1 /* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */ 2 /* 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 4 * Optimized by Bruce D. Evans. 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 "libm.h" 17 18 /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ 19 static const double T[] = { 20 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ 21 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ 22 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */ 23 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */ 24 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */ 25 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ 26 }; 27 28 float __tandf(double x, int odd) 29 { 30 double_t z,r,w,s,t,u; 31 32 z = x*x; 33 /* 34 * Split up the polynomial into small independent terms to give 35 * opportunities for parallel evaluation. The chosen splitting is 36 * micro-optimized for Athlons (XP, X64). It costs 2 multiplications 37 * relative to Horner's method on sequential machines. 38 * 39 * We add the small terms from lowest degree up for efficiency on 40 * non-sequential machines (the lowest degree terms tend to be ready 41 * earlier). Apart from this, we don't care about order of 42 * operations, and don't need to to care since we have precision to 43 * spare. However, the chosen splitting is good for accuracy too, 44 * and would give results as accurate as Horner's method if the 45 * small terms were added from highest degree down. 46 */ 47 r = T[4] + z*T[5]; 48 t = T[2] + z*T[3]; 49 w = z*z; 50 s = z*x; 51 u = T[0] + z*T[1]; 52 r = (x + s*u) + (s*w)*(t + w*r); 53 return odd ? -1.0/r : r; 54 } 55