12116Sjkh/* s_cbrtf.c -- float version of s_cbrt.c. 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3153386Sbde * Debugged and optimized by Bruce D. Evans. 42116Sjkh */ 52116Sjkh 62116Sjkh/* 72116Sjkh * ==================================================== 82116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 92116Sjkh * 102116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 112116Sjkh * Permission to use, copy, modify, and distribute this 128870Srgrimes * software is freely granted, provided that this notice 132116Sjkh * is preserved. 142116Sjkh * ==================================================== 152116Sjkh */ 162116Sjkh 17176451Sdas#include <sys/cdefs.h> 18176451Sdas__FBSDID("$FreeBSD$"); 192116Sjkh 202116Sjkh#include "math.h" 212116Sjkh#include "math_private.h" 222116Sjkh 232116Sjkh/* cbrtf(x) 242116Sjkh * Return cube root of x 252116Sjkh */ 268870Srgrimesstatic const unsigned 27153306Sbde B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ 28153306Sbde B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ 292116Sjkh 3097413Salfredfloat 3197413Salfredcbrtf(float x) 322116Sjkh{ 33154049Sbde double r,T; 34154049Sbde float t; 352116Sjkh int32_t hx; 362116Sjkh u_int32_t sign; 372116Sjkh u_int32_t high; 382116Sjkh 392116Sjkh GET_FLOAT_WORD(hx,x); 402116Sjkh sign=hx&0x80000000; /* sign= sign(x) */ 412116Sjkh hx ^=sign; 422116Sjkh if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ 432116Sjkh 442116Sjkh /* rough cbrt to 5 bits */ 45170089Sbde if(hx<0x00800000) { /* zero or subnormal? */ 46170089Sbde if(hx==0) 47170089Sbde return(x); /* cbrt(+-0) is itself */ 48153382Sbde SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ 49153382Sbde t*=x; 50153382Sbde GET_FLOAT_WORD(high,t); 51153386Sbde SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2)); 52153382Sbde } else 53153386Sbde SET_FLOAT_WORD(t,sign|(hx/3+B1)); 542116Sjkh 55154051Sbde /* 56154051Sbde * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In 57154051Sbde * double precision so that its terms can be arranged for efficiency 58154051Sbde * without causing overflow or underflow. 59154051Sbde */ 60154049Sbde T=t; 61154049Sbde r=T*T*T; 62154051Sbde T=T*((double)x+x+r)/(x+r+r); 632116Sjkh 64154051Sbde /* 65154051Sbde * Second step Newton iteration to 47 bits. In double precision for 66154051Sbde * efficiency and accuracy. 67154051Sbde */ 68154049Sbde r=T*T*T; 69154051Sbde T=T*((double)x+x+r)/(x+r+r); 70153303Sbde 71154049Sbde /* rounding to 24 bits is perfect in round-to-nearest mode */ 72154049Sbde return(T); 732116Sjkh} 74