1 /* s_cbrtf.c -- float version of s_cbrt.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 * Debugged and optimized by Bruce D. Evans. 4 */ 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 17 #include "cdefs-compat.h" 18 //__FBSDID("$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.18 2008/02/22 02:30:35 das Exp $"); 19 20 #include <openlibm_math.h> 21 22 #include "math_private.h" 23 24 /* cbrtf(x) 25 * Return cube root of x 26 */ 27 static const unsigned 28 B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ 29 B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ 30 31 DLLEXPORT float 32 cbrtf(float x) 33 { 34 double r,T; 35 float t; 36 int32_t hx; 37 u_int32_t sign; 38 u_int32_t high; 39 40 GET_FLOAT_WORD(hx,x); 41 sign=hx&0x80000000; /* sign= sign(x) */ 42 hx ^=sign; 43 if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ 44 45 /* rough cbrt to 5 bits */ 46 if(hx<0x00800000) { /* zero or subnormal? */ 47 if(hx==0) 48 return(x); /* cbrt(+-0) is itself */ 49 SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ 50 t*=x; 51 GET_FLOAT_WORD(high,t); 52 SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2)); 53 } else 54 SET_FLOAT_WORD(t,sign|(hx/3+B1)); 55 56 /* 57 * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In 58 * double precision so that its terms can be arranged for efficiency 59 * without causing overflow or underflow. 60 */ 61 T=t; 62 r=T*T*T; 63 T=T*((double)x+x+r)/(x+r+r); 64 65 /* 66 * Second step Newton iteration to 47 bits. In double precision for 67 * efficiency and accuracy. 68 */ 69 r=T*T*T; 70 T=T*((double)x+x+r)/(x+r+r); 71 72 /* rounding to 24 bits is perfect in round-to-nearest mode */ 73 return(T); 74 } 75