1 | /* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */
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2 | /*
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3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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4 | * Optimized by Bruce D. Evans.
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5 | */
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6 | /*
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7 | * ====================================================
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8 | * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
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9 | *
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10 | * Permission to use, copy, modify, and distribute this
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11 | * software is freely granted, provided that this notice
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12 | * is preserved.
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13 | * ====================================================
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14 | */
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15 |
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16 | #include "libm.h"
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17 |
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18 | /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
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19 | static const double T[] = {
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20 | 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
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21 | 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
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22 | 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
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23 | 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
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24 | 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
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25 | 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
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26 | };
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27 |
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28 | float __tandf(double x, int odd)
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29 | {
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30 | double_t z,r,w,s,t,u;
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31 |
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32 | z = x*x;
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33 | /*
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34 | * Split up the polynomial into small independent terms to give
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35 | * opportunities for parallel evaluation. The chosen splitting is
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36 | * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
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37 | * relative to Horner's method on sequential machines.
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38 | *
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39 | * We add the small terms from lowest degree up for efficiency on
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40 | * non-sequential machines (the lowest degree terms tend to be ready
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41 | * earlier). Apart from this, we don't care about order of
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42 | * operations, and don't need to to care since we have precision to
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43 | * spare. However, the chosen splitting is good for accuracy too,
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44 | * and would give results as accurate as Horner's method if the
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45 | * small terms were added from highest degree down.
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46 | */
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47 | r = T[4] + z*T[5];
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48 | t = T[2] + z*T[3];
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49 | w = z*z;
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50 | s = z*x;
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51 | u = T[0] + z*T[1];
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52 | r = (x + s*u) + (s*w)*(t + w*r);
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53 | return odd ? -1.0/r : r;
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54 | }
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