diff options
Diffstat (limited to 'sysdeps/libm-ieee754')
| -rw-r--r-- | sysdeps/libm-ieee754/s_cbrtl.c | 123 |
1 files changed, 123 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/s_cbrtl.c b/sysdeps/libm-ieee754/s_cbrtl.c new file mode 100644 index 0000000000..03ebfe7eb8 --- /dev/null +++ b/sysdeps/libm-ieee754/s_cbrtl.c @@ -0,0 +1,123 @@ +/* s_cbrtl.c -- long double version of s_cbrt.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * 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. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include "math.h" +#include "math_private.h" + +/* cbrtl(x) + * Return cube root of x + */ +#ifdef __STDC__ +static const u_int32_t +#else +static u_int32_t +#endif + B1_EXP = 10921, /* = Int(B1) */ + B1_MANT = 0x7bc4b064, /* = Int(1.0-0.03306235651)*2**31 */ + + B2_EXP = 10900, + B2_MANT = 0x7bc4b064; /* = Int(1.0-0.03306235651)*2**31 */ + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +C = 5.42857142857142815906e-01L, /* 19/35 */ +D = -7.05306122448979611050e-01L, /* -864/1225 */ +E = 1.41428571428571436819e+00L, /* 99/70 */ +F = 1.60714285714285720630e+00L, /* 45/28 */ +G = 3.57142857142857150787e-01L; /* 5/14 */ + +#ifdef __STDC__ + long double __cbrtl(long double x) +#else + long double __cbrtl(x) + long double x; +#endif +{ + int32_t hx; + long double r,s,t=0.0,w; + u_int32_t sign, se, x0, x1; + + GET_LDOUBLE_WORDS(se,x0,x1,x); + sign=se&0x8000; /* sign= sign(x) */ + se ^= sign; + if(se==0x7fff) return(x+x); /* cbrt(NaN,INF) is itself */ + if((se|x0|x1)==0) + return(x); /* cbrt(0) is itself */ + + SET_LDOUBLE_EXP(x,se); /* x <- |x| */ + +/* XXX I don't know whether the numbers for correct are correct. The + precalculation is extended from 20 bits to 32 bits. This hopefully + gives us the needed bits to get us still along with one iteration + step. */ + + /* rough cbrt to 5 bits */ + if(se==0) /* subnormal number */ + { + u_int64_t xxl; + u_int32_t set,t0,t1; + SET_LDOUBLE_EXP(t,0x4035); /* set t= 2**54 */ + SET_LDOUBLE_MSW(t,0x80000000); + t*=x; + GET_LDOUBLE_WORDS(set,t0,t1,t); + xxl = ((u_int64_t) set) << 32 | t0; + xxl /= 3; + xxl += B2_EXP << 16 | B2_MANT; + t0 = xxl & 0xffffffffu; + set = xxl >> 32; + SET_LDOUBLE_WORDS(t,set,t0,t1); + } + else + { + u_int64_t xxl = ((u_int64_t) se) << 32 | x0; + xxl /= 3; + xxl += B1_EXP << 16 | B1_MANT; + SET_LDOUBLE_MSW(t,xxl&0xffffffffu); + xxl >>= 32; + SET_LDOUBLE_EXP(t,xxl); + } + + + /* 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 32 bits and make it larger than cbrt(x) */ + GET_LDOUBLE_WORDS(se,x0,x1,t); + SET_LDOUBLE_WORDS(t,se,x0+1,0); + + + /* 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_LDOUBLE_EXP(se,t); + SET_LDOUBLE_EXP(t,se|sign); + return(t); +} +weak_alias (__cbrtl, cbrtl) |