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1/*2 * Single-precision 2^x function.3 *4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.5 * See https://llvm.org/LICENSE.txt for license information.6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception7 */8 9#include <math.h>10#include <stdint.h>11#include "math_config.h"12 13/*14EXP2F_TABLE_BITS = 515EXP2F_POLY_ORDER = 316 17ULP error: 0.502 (nearest rounding.)18Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)19Wrong count: 168353 (all nearest rounding wrong results with fma.)20Non-nearest ULP error: 1 (rounded ULP error)21*/22 23#define N (1 << EXP2F_TABLE_BITS)24#define T __exp2f_data.tab25#define C __exp2f_data.poly26#define SHIFT __exp2f_data.shift_scaled27 28static inline uint32_t29top12 (float x)30{31 return asuint (x) >> 20;32}33 34float35exp2f (float x)36{37 uint32_t abstop;38 uint64_t ki, t;39 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */40 double_t kd, xd, z, r, r2, y, s;41 42 xd = (double_t) x;43 abstop = top12 (x) & 0x7ff;44 if (unlikely (abstop >= top12 (128.0f)))45 {46 /* |x| >= 128 or x is nan. */47 if (asuint (x) == asuint (-INFINITY))48 return 0.0f;49 if (abstop >= top12 (INFINITY))50 return x + x;51 if (x > 0.0f)52 return __math_oflowf (0);53 if (x <= -150.0f)54 return __math_uflowf (0);55#if WANT_ERRNO_UFLOW56 if (x < -149.0f)57 return __math_may_uflowf (0);58#endif59 }60 61 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */62 kd = eval_as_double (xd + SHIFT);63 ki = asuint64 (kd);64 kd -= SHIFT; /* k/N for int k. */65 r = xd - kd;66 67 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */68 t = T[ki % N];69 t += ki << (52 - EXP2F_TABLE_BITS);70 s = asdouble (t);71 z = C[0] * r + C[1];72 r2 = r * r;73 y = C[2] * r + 1;74 y = z * r2 + y;75 y = y * s;76 return eval_as_float (y);77}78#if USE_GLIBC_ABI79strong_alias (exp2f, __exp2f_finite)80hidden_alias (exp2f, __ieee754_exp2f)81#endif82