mirror of
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653 lines
20 KiB
C++
653 lines
20 KiB
C++
// SPDX-FileCopyrightText: 2015 Evan Teran
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// SPDX-License-Identifier: MIT
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// From: https://github.com/eteran/cpp-utilities/blob/master/fixed/include/cpp-utilities/fixed.h
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// See also: http://stackoverflow.com/questions/79677/whats-the-best-way-to-do-fixed-point-math
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#pragma once
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#include <cstddef> // for size_t
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#include <cstdint>
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#include <exception>
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#include <ostream>
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#include <type_traits>
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#include <common/concepts.h>
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namespace Common {
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template <size_t I, size_t F>
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class FixedPoint;
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namespace detail {
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// helper templates to make magic with types :)
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// these allow us to determine reasonable types from
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// a desired size, they also let us infer the next largest type
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// from a type which is nice for the division op
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template <size_t T>
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struct type_from_size {
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using value_type = void;
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using unsigned_type = void;
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using signed_type = void;
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static constexpr bool is_specialized = false;
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};
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#if defined(__GNUC__) && defined(__x86_64__) && !defined(__STRICT_ANSI__)
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template <>
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struct type_from_size<128> {
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static constexpr bool is_specialized = true;
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static constexpr size_t size = 128;
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using value_type = __int128;
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using unsigned_type = unsigned __int128;
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using signed_type = __int128;
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using next_size = type_from_size<256>;
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};
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#endif
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template <>
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struct type_from_size<64> {
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static constexpr bool is_specialized = true;
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static constexpr size_t size = 64;
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using value_type = int64_t;
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using unsigned_type = std::make_unsigned_t<value_type>;
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using signed_type = std::make_signed_t<value_type>;
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using next_size = type_from_size<128>;
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};
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template <>
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struct type_from_size<32> {
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static constexpr bool is_specialized = true;
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static constexpr size_t size = 32;
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using value_type = int32_t;
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using unsigned_type = std::make_unsigned_t<value_type>;
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using signed_type = std::make_signed_t<value_type>;
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using next_size = type_from_size<64>;
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};
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template <>
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struct type_from_size<16> {
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static constexpr bool is_specialized = true;
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static constexpr size_t size = 16;
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using value_type = int16_t;
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using unsigned_type = std::make_unsigned_t<value_type>;
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using signed_type = std::make_signed_t<value_type>;
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using next_size = type_from_size<32>;
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};
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template <>
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struct type_from_size<8> {
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static constexpr bool is_specialized = true;
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static constexpr size_t size = 8;
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using value_type = int8_t;
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using unsigned_type = std::make_unsigned_t<value_type>;
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using signed_type = std::make_signed_t<value_type>;
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using next_size = type_from_size<16>;
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};
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// this is to assist in adding support for non-native base
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// types (for adding big-int support), this should be fine
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// unless your bit-int class doesn't nicely support casting
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template <class B, class N>
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constexpr B next_to_base(N rhs) {
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return static_cast<B>(rhs);
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}
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struct divide_by_zero : std::exception {};
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template <size_t I, size_t F>
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constexpr FixedPoint<I, F> divide(
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FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
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std::enable_if_t<type_from_size<I + F>::next_size::is_specialized>* = nullptr) {
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using next_type = typename FixedPoint<I, F>::next_type;
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using base_type = typename FixedPoint<I, F>::base_type;
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constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
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next_type t(numerator.to_raw());
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t <<= fractional_bits;
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FixedPoint<I, F> quotient;
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quotient = FixedPoint<I, F>::from_base(next_to_base<base_type>(t / denominator.to_raw()));
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remainder = FixedPoint<I, F>::from_base(next_to_base<base_type>(t % denominator.to_raw()));
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return quotient;
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}
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template <size_t I, size_t F>
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constexpr FixedPoint<I, F> divide(
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FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
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std::enable_if_t<!type_from_size<I + F>::next_size::is_specialized>* = nullptr) {
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using unsigned_type = typename FixedPoint<I, F>::unsigned_type;
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constexpr int bits = FixedPoint<I, F>::total_bits;
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if (denominator == 0) {
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throw divide_by_zero();
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} else {
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int sign = 0;
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FixedPoint<I, F> quotient;
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if (numerator < 0) {
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sign ^= 1;
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numerator = -numerator;
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}
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if (denominator < 0) {
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sign ^= 1;
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denominator = -denominator;
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}
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unsigned_type n = numerator.to_raw();
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unsigned_type d = denominator.to_raw();
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unsigned_type x = 1;
