| /* |
| * Copyright (c) 2017 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_compute/core/Error.h" |
| |
| #include <cmath> |
| #include <limits> |
| |
| namespace |
| { |
| template <typename TpIn, typename TpSat> |
| inline TpSat saturate_convert(TpIn a) |
| { |
| if(a > std::numeric_limits<TpSat>::max()) |
| { |
| a = std::numeric_limits<TpSat>::max(); |
| } |
| if(a < std::numeric_limits<TpSat>::min()) |
| { |
| a = std::numeric_limits<TpSat>::min(); |
| } |
| return static_cast<TpSat>(a); |
| } |
| } // namespace |
| |
| namespace arm_compute |
| { |
| inline qint8_t sqshl_qs8(qint8_t a, int shift) |
| { |
| qint16_t tmp = static_cast<qint16_t>(a) << shift; |
| |
| // Saturate the result in case of overflow and cast to qint8_t |
| return saturate_convert<qint16_t, qint8_t>(tmp); |
| } |
| |
| inline qint16_t sqshl_qs16(qint16_t a, int shift) |
| { |
| qint32_t tmp = static_cast<qint32_t>(a) << shift; |
| |
| // Saturate the result in case of overflow and cast to qint16_t |
| return saturate_convert<qint32_t, qint16_t>(tmp); |
| } |
| |
| inline qint8_t sshr_qs8(qint8_t a, int shift) |
| { |
| ARM_COMPUTE_ERROR_ON_MSG(shift == 0, "Shift should not be zero"); |
| const qint8_t round_val = 1 << (shift - 1); |
| return sqadd_qs8(a, round_val) >> shift; |
| } |
| |
| inline qint16_t sshr_qs16(qint16_t a, int shift) |
| { |
| ARM_COMPUTE_ERROR_ON_MSG(shift == 0, "Shift should not be zero"); |
| const qint16_t round_val = 1 << (shift - 1); |
| return sqadd_qs16(a, round_val) >> shift; |
| } |
| |
| inline qint8_t sabs_qs8(qint8_t a) |
| { |
| return (a < 0) ? (a == std::numeric_limits<int8_t>::min()) ? std::numeric_limits<int8_t>::max() : -a : a; |
| } |
| |
| inline qint16_t sabs_qs16(qint16_t a) |
| { |
| return (a < 0) ? (a == std::numeric_limits<int16_t>::min()) ? std::numeric_limits<int16_t>::max() : -a : a; |
| } |
| |
| inline qint8_t sadd_qs8(qint8_t a, qint8_t b) |
| { |
| return a + b; |
| } |
| |
| inline qint16_t sadd_qs16(qint16_t a, qint16_t b) |
| { |
| return a + b; |
| } |
| |
| inline qint8_t sqadd_qs8(qint8_t a, qint8_t b) |
| { |
| // We need to store the temporary result in qint16_t otherwise we cannot evaluate the overflow |
| qint16_t tmp = (static_cast<qint16_t>(a) + static_cast<qint16_t>(b)); |
| |
| // Saturate the result in case of overflow and cast to qint8_t |
| return saturate_convert<qint16_t, qint8_t>(tmp); |
| } |
| |
| inline qint16_t sqadd_qs16(qint16_t a, qint16_t b) |
| { |
| // We need to store the temporary result in qint32_t otherwise we cannot evaluate the overflow |
| qint32_t tmp = (static_cast<qint32_t>(a) + static_cast<qint32_t>(b)); |
| |
| // Saturate the result in case of overflow and cast to qint16_t |
| return saturate_convert<qint32_t, qint16_t>(tmp); |
| } |
| |
| inline qint32_t sqadd_qs32(qint32_t a, qint32_t b) |
| { |
| // We need to store the temporary result in qint64_t otherwise we cannot evaluate the overflow |
| qint64_t tmp = (static_cast<qint64_t>(a) + static_cast<qint64_t>(b)); |
| |
| // Saturate the result in case of overflow and cast to qint32_t |
| return saturate_convert<qint64_t, qint32_t>(tmp); |
| } |
| |
| inline qint8_t ssub_qs8(qint8_t a, qint8_t b) |
| { |
| return a - b; |
| } |
| |
| inline qint16_t ssub_qs16(qint16_t a, qint16_t b) |
| { |
| return a - b; |
| } |
| |
| inline qint8_t sqsub_qs8(qint8_t a, qint8_t b) |
| { |
| // We need to store the temporary result in uint16_t otherwise we cannot evaluate the overflow |
| qint16_t tmp = static_cast<qint16_t>(a) - static_cast<qint16_t>(b); |
