Add a "fork" of musl as //fusl.

fusl/src/math/exp2f.c

+/* origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c */
+/*-
+ * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include "libm.h"
+
+#define TBLSIZE 16
+
+static const float
+redux = 0x1.8p23f / TBLSIZE,
+P1    = 0x1.62e430p-1f,
+P2    = 0x1.ebfbe0p-3f,
+P3    = 0x1.c6b348p-5f,
+P4    = 0x1.3b2c9cp-7f;
+
+static const double exp2ft[TBLSIZE] = {
+  0x1.6a09e667f3bcdp-1,
+  0x1.7a11473eb0187p-1,
+  0x1.8ace5422aa0dbp-1,
+  0x1.9c49182a3f090p-1,
+  0x1.ae89f995ad3adp-1,
+  0x1.c199bdd85529cp-1,
+  0x1.d5818dcfba487p-1,
+  0x1.ea4afa2a490dap-1,
+  0x1.0000000000000p+0,
+  0x1.0b5586cf9890fp+0,
+  0x1.172b83c7d517bp+0,
+  0x1.2387a6e756238p+0,
+  0x1.306fe0a31b715p+0,
+  0x1.3dea64c123422p+0,
+  0x1.4bfdad5362a27p+0,
+  0x1.5ab07dd485429p+0,
+};
+
+/*
+ * exp2f(x): compute the base 2 exponential of x
+ *
+ * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
+ *
+ * Method: (equally-spaced tables)
+ *
+ *   Reduce x:
+ *     x = k + y, for integer k and |y| <= 1/2.
+ *     Thus we have exp2f(x) = 2**k * exp2(y).
+ *
+ *   Reduce y:
+ *     y = i/TBLSIZE + z for integer i near y * TBLSIZE.
+ *     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
+ *     with |z| <= 2**-(TBLSIZE+1).
+ *
+ *   We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
+ *   degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
+ *   Using double precision for everything except the reduction makes
+ *   roundoff error insignificant and simplifies the scaling step.
+ *
+ *   This method is due to Tang, but I do not use his suggested parameters:
+ *
+ *      Tang, P.  Table-driven Implementation of the Exponential Function
+ *      in IEEE Floating-Point Arithmetic.  TOMS 15(2), 144-157 (1989).
+ */
+float exp2f(float x)
+{
+        double_t t, r, z;
+        union {float f; uint32_t i;} u = {x};
+        union {double f; uint64_t i;} uk;
+        uint32_t ix, i0, k;
+
+        /* Filter out exceptional cases. */
+        ix = u.i & 0x7fffffff;
+        if (ix > 0x42fc0000) {  /* |x| > 126 */
+                if (u.i >= 0x43000000 && u.i < 0x80000000) {  /* x >= 128 */
+                        x *= 0x1p127f;
+                        return x;
+                }
+                if (u.i >= 0x80000000) {  /* x < -126 */
+                        if (u.i >= 0xc3160000 || (u.i & 0x0000ffff))
+                                FORCE_EVAL(-0x1p-149f/x);
+                        if (u.i >= 0xc3160000)  /* x <= -150 */
+                                return 0;
+                }
+        } else if (ix <= 0x33000000) {  /* |x| <= 0x1p-25 */
+                return 1.0f + x;
+        }
+
+        /* Reduce x, computing z, i0, and k. */
+        u.f = x + redux;
+        i0 = u.i;
+        i0 += TBLSIZE / 2;
+        k = i0 / TBLSIZE;
+        uk.i = (uint64_t)(0x3ff + k)<<52;
+        i0 &= TBLSIZE - 1;
+        u.f -= redux;
+        z = x - u.f;
+        /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
+        r = exp2ft[i0];
+        t = r * z;
+        r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
+
+        /* Scale by 2**k */
+        return r * uk.f;
+}