/* * 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. */ #ifndef ARM_COMPUTE_ASYMM_HELPER_H #define ARM_COMPUTE_ASYMM_HELPER_H // TODO These functions were implemented to be used in softmax-uint8 kernel and therefore process only vectors of length 16. // But they can be managed to process arbitrary vector length using VEC_DATA_TYPE(int, size) definition to be more reusable. // Algoriths for these functions were taken from // https://github.com/google/gemmlowp/blob/master/fixedpoint/fixedpoint.h // and adapted to operate on integer vectors. /** For each element of input vector, the corresponding bits of the result item are set * if the input item is zero. * * @param[in] a Input vector whose zero bits define which corresponding bits in result will be set. * * @returns Output vector with bits set when corresponding bit in @p a is zero. */ inline int16 asymm_mask_if_zero(int16 a) { const int16 all_zeros = 0; const int16 all_ones = ~0; return select(all_zeros, all_ones, a == 0); } /** For each element of input vector, the corresponding bits of the result item are set * if the input item is non-zero. * * @param[in] a Input vector whose non-zero bits define which corresponding bits in result will be set. * * @returns Output vector with bits set when corresponding bit in @p a is non zero. */ inline int16 asymm_mask_if_non_zero(int16 a) { const int16 all_zeros = 0; const int16 all_ones = ~0; return select(all_zeros, all_ones, a != 0); } /** Each bit of the result is set to the corresponding bit of either then_val or * else_val depending on whether the corresponding bit of if_mask is set. * Equivalent to the VBSL instruction in ARM NEON. * * @param[in] if_mask Mask defines will bit be taken from @p then_val or @p else_val depending on corresponding bit in mask is set or not. * @param[in] then_val Value whose bit will be used for result when corresponding bit in @p if_mask is set. * @param[in] else_val Value whose bit will be used for result when corresponding bit in @p if_mask is not set. * * @returns Result contaning bits from @p then_val or from @p else_val depending on corresponding bit in @p if_mask is set or not. */ inline int16 asymm_select_using_mask(int16 if_mask, int16 then_val, int16 else_val) { return (if_mask & then_val) ^ (~if_mask & else_val); } /** Correctly rounded to nearest division by a power of two. * Also known as a rounding arithmetic right shift. * * @param[in] x Value needed to be divided by power of two. * @param[in] exponent Power of two, must be positive number. * * @return Arithmetic right shift. */ inline int16 asymm_rounding_divide_by_pow2(int16 x, int exponent) { int16 mask = (1 << exponent) - 1; const int16 zero = 0; const int16 one = 1; int16 threshold = (mask >> 1) + select(zero, one, x < 0); return (x >> exponent) + select(zero, one, (x & mask) > threshold); } /** Calculates the product of a integer value by a power of two, with either a positive exponent * (equivalent to an arithmetic left shift, saturating) or a negative exponent * (equivalent to an arithmetic right shift, rounding to nearest). * * @param[in] x Value needed to be multiplied or divided by power of two depending on sign of @p exponent. * @param[in] exponent Power of two, can be positive or negative number. * * @return Arithmetic left or right shift. */ inline int16 asymm_saturating_rounding_mult_by_pow2(int16 x, int exponent) { if(exponent < 0) { return asymm_rounding_divide_by_pow2(x, -exponent); } const int16 min = INT_MIN; const int16 max = INT_MAX; int threshold = ((1 << (31 - exponent)) - 1); int16 positive_mask = asymm_mask_if_non_zero(x > threshold); int16 negative_mask = asymm_mask_if_non_zero(x < -threshold); int16 result = x << exponent; result = asymm_select_using_mask(positive_mask, max, result); result = asymm_select_using_mask(negative_mask, min, result); return result; } /** Calculates (a+b)/2, rounded to the nearest integer. * Equivalent to VRHADD in the ARM NEON instruction set. * * @param[in] a First term of half-sum. * @param[in] b Second term of half-sum. * * @return (a+b)/2, rounded to the nearest integer. */ inline int16 asymm_rounding_half_sum(int16 a, int16 b) { long16 a64 = convert_long16(a); long16 b64 = convert_long16(b); long16 sum = a64 + b64; const long16 one = 1; const long16 minus_one = -1; long16 sign = select(minus_one, one, sum >= 0); return convert_int16((sum + sign) / 2); } /** Product of two numbers, interpreting them as fixed-point values in the interval [-1, 1), * rounding to the nearest value, and saturating -1 * -1 to the maximum value. * This is equivalent to the VQRDMULH instruction in ARM NEON. * * @param[in] a First term of product. * @param[in] b Second term