| /* |
| * 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_TEST_VALIDATION_FIXEDPOINT_H__ |
| #define __ARM_COMPUTE_TEST_VALIDATION_FIXEDPOINT_H__ |
| |
| #include "support/ToolchainSupport.h" |
| #include "tests/Utils.h" |
| |
| #include <cassert> |
| #include <cstdint> |
| #include <cstdlib> |
| #include <limits> |
| #include <string> |
| #include <type_traits> |
| |
| namespace arm_compute |
| { |
| namespace test |
| { |
| namespace fixed_point_arithmetic |
| { |
| namespace detail |
| { |
| // Forward declare structs |
| struct functions; |
| template <typename T> |
| struct constant_expr; |
| } |
| |
| /** Fixed point traits */ |
| namespace traits |
| { |
| // Promote types |
| // *INDENT-OFF* |
| // clang-format off |
| template <typename T> struct promote { }; |
| template <> struct promote<uint8_t> { using type = uint16_t; }; |
| template <> struct promote<int8_t> { using type = int16_t; }; |
| template <> struct promote<uint16_t> { using type = uint32_t; }; |
| template <> struct promote<int16_t> { using type = int32_t; }; |
| template <> struct promote<uint32_t> { using type = uint64_t; }; |
| template <> struct promote<int32_t> { using type = int64_t; }; |
| template <> struct promote<uint64_t> { using type = uint64_t; }; |
| template <> struct promote<int64_t> { using type = int64_t; }; |
| template <typename T> |
| using promote_t = typename promote<T>::type; |
| // clang-format on |
| // *INDENT-ON* |
| } |
| |
| /** Strongly typed enum class representing the overflow policy */ |
| enum class OverflowPolicy |
| { |
| WRAP, /**< Wrap policy */ |
| SATURATE /**< Saturate policy */ |
| }; |
| /** Strongly typed enum class representing the rounding policy */ |
| enum class RoundingPolicy |
| { |
| TO_ZERO, /**< Round to zero policy */ |
| TO_NEAREST_EVEN /**< Round to nearest even policy */ |
| }; |
| |
| /** Arbitrary fixed-point arithmetic class */ |
| template <typename T> |
| class fixed_point |
| { |
| public: |
| // Static Checks |
| static_assert(std::is_integral<T>::value, "Type is not an integer"); |
| |
| /** Constructor (from different fixed point type) |
| * |
| * @param[in] val Fixed point |
| * @param[in] p Fixed point precision |
| */ |
| template <typename U> |
| fixed_point(fixed_point<U> val, uint8_t p) |
| : _value(0), _fixed_point_position(p) |
| { |
| assert(p > 0 && p < std::numeric_limits<T>::digits); |
| T v = 0; |
| |
| if(std::numeric_limits<T>::digits < std::numeric_limits<U>::digits) |
| { |
| val.rescale(p); |
| v = detail::constant_expr<T>::saturate_cast(val.raw()); |
| } |
| else |
| { |
| auto v_cast = static_cast<fixed_point<T>>(val); |
| v_cast.rescale(p); |
| v = v_cast.raw(); |
| } |
| _value = static_cast<T>(v); |
| } |
| /** Constructor (from integer) |
| * |
| * @param[in] val Integer value to be represented as fixed point |
| * @param[in] p Fixed point precision |
| * @param[in] is_raw If true val is a raw fixed point value else an integer |
| */ |
| template <typename U, typename = typename std::enable_if<std::is_integral<U>::value>::type> |
| fixed_point(U val, uint8_t p, bool is_raw = false) |
| : _value(val << p), _fixed_point_position(p) |
| { |
| if(is_raw) |
| { |
| _value = val; |
| } |
| } |
| /** Constructor (from float) |
| * |
| * @param[in] val Float value to be represented as fixed point |
| * @param[in] p Fixed point precision |
| */ |
| fixed_point(float val, uint8_t p) |
| : _value(detail::constant_expr<T>::to_fixed(val, p)), _fixed_point_position(p) |
| { |
| assert(p > 0 && p < std::numeric_limits<T>::digits); |
| } |
| /** Constructor (from float string) |
| * |
| * @param[in] str Float string to be represented as fixed point |
| * @param[in] p Fixed point precision |
| */ |
| fixed_point(std::string str, uint8_t p) |
| : _value(detail::constant_expr<T>::to_fixed(support::cpp11::stof(str), p)), _fixed_point_position(p) |
| { |
| assert(p > 0 && p < std::numeric_limits<T>::digits); |
| } |
| /** Default copy constructor */ |
