415 lines
14 KiB
C
415 lines
14 KiB
C
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/*
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* Copyright (c) 2016, 2019 ARM Limited.
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*
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* SPDX-License-Identifier: MIT
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to
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* deal in the Software without restriction, including without limitation the
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* rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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* sell copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in all
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* copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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#ifndef __ARM_COMPUTE_NEMATH_H__
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#define __ARM_COMPUTE_NEMATH_H__
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#if defined(ARM_MATH_NEON)
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/** Calculate floor of a vector.
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*
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* @param[in] val Input vector value in F32 format.
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*
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* @return The calculated floor vector.
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*/
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static inline float32x4_t vfloorq_f32(float32x4_t val);
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/** Calculate inverse square root.
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*
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* @param[in] x Input value.
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*
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* @return The calculated inverse square root.
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*/
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static inline float32x2_t vinvsqrt_f32(float32x2_t x);
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/** Calculate inverse square root.
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*
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* @param[in] x Input value.
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*
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* @return The calculated inverse square root.
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*/
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static inline float32x4_t vinvsqrtq_f32(float32x4_t x);
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/** Calculate reciprocal.
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*
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* @param[in] x Input value.
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*
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* @return The calculated reciprocal.
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*/
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static inline float32x2_t vinv_f32(float32x2_t x);
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/** Calculate reciprocal.
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*
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* @param[in] x Input value.
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*
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* @return The calculated reciprocal.
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*/
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static inline float32x4_t vinvq_f32(float32x4_t x);
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/** Perform a 7th degree polynomial approximation using Estrin's method.
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*
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* @param[in] x Input vector value in F32 format.
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* @param[in] coeffs Polynomial coefficients table. (array of flattened float32x4_t vectors)
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*
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* @return The calculated approximation.
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*/
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static inline float32x4_t vtaylor_polyq_f32(float32x4_t x, const float32_t *coeffs);
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/** Calculate exponential
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*
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* @param[in] x Input vector value in F32 format.
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*
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* @return The calculated exponent.
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*/
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static inline float32x4_t vexpq_f32(float32x4_t x);
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/** Calculate logarithm
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*
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* @param[in] x Input vector value in F32 format.
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*
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* @return The calculated logarithm.
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*/
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static inline float32x4_t vlogq_f32(float32x4_t x);
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/** Calculate hyperbolic tangent.
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*
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* tanh(x) = (e^2x - 1)/(e^2x + 1)
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*
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* @note We clamp x to [-5,5] to avoid overflowing issues.
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*
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* @param[in] val Input vector value in F32 format.
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*
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* @return The calculated Hyperbolic Tangent.
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*/
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static inline float32x4_t vtanhq_f32(float32x4_t val);
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/** Calculate n power of a number.
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*
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* pow(x,n) = e^(n*log(x))
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*
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* @param[in] val Input vector value in F32 format.
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* @param[in] n Powers to raise the input to.
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*
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* @return The calculated power.
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*/
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static inline float32x4_t vpowq_f32(float32x4_t val, float32x4_t n);
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#ifdef __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
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/** Calculate hyperbolic tangent.
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*
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* tanh(x) = (e^2x - 1)/(e^2x + 1)
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*
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* @note We clamp x to [-5,5] to avoid overflowing issues.
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*
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* @param[in] val Input vector value in F32 format.
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*
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* @return The calculated Hyperbolic Tangent.
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*/
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static inline float16x8_t vtanhq_f16(float16x8_t val);
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/** Calculate reciprocal.
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*
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* @param[in] x Input value.
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*
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* @return The calculated reciprocal.
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*/
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static inline float16x4_t vinv_f16(float16x4_t x);
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/** Calculate reciprocal.
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*
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* @param[in] x Input value.
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*
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* @return The calculated reciprocal.
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*/
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static inline float16x8_t vinvq_f16(float16x8_t x);
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/** Calculate inverse square root.
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*
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* @param[in] x Input value.
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*
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* @return The calculated inverse square root.
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*/
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static inline float16x4_t vinvsqrt_f16(float16x4_t x);
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/** Calculate inverse square root.
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*
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* @param[in] x Input value.
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*
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* @return The calculated inverse square root.
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*/
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static inline float16x8_t vinvsqrtq_f16(float16x8_t x);
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/** Calculate exponential
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*
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* @param[in] x Input vector value in F16 format.
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*
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* @return The calculated exponent.
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*/
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static inline float16x8_t vexpq_f16(float16x8_t x);
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/** Calculate n power of a number.
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*
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* pow(x,n) = e^(n*log(x))
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*
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* @param[in] val Input vector value in F16 format.
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* @param[in] n Powers to raise the input to.
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*
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* @return The calculated power.
