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+/* 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 -8,8 100000 1.3e-34 3.9e-35
+ * IEEE exp(+-707) 100000 1.3e-34 4.3e-35
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: January, 1991
+Copyright 1984, 1991 by Stephen L. Moshier
+Adapted for glibc October, 2001.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+
+#include <math.h>
+#include <math_private.h>
+
+static const _Float128 CBRT2 = L(1.259921049894873164767210607278228350570251);
+static const _Float128 CBRT4 = L(1.587401051968199474751705639272308260391493);
+static const _Float128 CBRT2I = L(0.7937005259840997373758528196361541301957467);
+static const _Float128 CBRT4I = L(0.6299605249474365823836053036391141752851257);
+
+
+_Float128
+__cbrtl (_Float128 x)
+{
+ int e, rem, sign;
+ _Float128 z;
+
+ if (!isfinite (x))
+ return x + x;
+
+ 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 = ((((L(1.3584464340920900529734e-1) * x
+ - L(6.3986917220457538402318e-1)) * x
+ + L(1.2875551670318751538055e0)) * x
+ - L(1.4897083391357284957891e0)) * x
+ + L(1.3304961236013647092521e0)) * x + L(3.7568280825958912391243e-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;
+ }
+ 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))) * L(0.3333333333333333333333333333333333333333);
+ x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333);
+ x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333);
+
+ if (sign < 0)
+ x = -x;
+ return (x);
+}
+
+weak_alias (__cbrtl, cbrtl)