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| 2 | /* @(#)k_sin.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | */ |
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| 13 | |
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| 14 | /* __kernel_sin( x, y, iy) |
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| 15 | * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
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| 16 | * Input x is assumed to be bounded by ~pi/4 in magnitude. |
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| 17 | * Input y is the tail of x. |
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| 18 | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
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| 19 | * |
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| 20 | * Algorithm |
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| 21 | * 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
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| 22 | * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. |
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| 23 | * 3. sin(x) is approximated by a polynomial of degree 13 on |
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| 24 | * [0,pi/4] |
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| 25 | * 3 13 |
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| 26 | * sin(x) ~ x + S1*x + ... + S6*x |
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| 27 | * where |
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| 28 | * |
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| 29 | * |sin(x) 2 4 6 8 10 12 | -58 |
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| 30 | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
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| 31 | * | x | |
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| 32 | * |
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| 33 | * 4. sin(x+y) = sin(x) + sin'(x')*y |
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| 34 | * ~ sin(x) + (1-x*x/2)*y |
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| 35 | * For better accuracy, let |
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| 36 | * 3 2 2 2 2 |
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| 37 | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
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| 38 | * then 3 2 |
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| 39 | * sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
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| 40 | */ |
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| 41 | |
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| 42 | #include "fdlibm.h" |
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| 43 | |
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| 44 | #ifndef _DOUBLE_IS_32BITS |
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| 45 | |
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| 46 | #ifdef __STDC__ |
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| 47 | static const double |
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| 48 | #else |
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| 49 | static double |
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| 50 | #endif |
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| 51 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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| 52 | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
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| 53 | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
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| 54 | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
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| 55 | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
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| 56 | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
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| 57 | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
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| 58 | |
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| 59 | #ifdef __STDC__ |
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| 60 | double __kernel_sin(double x, double y, int iy) |
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| 61 | #else |
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| 62 | double __kernel_sin(x, y, iy) |
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| 63 | double x,y; int iy; /* iy=0 if y is zero */ |
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| 64 | #endif |
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| 65 | { |
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| 66 | double z,r,v; |
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| 67 | __int32_t ix; |
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| 68 | GET_HIGH_WORD(ix,x); |
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| 69 | ix &= 0x7fffffff; /* high word of x */ |
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| 70 | if(ix<0x3e400000) /* |x| < 2**-27 */ |
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| 71 | {if((int)x==0) return x;} /* generate inexact */ |
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| 72 | z = x*x; |
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| 73 | v = z*x; |
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| 74 | r = S2+z*(S3+z*(S4+z*(S5+z*S6))); |
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| 75 | if(iy==0) return x+v*(S1+z*r); |
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| 76 | else return x-((z*(half*y-v*r)-y)-v*S1); |
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| 77 | } |
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| 78 | |
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| 79 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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