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unsigned_type answer = 0;
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// egyptian division algorithm
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while ((n >= d) && (((d >> (bits - 1)) & 1) == 0)) {
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x <<= 1;
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d <<= 1;
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}
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while (x != 0) {
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if (n >= d) {
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n -= d;
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answer += x;
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}
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x >>= 1;
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d >>= 1;
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}
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unsigned_type l1 = n;
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unsigned_type l2 = denominator.to_raw();
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// calculate the lower bits (needs to be unsigned)
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while (l1 >> (bits - F) > 0) {
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l1 >>= 1;
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l2 >>= 1;
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}
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const unsigned_type lo = (l1 << F) / l2;
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quotient = FixedPoint<I, F>::from_base((answer << F) | lo);
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remainder = n;
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if (sign) {
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quotient = -quotient;
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}
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return quotient;
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}
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}
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// this is the usual implementation of multiplication
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template <size_t I, size_t F>
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constexpr FixedPoint<I, F> multiply(
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FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
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std::enable_if_t<type_from_size<I + F>::next_size::is_specialized>* = nullptr) {
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using next_type = typename FixedPoint<I, F>::next_type;
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using base_type = typename FixedPoint<I, F>::base_type;
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constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
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next_type t(static_cast<next_type>(lhs.to_raw()) * static_cast<next_type>(rhs.to_raw()));
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t >>= fractional_bits;
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return FixedPoint<I, F>::from_base(next_to_base<base_type>(t));
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}
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// this is the fall back version we use when we don't have a next size
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// it is slightly slower, but is more robust since it doesn't
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// require and upgraded type
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template <size_t I, size_t F>
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constexpr FixedPoint<I, F> multiply(
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FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
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std::enable_if_t<!type_from_size<I + F>::next_size::is_specialized>* = nullptr) {
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using base_type = typename FixedPoint<I, F>::base_type;
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constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
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constexpr base_type integer_mask = FixedPoint<I, F>::integer_mask;
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constexpr base_type fractional_mask = FixedPoint<I, F>::fractional_mask;
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// more costly but doesn't need a larger type
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const base_type a_hi = (lhs.to_raw() & integer_mask) >> fractional_bits;
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const base_type b_hi = (rhs.to_raw() & integer_mask) >> fractional_bits;
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const base_type a_lo = (lhs.to_raw() & fractional_mask);
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const base_type b_lo = (rhs.to_raw() & fractional_mask);
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const base_type x1 = a_hi * b_hi;
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const base_type x2 = a_hi * b_lo;
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const base_type x3 = a_lo * b_hi;
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const base_type x4 = a_lo * b_lo;
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return FixedPoint<I, F>::from_base((x1 << fractional_bits) + (x3 + x2) +
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(x4 >> fractional_bits));
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}
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} // namespace detail
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template <size_t I, size_t F>
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class FixedPoint {
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static_assert(detail::type_from_size<I + F>::is_specialized, "invalid combination of sizes");
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public:
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static constexpr size_t fractional_bits = F;
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static constexpr size_t integer_bits = I;
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static constexpr size_t total_bits = I + F;
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using base_type_info = detail::type_from_size<total_bits>;
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using base_type = typename base_type_info::value_type;
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using next_type = typename base_type_info::next_size::value_type;
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using unsigned_type = typename base_type_info::unsigned_type;
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public:
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#ifdef __GNUC__
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#pragma GCC diagnostic push
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#pragma GCC diagnostic ignored "-Woverflow"
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#endif
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static constexpr base_type fractional_mask =
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~(static_cast<unsigned_type>(~base_type(0)) << fractional_bits);
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static constexpr base_type integer_mask = ~fractional_mask;
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#ifdef __GNUC__
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#pragma GCC diagnostic pop
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#endif
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public:
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static constexpr base_type one = base_type(1) << fractional_bits;
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public: // constructors
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constexpr FixedPoint() = default;
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constexpr FixedPoint(const FixedPoint&) = default;
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constexpr FixedPoint& operator=(const FixedPoint&) = default;
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constexpr FixedPoint(FixedPoint&&) noexcept = default;
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constexpr FixedPoint& operator=(FixedPoint&&) noexcept = default;
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template <IsArithmetic Number>
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constexpr FixedPoint(Number n) : data_(static_cast<base_type>(n * one)) {}
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public: // conversion
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template <size_t I2, size_t F2>
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constexpr explicit FixedPoint(FixedPoint<I2, F2> other) {
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static_assert(I2 <= I && F2 <= F, "Scaling conversion can only upgrade types");
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using T = FixedPoint<I2, F2>;
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const base_type fractional = (other.data_ & T::fractional_mask);
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const base_type integer = (other.data_ & T::integer_mask) >> T::fractional_bits;
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data_ =
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(integer << fractional_bits) | (fractional << (fractional_bits - T::fractional_bits));
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}
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private:
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// this makes it simpler to create a FixedPoint point object from
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// a native type without scaling
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// use "FixedPoint::from_base" in order to perform this.
