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| 2 | /* @(#)k_sin.c 1.3 95/01/18 */
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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 SunSoft, 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 | #ifndef lint
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| 15 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_sin.c,v 1.8 2005/02/04 18:26:06 das Exp $";
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| 16 | #endif
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| 17 |
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| 18 | /* __kernel_sin( x, y, iy)
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| 19 | * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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| 20 | * Input x is assumed to be bounded by ~pi/4 in magnitude.
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| 21 | * Input y is the tail of x.
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| 22 | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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| 23 | *
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| 24 | * Algorithm
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| 25 | * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
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| 26 | * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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| 27 | * 3. sin(x) is approximated by a polynomial of degree 13 on
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| 28 | * [0,pi/4]
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| 29 | * 3 13
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| 30 | * sin(x) ~ x + S1*x + ... + S6*x
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| 31 | * where
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| 32 | *
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| 33 | * |sin(x) 2 4 6 8 10 12 | -58
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| 34 | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
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| 35 | * | x |
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| 36 | *
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| 37 | * 4. sin(x+y) = sin(x) + sin'(x')*y
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| 38 | * ~ sin(x) + (1-x*x/2)*y
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| 39 | * For better accuracy, let
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| 40 | * 3 2 2 2 2
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| 41 | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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| 42 | * then 3 2
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| 43 | * sin(x) = x + (S1*x + (x *(r-y/2)+y))
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| 44 | */
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| 45 |
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| 46 | #include "math.h"
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| 47 | #include "math_private.h"
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| 48 |
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| 49 | static const double
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| 50 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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| 51 | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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| 52 | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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| 53 | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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| 54 | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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| 55 | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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| 56 | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
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| 57 |
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| 58 | double
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| 59 | __kernel_sin(double x, double y, int iy)
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| 60 | {
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| 61 | double z,r,v;
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| 62 | int32_t ix;
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| 63 | GET_HIGH_WORD(ix,x);
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| 64 | ix &= 0x7fffffff; /* high word of x */
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| 65 | if(ix<0x3e400000) /* |x| < 2**-27 */
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| 66 | {if((int)x==0) return x;} /* generate inexact */
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| 67 | z = x*x;
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| 68 | v = z*x;
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| 69 | r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
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| 70 | if(iy==0) return x+v*(S1+z*r);
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| 71 | else return x-((z*(half*y-v*r)-y)-v*S1);
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| 72 | }
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