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| 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 } |
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