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*/
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static inline float16x8_t vpowq_f16(float16x8_t val, float16x8_t n);
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#endif /* __ARM_FEATURE_FP16_VECTOR_ARITHMETIC */
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/** Exponent polynomial coefficients */
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extern const float32_t exp_tab[4*8];
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/** Logarithm polynomial coefficients */
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extern const float32_t log_tab[4*8];
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#ifndef DOXYGEN_SKIP_THIS
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inline float32x4_t vfloorq_f32(float32x4_t val)
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{
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static const float32_t CONST_1[4] = {1.f,1.f,1.f,1.f};
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const int32x4_t z = vcvtq_s32_f32(val);
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const float32x4_t r = vcvtq_f32_s32(z);
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return vbslq_f32(vcgtq_f32(r, val), vsubq_f32(r, vld1q_f32(CONST_1)), r);
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}
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inline float32x2_t vinvsqrt_f32(float32x2_t x)
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{
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float32x2_t sqrt_reciprocal = vrsqrte_f32(x);
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sqrt_reciprocal = vmul_f32(vrsqrts_f32(vmul_f32(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
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sqrt_reciprocal = vmul_f32(vrsqrts_f32(vmul_f32(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
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return sqrt_reciprocal;
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}
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inline float32x4_t vinvsqrtq_f32(float32x4_t x)
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{
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float32x4_t sqrt_reciprocal = vrsqrteq_f32(x);
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sqrt_reciprocal = vmulq_f32(vrsqrtsq_f32(vmulq_f32(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
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sqrt_reciprocal = vmulq_f32(vrsqrtsq_f32(vmulq_f32(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
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return sqrt_reciprocal;
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}
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inline float32x2_t vinv_f32(float32x2_t x)
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{
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float32x2_t recip = vrecpe_f32(x);
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recip = vmul_f32(vrecps_f32(x, recip), recip);
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recip = vmul_f32(vrecps_f32(x, recip), recip);
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return recip;
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}
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inline float32x4_t vinvq_f32(float32x4_t x)
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{
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float32x4_t recip = vrecpeq_f32(x);
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recip = vmulq_f32(vrecpsq_f32(x, recip), recip);
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recip = vmulq_f32(vrecpsq_f32(x, recip), recip);
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return recip;
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}
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inline float32x4_t vtaylor_polyq_f32(float32x4_t x, const float32_t *coeffs)
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{
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float32x4_t A = vmlaq_f32(vld1q_f32(&coeffs[4*0]), vld1q_f32(&coeffs[4*4]), x);
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float32x4_t B = vmlaq_f32(vld1q_f32(&coeffs[4*2]), vld1q_f32(&coeffs[4*6]), x);
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float32x4_t C = vmlaq_f32(vld1q_f32(&coeffs[4*1]), vld1q_f32(&coeffs[4*5]), x);
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float32x4_t D = vmlaq_f32(vld1q_f32(&coeffs[4*3]), vld1q_f32(&coeffs[4*7]), x);
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float32x4_t x2 = vmulq_f32(x, x);
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float32x4_t x4 = vmulq_f32(x2, x2);
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float32x4_t res = vmlaq_f32(vmlaq_f32(A, B, x2), vmlaq_f32(C, D, x2), x4);
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return res;
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}
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inline float32x4_t vexpq_f32(float32x4_t x)
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{