| |
| // Saturate the result in case of overflow and cast to qint8_t |
| return saturate_convert<qint16_t, qint8_t>(tmp); |
| } |
| |
| inline qint16_t sqsub_qs16(qint16_t a, qint16_t b) |
| { |
| // We need to store the temporary result in qint32_t otherwise we cannot evaluate the overflow |
| qint32_t tmp = static_cast<qint32_t>(a) - static_cast<qint32_t>(b); |
| |
| // Saturate the result in case of overflow and cast to qint16_t |
| return saturate_convert<qint32_t, qint16_t>(tmp); |
| } |
| |
| inline qint8_t smul_qs8(qint8_t a, qint8_t b, int fixed_point_position) |
| { |
| const qint16_t round_up_const = (1 << (fixed_point_position - 1)); |
| |
| qint16_t tmp = static_cast<qint16_t>(a) * static_cast<qint16_t>(b); |
| |
| // Rounding up |
| tmp += round_up_const; |
| |
| return static_cast<qint8_t>(tmp >> fixed_point_position); |
| } |
| |
| inline qint16_t smul_qs16(qint16_t a, qint16_t b, int fixed_point_position) |
| { |
| const qint32_t round_up_const = (1 << (fixed_point_position - 1)); |
| |
| qint32_t tmp = static_cast<qint32_t>(a) * static_cast<qint32_t>(b); |
| |
| // Rounding up |
| tmp += round_up_const; |
| |
| return static_cast<qint16_t>(tmp >> fixed_point_position); |
| } |
| |
| inline qint8_t sqmul_qs8(qint8_t a, qint8_t b, int fixed_point_position) |
| { |
| const qint16_t round_up_const = (1 << (fixed_point_position - 1)); |
| |
| qint16_t tmp = static_cast<qint16_t>(a) * static_cast<qint16_t>(b); |
| |
| // Rounding up |
| tmp += round_up_const; |
| |
| return saturate_convert<qint16_t, qint8_t>(tmp >> fixed_point_position); |
| } |
| |
| inline qint16_t sqmul_qs16(qint16_t a, qint16_t b, int fixed_point_position) |
| { |
| const qint32_t round_up_const = (1 << (fixed_point_position - 1)); |
| |
| qint32_t tmp = static_cast<qint32_t>(a) * static_cast<qint32_t>(b); |
| |
| // Rounding up |
| tmp += round_up_const; |
| |
| return saturate_convert<qint32_t, qint16_t>(tmp >> fixed_point_position); |
| } |
| |
| inline qint16_t sqmull_qs8(qint8_t a, qint8_t b, int fixed_point_position) |
| { |
| const qint16_t round_up_const = (1 << (fixed_point_position - 1)); |
| |
| qint16_t tmp = static_cast<qint16_t>(a) * static_cast<qint16_t>(b); |
| |
| // Rounding up |
| tmp += round_up_const; |
| |
| return tmp >> fixed_point_position; |
| } |
| |
| inline qint32_t sqmull_qs16(qint16_t a, qint16_t b, int fixed_point_position) |
| { |
| const qint32_t round_up_const = (1 << (fixed_point_position - 1)); |
| |
| qint32_t tmp = static_cast<qint32_t>(a) * static_cast<qint32_t>(b); |
| |
| // Rounding up |
| tmp += round_up_const; |
| |
| return tmp >> fixed_point_position; |
| } |
| |
| inline qint8_t sinvsqrt_qs8(qint8_t a, int fixed_point_position) |
| { |
| const qint8_t shift = 8 - (fixed_point_position + (__builtin_clz(a) - 24)); |
| |
| const qint8_t const_three = (3 << fixed_point_position); |
| qint8_t temp = shift < 0 ? (a << -shift) : (a >> shift); |
| qint8_t x2 = temp; |
| |
| // We need three iterations to find the result |
| for(int i = 0; i < 3; ++i) |
| { |
| qint8_t three_minus_dx = ssub_qs8(const_three, smul_qs8(temp, smul_qs8(x2, x2, fixed_point_position), fixed_point_position)); |
| x2 = (smul_qs8(x2, three_minus_dx, fixed_point_position) >> 1); |
| } |
| |
| temp = shift < 0 ? (x2 << (-shift >> 1)) : (x2 >> (shift >> 1)); |
| |
| return temp; |
| } |
| |
| inline qint16_t sinvsqrt_qs16(qint16_t a, int fixed_point_position) |
| { |
| const qint16_t shift = 16 - (fixed_point_position + (__builtin_clz(a) - 16)); |