of product. * * @return Product of two numbers. */ inline int16 asymm_saturating_rounding_doubling_high_mul(int16 a, int16 b) { int16 overflow = (a == b) && (a == INT_MIN); long16 a_64 = convert_long16(a); long16 b_64 = convert_long16(b); long16 ab_64 = a_64 * b_64; long16 mask1 = 1 << 30; long16 mask2 = 1 - (1 << 30); long16 nudge = select(mask2, mask1, ab_64 >= 0); long16 mask = 1ll << 31; int16 ab_x2_high32 = convert_int16((ab_64 + nudge) / mask); return select(ab_x2_high32, INT_MAX, overflow); } /** Fixed-point multiplication. * * @param[in] a Argument 1 in fixed-point format Q(a). * @param[in] b Argument 2 in fixed-point format Q(b). * * @return Result in fixed-point format Q(a+b). */ inline int16 asymm_mult(int16 a, int16 b) { return asymm_saturating_rounding_doubling_high_mul(a, b); } /** Calculates \f$ exp(x) \f$ for x in [-1/4, 0). * * @param[in] a Argument in fixed-point format Q0. * * @return Result in fixed-point format Q0. */ inline int16 asymm_exp_on_interval_between_negative_one_quarter_and_0_excl(int16 a) { const int16 constant_term = 1895147668; const int16 constant_1_over_3 = 715827883; const int k_fractional_bits = 31; int16 x = a + (1 << (k_fractional_bits - 3)); int16 x2 = asymm_mult(x, x); int16 x3 = asymm_mult(x2, x); int16 x4 = asymm_mult(x2, x2); int16 x4_over_4 = asymm_rounding_divide_by_pow2(x4, 2); int16 x4_over_24_plus_x3_over_6_plus_x2 = asymm_mult((x4_over_4 + x3), constant_1_over_3) + x2; int16 x4_over_24_plus_x3_over_6_plus_x2_over_2 = asymm_rounding_divide_by_pow2(x4_over_24_plus_x3_over_6_plus_x2, 1); return constant_term + asymm_mult(constant_term, x + x4_over_24_plus_x3_over_6_plus_x2_over_2); } /** Calculates \f$ exp(x) \f$ for x < 0. * * @param[in] a Argument in fixed-point format Q(k_integer_bits). * @param[in] k_integer_bits Number of integer bit in argument. * * @return Result in fixed-point format Q0. */ inline int16 asymm_exp_on_negative_values(int16 a, int k_integer_bits) { const int k_fractional_bits = 31 - k_integer_bits; int16 k_one_quarter = 1 << (k_fractional_bits - 2); int16 mask = k_one_quarter - 1; int16 a_mod_quarter_minus_one_quarter = (a & mask) - k_one_quarter; int16 a_mod_quarter_minus_one_quarter_scaled = a_mod_quarter_minus_one_quarter << k_integer_bits; int16 result = asymm_exp_on_interval_between_negative_one_quarter_and_0_excl(a_mod_quarter_minus_one_quarter_scaled); int16 remainder = a_mod_quarter_minus_one_quarter - a; #define EXP_BARREL_SHIFTER(Exponent, FixedPointMultiplier) \ if(k_integer_bits > Exponent) \ { \ const int k_shift_amount = k_integer_bits > Exponent ? k_fractional_bits + Exponent : 0; \ result = asymm_select_using_mask( \ asymm_mask_if_non_zero(remainder & (1 << k_shift_amount)), \ asymm_mult(result, FixedPointMultiplier), result); \ } EXP_BARREL_SHIFTER(-2, 1672461947); EXP_BARREL_SHIFTER(-1, 1302514674); EXP_BARREL_SHIFTER(+0, 790015084); EXP_BARREL_SHIFTER(+1, 290630308); EXP_BARREL_SHIFTER(+2, 39332535); EXP_BARREL_SHIFTER(+3, 720401); EXP_BARREL_SHIFTER(+4, 242); #undef EXP_BARREL_SHIFTER if(k_integer_bits > 5) { const int16 clamp = -(1 << (k_fractional_bits + 5)); result = asymm_select_using_mask(asymm_mask_if_non_zero(a < clamp), 0, result); } const int16 Q0_one = INT_MAX; return asymm_select_using_mask(asymm_mask_if_zero(a), Q0_one, result); } /** Calculates \f$ 1 / (1 + x) \f$ for x in (0, 1). * * @param[in] a Argument in fixed-point format Q0. * * @return Result in fixed-point format Q0. */ inline int16 asymm_one_over_one_plus_x_for_x_in_0_1(int16 a) { const int16 Q0_one = INT_MAX; const int16 Q2_one = 1 << (31 - 2); int16 half_denominator = asymm_rounding_half_sum(a, Q0_one); const int16 Q2_48_over_17 = 1515870810; const int16 Q2_neg_32_over_17 = -1010580540; int16 x = Q2_48_over_17 + asymm_mult(half_denominator, Q2_neg_32_over_17); for(int i = 0; i < 3; i++) { int16 half_denominator_times_x = asymm_mult(half_denominator, x); int16 one_minus_half_denominator_times_x = Q2_one - half_denominator_times_x; int16 tmp = asymm_mult(x, one_minus_half_denominator_times_x); x = x + asymm_saturating_rounding_mult_by_pow2(tmp, 2); } return asymm_saturating_rounding_mult_by_pow2(x, 1); } /** Considering the integer value as fixed-point, change the number of integer bits and update value accordingly. * * @param[in] value Value to be rescaled. * @param[in] src_integer_bits Old number of integer bits. * @param[in] dst_integer_bits New number of integer bits. * * @return Rescaled value. */ inline int16 asymm_rescale(int16 value, int src_integer_bits, int dst_integer_bits) { int exponent = src_integer_bits - dst_integer_bits; return asymm_saturating_rounding_mult_by_pow2(value, exponent); } #endif // ARM_COMPUTE_ASYMM_HELPER_H