| /* k_tanf.c -- float version of k_tan.c |

| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |

| * Optimized by Bruce D. Evans. |

| */ |

| |

| /* |

| * ==================================================== |

| * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. |

| * |

| * Permission to use, copy, modify, and distribute this |

| * software is freely granted, provided that this notice |

| * is preserved. |

| * ==================================================== |

| */ |

| |

| #ifndef INLINE_KERNEL_TANDF |

| #ifndef lint |

| static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_tanf.c,v 1.20 2005/11/28 11:46:20 bde Exp $"; |

| #endif |

| #endif |

| |

| #include "math.h" |

| #include "math_private.h" |

| |

| /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ |

| static const double |

| T[] = { |

| 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ |

| 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ |

| 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */ |

| 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */ |

| 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */ |

| 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ |

| }; |

| |

| #ifdef INLINE_KERNEL_TANDF |

| extern inline |

| #endif |

| float |

| __kernel_tandf(double x, int iy) |

| { |

| double z,r,w,s,t,u; |

| |

| z = x*x; |

| /* |

| * Split up the polynomial into small independent terms to give |

| * opportunities for parallel evaluation. The chosen splitting is |

| * micro-optimized for Athlons (XP, X64). It costs 2 multiplications |

| * relative to Horner's method on sequential machines. |

| * |

| * We add the small terms from lowest degree up for efficiency on |

| * non-sequential machines (the lowest degree terms tend to be ready |

| * earlier). Apart from this, we don't care about order of |

| * operations, and don't need to to care since we have precision to |

| * spare. However, the chosen splitting is good for accuracy too, |

| * and would give results as accurate as Horner's method if the |

| * small terms were added from highest degree down. |

| */ |

| r = T[4]+z*T[5]; |

| t = T[2]+z*T[3]; |

| w = z*z; |

| s = z*x; |

| u = T[0]+z*T[1]; |

| r = (x+s*u)+(s*w)*(t+w*r); |

| if(iy==1) return r; |

| else return -1.0/r; |

| } |