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