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/*
* Double-precision vector e^(x+tail) function.
*
* Copyright (c) 2019-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "math_config.h"
#if V_SUPPORTED
#include "v_exp_tail.h"
#define C1 v_f64 (C1_scal)
#define C2 v_f64 (C2_scal)
#define C3 v_f64 (C3_scal)
#define InvLn2 v_f64 (InvLn2_scal)
#define Ln2hi v_f64 (Ln2hi_scal)
#define Ln2lo v_f64 (Ln2lo_scal)
#define IndexMask v_u64 (IndexMask_scal)
#define Shift v_f64 (Shift_scal)
#define Thres v_f64 (Thres_scal)
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_tail) (v_f64_t x, v_f64_t xtail)
{
v_f64_t n, r, 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_TAIL_TABLE_BITS);
i = u & IndexMask;
/* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
y = v_fma_f64 (C3, r, C2);
y = v_fma_f64 (y, r, C1);
y = v_fma_f64 (y, r, v_f64 (1.0));
y = v_fma_f64 (y, r, xtail);
/* 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);
}
#endif
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