1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.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 | * Debugged and 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 (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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9 | *
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10 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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11 | * Permission to use, copy, modify, and distribute this
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12 | * software is freely granted, provided that this notice
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13 | * is preserved.
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14 | * ====================================================
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15 | */
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16 | /* cbrtf(x)
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17 | * Return cube root of x
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18 | */
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19 |
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20 | #include <math.h>
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21 | #include <stdint.h>
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22 |
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23 | static const unsigned
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24 | B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
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25 | B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
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26 |
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27 | float cbrtf(float x)
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28 | {
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29 | double_t r,T;
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30 | union {float f; uint32_t i;} u = {x};
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31 | uint32_t hx = u.i & 0x7fffffff;
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32 |
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33 | if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */
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34 | return x + x;
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35 |
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36 | /* rough cbrt to 5 bits */
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37 | if (hx < 0x00800000) { /* zero or subnormal? */
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38 | if (hx == 0)
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39 | return x; /* cbrt(+-0) is itself */
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40 | u.f = x*0x1p24f;
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41 | hx = u.i & 0x7fffffff;
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42 | hx = hx/3 + B2;
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43 | } else
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44 | hx = hx/3 + B1;
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45 | u.i &= 0x80000000;
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46 | u.i |= hx;
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47 |
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48 | /*
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49 | * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
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50 | * double precision so that its terms can be arranged for efficiency
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51 | * without causing overflow or underflow.
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52 | */
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53 | T = u.f;
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54 | r = T*T*T;
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55 | T = T*((double_t)x+x+r)/(x+r+r);
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56 |
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57 | /*
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58 | * Second step Newton iteration to 47 bits. In double precision for
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59 | * efficiency and accuracy.
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60 | */
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61 | r = T*T*T;
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62 | T = T*((double_t)x+x+r)/(x+r+r);
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63 |
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64 | /* rounding to 24 bits is perfect in round-to-nearest mode */
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65 | return T;
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66 | }
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