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.
7 * ====================================================
8 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
13 * ====================================================
15 * $FreeBSD: head/lib/msun/src/k_tanf.c 239192 2012-08-11 11:13:48Z dim $
19 #include "math_private.h"
21 /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
24 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
25 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
26 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
27 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
28 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
29 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
32 #ifdef INLINE_KERNEL_TANDF
36 __kernel_tandf(double x, int iy)
42 * Split up the polynomial into small independent terms to give
43 * opportunities for parallel evaluation. The chosen splitting is
44 * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
45 * relative to Horner's method on sequential machines.
47 * We add the small terms from lowest degree up for efficiency on
48 * non-sequential machines (the lowest degree terms tend to be ready
49 * earlier). Apart from this, we don't care about order of
50 * operations, and don't need to to care since we have precision to
51 * spare. However, the chosen splitting is good for accuracy too,
52 * and would give results as accurate as Horner's method if the
53 * small terms were added from highest degree down.
60 r = (x+s*u)+(s*w)*(t+w*r);