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Diffstat (limited to 'libm/ldouble/cbrtl.c')
-rw-r--r-- | libm/ldouble/cbrtl.c | 143 |
1 files changed, 143 insertions, 0 deletions
diff --git a/libm/ldouble/cbrtl.c b/libm/ldouble/cbrtl.c new file mode 100644 index 000000000..89ed11a06 --- /dev/null +++ b/libm/ldouble/cbrtl.c @@ -0,0 +1,143 @@ +/* cbrtl.c + * + * Cube root, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, cbrtl(); + * + * y = cbrtl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the cube root of the argument, which may be negative. + * + * Range reduction involves determining the power of 2 of + * the argument. A polynomial of degree 2 applied to the + * mantissa, and multiplication by the cube root of 1, 2, or 4 + * approximates the root to within about 0.1%. Then Newton's + * iteration is used three times to converge to an accurate + * result. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE .125,8 80000 7.0e-20 2.2e-20 + * IEEE exp(+-707) 100000 7.0e-20 2.4e-20 + * + */ + + +/* +Cephes Math Library Release 2.2: January, 1991 +Copyright 1984, 1991 by Stephen L. Moshier +Direct inquiries to 30 Frost Street, Cambridge, MA 02140 +*/ + + +#include <math.h> + +static long double CBRT2 = 1.2599210498948731647672L; +static long double CBRT4 = 1.5874010519681994747517L; +static long double CBRT2I = 0.79370052598409973737585L; +static long double CBRT4I = 0.62996052494743658238361L; + +#ifdef ANSIPROT +extern long double frexpl ( long double, int * ); +extern long double ldexpl ( long double, int ); +extern int isnanl ( long double ); +#else +long double frexpl(), ldexpl(); +extern int isnanl(); +#endif + +#ifdef INFINITIES +extern long double INFINITYL; +#endif + +long double cbrtl(x) +long double x; +{ +int e, rem, sign; +long double z; + + +#ifdef NANS +if(isnanl(x)) + return(x); +#endif +#ifdef INFINITIES +if( x == INFINITYL) + return(x); +if( x == -INFINITYL) + return(x); +#endif +if( x == 0 ) + return( x ); +if( x > 0 ) + sign = 1; +else + { + sign = -1; + x = -x; + } + +z = x; +/* extract power of 2, leaving + * mantissa between 0.5 and 1 + */ +x = frexpl( x, &e ); + +/* Approximate cube root of number between .5 and 1, + * peak relative error = 1.2e-6 + */ +x = (((( 1.3584464340920900529734e-1L * x + - 6.3986917220457538402318e-1L) * x + + 1.2875551670318751538055e0L) * x + - 1.4897083391357284957891e0L) * x + + 1.3304961236013647092521e0L) * x + + 3.7568280825958912391243e-1L; + +/* exponent divided by 3 */ +if( e >= 0 ) + { + rem = e; + e /= 3; + rem -= 3*e; + if( rem == 1 ) + x *= CBRT2; + else if( rem == 2 ) + x *= CBRT4; + } +else + { /* argument less than 1 */ + e = -e; + rem = e; + e /= 3; + rem -= 3*e; + if( rem == 1 ) + x *= CBRT2I; + else if( rem == 2 ) + x *= CBRT4I; + e = -e; + } + +/* multiply by power of 2 */ +x = ldexpl( x, e ); + +/* Newton iteration */ + +x -= ( x - (z/(x*x)) )*0.3333333333333333333333L; +x -= ( x - (z/(x*x)) )*0.3333333333333333333333L; + +if( sign < 0 ) + x = -x; +return(x); +} |