1*f504f610SAugustin Cavalier /* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */
2*f504f610SAugustin Cavalier /*
3*f504f610SAugustin Cavalier * ====================================================
4*f504f610SAugustin Cavalier * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*f504f610SAugustin Cavalier *
6*f504f610SAugustin Cavalier * Developed at SunSoft, a Sun Microsystems, Inc. business.
7*f504f610SAugustin Cavalier * Permission to use, copy, modify, and distribute this
8*f504f610SAugustin Cavalier * software is freely granted, provided that this notice
9*f504f610SAugustin Cavalier * is preserved.
10*f504f610SAugustin Cavalier * ====================================================
11*f504f610SAugustin Cavalier */
12*f504f610SAugustin Cavalier /* __sin( x, y, iy)
13*f504f610SAugustin Cavalier * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
14*f504f610SAugustin Cavalier * Input x is assumed to be bounded by ~pi/4 in magnitude.
15*f504f610SAugustin Cavalier * Input y is the tail of x.
16*f504f610SAugustin Cavalier * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
17*f504f610SAugustin Cavalier *
18*f504f610SAugustin Cavalier * Algorithm
19*f504f610SAugustin Cavalier * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
20*f504f610SAugustin Cavalier * 2. Callers must return sin(-0) = -0 without calling here since our
21*f504f610SAugustin Cavalier * odd polynomial is not evaluated in a way that preserves -0.
22*f504f610SAugustin Cavalier * Callers may do the optimization sin(x) ~ x for tiny x.
23*f504f610SAugustin Cavalier * 3. sin(x) is approximated by a polynomial of degree 13 on
24*f504f610SAugustin Cavalier * [0,pi/4]
25*f504f610SAugustin Cavalier * 3 13
26*f504f610SAugustin Cavalier * sin(x) ~ x + S1*x + ... + S6*x
27*f504f610SAugustin Cavalier * where
28*f504f610SAugustin Cavalier *
29*f504f610SAugustin Cavalier * |sin(x) 2 4 6 8 10 12 | -58
30*f504f610SAugustin Cavalier * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
31*f504f610SAugustin Cavalier * | x |
32*f504f610SAugustin Cavalier *
33*f504f610SAugustin Cavalier * 4. sin(x+y) = sin(x) + sin'(x')*y
34*f504f610SAugustin Cavalier * ~ sin(x) + (1-x*x/2)*y
35*f504f610SAugustin Cavalier * For better accuracy, let
36*f504f610SAugustin Cavalier * 3 2 2 2 2
37*f504f610SAugustin Cavalier * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
38*f504f610SAugustin Cavalier * then 3 2
39*f504f610SAugustin Cavalier * sin(x) = x + (S1*x + (x *(r-y/2)+y))
40*f504f610SAugustin Cavalier */
41*f504f610SAugustin Cavalier
42*f504f610SAugustin Cavalier #include "libm.h"
43*f504f610SAugustin Cavalier
44*f504f610SAugustin Cavalier static const double
45*f504f610SAugustin Cavalier S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
46*f504f610SAugustin Cavalier S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
47*f504f610SAugustin Cavalier S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
48*f504f610SAugustin Cavalier S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
49*f504f610SAugustin Cavalier S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
50*f504f610SAugustin Cavalier S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
51*f504f610SAugustin Cavalier
__sin(double x,double y,int iy)52*f504f610SAugustin Cavalier double __sin(double x, double y, int iy)
53*f504f610SAugustin Cavalier {
54*f504f610SAugustin Cavalier double_t z,r,v,w;
55*f504f610SAugustin Cavalier
56*f504f610SAugustin Cavalier z = x*x;
57*f504f610SAugustin Cavalier w = z*z;
58*f504f610SAugustin Cavalier r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
59*f504f610SAugustin Cavalier v = z*x;
60*f504f610SAugustin Cavalier if (iy == 0)
61*f504f610SAugustin Cavalier return x + v*(S1 + z*r);
62*f504f610SAugustin Cavalier else
63*f504f610SAugustin Cavalier return x - ((z*(0.5*y - v*r) - y) - v*S1);
64*f504f610SAugustin Cavalier }
65