/* * 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_FIXED_POINT_H #define ARM_COMPUTE_FIXED_POINT_H #define TYPE_ALIAS(type, alias) \ typedef type alias; \ typedef type alias##x##1; \ typedef type##2 alias##x##2; \ typedef type##3 alias##x##3; \ typedef type##4 alias##x##4; \ typedef type##8 alias##x##8; \ typedef type##16 alias##x##16; TYPE_ALIAS(char, qs8) TYPE_ALIAS(short, qs16) #define qs8_MIN ((char)CHAR_MIN) #define qs8_MAX ((char)CHAR_MAX) #define qs16_MIN ((short)SHRT_MIN) #define qs16_MAX ((short)SHRT_MAX) #define qu8_MIN ((uchar)0) #define qu8_MAX ((uchar)UCHAR_MAX) #define qu16_MIN ((ushort)0) #define qu16_MAX ((ushort)USHRT_MAX) #define qs8_TYPE char #define qs8x1_TYPE char #define qs8x2_TYPE char2 #define qs8x4_TYPE char4 #define qs8x8_TYPE char8 #define qs8x16_TYPE char16 #define qs16_TYPE short #define qs16x1_TYPE short #define qs16x2_TYPE short2 #define qs16x4_TYPE short4 #define qs16x8_TYPE short8 #define qs16x16_TYPE short16 #undef VEC_DATA_TYPE_STR #undef VEC_DATA_TYPE #undef CONVERT_STR #undef CONVERT #undef CONVERT_SAT_STR #undef CONVERT_SAT #define VEC_DATA_TYPE_STR(type, size) type##x##size #define VEC_DATA_TYPE(type, size) VEC_DATA_TYPE_STR(type, size) #define CONVERT_STR3(x, type, rtype) (convert_##rtype((x))) #define CONVERT_STR2(x, type, rtype) CONVERT_STR3(x, type, rtype) #define CONVERT_STR(x, type) CONVERT_STR2(x, type, type##_TYPE) #define CONVERT(x, type) CONVERT_STR(x, type) #define CONVERT_SAT_STR3(x, type, rtype) (convert_##rtype##_sat((x))) #define CONVERT_SAT_STR2(x, type, rtype) CONVERT_SAT_STR3(x, type, rtype) #define CONVERT_SAT_STR(x, type) CONVERT_SAT_STR2(x, type, type##_TYPE) #define CONVERT_SAT(x, type) CONVERT_SAT_STR(x, type) /* Computes max of fixed point types. * * @param[in] type the actual data type. * * @return The result of the fixed point maximum. */ #define MAXQ_IMPL(type) \ inline type max_##type(type VopA, type VopB) \ { \ return max(VopA, VopB); \ } MAXQ_IMPL(qs8x1) MAXQ_IMPL(qs8x2) MAXQ_IMPL(qs8x4) MAXQ_IMPL(qs8x8) MAXQ_IMPL(qs8x16) #define MAX_OP_EXPAND_STR(a, b, type, size) max_##type##x##size((a), (b)) #define MAX_OP_EXPAND(a, b, type, size) MAX_OP_EXPAND_STR(a, b, type, size) /* Computes saturated addition of fixed point types. * * @param[in] type the actual data type. * * @return The result of the fixed point addition. The result is saturated in case of overflow */ #define ADDQ_SAT_IMPL(type) \ inline type add_sat_##type(type VopA, type VopB) \ { \ return add_sat(VopA, VopB); \ } ADDQ_SAT_IMPL(qs8x1) ADDQ_SAT_IMPL(qs8x2) ADDQ_SAT_IMPL(qs8x4) ADDQ_SAT_IMPL(qs8x8) ADDQ_SAT_IMPL(qs8x16) #define ADD_SAT_OP_EXPAND_STR(a, b, type, size) add_sat_##type##x##size((a), (b)) #define ADD_SAT_OP_EXPAND(a, b, type, size) ADD_SAT_OP_EXPAND_STR(a, b, type, size) /* Computes saturated subtraction of fixed point types. * * @param[in] type the actual data type. * * @return The result of the fixed point subtraction. The result is saturated in case of overflow */ #define SUBQ_SAT_IMPL(type) \ inline type sub_sat_##type(type VopA, type VopB) \ { \ return sub_sat(VopA, VopB); \ } SUBQ_SAT_IMPL(qs8x1) SUBQ_SAT_IMPL(qs8x2) SUBQ_SAT_IMPL(qs8x4) SUBQ_SAT_IMPL(qs8x8) SUBQ_SAT_IMPL(qs8x16) #define SUB_SAT_OP_EXPAND_STR(a, b, type, size) sub_sat_##type##x##size((a), (b)) #define SUB_SAT_OP_EXPAND(a, b, type, size) SUB_SAT_OP_EXPAND_STR(a, b, type, size) /* Saturate multiply of two fixed point numbers * * @param[in] type the actual data type. * @param[in] itype the intermediate data type. * * @return The result of the fixed point multiplication. The result is saturated in case of overflow */ #define MULQ_SAT_IMPL(type, itype) \ inline type mul_sat_##type(type VopA, type VopB, int fixed_point_position) \ { \ itype round_val = (itype)(1 << (fixed_point_position - 1)); \ itype res = mad_sat(CONVERT((VopA), itype), CONVERT((VopB), itype), round_val); \ return CONVERT_SAT((res >> (itype)fixed_point_position), type); \ } MULQ_SAT_IMPL(qs8x16, qs16x16) #define MUL_SAT_OP_EXPAND_STR(a, b, type, size, position) mul_sat_##type##x##size((a), (b), (position)) #define MUL_SAT_OP_EXPAND(a, b, type, size, position) MUL_SAT_OP_EXPAND_STR(a, b, type, size, position) /* Saturate multiply-accumulate * * @param[in] type the actual data type. * @param[in] itype the intermediate data type. * * @return The result of the fixed point multiply-accumulate. The result is saturated in case of overflow */ #define MLAQ_SAT_IMPL(type, itype) \ type mla_sat_##type(type