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.
79 lines
2.0 KiB
79 lines
2.0 KiB
/*
|
|
* Single-precision vector 2^x function.
|
|
*
|
|
* Copyright (c) 2019, Arm Limited.
|
|
* SPDX-License-Identifier: MIT
|
|
*/
|
|
|
|
#include "mathlib.h"
|
|
#include "v_math.h"
|
|
#if V_SUPPORTED
|
|
|
|
static const float Poly[] = {
|
|
/* maxerr: 1.962 ulp. */
|
|
0x1.59977ap-10f,
|
|
0x1.3ce9e4p-7f,
|
|
0x1.c6bd32p-5f,
|
|
0x1.ebf9bcp-3f,
|
|
0x1.62e422p-1f,
|
|
};
|
|
#define C0 v_f32 (Poly[0])
|
|
#define C1 v_f32 (Poly[1])
|
|
#define C2 v_f32 (Poly[2])
|
|
#define C3 v_f32 (Poly[3])
|
|
#define C4 v_f32 (Poly[4])
|
|
|
|
#define Shift v_f32 (0x1.8p23f)
|
|
|
|
VPCS_ATTR
|
|
static v_f32_t
|
|
specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
|
|
{
|
|
/* 2^n may overflow, break it up into s1*s2. */
|
|
v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
|
|
v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
|
|
v_f32_t s2 = v_as_f32_u32 (e - b);
|
|
v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
|
|
v_u32_t r2 = v_as_u32_f32 (s1 * s1);
|
|
v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
|
|
/* Similar to r1 but avoids double rounding in the subnormal range. */
|
|
v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
|
|
return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
|
|
}
|
|
|
|
VPCS_ATTR
|
|
v_f32_t
|
|
V_NAME(exp2f) (v_f32_t x)
|
|
{
|
|
v_f32_t n, r, r2, scale, p, q, poly, absn;
|
|
v_u32_t cmp, e;
|
|
|
|
/* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
|
|
x = n + r, with r in [-1/2, 1/2]. */
|
|
#if 0
|
|
v_f32_t z;
|
|
z = x + Shift;
|
|
n = z - Shift;
|
|
r = x - n;
|
|
e = v_as_u32_f32 (z) << 23;
|
|
#else
|
|
n = v_round_f32 (x);
|
|
r = x - n;
|
|
e = v_as_u32_s32 (v_round_s32 (x)) << 23;
|
|
#endif
|
|
scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
|
|
absn = v_abs_f32 (n);
|
|
cmp = v_cond_u32 (absn > v_f32 (126.0f));
|
|
r2 = r * r;
|
|
p = v_fma_f32 (C0, r, C1);
|
|
q = v_fma_f32 (C2, r, C3);
|
|
q = v_fma_f32 (p, r2, q);
|
|
p = C4 * r;
|
|
poly = v_fma_f32 (q, r2, p);
|
|
if (unlikely (v_any_u32 (cmp)))
|
|
return specialcase (poly, n, e, absn, cmp, scale);
|
|
return v_fma_f32 (poly, scale, scale);
|
|
}
|
|
VPCS_ALIAS
|
|
#endif
|