| fixed_point &operator=(const fixed_point &) = default; |
| /** Default move constructor */ |
| fixed_point &operator=(fixed_point &&) = default; |
| /** Default copy assignment operator */ |
| fixed_point(const fixed_point &) = default; |
| /** Default move assignment operator */ |
| fixed_point(fixed_point &&) = default; |
| |
| /** Float conversion operator |
| * |
| * @return Float representation of fixed point |
| */ |
| operator float() const |
| { |
| return detail::constant_expr<T>::to_float(_value, _fixed_point_position); |
| } |
| /** Integer conversion operator |
| * |
| * @return Integer representation of fixed point |
| */ |
| template <typename U, typename = typename std::enable_if<std::is_integral<T>::value>::type> |
| operator U() const |
| { |
| return detail::constant_expr<T>::to_int(_value, _fixed_point_position); |
| } |
| /** Convert to different fixed point of different type but same precision |
| * |
| * @note Down-conversion might fail. |
| */ |
| template <typename U> |
| operator fixed_point<U>() |
| { |
| U val = static_cast<U>(_value); |
| if(std::numeric_limits<U>::digits < std::numeric_limits<T>::digits) |
| { |
| val = detail::constant_expr<U>::saturate_cast(_value); |
| } |
| return fixed_point<U>(val, _fixed_point_position, true); |
| } |
| |
| /** Arithmetic += assignment operator |
| * |
| * @param[in] rhs Fixed point operand |
| * |
| * @return Reference to this fixed point |
| */ |
| template <typename U> |
| fixed_point<T> &operator+=(const fixed_point<U> &rhs) |
| { |
| fixed_point<T> val(rhs, _fixed_point_position); |
| _value += val.raw(); |
| return *this; |
| } |
| /** Arithmetic -= assignment operator |
| * |
| * @param[in] rhs Fixed point operand |
| * |
| * @return Reference to this fixed point |
| */ |
| template <typename U> |
| fixed_point<T> &operator-=(const fixed_point<U> &rhs) |
| { |
| fixed_point<T> val(rhs, _fixed_point_position); |
| _value -= val.raw(); |
| return *this; |
| } |
| |
| /** Raw value accessor |
| * |
| * @return Raw fixed point value |
| */ |
| T raw() const |
| { |
| return _value; |
| } |
| /** Precision accessor |
| * |
| * @return Precision of fixed point |
| */ |
| uint8_t precision() const |
| { |
| return _fixed_point_position; |
| } |
| /** Rescale a fixed point to a new precision |
| * |
| * @param[in] p New fixed point precision |
| */ |
| void rescale(uint8_t p) |
| { |
| assert(p > 0 && p < std::numeric_limits<T>::digits); |
| |
| using promoted_T = typename traits::promote<T>::type; |
| promoted_T val = _value; |
| if(p > _fixed_point_position) |
| { |
| val <<= (p - _fixed_point_position); |
| } |
| else if(p < _fixed_point_position) |
| { |
| uint8_t pbar = _fixed_point_position - p; |
| val += (pbar != 0) ? (1 << (pbar - 1)) : 0; |
| val >>= pbar; |
| } |
| |
| _value = detail::constant_expr<T>::saturate_cast(val); |
| _fixed_point_position = p; |
| } |
| |
| private: |
| T _value; /**< Fixed point raw value */ |
| uint8_t _fixed_point_position; /**< Fixed point precision */ |
| }; |
| |
| namespace detail |
| { |
| /** Count the number of leading zero bits in the given value. |
| * |
| * @param[in] value Input value. |
| * |
| * @return Number of leading zero bits. |
| */ |
| template <typename T> |
| constexpr int clz(T value) |
| { |
| using unsigned_T = typename std::make_unsigned<T>::type; |
| // __builtin_clz is available for int. Need to correct reported number to |
| // match the original type. |
| return __builtin_clz(value) - (32 - std::numeric_limits<unsigned_T>::digits); |
| } |
| |
| template <typename T> |
| struct constant_expr |
| { |
| /** Calculate representation of 1 in fixed point given a fixed point precision |
| * |
| * @param[in] p Fixed point precision |
| * |
| * @return Representation of value 1 in fixed point. |
| */ |
| static constexpr T fixed_one(uint8_t p) |
| { |
| return (1 << p); |
| } |
| /** Calculate fixed point precision step given a fixed point precision |
| * |
| * @param[in] p Fixed point precision |
