| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 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 | } |