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+/*-
+ * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
+ *
+ * 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 <sys/cdefs.h>
+//__FBSDID("$FreeBSD$");
+
+#include <float.h>
+
+#include "math_private.h"
+
+#define TBLBITS 4
+#define TBLSIZE (1 << TBLBITS)
+
+static const float
+ redux = 0x1.8p23f / TBLSIZE,
+ P1 = 0x1.62e430p-1f,
+ P2 = 0x1.ebfbe0p-3f,
+ P3 = 0x1.c6b348p-5f,
+ P4 = 0x1.3b2c9cp-7f;
+
+static volatile float
+ huge = 0x1p100f,
+ twom100 = 0x1p-100f;
+
+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 = 2**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 tv, twopk, u, z;
+ float t;
+ uint32_t hx, ix, i0;
+ int32_t k;
+
+ /* Filter out exceptional cases. */
+ GET_FLOAT_WORD(hx, x);
+ ix = hx & 0x7fffffff; /* high word of |x| */
+ if(ix >= 0x43000000) { /* |x| >= 128 */
+ if(ix >= 0x7f800000) {
+ if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
+ return (x + x); /* x is NaN or +Inf */
+ else
+ return (0.0); /* x is -Inf */
+ }
+ if(x >= 0x1.0p7f)
+ return (huge * huge); /* overflow */
+ if(x <= -0x1.2cp7f)
+ return (twom100 * twom100); /* underflow */
+ } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
+ return (1.0f + x);
+ }
+
+ /* Reduce x, computing z, i0, and k. */
+ STRICT_ASSIGN(float, t, x + redux);
+ GET_FLOAT_WORD(i0, t);
+ i0 += TBLSIZE / 2;
+ k = (i0 >> TBLBITS) << 20;
+ i0 &= TBLSIZE - 1;
+ t -= redux;
+ z = x - t;
+ INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
+
+ /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
+ tv = exp2ft[i0];
+ u = tv * z;
+ tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
+
+ /* Scale by 2**(k>>20). */
+ return (tv * twopk);
+}