You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
96 lines
2.6 KiB
96 lines
2.6 KiB
/*
|
|
* Double-precision vector e^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"
|
|
#if V_SUPPORTED
|
|
#include "v_exp.h"
|
|
|
|
#if V_EXP_TABLE_BITS == 7
|
|
/* maxerr: 1.88 +0.5 ulp
|
|
rel error: 1.4337*2^-53
|
|
abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */
|
|
#define C1 v_f64 (0x1.ffffffffffd43p-2)
|
|
#define C2 v_f64 (0x1.55555c75adbb2p-3)
|
|
#define C3 v_f64 (0x1.55555da646206p-5)
|
|
#define InvLn2 v_f64 (0x1.71547652b82fep7) /* N/ln2. */
|
|
#define Ln2hi v_f64 (0x1.62e42fefa39efp-8) /* ln2/N. */
|
|
#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-63)
|
|
#elif V_EXP_TABLE_BITS == 8
|
|
/* maxerr: 0.54 +0.5 ulp
|
|
rel error: 1.4318*2^-58
|
|
abs error: 1.4299*2^-58 in [ -ln2/512, ln2/512 ]. */
|
|
#define C1 v_f64 (0x1.fffffffffffd4p-2)
|
|
#define C2 v_f64 (0x1.5555571d6b68cp-3)
|
|
#define C3 v_f64 (0x1.5555576a59599p-5)
|
|
#define InvLn2 v_f64 (0x1.71547652b82fep8)
|
|
#define Ln2hi v_f64 (0x1.62e42fefa39efp-9)
|
|
#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-64)
|
|
#endif
|
|
|
|
#define N (1 << V_EXP_TABLE_BITS)
|
|
#define Tab __v_exp_data
|
|
#define IndexMask v_u64 (N - 1)
|
|
#define Shift v_f64 (0x1.8p+52)
|
|
#define Thres v_f64 (704.0)
|
|
|
|
VPCS_ATTR
|
|
static v_f64_t
|
|
specialcase (v_f64_t s, v_f64_t y, v_f64_t n)
|
|
{
|
|
v_f64_t absn = v_abs_f64 (n);
|
|
|
|
/* 2^(n/N) may overflow, break it up into s1*s2. */
|
|
v_u64_t b = v_cond_u64 (n <= v_f64 (0.0)) & v_u64 (0x6000000000000000);
|
|
v_f64_t s1 = v_as_f64_u64 (v_u64 (0x7000000000000000) - b);
|
|
v_f64_t s2 = v_as_f64_u64 (v_as_u64_f64 (s) - v_u64 (0x3010000000000000) + b);
|
|
v_u64_t cmp = v_cond_u64 (absn > v_f64 (1280.0 * N));
|
|
v_f64_t r1 = s1 * s1;
|
|
v_f64_t r0 = v_fma_f64 (y, s2, s2) * s1;
|
|
return v_as_f64_u64 ((cmp & v_as_u64_f64 (r1)) | (~cmp & v_as_u64_f64 (r0)));
|
|
}
|
|
|
|
VPCS_ATTR
|
|
v_f64_t
|
|
V_NAME(exp) (v_f64_t x)
|
|
{
|
|
v_f64_t n, r, r2, s, y, z;
|
|
v_u64_t cmp, u, e, i;
|
|
|
|
cmp = v_cond_u64 (v_abs_f64 (x) > Thres);
|
|
|
|
/* n = round(x/(ln2/N)). */
|
|
z = v_fma_f64 (x, InvLn2, Shift);
|
|
u = v_as_u64_f64 (z);
|
|
n = z - Shift;
|
|
|
|
/* r = x - n*ln2/N. */
|
|
r = x;
|
|
r = v_fma_f64 (-Ln2hi, n, r);
|
|
r = v_fma_f64 (-Ln2lo, n, r);
|
|
|
|
e = u << (52 - V_EXP_TABLE_BITS);
|
|
i = u & IndexMask;
|
|
|
|
/* y = exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
|
|
r2 = r * r;
|
|
y = v_fma_f64 (C2, r, C1);
|
|
y = v_fma_f64 (C3, r2, y);
|
|
y = v_fma_f64 (y, r2, r);
|
|
|
|
/* s = 2^(n/N). */
|
|
u = v_lookup_u64 (Tab, i);
|
|
s = v_as_f64_u64 (u + e);
|
|
|
|
if (unlikely (v_any_u64 (cmp)))
|
|
return specialcase (s, y, n);
|
|
return v_fma_f64 (y, s, s);
|
|
}
|
|
VPCS_ALIAS
|
|
#endif
|