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/*
* Helper for single-precision routines which calculate exp(x) and do not
* need special-case handling
*
* Copyright (c) 2019-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#ifndef PL_MATH_V_EXPF_INLINE_H
#define PL_MATH_V_EXPF_INLINE_H
#include "v_math.h"
struct v_expf_data
{
float32x4_t poly[5];
float32x4_t shift, invln2, ln2_hi, ln2_lo;
};
/* maxerr: 1.45358 +0.5 ulp. */
#define V_EXPF_DATA \
{ \
.poly = { V4 (0x1.0e4020p-7f), V4 (0x1.573e2ep-5f), V4 (0x1.555e66p-3f), \
V4 (0x1.fffdb6p-2f), V4 (0x1.ffffecp-1f) }, \
\
.shift = V4 (0x1.8p23f), .invln2 = V4 (0x1.715476p+0f), \
.ln2_hi = V4 (0x1.62e4p-1f), .ln2_lo = V4 (0x1.7f7d1cp-20f), \
}
#define ExponentBias v_u32 (0x3f800000) /* asuint(1.0f). */
#define C(i) d->poly[i]
static inline float32x4_t
v_expf_inline (float32x4_t x, const struct v_expf_data *d)
{
/* Helper routine for calculating exp(x).
Copied from v_expf.c, with all special-case handling removed - the
calling routine should handle special values if required. */
/* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
float32x4_t n, r, z;
z = vfmaq_f32 (d->shift, x, d->invln2);
n = vsubq_f32 (z, d->shift);
r = vfmsq_f32 (x, n, d->ln2_hi);
r = vfmsq_f32 (r, n, d->ln2_lo);
uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23);
float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, ExponentBias));
/* Custom order-4 Estrin avoids building high order monomial. */
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t p, q, poly;
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);
return vfmaq_f32 (scale, poly, scale);
}
#endif // PL_MATH_V_EXPF_INLINE_H
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