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 } 67