X-Git-Url: http://nsz.repo.hu/git/?a=blobdiff_plain;f=src%2Fmath%2Fexp2f.c;h=0360482cae0a371d43a0b8f9faf5569eea87a18c;hb=97d35a552ec5b6ddf7923dd2f9a8eb973526acea;hp=ea50db4afa42a923ff69f6d0430f87a76c03e23e;hpb=5d5ab51862cbd010bdf52dc3b04b0967450bcd1a;p=musl diff --git a/src/math/exp2f.c b/src/math/exp2f.c index ea50db4a..0360482c 100644 --- a/src/math/exp2f.c +++ b/src/math/exp2f.c @@ -1,128 +1,69 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c */ -/*- - * Copyright (c) 2005 David Schultz - * 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. +/* + * Single-precision 2^x function. * - * 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. + * Copyright (c) 2017-2018, Arm Limited. + * SPDX-License-Identifier: MIT */ +#include +#include #include "libm.h" +#include "exp2f_data.h" -#define TBLSIZE 16 +/* +EXP2F_TABLE_BITS = 5 +EXP2F_POLY_ORDER = 3 -static const float -redux = 0x1.8p23f / TBLSIZE, -P1 = 0x1.62e430p-1f, -P2 = 0x1.ebfbe0p-3f, -P3 = 0x1.c6b348p-5f, -P4 = 0x1.3b2c9cp-7f; +ULP error: 0.502 (nearest rounding.) +Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.) +Wrong count: 168353 (all nearest rounding wrong results with fma.) +Non-nearest ULP error: 1 (rounded ULP error) +*/ -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, -}; +#define N (1 << EXP2F_TABLE_BITS) +#define T __exp2f_data.tab +#define C __exp2f_data.poly +#define SHIFT __exp2f_data.shift_scaled + +static inline uint32_t top12(float x) +{ + return asuint(x) >> 20; +} -/* - * 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, k; + uint32_t abstop; + uint64_t ki, t; + double_t kd, xd, z, r, r2, y, s; - /* Filter out exceptional cases. */ - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; - if (ix >= 0x43000000) { /* |x| >= 128 */ - if (ix >= 0x7f800000) { - if (hx == 0xff800000) /* -inf */ - return 0; - return x; - } - if (x >= 128) { - STRICT_ASSIGN(float, x, x * 0x1p127f); - return x; - } - if (x <= -150) { - STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f); - return x; - } - } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */ - return 1.0f + x; + xd = (double_t)x; + abstop = top12(x) & 0x7ff; + if (predict_false(abstop >= top12(128.0f))) { + /* |x| >= 128 or x is nan. */ + if (asuint(x) == asuint(-INFINITY)) + return 0.0f; + if (abstop >= top12(INFINITY)) + return x + x; + if (x > 0.0f) + return __math_oflowf(0); + if (x <= -150.0f) + return __math_uflowf(0); } - /* Reduce x, computing z, i0, and k. */ - STRICT_ASSIGN(float, t, x + redux); - GET_FLOAT_WORD(i0, t); - i0 += TBLSIZE / 2; - k = (i0 / TBLSIZE) << 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); + /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ + kd = eval_as_double(xd + SHIFT); + ki = asuint64(kd); + kd -= SHIFT; /* k/N for int k. */ + r = xd - kd; - /* Scale by 2**(k>>20). */ - return tv * twopk; + /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ + t = T[ki % N]; + t += ki << (52 - EXP2F_TABLE_BITS); + s = asdouble(t); + z = C[0] * r + C[1]; + r2 = r * r; + y = C[2] * r + 1; + y = z * r2 + y; + y = y * s; + return eval_as_float(y); }