1 /* k_tanf.c -- float version of k_tan.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Optimized by Bruce D. Evans.
4 */
5
6 /*
7 * ====================================================
8 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
9 *
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16 #include "math.h"
17 #include "math_private.h"
18
19 /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
20 static const double
21 T[] = {
22 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
23 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
24 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
25 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
26 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
27 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
28 };
29
30 #ifdef INLINE_KERNEL_TANDF
31 static __inline
32 #endif
33 float
__kernel_tandf(double x,int iy)34 __kernel_tandf(double x, int iy)
35 {
36 double z,r,w,s,t,u;
37
38 z = x*x;
39 /*
40 * Split up the polynomial into small independent terms to give
41 * opportunities for parallel evaluation. The chosen splitting is
42 * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
43 * relative to Horner's method on sequential machines.
44 *
45 * We add the small terms from lowest degree up for efficiency on
46 * non-sequential machines (the lowest degree terms tend to be ready
47 * earlier). Apart from this, we don't care about order of
48 * operations, and don't need to care since we have precision to
49 * spare. However, the chosen splitting is good for accuracy too,
50 * and would give results as accurate as Horner's method if the
51 * small terms were added from highest degree down.
52 */
53 r = T[4]+z*T[5];
54 t = T[2]+z*T[3];
55 w = z*z;
56 s = z*x;
57 u = T[0]+z*T[1];
58 r = (x+s*u)+(s*w)*(t+w*r);
59 if(iy==1) return r;
60 else return -1.0/r;
61 }
62