132 lines
3.3 KiB
C++
132 lines
3.3 KiB
C++
/* Translated into C++ by SciPy developers in 2024.
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* Original header with Copyright information appears below.
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*/
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/* cbrt.c
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*
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* Cube root
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, cbrt();
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*
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* y = cbrt( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the cube root of the argument, which may be negative.
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*
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* Range reduction involves determining the power of 2 of
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* the argument. A polynomial of degree 2 applied to the
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* mantissa, and multiplication by the cube root of 1, 2, or 4
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* approximates the root to within about 0.1%. Then Newton's
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* iteration is used three times to converge to an accurate
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* result.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,1e308 30000 1.5e-16 5.0e-17
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*
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*/
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/* cbrt.c */
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/*
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* Cephes Math Library Release 2.2: January, 1991
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* Copyright 1984, 1991 by Stephen L. Moshier
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* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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#pragma once
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#include "../config.h"
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namespace xsf {
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namespace cephes {
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namespace detail {
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constexpr double CBRT2 = 1.2599210498948731647672;
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constexpr double CBRT4 = 1.5874010519681994747517;
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constexpr double CBRT2I = 0.79370052598409973737585;
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constexpr double CBRT4I = 0.62996052494743658238361;
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XSF_HOST_DEVICE inline double cbrt(double x) {
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int e, rem, sign;
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double z;
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if (!std::isfinite(x)) {
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return x;
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}
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if (x == 0) {
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return (x);
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}
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if (x > 0) {
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sign = 1;
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} else {
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sign = -1;
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x = -x;
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}
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z = x;
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/* extract power of 2, leaving
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* mantissa between 0.5 and 1
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*/
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x = std::frexp(x, &e);
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/* Approximate cube root of number between .5 and 1,
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* peak relative error = 9.2e-6
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*/
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x = (((-1.3466110473359520655053e-1 * x + 5.4664601366395524503440e-1) * x - 9.5438224771509446525043e-1) *
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x +
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1.1399983354717293273738e0) *
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x +
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4.0238979564544752126924e-1;
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/* exponent divided by 3 */
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if (e >= 0) {
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rem = e;
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e /= 3;
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rem -= 3 * e;
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if (rem == 1) {
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x *= CBRT2;
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} else if (rem == 2) {
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x *= CBRT4;
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}
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}
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/* argument less than 1 */
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else {
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e = -e;
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rem = e;
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e /= 3;
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rem -= 3 * e;
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if (rem == 1) {
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x *= CBRT2I;
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} else if (rem == 2) {
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x *= CBRT4I;
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}
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e = -e;
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}
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/* multiply by power of 2 */
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x = std::ldexp(x, e);
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/* Newton iteration */
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x -= (x - (z / (x * x))) * 0.33333333333333333333;
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x -= (x - (z / (x * x))) * 0.33333333333333333333;
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if (sign < 0)
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x = -x;
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return (x);
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}
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} // namespace detail
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} // namespace cephes
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} // namespace xsf
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