| * |
| * @return Fixed point precision step |
| */ |
| static constexpr float fixed_step(uint8_t p) |
| { |
| return (1.0f / static_cast<float>(1 << p)); |
| } |
| |
| /** Convert a fixed point value to float given its precision. |
| * |
| * @param[in] val Fixed point value |
| * @param[in] p Fixed point precision |
| * |
| * @return Float representation of the fixed point number |
| */ |
| static constexpr float to_float(T val, uint8_t p) |
| { |
| return static_cast<float>(val * fixed_step(p)); |
| } |
| /** Convert a fixed point value to integer given its precision. |
| * |
| * @param[in] val Fixed point value |
| * @param[in] p Fixed point precision |
| * |
| * @return Integer of the fixed point number |
| */ |
| static constexpr T to_int(T val, uint8_t p) |
| { |
| return val >> p; |
| } |
| /** Convert a single precision floating point value to a fixed point representation given its precision. |
| * |
| * @param[in] val Floating point value |
| * @param[in] p Fixed point precision |
| * |
| * @return The raw fixed point representation |
| */ |
| static constexpr T to_fixed(float val, uint8_t p) |
| { |
| return static_cast<T>(saturate_cast<float>(val * fixed_one(p) + ((val >= 0) ? 0.5 : -0.5))); |
| } |
| /** Clamp value between two ranges |
| * |
| * @param[in] val Value to clamp |
| * @param[in] min Minimum value to clamp to |
| * @param[in] max Maximum value to clamp to |
| * |
| * @return clamped value |
| */ |
| static constexpr T clamp(T val, T min, T max) |
| { |
| return std::min(std::max(val, min), max); |
| } |
| /** Saturate given number |
| * |
| * @param[in] val Value to saturate |
| * |
| * @return Saturated value |
| */ |
| template <typename U> |
| static constexpr T saturate_cast(U val) |
| { |
| return static_cast<T>(std::min<U>(std::max<U>(val, static_cast<U>(std::numeric_limits<T>::min())), static_cast<U>(std::numeric_limits<T>::max()))); |
| } |
| }; |
| struct functions |
| { |
| /** Output stream operator |
| * |
| * @param[in] s Output stream |
| * @param[in] x Fixed point value |
| * |
| * @return Reference output to updated stream |
| */ |
| template <typename T, typename U, typename traits> |
| static std::basic_ostream<T, traits> &write(std::basic_ostream<T, traits> &s, fixed_point<U> &x) |
| { |
| return s << static_cast<float>(x); |
| } |
| /** Signbit of a fixed point number. |
| * |
| * @param[in] x Fixed point number |
| * |
| * @return True if negative else false. |
| */ |
| template <typename T> |
| static bool signbit(fixed_point<T> x) |
| { |
| return ((x.raw() >> std::numeric_limits<T>::digits) != 0); |
| } |
| /** Checks if two fixed point numbers are equal |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed points are equal else false |
| */ |
| template <typename T> |
| static bool isequal(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| return (x.raw() == y.raw()); |
| } |
| /** Checks if two fixed point number are not equal |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed points are not equal else false |
| */ |
| template <typename T> |
| static bool isnotequal(fixed_point<T> x, fixed_point<T> y) |
| { |
| return !isequal(x, y); |
| } |
| /** Checks if one fixed point is greater than the other |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed point is greater than other |
| */ |
| template <typename T> |
| static bool isgreater(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| return (x.raw() > y.raw()); |
| } |
| /** Checks if one fixed point is greater or equal than the other |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed point is greater or equal than other |
| */ |
| template <typename T> |
| static bool isgreaterequal(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| return (x.raw() >= y.raw()); |
| } |
| /** Checks if one fixed point is less than the other |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed point is less than other |
| */ |
| template <typename T> |
