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/******************************************************************************
* @file arm_vec_math_f16.h
* @brief Public header file for CMSIS DSP Library
* @version V1.10.0
* @date 08 July 2021
* Target Processor: Cortex-M and Cortex-A cores
******************************************************************************/
/*
* Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#ifndef _ARM_VEC_MATH_F16_H
#define _ARM_VEC_MATH_F16_H
#include "arm_math_types_f16.h"
#include "arm_common_tables_f16.h"
#include "arm_helium_utils.h"
#ifdef __cplusplus
extern "C"
{
#endif
#if defined(ARM_FLOAT16_SUPPORTED)
#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
static const float16_t __logf_rng_f16=0.693147180f16;
/* fast inverse approximation (3x newton) */
__STATIC_INLINE f16x8_t vrecip_medprec_f16(
f16x8_t x)
{
q15x8_t m;
f16x8_t b;
any16x8_t xinv;
f16x8_t ax = vabsq(x);
xinv.f = ax;
m = 0x03c00 - (xinv.i & 0x07c00);
xinv.i = xinv.i + m;
xinv.f = 1.41176471f16 - 0.47058824f16 * xinv.f;
xinv.i = xinv.i + m;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
xinv.f = vdupq_m_n_f16(xinv.f, F16INFINITY, vcmpeqq_n_f16(x, 0.0f));
/*
* restore sign
*/
xinv.f = vnegq_m(xinv.f, xinv.f, vcmpltq_n_f16(x, 0.0f));
return xinv.f;
}
/* fast inverse approximation (4x newton) */
__STATIC_INLINE f16x8_t vrecip_hiprec_f16(
f16x8_t x)
{
q15x8_t m;
f16x8_t b;
any16x8_t xinv;
f16x8_t ax = vabsq(x);
xinv.f = ax;
m = 0x03c00 - (xinv.i & 0x07c00);
xinv.i = xinv.i + m;
xinv.f = 1.41176471f16 - 0.47058824f16 * xinv.f;
xinv.i = xinv.i + m;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
b = 2.0f16 - xinv.f * ax;
xinv.f = xinv.f * b;
xinv.f = vdupq_m_n_f16(xinv.f, F16INFINITY, vcmpeqq_n_f16(x, 0.0f));
/*
* restore sign
*/
xinv.f = vnegq_m(xinv.f, xinv.f, vcmpltq_n_f16(x, 0.0f));
return xinv.f;
}
__STATIC_INLINE f16x8_t vdiv_f16(
f16x8_t num, f16x8_t den)
{
return vmulq(num, vrecip_hiprec_f16(den));
}
/**
@brief Single-precision taylor dev.
@param[in] x f16 vector input
@param[in] coeffs f16 vector coeffs
@return destination f16 vector
*/
__STATIC_INLINE float16x8_t vtaylor_polyq_f16(
float16x8_t x,
const float16_t * coeffs)
{
float16x8_t A = vfmasq(vdupq_n_f16(coeffs[4]), x, coeffs[0]);
float16x8_t B = vfmasq(vdupq_n_f16(coeffs[6]), x, coeffs[2]);
float16x8_t C = vfmasq(vdupq_n_f16(coeffs[5]), x, coeffs[1]);
float16x8_t D = vfmasq(vdupq_n_f16(coeffs[7]), x, coeffs[3]);
float16x8_t x2 = vmulq(x, x);
float16x8_t x4 = vmulq(x2, x2);
float16x8_t res = vfmaq(vfmaq_f16(A, B, x2), vfmaq_f16(C, D, x2), x4);
return res;
}
#define VMANT_EXP_F16(x) \
any16x8_t r; \
int16x8_t n; \
\
r.f = x; \
n = r.i >> 10; \
n = n - 15; \
r.i = r.i - (n << 10);\
\
vecExpUnBiased = n; \
vecTmpFlt1 = r.f;
__STATIC_INLINE float16x8_t vlogq_f16(float16x8_t vecIn)
{
q15x8_t vecExpUnBiased;
float16x8_t vecTmpFlt0, vecTmpFlt1;
float16x8_t vecAcc0, vecAcc1, vecAcc2, vecAcc3;
float16x8_t vecExpUnBiasedFlt;
/*
* extract exponent
*/
VMANT_EXP_F16(vecIn);
vecTmpFlt0 = vecTmpFlt1 * vecTmpFlt1;
/*
* a = (__logf_lut_f16[4] * r.f) + (__logf_lut_f16[0]);
*/
vecAcc0 = vdupq_n_f16(__logf_lut_f16[0]);
vecAcc0 = vfmaq(vecAcc0, vecTmpFlt1, __logf_lut_f16[4]);
/*
