src/libm/k_sin.c
 author Philipp Wiesemann Sat, 05 Apr 2014 23:32:41 +0200 changeset 8695 a672c01a4ab7 parent 6044 35448a5ea044 child 11683 48bcba563d9c permissions -rw-r--r--
Fixed names of four hint environment variables.
1 /* @(#)k_sin.c 5.1 93/09/24 */
2 /*
3  * ====================================================
5  *
6  * Developed at SunPro, a Sun Microsystems, Inc. business.
7  * Permission to use, copy, modify, and distribute this
8  * software is freely granted, provided that this notice
9  * is preserved.
10  * ====================================================
11  */
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static const char rcsid[] =
15     "\$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp \$";
16 #endif
18 /* __kernel_sin( x, y, iy)
19  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
20  * Input x is assumed to be bounded by ~pi/4 in magnitude.
21  * Input y is the tail of x.
22  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
23  *
24  * Algorithm
25  *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
26  *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
27  *	3. sin(x) is approximated by a polynomial of degree 13 on
28  *	   [0,pi/4]
29  *		  	         3            13
30  *	   	sin(x) ~ x + S1*x + ... + S6*x
31  *	   where
32  *
33  * 	|sin(x)         2     4     6     8     10     12  |     -58
34  * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
35  * 	|  x 					           |
36  *
37  *	4. sin(x+y) = sin(x) + sin'(x')*y
38  *		    ~ sin(x) + (1-x*x/2)*y
39  *	   For better accuracy, let
40  *		     3      2      2      2      2
41  *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
42  *	   then                   3    2
43  *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
44  */
46 #include "math_libm.h"
47 #include "math_private.h"
49 #ifdef __STDC__
50 static const double
51 #else
52 static double
53 #endif
54   half = 5.00000000000000000000e-01,    /* 0x3FE00000, 0x00000000 */
55     S1 = -1.66666666666666324348e-01,   /* 0xBFC55555, 0x55555549 */
56     S2 = 8.33333333332248946124e-03,    /* 0x3F811111, 0x1110F8A6 */
57     S3 = -1.98412698298579493134e-04,   /* 0xBF2A01A0, 0x19C161D5 */
58     S4 = 2.75573137070700676789e-06,    /* 0x3EC71DE3, 0x57B1FE7D */
59     S5 = -2.50507602534068634195e-08,   /* 0xBE5AE5E6, 0x8A2B9CEB */
60     S6 = 1.58969099521155010221e-10;    /* 0x3DE5D93A, 0x5ACFD57C */
62 #ifdef __STDC__
63 double attribute_hidden
64 __kernel_sin(double x, double y, int iy)
65 #else
66 double attribute_hidden
67 __kernel_sin(x, y, iy)
68      double x, y;
69      int iy;                    /* iy=0 if y is zero */
70 #endif
71 {
72     double z, r, v;
73     int32_t ix;
74     GET_HIGH_WORD(ix, x);
75     ix &= 0x7fffffff;           /* high word of x */
76     if (ix < 0x3e400000) {      /* |x| < 2**-27 */
77         if ((int) x == 0)
78             return x;
79     }                           /* generate inexact */
80     z = x * x;
81     v = z * x;
82     r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
83     if (iy == 0)
84         return x + v * (S1 + z * r);
85     else
86         return x - ((z * (half * y - v * r) - y) - v * S1);
87 }