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Diffstat (limited to 'newlib/libm/common/s_cbrt.c')
| -rw-r--r-- | newlib/libm/common/s_cbrt.c | 123 |
1 files changed, 123 insertions, 0 deletions
diff --git a/newlib/libm/common/s_cbrt.c b/newlib/libm/common/s_cbrt.c new file mode 100644 index 00000000000..95185d0fa0a --- /dev/null +++ b/newlib/libm/common/s_cbrt.c @@ -0,0 +1,123 @@ + +/* @(#)s_cbrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* +FUNCTION + <<cbrt>>, <<cbrtf>>---cube root + +INDEX + cbrt +INDEX + cbrtf + +ANSI_SYNOPSIS + #include <math.h> + double cbrt(double <[x]>); + float cbrtf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double cbrt(<[x]>); + float cbrtf(<[x]>); + +DESCRIPTION + <<cbrt>> computes the cube root of the argument. + +RETURNS + The cube root is returned. + +PORTABILITY + <<cbrt>> is in System V release 4. <<cbrtf>> is an extension. +*/ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +/* cbrt(x) + * Return cube root of x + */ +#ifdef __STDC__ +static const __uint32_t +#else +static __uint32_t +#endif + B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ + +#ifdef __STDC__ +static const double +#else +static double +#endif +C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ +D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ +E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ +F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ +G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ + +#ifdef __STDC__ + double cbrt(double x) +#else + double cbrt(x) + double x; +#endif +{ + __int32_t hx; + double r,s,t=0.0,w; + __uint32_t sign; + __uint32_t high,low; + + GET_HIGH_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ + GET_LOW_WORD(low,x); + if((hx|low)==0) + return(x); /* cbrt(0) is itself */ + + SET_HIGH_WORD(x,hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if(hx<0x00100000) /* subnormal number */ + {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ + t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); + } + else + SET_HIGH_WORD(t,hx/3+B1); + + + /* new cbrt to 23 bits, may be implemented in single precision */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* chopped to 20 bits and make it larger than cbrt(x) */ + GET_HIGH_WORD(high,t); + INSERT_WORDS(t,high+0x00000001,0); + + + /* one step newton iteration to 53 bits with error less than 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; + w=t+t; + r=(r-t)/(w+r); /* r-s is exact */ + t=t+t*r; + + /* retore the sign bit */ + GET_HIGH_WORD(high,t); + SET_HIGH_WORD(t,high|sign); + return(t); +} + +#endif /* _DOUBLE_IS_32BITS */ |