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