| The Android Open Source Project | b07e1d9 | 2009-03-03 19:29:30 -0800 | [diff] [blame] | 1 | |
| 2 | /* @(#)k_cos.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| 14 | /* |
| 15 | * __kernel_cos( x, y ) |
| 16 | * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 |
| 17 | * Input x is assumed to be bounded by ~pi/4 in magnitude. |
| 18 | * Input y is the tail of x. |
| 19 | * |
| 20 | * Algorithm |
| 21 | * 1. Since ieee_cos(-x) = ieee_cos(x), we need only to consider positive x. |
| 22 | * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. |
| 23 | * 3. ieee_cos(x) is approximated by a polynomial of degree 14 on |
| 24 | * [0,pi/4] |
| 25 | * 4 14 |
| 26 | * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x |
| 27 | * where the remez error is |
| 28 | * |
| 29 | * | 2 4 6 8 10 12 14 | -58 |
| 30 | * |ieee_cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 |
| 31 | * | | |
| 32 | * |
| 33 | * 4 6 8 10 12 14 |
| 34 | * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
| 35 | * ieee_cos(x) = 1 - x*x/2 + r |
| 36 | * since ieee_cos(x+y) ~ ieee_cos(x) - ieee_sin(x)*y |
| 37 | * ~ ieee_cos(x) - x*y, |
| 38 | * a correction term is necessary in ieee_cos(x) and hence |
| 39 | * cos(x+y) = 1 - (x*x/2 - (r - x*y)) |
| 40 | * For better accuracy when x > 0.3, let qx = |x|/4 with |
| 41 | * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. |
| 42 | * Then |
| 43 | * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). |
| 44 | * Note that 1-qx and (x*x/2-qx) is EXACT here, and the |
| 45 | * magnitude of the latter is at least a quarter of x*x/2, |
| 46 | * thus, reducing the rounding error in the subtraction. |
| 47 | */ |
| 48 | |
| 49 | #include "fdlibm.h" |
| 50 | |
| 51 | #ifdef __STDC__ |
| 52 | static const double |
| 53 | #else |
| 54 | static double |
| 55 | #endif |
| 56 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| 57 | C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ |
| 58 | C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ |
| 59 | C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ |
| 60 | C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ |
| 61 | C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ |
| 62 | C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ |
| 63 | |
| 64 | #ifdef __STDC__ |
| 65 | double __kernel_cos(double x, double y) |
| 66 | #else |
| 67 | double __kernel_cos(x, y) |
| 68 | double x,y; |
| 69 | #endif |
| 70 | { |
| 71 | double a,hz,z,r,qx; |
| 72 | int ix; |
| 73 | ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/ |
| 74 | if(ix<0x3e400000) { /* if x < 2**27 */ |
| 75 | if(((int)x)==0) return one; /* generate inexact */ |
| 76 | } |
| 77 | z = x*x; |
| 78 | r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); |
| 79 | if(ix < 0x3FD33333) /* if |x| < 0.3 */ |
| 80 | return one - (0.5*z - (z*r - x*y)); |
| 81 | else { |
| 82 | if(ix > 0x3fe90000) { /* x > 0.78125 */ |
| 83 | qx = 0.28125; |
| 84 | } else { |
| 85 | __HI(qx) = ix-0x00200000; /* x/4 */ |
| 86 | __LO(qx) = 0; |
| 87 | } |
| 88 | hz = 0.5*z-qx; |
| 89 | a = one-qx; |
| 90 | return a - (hz - (z*r-x*y)); |
| 91 | } |
| 92 | } |