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