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Diffstat (limited to 'src/core/CL/cl_kernels/asymm_helper.h')
| -rw-r--r-- | src/core/CL/cl_kernels/asymm_helper.h | 278 |
1 files changed, 278 insertions, 0 deletions
diff --git a/src/core/CL/cl_kernels/asymm_helper.h b/src/core/CL/cl_kernels/asymm_helper.h new file mode 100644 index 0000000000..10169a98ab --- /dev/null +++ b/src/core/CL/cl_kernels/asymm_helper.h @@ -0,0 +1,278 @@ +/* + * 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 |