| The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 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 | #ifndef INLINE_KERNEL_TANDF |
| 17 | #ifndef lint |
| 18 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_tanf.c,v 1.20 2005/11/28 11:46:20 bde Exp $"; |
| 19 | #endif |
| 20 | #endif |
| 21 | |
| 22 | #include "math.h" |
| 23 | #include "math_private.h" |
| 24 | |
| 25 | /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ |
| 26 | static const double |
| 27 | T[] = { |
| 28 | 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ |
| 29 | 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ |
| 30 | 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */ |
| 31 | 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */ |
| 32 | 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */ |
| 33 | 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ |
| 34 | }; |
| 35 | |
| 36 | #ifdef INLINE_KERNEL_TANDF |
| 37 | extern inline |
| 38 | #endif |
| 39 | float |
| 40 | __kernel_tandf(double x, int iy) |
| 41 | { |
| 42 | double z,r,w,s,t,u; |
| 43 | |
| 44 | z = x*x; |
| 45 | /* |
| 46 | * Split up the polynomial into small independent terms to give |
| 47 | * opportunities for parallel evaluation. The chosen splitting is |
| 48 | * micro-optimized for Athlons (XP, X64). It costs 2 multiplications |
| 49 | * relative to Horner's method on sequential machines. |
| 50 | * |
| 51 | * We add the small terms from lowest degree up for efficiency on |
| 52 | * non-sequential machines (the lowest degree terms tend to be ready |
| 53 | * earlier). Apart from this, we don't care about order of |
| 54 | * operations, and don't need to to care since we have precision to |
| 55 | * spare. However, the chosen splitting is good for accuracy too, |
| 56 | * and would give results as accurate as Horner's method if the |
| 57 | * small terms were added from highest degree down. |
| 58 | */ |
| 59 | r = T[4]+z*T[5]; |
| 60 | t = T[2]+z*T[3]; |
| 61 | w = z*z; |
| 62 | s = z*x; |
| 63 | u = T[0]+z*T[1]; |
| 64 | r = (x+s*u)+(s*w)*(t+w*r); |
| 65 | if(iy==1) return r; |
| 66 | else return -1.0/r; |
| 67 | } |