| static bool isless(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| return (x.raw() < y.raw()); |
| } |
| /** Checks if one fixed point is less or equal than the other |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed point is less or equal than other |
| */ |
| template <typename T> |
| static bool islessequal(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| return (x.raw() <= y.raw()); |
| } |
| /** Checks if one fixed point is less or greater than the other |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return True if fixed point is less or greater than other |
| */ |
| template <typename T> |
| static bool islessgreater(fixed_point<T> x, fixed_point<T> y) |
| { |
| return isnotequal(x, y); |
| } |
| /** Clamp fixed point to specific range. |
| * |
| * @param[in] x Fixed point operand |
| * @param[in] min Minimum value to clamp to |
| * @param[in] max Maximum value to clamp to |
| * |
| * @return Clamped result |
| */ |
| template <typename T> |
| static fixed_point<T> clamp(fixed_point<T> x, T min, T max) |
| { |
| return fixed_point<T>(constant_expr<T>::clamp(x.raw(), min, max), x.precision(), true); |
| } |
| /** Negate number |
| * |
| * @param[in] x Fixed point operand |
| * |
| * @return Negated fixed point result |
| */ |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| static fixed_point<T> negate(fixed_point<T> x) |
| { |
| using promoted_T = typename traits::promote<T>::type; |
| promoted_T val = -x.raw(); |
| if(OP == OverflowPolicy::SATURATE) |
| { |
| val = constant_expr<T>::saturate_cast(val); |
| } |
| return fixed_point<T>(static_cast<T>(val), x.precision(), true); |
| } |
| /** Perform addition among two fixed point numbers |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return Result fixed point with precision equal to minimum precision of both operands |
| */ |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| static fixed_point<T> add(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| if(OP == OverflowPolicy::SATURATE) |
| { |
| using type = typename traits::promote<T>::type; |
| type val = static_cast<type>(x.raw()) + static_cast<type>(y.raw()); |
| val = constant_expr<T>::saturate_cast(val); |
| return fixed_point<T>(static_cast<T>(val), p, true); |
| } |
| else |
| { |
| return fixed_point<T>(x.raw() + y.raw(), p, true); |
| } |
| } |
| /** Perform subtraction among two fixed point numbers |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return Result fixed point with precision equal to minimum precision of both operands |
| */ |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| static fixed_point<T> sub(fixed_point<T> x, fixed_point<T> y) |
| { |
| uint8_t p = std::min(x.precision(), y.precision()); |
| x.rescale(p); |
| y.rescale(p); |
| if(OP == OverflowPolicy::SATURATE) |
| { |
| using type = typename traits::promote<T>::type; |
| type val = static_cast<type>(x.raw()) - static_cast<type>(y.raw()); |
| val = constant_expr<T>::saturate_cast(val); |
| return fixed_point<T>(static_cast<T>(val), p, true); |
| } |
| else |
| { |
| return fixed_point<T>(x.raw() - y.raw(), p, true); |
| } |
| } |
| /** Perform multiplication among two fixed point numbers |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return Result fixed point with precision equal to minimum precision of both operands |
| */ |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| static fixed_point<T> mul(fixed_point<T> x, fixed_point<T> y) |
| { |
| using promoted_T = typename traits::promote<T>::type; |
| uint8_t p_min = std::min(x.precision(), y.precision()); |
| uint8_t p_max = std::max(x.precision(), y.precision()); |
| promoted_T round_factor = (1 << (p_max - 1)); |
| promoted_T val = ((static_cast<promoted_T>(x.raw()) * static_cast<promoted_T>(y.raw())) + round_factor) >> p_max; |
| if(OP == OverflowPolicy::SATURATE) |
| { |
| val = constant_expr<T>::saturate_cast(val); |
| } |
| return fixed_point<T>(static_cast<T>(val), p_min, true); |
| } |