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static const float32_t CONST_LN2[4] = {0.6931471805f,0.6931471805f,0.6931471805f,0.6931471805f}; // ln(2)
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static const float32_t CONST_INV_LN2[4] = {1.4426950408f,1.4426950408f,1.4426950408f,1.4426950408f}; // 1/ln(2)
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static const float32_t CONST_0[4] = {0.f,0.f,0.f,0.f};
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static const int32_t CONST_NEGATIVE_126[4] = {-126,-126,-126,-126};
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// Perform range reduction [-log(2),log(2)]
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int32x4_t m = vcvtq_s32_f32(vmulq_f32(x, vld1q_f32(CONST_INV_LN2)));
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float32x4_t val = vmlsq_f32(x, vcvtq_f32_s32(m), vld1q_f32(CONST_LN2));
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// Polynomial Approximation
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float32x4_t poly = vtaylor_polyq_f32(val, exp_tab);
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// Reconstruct
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poly = vreinterpretq_f32_s32(vqaddq_s32(vreinterpretq_s32_f32(poly), vqshlq_n_s32(m, 23)));
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poly = vbslq_f32(vcltq_s32(m, vld1q_s32(CONST_NEGATIVE_126)), vld1q_f32(CONST_0), poly);
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return poly;
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}
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inline float32x4_t vlogq_f32(float32x4_t x)
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{
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static const int32_t CONST_127[4] = {127,127,127,127}; // 127
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static const float32_t CONST_LN2[4] = {0.6931471805f,0.6931471805f,0.6931471805f,0.6931471805f}; // ln(2)
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// Extract exponent
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int32x4_t m = vsubq_s32(vreinterpretq_s32_u32(vshrq_n_u32(vreinterpretq_u32_f32(x), 23)), vld1q_s32(CONST_127));
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float32x4_t val = vreinterpretq_f32_s32(vsubq_s32(vreinterpretq_s32_f32(x), vshlq_n_s32(m, 23)));
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// Polynomial Approximation
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float32x4_t poly = vtaylor_polyq_f32(val, log_tab);
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// Reconstruct
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poly = vmlaq_f32(poly, vcvtq_f32_s32(m), vld1q_f32(CONST_LN2));
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return poly;
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}
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inline float32x4_t vtanhq_f32(float32x4_t val)
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{
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static const float32_t CONST_1[4] = {1.f,1.f,1.f,1.f};
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static const float32_t CONST_2[4] = {2.f,2.f,2.f,2.f};
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static const float32_t CONST_MIN_TANH[4] = {-10.f,-10.f,-10.f,-10.f};
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static const float32_t CONST_MAX_TANH[4] = {10.f,10.f,10.f,10.f};
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float32x4_t x = vminq_f32(vmaxq_f32(val, vld1q_f32(CONST_MIN_TANH)), vld1q_f32(CONST_MAX_TANH));
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float32x4_t exp2x = vexpq_f32(vmulq_f32(vld1q_f32(CONST_2), x));
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float32x4_t num = vsubq_f32(exp2x, vld1q_f32(CONST_1));
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float32x4_t den = vaddq_f32(exp2x, vld1q_f32(CONST_1));
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float32x4_t tanh = vmulq_f32(num, vinvq_f32(den));
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return tanh;
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}
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inline float32x4_t vpowq_f32(float32x4_t val, float32x4_t n)
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{
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return vexpq_f32(vmulq_f32(n, vlogq_f32(val)));
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}
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#endif /* DOXYGEN_SKIP_THIS */
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#ifdef __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
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/** Exponent polynomial coefficients */
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/** Logarithm polynomial coefficients */
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#ifndef DOXYGEN_SKIP_THIS
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inline float16x8_t vfloorq_f16(float16x8_t val)
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{
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static const float16_t CONST_1[8] = {1.f,1.f,1.f,1.f,1.f,1.f,1.f,1.f};