* b = (__logf_lut_f16[6] * r.f) + (__logf_lut_f16[2]);
*/
vecAcc1 = vdupq_n_f16(__logf_lut_f16[2]);
vecAcc1 = vfmaq(vecAcc1, vecTmpFlt1, __logf_lut_f16[6]);
/*
* c = (__logf_lut_f16[5] * r.f) + (__logf_lut_f16[1]);
*/
vecAcc2 = vdupq_n_f16(__logf_lut_f16[1]);
vecAcc2 = vfmaq(vecAcc2, vecTmpFlt1, __logf_lut_f16[5]);
/*
* d = (__logf_lut_f16[7] * r.f) + (__logf_lut_f16[3]);
*/
vecAcc3 = vdupq_n_f16(__logf_lut_f16[3]);
vecAcc3 = vfmaq(vecAcc3, vecTmpFlt1, __logf_lut_f16[7]);
/*
* a = a + b * xx;
*/
vecAcc0 = vfmaq(vecAcc0, vecAcc1, vecTmpFlt0);
/*
* c = c + d * xx;
*/
vecAcc2 = vfmaq(vecAcc2, vecAcc3, vecTmpFlt0);
/*
* xx = xx * xx;
*/
vecTmpFlt0 = vecTmpFlt0 * vecTmpFlt0;
vecExpUnBiasedFlt = vcvtq_f16_s16(vecExpUnBiased);
/*
* r.f = a + c * xx;
*/
vecAcc0 = vfmaq(vecAcc0, vecAcc2, vecTmpFlt0);
/*
* add exponent
* r.f = r.f + ((float32_t) m) * __logf_rng_f16;
*/
vecAcc0 = vfmaq(vecAcc0, vecExpUnBiasedFlt, __logf_rng_f16);
// set log0 down to -inf
vecAcc0 = vdupq_m_n_f16(vecAcc0, -(_Float16)F16INFINITY, vcmpeqq_n_f16(vecIn, 0.0f));
return vecAcc0;
}
__STATIC_INLINE float16x8_t vexpq_f16(
float16x8_t x)
{
// Perform range reduction [-log(2),log(2)]
int16x8_t m = vcvtq_s16_f16(vmulq_n_f16(x, 1.4426950408f16));
float16x8_t val = vfmsq_f16(x, vcvtq_f16_s16(m), vdupq_n_f16(0.6931471805f16));
// Polynomial Approximation
float16x8_t poly = vtaylor_polyq_f16(val, exp_tab_f16);
// Reconstruct
poly = (float16x8_t) (vqaddq_s16((int16x8_t) (poly), vqshlq_n_s16(m, 10)));
poly = vdupq_m_n_f16(poly, 0.0f16, vcmpltq_n_s16(m, -14));
return poly;
}
__STATIC_INLINE float16x8_t arm_vec_exponent_f16(float16x8_t x, int16_t nb)
{
float16x8_t r = x;
nb--;
while (nb > 0) {
r = vmulq(r, x);
nb--;
}
return (r);
}
__STATIC_INLINE f16x8_t vpowq_f16(
f16x8_t val,
f16x8_t n)
{
return vexpq_f16(vmulq_f16(n, vlogq_f16(val)));
}
#define INV_NEWTON_INIT_F16 0x7773
__STATIC_INLINE f16x8_t vrecip_f16(f16x8_t vecIn)
{
f16x8_t vecSx, vecW, vecTmp;
any16x8_t v;
vecSx = vabsq(vecIn);
v.f = vecIn;
v.i = vsubq(vdupq_n_s16(INV_NEWTON_INIT_F16), v.i);
vecW = vmulq(vecSx, v.f);
// v.f = v.f * (8 + w * (-28 + w * (56 + w * (-70 + w *(56 + w * (-28 + w * (8 - w)))))));
vecTmp = vsubq(vdupq_n_f16(8.0f16), vecW);
vecTmp = vfmasq_n_f16(vecW, vecTmp, -28.0f16);
vecTmp = vfmasq_n_f16(vecW, vecTmp, 56.0f16);
vecTmp = vfmasq_n_f16(vecW, vecTmp, -70.0f16);
vecTmp = vfmasq_n_f16(vecW, vecTmp, 56.0f16);
vecTmp = vfmasq_n_f16(vecW, vecTmp, -28.0f16);
vecTmp = vfmasq_n_f16(vecW, vecTmp, 8.0f16);
v.f = vmulq(v.f, vecTmp);
v.f = vdupq_m_n_f16(v.f, F16INFINITY, vcmpeqq_n_f16(vecIn, 0.0f));
/*
* restore sign
*/
v.f = vnegq_m(v.f, v.f, vcmpltq_n_f16(vecIn, 0.0f));
return v.f;
}
__STATIC_INLINE f16x8_t vtanhq_f16(
f16x8_t val)
{
f16x8_t x =
vminnmq_f16(vmaxnmq_f16(val, vdupq_n_f16(-10.f16)), vdupq_n_f16(10.0f16));
f16x8_t exp2x = vexpq_f16(vmulq_n_f16(x, 2.f16));
f16x8_t num = vsubq_n_f16(exp2x, 1.f16);
f16x8_t den = vaddq_n_f16(exp2x, 1.f16);
f16x8_t tanh = vmulq_f16(num, vrecip_f16(den));
return tanh;
}
#endif /* defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)*/
#ifdef __cplusplus
}
#endif
#endif /* ARM FLOAT16 SUPPORTED */
#endif /* _ARM_VEC_MATH_F16_H */
/**
*
* End of file.
*/
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