65 lines
2.3 KiB
C
65 lines
2.3 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */
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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 SunSoft, 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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/* __sin( x, y, iy)
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* kernel sin function on ~[-pi/4, pi/4] (except on -0), 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. Callers must return sin(-0) = -0 without calling here since our
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* odd polynomial is not evaluated in a way that preserves -0.
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* Callers may do the optimization sin(x) ~ x for tiny x.
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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 "libm.h"
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static const double
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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 __sin(double x, double y, int iy)
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{
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double_t z,r,v,w;
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z = x*x;
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w = z*z;
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r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
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v = z*x;
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if (iy == 0)
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return x + v*(S1 + z*r);
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else
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return x - ((z*(0.5*y - v*r) - y) - v*S1);
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}
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