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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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