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

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MIT License
Copyright (c) 2017-2019 ARM Software
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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/*
* Copyright (c) 2016, 2019 ARM Limited.
*
* SPDX-License-Identifier: MIT
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to
* deal in the Software without restriction, including without limitation the
* rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
* sell copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "arm_math.h"
#include "NEMath.h"
#if defined(ARM_MATH_NEON)
/** Exponent polynomial coefficients */
const float32_t exp_tab[4*8] =
{
1.f,1.f,1.f,1.f,
0.0416598916054f,0.0416598916054f,0.0416598916054f,0.0416598916054f,
0.500000596046f,0.500000596046f,0.500000596046f,0.500000596046f,
0.0014122662833f,0.0014122662833f,0.0014122662833f,0.0014122662833f,
1.00000011921f,1.00000011921f,1.00000011921f,1.00000011921f,
0.00833693705499f,0.00833693705499f,0.00833693705499f,0.00833693705499f,
0.166665703058f,0.166665703058f,0.166665703058f,0.166665703058f,
0.000195780929062f,0.000195780929062f,0.000195780929062f,0.000195780929062f
};
/** Logarithm polynomial coefficients */
const float32_t log_tab[4*8] =
{
-2.29561495781f,-2.29561495781f,-2.29561495781f,-2.29561495781f,
-2.47071170807f,-2.47071170807f,-2.47071170807f,-2.47071170807f,
-5.68692588806f,-5.68692588806f,-5.68692588806f,-5.68692588806f,
-0.165253549814f,-0.165253549814f,-0.165253549814f,-0.165253549814f,
5.17591238022f,5.17591238022f,5.17591238022f,5.17591238022f,
0.844007015228f,0.844007015228f,0.844007015228f,0.844007015228f,
4.58445882797f,4.58445882797f,4.58445882797f,4.58445882797f,
0.0141278216615f,0.0141278216615f,0.0141278216615f,0.0141278216615f
};
#endif