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const int16x8_t z = vcvtq_s16_f16(val);
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const float16x8_t r = vcvtq_f16_s16(z);
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return vbslq_f16(vcgtq_f16(r, val), vsubq_f16(r, vld1q_f16(CONST_1)), r);
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}
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inline float16x4_t vinvsqrt_f16(float16x4_t x)
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{
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float16x4_t sqrt_reciprocal = vrsqrte_f16(x);
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sqrt_reciprocal = vmul_f16(vrsqrts_f16(vmul_f16(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
|
||
|
|
sqrt_reciprocal = vmul_f16(vrsqrts_f16(vmul_f16(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
|
||
|
|
return sqrt_reciprocal;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vinvsqrtq_f16(float16x8_t x)
|
||
|
|
{
|
||
|
|
float16x8_t sqrt_reciprocal = vrsqrteq_f16(x);
|
||
|
|
sqrt_reciprocal = vmulq_f16(vrsqrtsq_f16(vmulq_f16(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
|
||
|
|
sqrt_reciprocal = vmulq_f16(vrsqrtsq_f16(vmulq_f16(x, sqrt_reciprocal), sqrt_reciprocal), sqrt_reciprocal);
|
||
|
|
return sqrt_reciprocal;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x4_t vinv_f16(float16x4_t x)
|
||
|
|
{
|
||
|
|
float16x4_t recip = vrecpe_f16(x);
|
||
|
|
recip = vmul_f16(vrecps_f16(x, recip), recip);
|
||
|
|
recip = vmul_f16(vrecps_f16(x, recip), recip);
|
||
|
|
return recip;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vinvq_f16(float16x8_t x)
|
||
|
|
{
|
||
|
|
float16x8_t recip = vrecpeq_f16(x);
|
||
|
|
recip = vmulq_f16(vrecpsq_f16(x, recip), recip);
|
||
|
|
recip = vmulq_f16(vrecpsq_f16(x, recip), recip);
|
||
|
|
return recip;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vtanhq_f16(float16x8_t val)
|
||
|
|
{
|
||
|
|
const float16_t CONST_1[8] = {1.f,1.f,1.f,1.f,1.f,1.f,1.f,1.f};
|
||
|
|
const float16_t CONST_2[8] = {2.f,2.f,2.f,2.f,2.f,2.f,2.f,2.f};
|
||
|
|
const float16_t CONST_MIN_TANH[8] = {-10.f,-10.f,-10.f,-10.f,-10.f,-10.f,-10.f,-10.f};
|
||
|
|
const float16_t CONST_MAX_TANH[8] = {10.f,10.f,10.f,10.f,10.f,10.f,10.f,10.f};
|
||
|
|
|
||
|
|
const float16x8_t x = vminq_f16(vmaxq_f16(val, vld1q_f16(CONST_MIN_TANH)), vld1q_f16(CONST_MAX_TANH));
|
||
|
|
const float16x8_t exp2x = vexpq_f16(vmulq_f16(vld1q_f16(CONST_2), x));
|
||
|
|
const float16x8_t num = vsubq_f16(exp2x, vld1q_f16(CONST_1));
|
||
|
|
const float16x8_t den = vaddq_f16(exp2x, vld1q_f16(CONST_1));
|
||
|
|
const float16x8_t tanh = vmulq_f16(num, vinvq_f16(den));
|
||
|
|
return tanh;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vtaylor_polyq_f16(float16x8_t x, const float16_t *coeffs)
|
||
|
|
{
|
||
|
|
const float16x8_t A = vaddq_f16(vld1q_f16(&coeffs[8*0]), vmulq_f16(vld1q_f16(&coeffs[8*4]), x));
|
||
|
|
const float16x8_t B = vaddq_f16(vld1q_f16(&coeffs[8*2]), vmulq_f16(vld1q_f16(&coeffs[8*6]), x));
|
||
|
|
const float16x8_t C = vaddq_f16(vld1q_f16(&coeffs[8*1]), vmulq_f16(vld1q_f16(&coeffs[8*5]), x));
|
||
|
|
const float16x8_t D = vaddq_f16(vld1q_f16(&coeffs[8*3]), vmulq_f16(vld1q_f16(&coeffs[8*7]), x));
|
||
|
|
const float16x8_t x2 = vmulq_f16(x, x);
|
||
|
|
const float16x8_t x4 = vmulq_f16(x2, x2);
|
||
|
|
const float16x8_t res = vaddq_f16(vaddq_f16(A, vmulq_f16(B, x2)), vmulq_f16(vaddq_f16(C, vmulq_f16(D, x2)), x4));
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vexpq_f16(float16x8_t x)
|
||
|
|
{
|
||
|
|
// TODO (COMPMID-1535) : Revisit FP16 approximations
|
||
|
|
const float32x4_t x_high = vcvt_f32_f16(vget_high_f16(x));
|
||
|
|
const float32x4_t x_low = vcvt_f32_f16(vget_low_f16(x));
|
||
|
|
|
||
|
|
const float16x8_t res = vcvt_high_f16_f32(vcvt_f16_f32(vexpq_f32(x_low)), vexpq_f32(x_high));
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vlogq_f16(float16x8_t x)
|
||
|
|
{
|
||
|
|
// TODO (COMPMID-1535) : Revisit FP16 approximations
|
||
|
|
const float32x4_t x_high = vcvt_f32_f16(vget_high_f16(x));
|
||
|
|
const float32x4_t x_low = vcvt_f32_f16(vget_low_f16(x));
|
||
|
|
|
||
|
|
const float16x8_t res = vcvt_high_f16_f32(vcvt_f16_f32(vlogq_f32(x_low)), vlogq_f32(x_high));
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline float16x8_t vpowq_f16(float16x8_t val, float16x8_t n)
|
||
|
|
{
|
||
|
|
// TODO (giaiod01) - COMPMID-1535
|
||
|
|
float32x4_t n0_f32 = vcvt_f32_f16(vget_low_f16(n));
|
||
|
|
float32x4_t n1_f32 = vcvt_f32_f16(vget_high_f16(n));
|
||
|
|
float32x4_t val0_f32 = vcvt_f32_f16(vget_low_f16(val));
|
||
|
|
float32x4_t val1_f32 = vcvt_f32_f16(vget_high_f16(val));
|
||
|
|
|
||
|
|
float32x4_t res0_f32 = vexpq_f32(vmulq_f32(n0_f32, vlogq_f32(val0_f32)));
|
||
|
|
float32x4_t res1_f32 = vexpq_f32(vmulq_f32(n1_f32, vlogq_f32(val1_f32)));
|
||
|
|
|
||
|
|
return vcombine_f16(vcvt_f16_f32(res0_f32), vcvt_f16_f32(res1_f32));
|
||
|
|
}
|
||
|
|
#endif /* DOXYGEN_SKIP_THIS */
|
||
|
|
#endif /* __ARM_FEATURE_FP16_VECTOR_ARITHMETIC */
|
||
|
|
#endif
|
||
|
|
#endif /* __ARM_COMPUTE_NEMATH_H__ */
|