| /** Perform division among two fixed point numbers |
| * |
| * @param[in] x First fixed point operand |
| * @param[in] y Second fixed point operand |
| * |
| * @return Result fixed point with precision equal to minimum precision of both operands |
| */ |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| static fixed_point<T> div(fixed_point<T> x, fixed_point<T> y) |
| { |
| using promoted_T = typename traits::promote<T>::type; |
| uint8_t p = std::min(x.precision(), y.precision()); |
| promoted_T denom = static_cast<promoted_T>(y.raw()); |
| if(denom != 0) |
| { |
| promoted_T val = (static_cast<promoted_T>(x.raw()) << std::max(x.precision(), y.precision())) / denom; |
| if(OP == OverflowPolicy::SATURATE) |
| { |
| val = constant_expr<T>::saturate_cast(val); |
| } |
| return fixed_point<T>(static_cast<T>(val), p, true); |
| } |
| else |
| { |
| T val = (x.raw() < 0) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max(); |
| return fixed_point<T>(val, p, true); |
| } |
| } |
| /** Shift left |
| * |
| * @param[in] x Fixed point operand |
| * @param[in] shift Shift value |
| * |
| * @return Shifted value |
| */ |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| static fixed_point<T> shift_left(fixed_point<T> x, size_t shift) |
| { |
| using promoted_T = typename traits::promote<T>::type; |
| promoted_T val = static_cast<promoted_T>(x.raw()) << shift; |
| if(OP == OverflowPolicy::SATURATE) |
| { |
| val = constant_expr<T>::saturate_cast(val); |
| } |
| return fixed_point<T>(static_cast<T>(val), x.precision(), true); |
| } |
| /** Shift right |
| * |
| * @param[in] x Fixed point operand |
| * @param[in] shift Shift value |
| * |
| * @return Shifted value |
| */ |
| template <typename T> |
| static fixed_point<T> shift_right(fixed_point<T> x, size_t shift) |
| { |
| return fixed_point<T>(x.raw() >> shift, x.precision(), true); |
| } |
| /** Calculate absolute value |
| * |
| * @param[in] x Fixed point operand |
| * |
| * @return Absolute value of operand |
| */ |
| template <typename T> |
| static fixed_point<T> abs(fixed_point<T> x) |
| { |
| using promoted_T = typename traits::promote<T>::type; |
| T val = (x.raw() < 0) ? constant_expr<T>::saturate_cast(-static_cast<promoted_T>(x.raw())) : x.raw(); |
| return fixed_point<T>(val, x.precision(), true); |
| } |
| /** Calculate the logarithm of a fixed point number |
| * |
| * @param[in] x Fixed point operand |
| * |
| * @return Logarithm value of operand |
| */ |
| template <typename T> |
| static fixed_point<T> log(fixed_point<T> x) |
| { |
| uint8_t p = x.precision(); |
| auto const_one = fixed_point<T>(static_cast<T>(1), p); |
| |
| // Logarithm of 1 is zero and logarithm of negative values is not defined in R, so return 0. |
| // Also, log(x) == -log(1/x) for 0 < x < 1. |
| if(isequal(x, const_one) || islessequal(x, fixed_point<T>(static_cast<T>(0), p))) |
| { |
| return fixed_point<T>(static_cast<T>(0), p, true); |
| } |
| else if(isless(x, const_one)) |
| { |
| return mul(log(div(const_one, x)), fixed_point<T>(-1, p)); |
| } |
| |
| // Remove even powers of 2 |
| T shift_val = 31 - __builtin_clz(x.raw() >> p); |
| x = shift_right(x, shift_val); |
| x = sub(x, const_one); |
| |
| // Constants |
| auto ln2 = fixed_point<T>(0.6931471, p); |
| auto A = fixed_point<T>(1.4384189, p); |
| auto B = fixed_point<T>(-0.67719, p); |
| auto C = fixed_point<T>(0.3218538, p); |
| auto D = fixed_point<T>(-0.0832229, p); |
| |
| // Polynomial expansion |
| auto sum = add(mul(x, D), C); |
| sum = add(mul(x, sum), B); |
| sum = add(mul(x, sum), A); |
| sum = mul(x, sum); |
| |
| return mul(add(sum, fixed_point<T>(static_cast<T>(shift_val), p)), ln2); |
| } |
| /** Calculate the exponential of a fixed point number. |
| * |
| * exp(x) = exp(floor(x)) * exp(x - floor(x)) |
| * = pow(2, floor(x) / ln(2)) * exp(x - floor(x)) |
| * = exp(x - floor(x)) << (floor(x) / ln(2)) |
| * |
| * @param[in] x Fixed point operand |
| * |
| * @return Exponential value of operand |
| */ |
| template <typename T> |