| |
| const qint16_t const_three = (3 << fixed_point_position); |
| qint16_t temp = shift < 0 ? (a << -shift) : (a >> shift); |
| qint16_t x2 = temp; |
| |
| // We need three iterations to find the result |
| for(int i = 0; i < 3; ++i) |
| { |
| qint16_t three_minus_dx = ssub_qs16(const_three, smul_qs16(temp, smul_qs16(x2, x2, fixed_point_position), fixed_point_position)); |
| x2 = smul_qs16(x2, three_minus_dx, fixed_point_position) >> 1; |
| } |
| |
| temp = shift < 0 ? (x2 << ((-shift) >> 1)) : (x2 >> (shift >> 1)); |
| |
| return temp; |
| } |
| |
| inline qint8_t sdiv_qs8(qint8_t a, qint8_t b, int fixed_point_position) |
| { |
| const qint16_t temp = a << fixed_point_position; |
| return static_cast<qint8_t>(temp / b); |
| } |
| |
| inline qint16_t sdiv_qs16(qint16_t a, qint16_t b, int fixed_point_position) |
| { |
| const qint32_t temp = a << fixed_point_position; |
| return static_cast<qint16_t>(temp / b); |
| } |
| |
| inline qint8_t sqexp_qs8(qint8_t a, int fixed_point_position) |
| { |
| // Constants |
| const qint8_t const_one = (1 << fixed_point_position); |
| const qint8_t ln2 = ((0x58 >> (6 - fixed_point_position)) + 1) >> 1; |
| const qint8_t inv_ln2 = (((0x38 >> (6 - fixed_point_position)) + 1) >> 1) | const_one; |
| const qint8_t A = ((0x7F >> (6 - fixed_point_position)) + 1) >> 1; |
| const qint8_t B = ((0x3F >> (6 - fixed_point_position)) + 1) >> 1; |
| const qint8_t C = ((0x16 >> (6 - fixed_point_position)) + 1) >> 1; |
| const qint8_t D = ((0x05 >> (6 - fixed_point_position)) + 1) >> 1; |
| |
| // Polynomial expansion |
| const int dec_a = (sqmul_qs8(a, inv_ln2, fixed_point_position) >> fixed_point_position); |
| const qint8_t alpha = sabs_qs8(sqsub_qs8(a, sqmul_qs8(ln2, sqshl_qs8(dec_a, fixed_point_position), fixed_point_position))); |
| qint8_t sum = sqadd_qs8(sqmul_qs8(alpha, D, fixed_point_position), C); |
| sum = sqadd_qs8(sqmul_qs8(alpha, sum, fixed_point_position), B); |
| sum = sqadd_qs8(sqmul_qs8(alpha, sum, fixed_point_position), A); |
| sum = sqmul_qs8(alpha, sum, fixed_point_position); |
| sum = sqadd_qs8(sum, const_one); |
| |
| return (dec_a < 0) ? (sum >> -dec_a) : sqshl_qs8(sum, dec_a); |
| } |
| |
| inline qint16_t sqexp_qs16(qint16_t a, int fixed_point_position) |
| { |
| // Constants |
| const qint16_t const_one = (1 << fixed_point_position); |
| const qint16_t ln2 = ((0x58B9 >> (14 - fixed_point_position)) + 1) >> 1; |
| const qint16_t inv_ln2 = (((0x38AA >> (14 - fixed_point_position)) + 1) >> 1) | const_one; |
| const qint16_t A = ((0x7FBA >> (14 - fixed_point_position)) + 1) >> 1; |
| const qint16_t B = ((0x3FE9 >> (14 - fixed_point_position)) + 1) >> 1; |
| const qint16_t C = ((0x1693 >> (14 - fixed_point_position)) + 1) >> 1; |
| const qint16_t D = ((0x0592 >> (14 - fixed_point_position)) + 1) >> 1; |
| |
| // Polynomial expansion |
| const int dec_a = (sqmul_qs16(a, inv_ln2, fixed_point_position) >> fixed_point_position); |
| const qint16_t alpha = sabs_qs16(sqsub_qs16(a, sqmul_qs16(ln2, sqshl_qs16(dec_a, fixed_point_position), fixed_point_position))); |
| qint16_t sum = sqadd_qs16(sqmul_qs16(alpha, D, fixed_point_position), C); |
| sum = sqadd_qs16(sqmul_qs16(alpha, sum, fixed_point_position), B); |
| sum = sqadd_qs16(sqmul_qs16(alpha, sum, fixed_point_position), A); |
| sum = sqmul_qs16(alpha, sum, fixed_point_position); |
| sum = sqadd_qs16(sum, const_one); |
| |
| return (dec_a < 0) ? (sum >> -dec_a) : sqshl_qs16(sum, dec_a); |
| } |
| |
