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1/*2 * Single-precision log2 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/*14LOG2F_TABLE_BITS = 415LOG2F_POLY_ORDER = 416 17ULP error: 0.752 (nearest rounding.)18Relative error: 1.9 * 2^-26 (before rounding.)19*/20 21#define N (1 << LOG2F_TABLE_BITS)22#define T __log2f_data.tab23#define A __log2f_data.poly24#define OFF 0x3f33000025 26float27log2f (float x)28{29 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */30 double_t z, r, r2, p, y, y0, invc, logc;31 uint32_t ix, iz, top, tmp;32 int k, i;33 34 ix = asuint (x);35#if WANT_ROUNDING36 /* Fix sign of zero with downward rounding when x==1. */37 if (unlikely (ix == 0x3f800000))38 return 0;39#endif40 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))41 {42 /* x < 0x1p-126 or inf or nan. */43 if (ix * 2 == 0)44 return __math_divzerof (1);45 if (ix == 0x7f800000) /* log2(inf) == inf. */46 return x;47 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)48 return __math_invalidf (x);49 /* x is subnormal, normalize it. */50 ix = asuint (x * 0x1p23f);51 ix -= 23 << 23;52 }53 54 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.55 The range is split into N subintervals.56 The ith subinterval contains z and c is near its center. */57 tmp = ix - OFF;58 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;59 top = tmp & 0xff800000;60 iz = ix - top;61 k = (int32_t) tmp >> 23; /* arithmetic shift */62 invc = T[i].invc;63 logc = T[i].logc;64 z = (double_t) asfloat (iz);65 66 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */67 r = z * invc - 1;68 y0 = logc + (double_t) k;69 70 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */71 r2 = r * r;72 y = A[1] * r + A[2];73 y = A[0] * r2 + y;74 p = A[3] * r + y0;75 y = y * r2 + p;76 return eval_as_float (y);77}78#if USE_GLIBC_ABI79strong_alias (log2f, __log2f_finite)80hidden_alias (log2f, __ieee754_log2f)81#endif82