src/libm/k_cos.c
 author Ryan C. Gordon Tue, 26 May 2015 21:19:23 -0400 changeset 9649 d7762e30ba24 parent 6044 35448a5ea044 child 11683 48bcba563d9c permissions -rw-r--r--
Stack hint should look for 0, not -1, and not care about environment variables.
1 /* @(#)k_cos.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_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp \$";
16 #endif
18 /*
19  * __kernel_cos( x,  y )
20  * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
21  * Input x is assumed to be bounded by ~pi/4 in magnitude.
22  * Input y is the tail of x.
23  *
24  * Algorithm
25  *	1. Since cos(-x) = cos(x), we need only to consider positive x.
26  *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
27  *	3. cos(x) is approximated by a polynomial of degree 14 on
28  *	   [0,pi/4]
29  *		  	                 4            14
30  *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
31  *	   where the remez error is
32  *
33  * 	|              2     4     6     8     10    12     14 |     -58
34  * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
35  * 	|    					               |
36  *
37  * 	               4     6     8     10    12     14
38  *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
39  *	       cos(x) = 1 - x*x/2 + r
40  *	   since cos(x+y) ~ cos(x) - sin(x)*y
41  *			  ~ cos(x) - x*y,
42  *	   a correction term is necessary in cos(x) and hence
43  *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
44  *	   For better accuracy when x > 0.3, let qx = |x|/4 with
45  *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
46  *	   Then
47  *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
48  *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
49  *	   magnitude of the latter is at least a quarter of x*x/2,
50  *	   thus, reducing the rounding error in the subtraction.
51  */
53 #include "math_libm.h"
54 #include "math_private.h"
56 #ifdef __STDC__
57 static const double
58 #else
59 static double
60 #endif
61   one = 1.00000000000000000000e+00,     /* 0x3FF00000, 0x00000000 */
62     C1 = 4.16666666666666019037e-02,    /* 0x3FA55555, 0x5555554C */
63     C2 = -1.38888888888741095749e-03,   /* 0xBF56C16C, 0x16C15177 */
64     C3 = 2.48015872894767294178e-05,    /* 0x3EFA01A0, 0x19CB1590 */
65     C4 = -2.75573143513906633035e-07,   /* 0xBE927E4F, 0x809C52AD */
66     C5 = 2.08757232129817482790e-09,    /* 0x3E21EE9E, 0xBDB4B1C4 */
67     C6 = -1.13596475577881948265e-11;   /* 0xBDA8FAE9, 0xBE8838D4 */
69 #ifdef __STDC__
70 double attribute_hidden
71 __kernel_cos(double x, double y)
72 #else
73 double attribute_hidden
74 __kernel_cos(x, y)
75      double x, y;
76 #endif
77 {
78     double a, hz, z, r, qx;
79     int32_t ix;
80     GET_HIGH_WORD(ix, x);
81     ix &= 0x7fffffff;           /* ix = |x|'s high word */
82     if (ix < 0x3e400000) {      /* if x < 2**27 */
83         if (((int) x) == 0)
84             return one;         /* generate inexact */
85     }
86     z = x * x;
87     r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
88     if (ix < 0x3FD33333)        /* if |x| < 0.3 */
89         return one - (0.5 * z - (z * r - x * y));
90     else {
91         if (ix > 0x3fe90000) {  /* x > 0.78125 */
92             qx = 0.28125;
93         } else {
94             INSERT_WORDS(qx, ix - 0x00200000, 0);       /* x/4 */
95         }
96         hz = 0.5 * z - qx;
97         a = one - qx;
98         return a - (hz - (z * r - x * y));
99     }
100 }