[469] | 1 | /* |
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| 2 | * ==================================================== |
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| 3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 4 | * |
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| 5 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 6 | * Permission to use, copy, modify, and distribute this |
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| 7 | * software is freely granted, provided that this notice |
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| 8 | * is preserved. |
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| 9 | * ==================================================== |
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| 10 | */ |
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| 11 | |
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| 12 | /* |
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| 13 | * Modified for ALMOS-MKH OS at UPMC, France, August 2018. (Alain Greiner) |
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| 14 | */ |
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| 15 | |
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| 16 | /* |
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| 17 | * __kernel_cos( x, y ) |
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| 18 | * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 |
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| 19 | * Input x is assumed to be bounded by ~pi/4 in magnitude. |
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| 20 | * Input y is the tail of x. |
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| 21 | * |
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| 22 | * Algorithm |
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| 23 | * 1. Since cos(-x) = cos(x), we need only to consider positive x. |
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| 24 | * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. |
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| 25 | * 3. cos(x) is approximated by a polynomial of degree 14 on |
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| 26 | * [0,pi/4] |
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| 27 | * 4 14 |
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| 28 | * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x |
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| 29 | * where the remez error is |
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| 30 | * |
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| 31 | * | 2 4 6 8 10 12 14 | -58 |
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| 32 | * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 |
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| 33 | * | | |
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| 34 | * |
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| 35 | * 4 6 8 10 12 14 |
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| 36 | * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
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| 37 | * cos(x) = 1 - x*x/2 + r |
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| 38 | * since cos(x+y) ~ cos(x) - sin(x)*y |
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| 39 | * ~ cos(x) - x*y, |
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| 40 | * a correction term is necessary in cos(x) and hence |
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| 41 | * cos(x+y) = 1 - (x*x/2 - (r - x*y)) |
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| 42 | * For better accuracy when x > 0.3, let qx = |x|/4 with |
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| 43 | * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. |
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| 44 | * Then |
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| 45 | * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). |
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| 46 | * Note that 1-qx and (x*x/2-qx) is EXACT here, and the |
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| 47 | * magnitude of the latter is at least a quarter of x*x/2, |
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| 48 | * thus, reducing the rounding error in the subtraction. |
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| 49 | */ |
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| 50 | |
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| 51 | #include "math.h" |
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| 52 | #include "math_private.h" |
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| 53 | |
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| 54 | static const double |
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| 55 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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| 56 | C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ |
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| 57 | C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ |
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| 58 | C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ |
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| 59 | C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ |
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| 60 | C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ |
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| 61 | C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ |
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| 62 | |
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| 63 | double __kernel_cos(double x, double y) |
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| 64 | { |
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| 65 | double a,hz,z,r,qx; |
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| 66 | int32_t ix; |
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| 67 | GET_HIGH_WORD(ix,x); |
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| 68 | ix &= 0x7fffffff; /* ix = |x|'s high word*/ |
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| 69 | if(ix<0x3e400000) { /* if x < 2**27 */ |
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| 70 | if(((int)x)==0) return one; /* generate inexact */ |
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| 71 | } |
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| 72 | z = x*x; |
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| 73 | r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); |
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| 74 | if(ix < 0x3FD33333) /* if |x| < 0.3 */ |
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| 75 | return one - (0.5*z - (z*r - x*y)); |
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| 76 | else { |
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| 77 | if(ix > 0x3fe90000) { /* x > 0.78125 */ |
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| 78 | qx = 0.28125; |
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| 79 | } else { |
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| 80 | INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ |
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| 81 | } |
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| 82 | hz = 0.5*z-qx; |
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| 83 | a = one-qx; |
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| 84 | return a - (hz - (z*r-x*y)); |
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| 85 | } |
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| 86 | } |
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