VopA, type VopB, type VopC, int fixed_point_position) \ { \ itype res = mad_sat(CONVERT(VopB, itype), CONVERT(VopC, itype), (itype)(1 << (fixed_point_position - 1))); \ return add_sat(VopA, CONVERT_SAT(res >> (itype)fixed_point_position, type)); \ } MLAQ_SAT_IMPL(qs8x8, qs16x8) MLAQ_SAT_IMPL(qs8x16, qs16x16) #define MLA_SAT_OP_EXPAND_STR(a, b, c, type, size, position) mla_sat_##type##x##size((a), (b), (c), (position)) #define MLA_SAT_OP_EXPAND(a, b, c, type, size, position) MLA_SAT_OP_EXPAND_STR(a, b, c, type, size, position) /* Saturate multiply-accumulate long * * @param[in] type the actual data type. * @param[in] itype the intermediate data type. * * @return The result of the fixed point multiply-accumulate long. The result is saturated in case of overflow */ #define MLALQ_SAT_IMPL(type, itype) \ itype mlal_sat_##type(itype VopA, type VopB, type VopC, int fixed_point_position) \ { \ itype res = mad_sat(CONVERT(VopB, itype), CONVERT(VopC, itype), (itype)(1 << (fixed_point_position - 1))); \ return add_sat(VopA, res >> (itype)fixed_point_position); \ } MLALQ_SAT_IMPL(qs8x8, qs16x8) #define MLAL_SAT_OP_EXPAND_STR(a, b, c, type, size, position) mlal_sat_##type##x##size((a), (b), (c), (position)) #define MLAL_SAT_OP_EXPAND(a, b, c, type, size, position) MLAL_SAT_OP_EXPAND_STR(a, b, c, type, size, position) /** Saturate division of two fixed point numbers * * @param[in] stype the actual scalar data type. * @param[in] type the actual data type. * @param[in] itype the intermediate data type. * * @return The result of the fixed point division. The result is saturated in case of overflow */ #define DIVQ_SAT_IMPL(stype, type, itype) \ inline type div_sat_##type(type VopA, type VopB, int fixed_point_position) \ { \ itype conv_a = CONVERT((VopA), itype); \ itype denominator = CONVERT((VopB), itype); \ itype numerator = conv_a << (itype)(fixed_point_position); \ itype res = select(numerator / denominator, select((itype)stype##_MAX, (itype)stype##_MIN, conv_a < (itype)0), denominator == (itype)0); \ return CONVERT_SAT((res), type); \ } DIVQ_SAT_IMPL(qs8, qs8x16, qs16x16) #define DIV_SAT_OP_EXPAND_STR(a, b, type, size, position) div_sat_##type##x##size((a), (b), (position)) #define DIV_SAT_OP_EXPAND(a, b, type, size, position) DIV_SAT_OP_EXPAND_STR(a, b, type, size, position) /** Saturate exponential fixed point 8 bit (16 elements) * * @param[in] a 8 bit fixed point input vector * @param[in] fixed_point_position Fixed point position that expresses the number of bits for the fractional part of the number * * @return The result of the 8 bit fixed point exponential. The result is saturated in case of overflow */ qs8x16 inline exp_qs8x16(qs8x16 a, int fixed_point_position) { // Constants (literal constants are calculated by converting the respective float to the fixed point with the highest supported fixed point position) char16 const_one = (char16)(1 << (fixed_point_position)); char16 ln2 = (char16)(((0x58 >> (6 - fixed_point_position)) + 1) >> 1); // 0.693147 char16 inv_ln2 = ((char16)(((0x38 >> (6 - (fixed_point_position))) + 1) >> 1)) | const_one; // 1.442695 char16 A = (char16)(((0x7F >> (6 - (fixed_point_position))) + 1) >> 1); // 0.9978546 char16 B = (char16)(((0x3F >> (6 - (fixed_point_position))) + 1) >> 1); // 0.4994721 char16 C = (char16)(((0x16 >> (6 - (fixed_point_position))) + 1) >> 1); // 0.1763723 char16 D = (char16)(((0x05 >> (6 - (fixed_point_position))) + 1) >> 1); // 0.0435108 // Perform range reduction [-log(2),log(2)] char16 m = mul_sat_qs8x16(a, inv_ln2, fixed_point_position); // get decimal part of m char16 dec_m = m >> (char16)fixed_point_position; char16 alpha = mul_sat_qs8x16(dec_m << (char16)fixed_point_position, ln2, fixed_point_position); alpha = convert_char16(abs_diff(a, alpha)); // Polynomial expansion char16 sum = add_sat_qs8x16(mul_sat_qs8x16(alpha, D, fixed_point_position), C); sum = add_sat_qs8x16(mul_sat_qs8x16(alpha, sum, fixed_point_position), B); sum = add_sat_qs8x16(mul_sat_qs8x16(alpha, sum, fixed_point_position), A); sum = add_sat_qs8x16(mul_sat_qs8x16(alpha, sum, fixed_point_position), const_one); // Reconstruct and saturate result return select(select(sum << dec_m, sum >> -dec_m, dec_m < (char16)0), (char16)0x7F, clz(sum) <= dec_m); } #define EXP_OP_EXPAND_STR(a, type, size, position) exp_##type##x##size((a), (position)) #define EXP_OP_EXPAND(a, type, size, position) EXP_OP_EXPAND_STR(a, type, size, position) #endif // ARM_COMPUTE_FIXED_POINT_H