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-rw-r--r--libm/double/cbrt.c142
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diff --git a/libm/double/cbrt.c b/libm/double/cbrt.c
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-/* cbrt.c
- *
- * Cube root
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, cbrt();
- *
- * y = cbrt( 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
- * DEC -10,10 200000 1.8e-17 6.2e-18
- * IEEE 0,1e308 30000 1.5e-16 5.0e-17
- *
- */
- /* cbrt.c */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1991, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-static double CBRT2 = 1.2599210498948731647672;
-static double CBRT4 = 1.5874010519681994747517;
-static double CBRT2I = 0.79370052598409973737585;
-static double CBRT4I = 0.62996052494743658238361;
-
-#ifdef ANSIPROT
-extern double frexp ( double, int * );
-extern double ldexp ( double, int );
-extern int isnan ( double );
-extern int isfinite ( double );
-#else
-double frexp(), ldexp();
-int isnan(), isfinite();
-#endif
-
-double cbrt(x)
-double x;
-{
-int e, rem, sign;
-double z;
-
-#ifdef NANS
-if( isnan(x) )
- return x;
-#endif
-#ifdef INFINITIES
-if( !isfinite(x) )
- 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 = frexp( x, &e );
-
-/* Approximate cube root of number between .5 and 1,
- * peak relative error = 9.2e-6
- */
-x = (((-1.3466110473359520655053e-1 * x
- + 5.4664601366395524503440e-1) * x
- - 9.5438224771509446525043e-1) * x
- + 1.1399983354717293273738e0 ) * x
- + 4.0238979564544752126924e-1;
-
-/* 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;
- }
-
-
-/* argument less than 1 */
-
-else
- {
- 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 = ldexp( x, e );
-
-/* Newton iteration */
-x -= ( x - (z/(x*x)) )*0.33333333333333333333;
-#ifdef DEC
-x -= ( x - (z/(x*x)) )/3.0;
-#else
-x -= ( x - (z/(x*x)) )*0.33333333333333333333;
-#endif
-
-if( sign < 0 )
- x = -x;
-return(x);
-}