fixes to compile without warnings.

src/cbrt.h

+/*******************************************************************************
+ * This file is part of SWIFT.
+ * Copyright (c) 2016 Pedro Gonnet (pedro.gonnet@durham.ac.uk)
+ *                    Matthieu Schaller (matthieu.schaller@durham.ac.uk)
+ *
+ * This program 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 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program 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 General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ ******************************************************************************/
+#ifndef SWIFT_CBRT_H
+#define SWIFT_CBRT_H
+
+/* Config parameters. */
+#include "../config.h"
+
+/* Some standard headers. */
+#include <math.h>
+
+/**
+ * @brief Compute the inverse cube root of a single-precision floating-point
+ * number.
+ *
+ * @param x_in The input value.
+ *
+ * @return The inverse cubic root of @c x_in. Note that this function
+ *         does not care about non-finite inputs.
+ */
+__attribute__((always_inline)) inline float icbrtf(float x_in) {
+
+  // Extract the exponent.
+  const unsigned int x_as_uint = *((char *)&x_in);
+  const int exponent = ((x_as_uint & 0x7f800000) >> 23) - 127;
+
+  // Clear the exponent and sign to get the mantissa.
+  const unsigned int x_norm_as_int = (x_as_uint & ~0xff800000) | 0x3f800000;
+  const float x_norm = *((char *)&x_norm_as_int);
+
+  // Multiply by sqrt(1/2) and subtract one, should then be in the
+  // range [sqrt(1/2) - 1, sqrt(2) - 1).
+  const float x = x_norm * (float)M_SQRT1_2 - 1.0f;
+
+  // Compute the polynomial interpolant.
+  float res =
+      9.99976591940035e-01f +
+      x * (-3.32901212909283e-01f +
+           x * (2.24361110929912e-01f +
+                x * (-1.88913279594895e-01f + x * 1.28384036492344e-01f)));
+
+  // Compute the new exponent and the correction factor.
+  int exponent_new = exponent;
+  if (exponent_new < 0) exponent_new -= 2;
+  exponent_new = -exponent_new / 3;
+  const int exponent_rem = exponent + 3 * exponent_new;
+  const unsigned int exponent_scale_as_int = (exponent_new + 127) << 23;
+  float exponent_scale = *((char *)&exponent_scale_as_int);
+  exponent_scale *=
+      exponent_rem > 0
+          ? (exponent_rem > 1 ? 5.61231024154687e-01f : 7.07106781186548e-01f)
+          : 8.90898718140339e-01f;
+  res *= exponent_scale;
+
+  // One step of Newton iteration to refine the result.
+  res *= (1.0f / 3.0f) * (4.0f - x_in * res * res * res);
+
+  // We're done.
+  return copysignf(res, x_in);
+}
+
+#endif /* SWIFT_CBRT_H */