assumed to be bounded by ~pi/4 in magnitude. |
| | 21 | * Input y is the tail of x. |
| | 22 | * |
| | 23 | * Algorithm |
| | 24 | * 1. Since cos(-x) = cos(x), we need only to consider positive x. |
| | 25 | * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. |
| | 26 | * 3. cos(x) is approximated by a polynomial of degree 14 on |
| | 27 | * [0,pi/4] |
| | 28 | * 4 14 |
| | 29 | * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x |
| | 30 | * where the remez error is |
| | 31 | * |
| | 32 | * | 2 4 6 8 10 12 14 | -58 |
| | 33 | * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 |
| | 34 | * | | |
| | 35 | * |
| | 36 | * 4 6 8 10 12 14 |
| | 37 | * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
| | 38 | * cos(x) = 1 - x*x/2 + r |
| | 39 | * since cos(x+y) ~ cos(x) - sin(x)*y |
| | 40 | * ~ cos(x) - x*y, |
| | 41 | * a correction term is necessary in cos(x) and hence |
| | 42 | * cos(x+y) = 1 - (x*x/2 - (r - x*y)) |
| | 43 | * For better accuracy when x > 0.3, let qx = |x|/4 with |
| | 44 | * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. |
| | 45 | * Then |
| | 46 | * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). |
| | 47 | * Note that 1-qx and (x*x/2-qx) is EXACT here, and the |
| | 48 | * magnitude of the latter is at least a quarter of x*x/2, |
| | 49 | * thus, reducing the rounding error in the subtraction. |
| | 50 | */ |
| | 51 | |
| | 52 | #include "math.h" |
| | 53 | #include "math_private.h" |
| | 54 | |
| | 55 | #ifdef __STDC__ |
| | 56 | static const double |
| | 57 | #else |
| | 58 | static double |
| | 59 | #endif |
| | 60 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| | 61 | C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ |
| | 62 | C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ |
| | 63 | C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ |
| | 64 | C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ |
| | 65 | C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ |
| | 66 | C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ |
| | 67 | |
| | 68 | #ifdef __STDC__ |
| | 69 | double __kernel_cos(double x, double y) |
| | 70 | #else |
| | 71 | double __kernel_cos(x, y) |
| | 72 | double x,y; |
| | 73 | #endif |
| | 74 | { |
| | 75 | double a,hz,z,r,qx; |
| | 76 | int32_t ix; |
| | 77 | GET_HIGH_WORD(ix,x); |
| | 78 | ix &= 0x7fffffff; /* ix = |x|'s high word*/ |
| | 79 | if(ix<0x3e400000) { /* if x < 2**27 */ |
| | 80 | if(((int)x)==0) return one; /* generate inexact */ |
| | 81 | } |
| | 82 | z = x*x; |
| | 83 | r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); |
| | 84 | if(ix < 0x3FD33333) /* if |x| < 0.3 */ |
| | 85 | return one - (0.5*z - (z*r - x*y)); |
| | 86 | else { |
| | 87 | if(ix > 0x3fe90000) { /* x > 0.78125 */ |
| | 88 | qx = 0.28125; |
| | 89 | } else { |
| | 90 | INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ |
| | 91 | } |
| | 92 | hz = 0.5*z-qx; |
| | 93 | a = one-qx; |
| | 94 | return a - (hz - (z*r-x*y)); |
| | 95 | } |
| | 96 | } |
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