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1/*2 * Double-precision vector log(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 "mathlib.h"10#include "v_math.h"11#include "v_log.h"12#if V_SUPPORTED13 14/* Worst-case error: 1.17 + 0.5 ulp. */15 16static const f64_t Poly[] = {17 /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */18 -0x1.ffffffffffff7p-2,19 0x1.55555555170d4p-2,20 -0x1.0000000399c27p-2,21 0x1.999b2e90e94cap-3,22 -0x1.554e550bd501ep-3,23};24 25#define A0 v_f64 (Poly[0])26#define A1 v_f64 (Poly[1])27#define A2 v_f64 (Poly[2])28#define A3 v_f64 (Poly[3])29#define A4 v_f64 (Poly[4])30#define Ln2 v_f64 (0x1.62e42fefa39efp-1)31#define N (1 << V_LOG_TABLE_BITS)32#define OFF v_u64 (0x3fe6900900000000)33 34struct entry35{36 v_f64_t invc;37 v_f64_t logc;38};39 40static inline struct entry41lookup (v_u64_t i)42{43 struct entry e;44#ifdef SCALAR45 e.invc = __v_log_data[i].invc;46 e.logc = __v_log_data[i].logc;47#else48 e.invc[0] = __v_log_data[i[0]].invc;49 e.logc[0] = __v_log_data[i[0]].logc;50 e.invc[1] = __v_log_data[i[1]].invc;51 e.logc[1] = __v_log_data[i[1]].logc;52#endif53 return e;54}55 56VPCS_ATTR57__attribute__ ((noinline)) static v_f64_t58specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)59{60 return v_call_f64 (log, x, y, cmp);61}62 63VPCS_ATTR64v_f64_t65V_NAME(log) (v_f64_t x)66{67 v_f64_t z, r, r2, p, y, kd, hi;68 v_u64_t ix, iz, tmp, top, i, cmp;69 v_s64_t k;70 struct entry e;71 72 ix = v_as_u64_f64 (x);73 top = ix >> 48;74 cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));75 76 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.77 The range is split into N subintervals.78 The ith subinterval contains z and c is near its center. */79 tmp = ix - OFF;80 i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;81 k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */82 iz = ix - (tmp & v_u64 (0xfffULL << 52));83 z = v_as_f64_u64 (iz);84 e = lookup (i);85 86 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */87 r = v_fma_f64 (z, e.invc, v_f64 (-1.0));88 kd = v_to_f64_s64 (k);89 90 /* hi = r + log(c) + k*Ln2. */91 hi = v_fma_f64 (kd, Ln2, e.logc + r);92 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */93 r2 = r * r;94 y = v_fma_f64 (A3, r, A2);95 p = v_fma_f64 (A1, r, A0);96 y = v_fma_f64 (A4, r2, y);97 y = v_fma_f64 (y, r2, p);98 y = v_fma_f64 (y, r2, hi);99 100 if (unlikely (v_any_u64 (cmp)))101 return specialcase (x, y, cmp);102 return y;103}104VPCS_ALIAS105#endif106