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/*
* Double-precision SVE e^(x+tail) function.
*
* Copyright (c) 2021-2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#ifndef SV_EXP_TAIL_H
#define SV_EXP_TAIL_H
#include "sv_math.h"
#if SV_SUPPORTED
#include "v_exp_tail.h"
#define C1 sv_f64 (C1_scal)
#define C2 sv_f64 (C2_scal)
#define C3 sv_f64 (C3_scal)
#define MinusLn2hi (-Ln2hi_scal)
#define MinusLn2lo (-Ln2lo_scal)
#define N (1 << V_EXP_TAIL_TABLE_BITS)
#define Tab __v_exp_tail_data
#define IndexMask (N - 1)
#define Shift sv_f64 (0x1.8p+52)
#define Thres 704.0
static inline sv_f64_t
sv_exp_tail_special_case (svbool_t pg, sv_f64_t s, sv_f64_t y, sv_f64_t n)
{
sv_f64_t absn = svabs_f64_x (pg, n);
/* 2^(n/N) may overflow, break it up into s1*s2. */
sv_u64_t b = svsel_u64 (svcmple_n_f64 (pg, n, 0), sv_u64 (0x6000000000000000),
sv_u64 (0));
sv_f64_t s1 = sv_as_f64_u64 (svsubr_n_u64_x (pg, b, 0x7000000000000000));
sv_f64_t s2 = sv_as_f64_u64 (
svadd_u64_x (pg, svsub_n_u64_x (pg, sv_as_u64_f64 (s), 0x3010000000000000),
b));
svbool_t cmp = svcmpgt_n_f64 (pg, absn, 1280.0 * N);
sv_f64_t r1 = svmul_f64_x (pg, s1, s1);
sv_f64_t r0 = svmul_f64_x (pg, sv_fma_f64_x (pg, y, s2, s2), s1);
return svsel_f64 (cmp, r1, r0);
}
static inline sv_f64_t
sv_exp_tail (const svbool_t pg, sv_f64_t x, sv_f64_t xtail)
{
/* Calculate exp(x + xtail). */
sv_f64_t z = sv_fma_n_f64_x (pg, InvLn2_scal, x, Shift);
sv_f64_t n = svsub_f64_x (pg, z, Shift);
sv_f64_t r = sv_fma_n_f64_x (pg, MinusLn2hi, n, x);
r = sv_fma_n_f64_x (pg, MinusLn2lo, n, r);
sv_u64_t u = sv_as_u64_f64 (z);
sv_u64_t e = svlsl_n_u64_x (pg, u, 52 - V_EXP_TAIL_TABLE_BITS);
sv_u64_t i = svand_n_u64_x (pg, u, IndexMask);
sv_f64_t y = sv_fma_f64_x (pg, C3, r, C2);
y = sv_fma_f64_x (pg, y, r, C1);
y = sv_fma_f64_x (pg, y, r, sv_f64 (1.0));
y = sv_fma_f64_x (pg, y, r, xtail);
/* s = 2^(n/N). */
u = sv_lookup_u64_x (pg, Tab, i);
sv_f64_t s = sv_as_f64_u64 (svadd_u64_x (pg, u, e));
svbool_t cmp = svcmpgt_n_f64 (pg, svabs_f64_x (pg, x), Thres);
if (unlikely (svptest_any (pg, cmp)))
{
return sv_exp_tail_special_case (pg, s, y, n);
}
return sv_fma_f64_x (pg, y, s, s);
}
#endif
#endif
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