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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */ |
| 2 /* |
| 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| 4 * Debugged and optimized by Bruce D. Evans. |
| 5 */ |
| 6 /* |
| 7 * ==================================================== |
| 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 9 * |
| 10 * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 11 * Permission to use, copy, modify, and distribute this |
| 12 * software is freely granted, provided that this notice |
| 13 * is preserved. |
| 14 * ==================================================== |
| 15 */ |
| 16 /* cbrtf(x) |
| 17 * Return cube root of x |
| 18 */ |
| 19 |
| 20 #include <math.h> |
| 21 #include <stdint.h> |
| 22 |
| 23 static const unsigned |
| 24 B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ |
| 25 B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ |
| 26 |
| 27 float cbrtf(float x) |
| 28 { |
| 29 double_t r,T; |
| 30 union {float f; uint32_t i;} u = {x}; |
| 31 uint32_t hx = u.i & 0x7fffffff; |
| 32 |
| 33 if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */ |
| 34 return x + x; |
| 35 |
| 36 /* rough cbrt to 5 bits */ |
| 37 if (hx < 0x00800000) { /* zero or subnormal? */ |
| 38 if (hx == 0) |
| 39 return x; /* cbrt(+-0) is itself */ |
| 40 u.f = x*0x1p24f; |
| 41 hx = u.i & 0x7fffffff; |
| 42 hx = hx/3 + B2; |
| 43 } else |
| 44 hx = hx/3 + B1; |
| 45 u.i &= 0x80000000; |
| 46 u.i |= hx; |
| 47 |
| 48 /* |
| 49 * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In |
| 50 * double precision so that its terms can be arranged for efficiency |
| 51 * without causing overflow or underflow. |
| 52 */ |
| 53 T = u.f; |
| 54 r = T*T*T; |
| 55 T = T*((double_t)x+x+r)/(x+r+r); |
| 56 |
| 57 /* |
| 58 * Second step Newton iteration to 47 bits. In double precision for |
| 59 * efficiency and accuracy. |
| 60 */ |
| 61 r = T*T*T; |
| 62 T = T*((double_t)x+x+r)/(x+r+r); |
| 63 |
| 64 /* rounding to 24 bits is perfect in round-to-nearest mode */ |
| 65 return T; |
| 66 } |
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