forked from OSchip/llvm-project
106 lines
2.5 KiB
C
106 lines
2.5 KiB
C
|
/*
|
||
|
|
* 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
|