| /* |
| * Double-precision vector log(x) function. |
| * |
| * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| * See https://llvm.org/LICENSE.txt for license information. |
| * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| */ |
| |
| #include "mathlib.h" |
| #include "v_math.h" |
| #include "v_log.h" |
| #if V_SUPPORTED |
| |
| /* Worst-case error: 1.17 + 0.5 ulp. */ |
| |
| static const f64_t Poly[] = { |
| /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */ |
| -0x1.ffffffffffff7p-2, |
| 0x1.55555555170d4p-2, |
| -0x1.0000000399c27p-2, |
| 0x1.999b2e90e94cap-3, |
| -0x1.554e550bd501ep-3, |
| }; |
| |
| #define A0 v_f64 (Poly[0]) |
| #define A1 v_f64 (Poly[1]) |
| #define A2 v_f64 (Poly[2]) |
| #define A3 v_f64 (Poly[3]) |
| #define A4 v_f64 (Poly[4]) |
| #define Ln2 v_f64 (0x1.62e42fefa39efp-1) |
| #define N (1 << V_LOG_TABLE_BITS) |
| #define OFF v_u64 (0x3fe6900900000000) |
| |
| struct entry |
| { |
| v_f64_t invc; |
| v_f64_t logc; |
| }; |
| |
| static inline struct entry |
| lookup (v_u64_t i) |
| { |
| struct entry e; |
| #ifdef SCALAR |
| e.invc = __v_log_data[i].invc; |
| e.logc = __v_log_data[i].logc; |
| #else |
| e.invc[0] = __v_log_data[i[0]].invc; |
| e.logc[0] = __v_log_data[i[0]].logc; |
| e.invc[1] = __v_log_data[i[1]].invc; |
| e.logc[1] = __v_log_data[i[1]].logc; |
| #endif |
| return e; |
| } |
| |
| VPCS_ATTR |
| __attribute__ ((noinline)) static v_f64_t |
| specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp) |
| { |
| return v_call_f64 (log, x, y, cmp); |
| } |
| |
| VPCS_ATTR |
| v_f64_t |
| V_NAME(log) (v_f64_t x) |
| { |
| v_f64_t z, r, r2, p, y, kd, hi; |
| v_u64_t ix, iz, tmp, top, i, cmp; |
| v_s64_t k; |
| struct entry e; |
| |
| ix = v_as_u64_f64 (x); |
| top = ix >> 48; |
| cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010)); |
| |
| /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. |
| The range is split into N subintervals. |
| The ith subinterval contains z and c is near its center. */ |
| tmp = ix - OFF; |
| i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N; |
| k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */ |
| iz = ix - (tmp & v_u64 (0xfffULL << 52)); |
| z = v_as_f64_u64 (iz); |
| e = lookup (i); |
| |
| /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ |
| r = v_fma_f64 (z, e.invc, v_f64 (-1.0)); |
| kd = v_to_f64_s64 (k); |
| |
| /* hi = r + log(c) + k*Ln2. */ |
| hi = v_fma_f64 (kd, Ln2, e.logc + r); |
| /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ |
| r2 = r * r; |
| y = v_fma_f64 (A3, r, A2); |
| p = v_fma_f64 (A1, r, A0); |
| y = v_fma_f64 (A4, r2, y); |
| y = v_fma_f64 (y, r2, p); |
| y = v_fma_f64 (y, r2, hi); |
| |
| if (unlikely (v_any_u64 (cmp))) |
| return specialcase (x, y, cmp); |
| return y; |
| } |
| VPCS_ALIAS |
| #endif |