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/* @(#)k_sin.c 5.1 93/09/24 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* __kernel_sin( x, y, iy) |
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* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
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* Input x is assumed to be bounded by ~pi/4 in magnitude. |
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* Input y is the tail of x. |
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* Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
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* |
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* Algorithm |
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* 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
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* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. |
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* 3. sin(x) is approximated by a polynomial of degree 13 on |
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* [0,pi/4] |
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* 3 13 |
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* sin(x) ~ x + S1*x + ... + S6*x |
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* where |
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* |
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* |sin(x) 2 4 6 8 10 12 | -58 |
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* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
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* | x | |
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* |
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* 4. sin(x+y) = sin(x) + sin'(x')*y |
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* ~ sin(x) + (1-x*x/2)*y |
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* For better accuracy, let |
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* 3 2 2 2 2 |
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* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
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* then 3 2 |
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* sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
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*/ |
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#include "math.h" |
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#include "math_private.h" |
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static const double |
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
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S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
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S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
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S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
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S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
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S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
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double |
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__kernel_sin(double x, double y, int iy) |
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{ |
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double z,r,v; |
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int32_t ix; |
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GET_HIGH_WORD(ix,x); |
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ix &= 0x7fffffff; /* high word of x */ |
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✓✓ |
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if(ix<0x3e400000) /* |x| < 2**-27 */ |
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✓✗ |
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{if((int)x==0) return x;} /* generate inexact */ |
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z = x*x; |
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v = z*x; |
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r = S2+z*(S3+z*(S4+z*(S5+z*S6))); |
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✓✗ |
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if(iy==0) return x+v*(S1+z*r); |
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else return x-((z*(half*y-v*r)-y)-v*S1); |
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} |