| static fixed_point<T> exp(fixed_point<T> x) |
| { |
| uint8_t p = x.precision(); |
| // Constants |
| auto const_one = fixed_point<T>(1, p); |
| auto ln2 = fixed_point<T>(0.6931471, p); |
| auto inv_ln2 = fixed_point<T>(1.442695, p); |
| auto A = fixed_point<T>(0.9978546, p); |
| auto B = fixed_point<T>(0.4994721, p); |
| auto C = fixed_point<T>(0.1763723, p); |
| auto D = fixed_point<T>(0.0435108, p); |
| |
| T scaled_int_part = detail::constant_expr<T>::to_int(mul(x, inv_ln2).raw(), p); |
| |
| // Polynomial expansion |
| auto frac_part = sub(x, mul(ln2, fixed_point<T>(scaled_int_part, p))); |
| auto taylor = add(mul(frac_part, D), C); |
| taylor = add(mul(frac_part, taylor), B); |
| taylor = add(mul(frac_part, taylor), A); |
| taylor = mul(frac_part, taylor); |
| taylor = add(taylor, const_one); |
| |
| // Saturate value |
| if(static_cast<T>(clz(taylor.raw())) <= scaled_int_part) |
| { |
| return fixed_point<T>(std::numeric_limits<T>::max(), p, true); |
| } |
| |
| return (scaled_int_part < 0) ? shift_right(taylor, -scaled_int_part) : shift_left(taylor, scaled_int_part); |
| } |
| /** Calculate the inverse square root of a fixed point number |
| * |
| * @param[in] x Fixed point operand |
| * |
| * @return Inverse square root value of operand |
| */ |
| template <typename T> |
| static fixed_point<T> inv_sqrt(fixed_point<T> x) |
| { |
| const uint8_t p = x.precision(); |
| int8_t shift = std::numeric_limits<T>::digits - (p + detail::clz(x.raw())); |
| |
| shift += std::numeric_limits<T>::is_signed ? 1 : 0; |
| |
| // Use volatile to restrict compiler optimizations on shift as compiler reports maybe-uninitialized error on Android |
| volatile int8_t *shift_ptr = &shift; |
| |
| auto const_three = fixed_point<T>(3, p); |
| auto a = (*shift_ptr < 0) ? shift_left(x, -(shift)) : shift_right(x, shift); |
| fixed_point<T> x2 = a; |
| |
| // We need three iterations to find the result for QS8 and five for QS16 |
| constexpr int num_iterations = std::is_same<T, int8_t>::value ? 3 : 5; |
| for(int i = 0; i < num_iterations; ++i) |
| { |
| fixed_point<T> three_minus_dx = sub(const_three, mul(a, mul(x2, x2))); |
| x2 = shift_right(mul(x2, three_minus_dx), 1); |
| } |
| |
| return (shift < 0) ? shift_left(x2, (-shift) >> 1) : shift_right(x2, shift >> 1); |
| } |
| /** Calculate the hyperbolic tangent of a fixed point number |
| * |
| * @param[in] x Fixed point operand |
| * |
| * @return Hyperbolic tangent of the operand |
| */ |
| template <typename T> |
| static fixed_point<T> tanh(fixed_point<T> x) |
| { |
| uint8_t p = x.precision(); |
| // Constants |
| auto const_one = fixed_point<T>(1, p); |
| auto const_two = fixed_point<T>(2, p); |
| |
| auto exp2x = exp(const_two * x); |
| auto num = exp2x - const_one; |
| auto den = exp2x + const_one; |
| auto tanh = num / den; |
| |
| return tanh; |
| } |
| /** Calculate the a-th power of a fixed point number. |
| * |
| * The power is computed as x^a = e^(log(x) * a) |
| * |
| * @param[in] x Fixed point operand |
| * @param[in] a Fixed point exponent |
| * |
| * @return a-th power of the operand |
| */ |
| template <typename T> |
| static fixed_point<T> pow(fixed_point<T> x, fixed_point<T> a) |
| { |
| return exp(log(x) * a); |
| } |
| }; |
| |
| template <typename T> |
| bool operator==(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return functions::isequal(lhs, rhs); |
| } |
| template <typename T> |
| bool operator!=(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return !operator==(lhs, rhs); |
| } |
| template <typename T> |
| bool operator<(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return functions::isless(lhs, rhs); |
| } |
| template <typename T> |
| bool operator>(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return operator<(rhs, lhs); |
| } |
| template <typename T> |
| bool operator<=(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return !operator>(lhs, rhs); |
| } |
| template <typename T> |
