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1/*2 * Single-precision log 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/*14LOGF_TABLE_BITS = 415LOGF_POLY_ORDER = 416 17ULP error: 0.818 (nearest rounding.)18Relative error: 1.957 * 2^-26 (before rounding.)19*/20 21#define T __logf_data.tab22#define A __logf_data.poly23#define Ln2 __logf_data.ln224#define N (1 << LOGF_TABLE_BITS)25#define OFF 0x3f33000026 27float28logf (float x)29{30 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */31 double_t z, r, r2, y, y0, invc, logc;32 uint32_t ix, iz, tmp;33 int k, i;34 35 ix = asuint (x);36#if WANT_ROUNDING37 /* Fix sign of zero with downward rounding when x==1. */38 if (unlikely (ix == 0x3f800000))39 return 0;40#endif41 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))42 {43 /* x < 0x1p-126 or inf or nan. */44 if (ix * 2 == 0)45 return __math_divzerof (1);46 if (ix == 0x7f800000) /* log(inf) == inf. */47 return x;48 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)49 return __math_invalidf (x);50 /* x is subnormal, normalize it. */51 ix = asuint (x * 0x1p23f);52 ix -= 23 << 23;53 }54 55 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.56 The range is split into N subintervals.57 The ith subinterval contains z and c is near its center. */58 tmp = ix - OFF;59 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;60 k = (int32_t) tmp >> 23; /* arithmetic shift */61 iz = ix - (tmp & 0x1ff << 23);62 invc = T[i].invc;63 logc = T[i].logc;64 z = (double_t) asfloat (iz);65 66 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */67 r = z * invc - 1;68 y0 = logc + (double_t) k * Ln2;69 70 /* Pipelined polynomial evaluation to approximate log1p(r). */71 r2 = r * r;72 y = A[1] * r + A[2];73 y = A[0] * r2 + y;74 y = y * r2 + (y0 + r);75 return eval_as_float (y);76}77#if USE_GLIBC_ABI78strong_alias (logf, __logf_finite)79hidden_alias (logf, __ieee754_logf)80#endif81