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