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/*
* Single-precision vector 2^x function.
*
* Copyright (c) 2019-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "mathlib.h"
#include "v_math.h"
static const struct data
{
float32x4_t poly[5];
uint32x4_t exponent_bias;
#if !WANT_SIMD_EXCEPT
float32x4_t special_bound, scale_thresh;
#endif
} data = {
/* maxerr: 1.962 ulp. */
.poly = { V4 (0x1.59977ap-10f), V4 (0x1.3ce9e4p-7f), V4 (0x1.c6bd32p-5f),
V4 (0x1.ebf9bcp-3f), V4 (0x1.62e422p-1f) },
.exponent_bias = V4 (0x3f800000),
#if !WANT_SIMD_EXCEPT
.special_bound = V4 (126.0f),
.scale_thresh = V4 (192.0f),
#endif
};
#define C(i) d->poly[i]
#if WANT_SIMD_EXCEPT
# define TinyBound v_u32 (0x20000000) /* asuint (0x1p-63). */
# define BigBound v_u32 (0x42800000) /* asuint (0x1p6). */
# define SpecialBound v_u32 (0x22800000) /* BigBound - TinyBound. */
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
{
/* If fenv exceptions are to be triggered correctly, fall back to the scalar
routine for special lanes. */
return v_call_f32 (exp2f, x, y, cmp);
}
#else
# define SpecialOffset v_u32 (0x82000000)
# define SpecialBias v_u32 (0x7f000000)
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t poly, float32x4_t n, uint32x4_t e, uint32x4_t cmp1,
float32x4_t scale, const struct data *d)
{
/* 2^n may overflow, break it up into s1*s2. */
uint32x4_t b = vandq_u32 (vclezq_f32 (n), SpecialOffset);
float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, SpecialBias));
float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b));
uint32x4_t cmp2 = vcagtq_f32 (n, d->scale_thresh);
float32x4_t r2 = vmulq_f32 (s1, s1);
float32x4_t r1 = vmulq_f32 (vfmaq_f32 (s2, poly, s2), s1);
/* Similar to r1 but avoids double rounding in the subnormal range. */
float32x4_t r0 = vfmaq_f32 (scale, poly, scale);
float32x4_t r = vbslq_f32 (cmp1, r1, r0);
return vbslq_f32 (cmp2, r2, r);
}
#endif
float32x4_t VPCS_ATTR V_NAME_F1 (exp2) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
float32x4_t n, r, r2, scale, p, q, poly;
uint32x4_t cmp, e;
#if WANT_SIMD_EXCEPT
/* asuint(|x|) - TinyBound >= BigBound - TinyBound. */
uint32x4_t ia = vreinterpretq_u32_f32 (vabsq_f32 (x));
cmp = vcgeq_u32 (vsubq_u32 (ia, TinyBound), SpecialBound);
float32x4_t xm = x;
/* If any lanes are special, mask them with 1 and retain a copy of x to allow
special_case to fix special lanes later. This is only necessary if fenv
exceptions are to be triggered correctly. */
if (unlikely (v_any_u32 (cmp)))
x = vbslq_f32 (cmp, v_f32 (1), x);
#endif
/* 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]. */
n = vrndaq_f32 (x);
r = vsubq_f32 (x, n);
e = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (x)), 23);
scale = vreinterpretq_f32_u32 (vaddq_u32 (e, d->exponent_bias));
#if !WANT_SIMD_EXCEPT
cmp = vcagtq_f32 (n, d->special_bound);
#endif
r2 = vmulq_f32 (r, r);
p = vfmaq_f32 (C (1), C (0), r);
q = vfmaq_f32 (C (3), C (2), r);
q = vfmaq_f32 (q, p, r2);
p = vmulq_f32 (C (4), r);
poly = vfmaq_f32 (p, q, r2);
if (unlikely (v_any_u32 (cmp)))
#if WANT_SIMD_EXCEPT
return special_case (xm, vfmaq_f32 (scale, poly, scale), cmp);
#else
return special_case (poly, n, e, cmp, scale, d);
#endif
return vfmaq_f32 (scale, poly, scale);
}
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