| bool operator>=(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return !operator<(lhs, rhs); |
| } |
| template <typename T> |
| fixed_point<T> operator+(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return functions::add(lhs, rhs); |
| } |
| template <typename T> |
| fixed_point<T> operator-(const fixed_point<T> &lhs, const fixed_point<T> &rhs) |
| { |
| return functions::sub(lhs, rhs); |
| } |
| template <typename T> |
| fixed_point<T> operator-(const fixed_point<T> &rhs) |
| { |
| return functions::negate(rhs); |
| } |
| template <typename T> |
| fixed_point<T> operator*(fixed_point<T> x, fixed_point<T> y) |
| { |
| return functions::mul(x, y); |
| } |
| template <typename T> |
| fixed_point<T> operator/(fixed_point<T> x, fixed_point<T> y) |
| { |
| return functions::div(x, y); |
| } |
| template <typename T> |
| fixed_point<T> operator>>(fixed_point<T> x, size_t shift) |
| { |
| return functions::shift_right(x, shift); |
| } |
| template <typename T> |
| fixed_point<T> operator<<(fixed_point<T> x, size_t shift) |
| { |
| return functions::shift_left(x, shift); |
| } |
| template <typename T, typename U, typename traits> |
| std::basic_ostream<T, traits> &operator<<(std::basic_ostream<T, traits> &s, fixed_point<U> x) |
| { |
| return functions::write(s, x); |
| } |
| template <typename T> |
| inline fixed_point<T> min(fixed_point<T> x, fixed_point<T> y) |
| { |
| return x > y ? y : x; |
| } |
| template <typename T> |
| inline fixed_point<T> max(fixed_point<T> x, fixed_point<T> y) |
| { |
| return x > y ? x : y; |
| } |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| inline fixed_point<T> add(fixed_point<T> x, fixed_point<T> y) |
| { |
| return functions::add<OP>(x, y); |
| } |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| inline fixed_point<T> sub(fixed_point<T> x, fixed_point<T> y) |
| { |
| return functions::sub<OP>(x, y); |
| } |
| template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T> |
| inline fixed_point<T> mul(fixed_point<T> x, fixed_point<T> y) |
| { |
| return functions::mul<OP>(x, y); |
| } |
| template <typename T> |
| inline fixed_point<T> div(fixed_point<T> x, fixed_point<T> y) |
| { |
| return functions::div(x, y); |
| } |
| template <typename T> |
| inline fixed_point<T> abs(fixed_point<T> x) |
| { |
| return functions::abs(x); |
| } |
| template <typename T> |
| inline fixed_point<T> clamp(fixed_point<T> x, T min, T max) |
| { |
| return functions::clamp(x, min, max); |
| } |
| template <typename T> |
| inline fixed_point<T> exp(fixed_point<T> x) |
| { |
| return functions::exp(x); |
| } |
| template <typename T> |
| inline fixed_point<T> log(fixed_point<T> x) |
| { |
| return functions::log(x); |
| } |
| template <typename T> |
| inline fixed_point<T> inv_sqrt(fixed_point<T> x) |
| { |
| return functions::inv_sqrt(x); |
| } |
| template <typename T> |
| inline fixed_point<T> tanh(fixed_point<T> x) |
| { |
| return functions::tanh(x); |
| } |
| template <typename T> |
| inline fixed_point<T> pow(fixed_point<T> x, fixed_point<T> a) |
| { |
| return functions::pow(x, a); |
| } |
| } // namespace detail |
| |
| // Expose operators |
| using detail::operator==; |
| using detail::operator!=; |
| using detail::operator<; |
| using detail::operator>; |
| using detail::operator<=; |
| using detail::operator>=; |
| using detail::operator+; |
| using detail::operator-; |
| using detail::operator*; |
| using detail::operator/; |
| using detail::operator>>; |
| using detail::operator<<; |
| |
| // Expose additional functions |
| using detail::min; |
| using detail::max; |
| using detail::add; |
| using detail::sub; |
| using detail::mul; |
| using detail::div; |
| using detail::abs; |
| using detail::clamp; |
| using detail::exp; |
| using detail::log; |
| using detail::inv_sqrt; |
| using detail::tanh; |
| using detail::pow; |
| } // namespace fixed_point_arithmetic |
| } // namespace test |
| } // namespace arm_compute |
| #endif /*__ARM_COMPUTE_TEST_VALIDATION_FIXEDPOINT_H__ */ |
