[352] | 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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