| inline qint8_t slog_qs8(qint8_t a, int fixed_point_position) |
| { |
| // Constants |
| qint8_t const_one = (1 << fixed_point_position); |
| qint8_t ln2 = (0x58 >> (7 - fixed_point_position)); |
| qint8_t A = (0x5C >> (7 - fixed_point_position - 1)); |
| qint8_t B = -(0x56 >> (7 - fixed_point_position)); |
| qint8_t C = (0x29 >> (7 - fixed_point_position)); |
| qint8_t D = -(0x0A >> (7 - fixed_point_position)); |
| |
| if((const_one == a) || (a < 0)) |
| { |
| return 0; |
| } |
| else if(a < const_one) |
| { |
| return -slog_qs8(sdiv_qs8(const_one, a, fixed_point_position), fixed_point_position); |
| } |
| |
| // Remove even powers of 2 |
| qint8_t shift_val = 31 - __builtin_clz(a >> fixed_point_position); |
| a >>= shift_val; |
| a = ssub_qs8(a, const_one); |
| |
| // Polynomial expansion |
| qint8_t sum = sqadd_qs8(sqmul_qs8(a, D, fixed_point_position), C); |
| sum = sqadd_qs8(sqmul_qs8(a, sum, fixed_point_position), B); |
| sum = sqadd_qs8(sqmul_qs8(a, sum, fixed_point_position), A); |
| sum = sqmul_qs8(a, sum, fixed_point_position); |
| |
| return smul_qs8(sadd_qs8(sum, shift_val << fixed_point_position), ln2, fixed_point_position); |
| } |
| |
| inline qint16_t slog_qs16(qint16_t a, int fixed_point_position) |
| { |
| // Constants |
| qint16_t const_one = (1 << fixed_point_position); |
| qint16_t ln2 = (0x58B9 >> (7 - fixed_point_position)); |
| qint16_t A = (0x5C0F >> (7 - fixed_point_position - 1)); |
| qint16_t B = -(0x56AE >> (7 - fixed_point_position)); |
| qint16_t C = (0x2933 >> (7 - fixed_point_position)); |
| qint16_t D = -(0x0AA7 >> (7 - fixed_point_position)); |
| |
| if((const_one == a) || (a < 0)) |
| { |
| return 0; |
| } |
| else if(a < const_one) |
| { |
| return -slog_qs16(sdiv_qs16(const_one, a, fixed_point_position), fixed_point_position); |
| } |
| |
| // Remove even powers of 2 |
| qint16_t shift_val = 31 - __builtin_clz(a >> fixed_point_position); |
| a >>= shift_val; |
| a = ssub_qs16(a, const_one); |
| |
| // Polynomial expansion |
| qint16_t sum = sqadd_qs16(sqmul_qs16(a, D, fixed_point_position), C); |
| sum = sqadd_qs16(sqmul_qs16(a, sum, fixed_point_position), B); |
| sum = sqadd_qs16(sqmul_qs16(a, sum, fixed_point_position), A); |
| sum = sqmul_qs16(a, sum, fixed_point_position); |
| |
| return smul_qs16(sadd_qs16(sum, shift_val << fixed_point_position), ln2, fixed_point_position); |
| } |
| |
| inline float scvt_f32_qs8(qint8_t a, int fixed_point_position) |
| { |
| return static_cast<float>(a) / (1 << fixed_point_position); |
| } |
| |
| inline qint8_t sqcvt_qs8_f32(float a, int fixed_point_position) |
| { |
| // round_nearest_integer(a * 2^(fixed_point_position)) |
| return saturate_convert<float, qint8_t>(a * (1 << fixed_point_position) + ((a >= 0) ? 0.5 : -0.5)); |
| } |
| |
| inline float scvt_f32_qs16(qint16_t a, int fixed_point_position) |
| { |
| return static_cast<float>(a) / (1 << fixed_point_position); |
| } |
| |
| inline qint16_t sqcvt_qs16_f32(float a, int fixed_point_position) |
| { |
| // round_nearest_integer(a * 2^(fixed_point_position)) |
| return saturate_convert<float, qint16_t>(a * (1 << fixed_point_position) + ((a >= 0) ? 0.5 : -0.5)); |
| } |
| |
| inline qint8_t sqmovn_qs16(qint16_t a) |
| { |
| // Saturate the result in case of overflow and cast to qint8_t |
| return saturate_convert<qint16_t, qint8_t>(a); |
| } |
| |
| inline qint16_t sqmovn_qs32(qint32_t a) |
| { |
| // Saturate the result in case of overflow and cast to qint16_t |
| return saturate_convert<qint32_t, qint16_t>(a); |
| } |
| } |