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struct NoScale {};
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constexpr FixedPoint(base_type n, const NoScale&) : data_(n) {}
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public:
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static constexpr FixedPoint from_base(base_type n) {
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return FixedPoint(n, NoScale());
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}
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public: // comparison operators
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friend constexpr auto operator<=>(FixedPoint lhs, FixedPoint rhs) = default;
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public: // unary operators
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[[nodiscard]] constexpr bool operator!() const {
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return !data_;
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}
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[[nodiscard]] constexpr FixedPoint operator~() const {
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// NOTE(eteran): this will often appear to "just negate" the value
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// that is not an error, it is because -x == (~x+1)
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// and that "+1" is adding an infinitesimally small fraction to the
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// complimented value
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return FixedPoint::from_base(~data_);
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}
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[[nodiscard]] constexpr FixedPoint operator-() const {
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return FixedPoint::from_base(-data_);
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}
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[[nodiscard]] constexpr FixedPoint operator+() const {
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return FixedPoint::from_base(+data_);
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}
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constexpr FixedPoint& operator++() {
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data_ += one;
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return *this;
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}
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constexpr FixedPoint& operator--() {
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data_ -= one;
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return *this;
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}
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constexpr FixedPoint operator++(int) {
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FixedPoint tmp(*this);
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data_ += one;
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return tmp;
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}
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constexpr FixedPoint operator--(int) {
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FixedPoint tmp(*this);
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data_ -= one;
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return tmp;
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}
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public: // basic math operators
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constexpr FixedPoint& operator+=(FixedPoint n) {
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data_ += n.data_;
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return *this;
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}
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constexpr FixedPoint& operator-=(FixedPoint n) {
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data_ -= n.data_;
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return *this;
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}
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constexpr FixedPoint& operator*=(FixedPoint n) {
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return assign(detail::multiply(*this, n));
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}
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constexpr FixedPoint& operator/=(FixedPoint n) {
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FixedPoint temp;
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return assign(detail::divide(*this, n, temp));
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}
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private:
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constexpr FixedPoint& assign(FixedPoint rhs) {
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data_ = rhs.data_;
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return *this;
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}
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public: // binary math operators, effects underlying bit pattern since these
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// don't really typically make sense for non-integer values
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constexpr FixedPoint& operator&=(FixedPoint n) {
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data_ &= n.data_;
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return *this;
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}
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constexpr FixedPoint& operator|=(FixedPoint n) {
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data_ |= n.data_;
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return *this;
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}
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constexpr FixedPoint& operator^=(FixedPoint n) {
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data_ ^= n.data_;
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return *this;
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}
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template <IsIntegral Integer>
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constexpr FixedPoint& operator>>=(Integer n) {
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data_ >>= n;
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return *this;
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}
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template <IsIntegral Integer>
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constexpr FixedPoint& operator<<=(Integer n) {
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data_ <<= n;
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return *this;
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}
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public: // conversion to basic types
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constexpr void round_up() {
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data_ += (data_ & fractional_mask) >> 1;
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}
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[[nodiscard]] constexpr int to_int() {
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round_up();
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return static_cast<int>((data_ & integer_mask) >> fractional_bits);
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}
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[[nodiscard]] constexpr unsigned int to_uint() {
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round_up();
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return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
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}
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[[nodiscard]] constexpr int64_t to_long() {
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round_up();
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return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
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}
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[[nodiscard]] constexpr int to_int_floor() const {
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return static_cast<int>((data_ & integer_mask) >> fractional_bits);
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}
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[[nodiscard]] constexpr int64_t to_long_floor() const {
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return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
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}
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[[nodiscard]] constexpr unsigned int to_uint_floor() const {
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return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
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}
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[[nodiscard]] constexpr float to_float() const {
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return static_cast<float>(data_) / FixedPoint::one;
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}
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[[nodiscard]] constexpr double to_double() const {
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return static_cast<double>(data_) / FixedPoint::one;
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}
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[[nodiscard]] constexpr base_type to_raw() const {
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return data_;
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}
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constexpr void clear_int() {
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data_ &= fractional_mask;
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}
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[[nodiscard]] constexpr base_type get_frac() const {
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return data_ & fractional_mask;
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}
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public:
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constexpr void swap(FixedPoint& rhs) noexcept {
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using std::swap;
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swap(data_, rhs.data_);
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}
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public:
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base_type data_{};
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};
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// if we have the same fractional portion, but differing integer portions, we trivially upgrade the
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// smaller type
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template <size_t I1, size_t I2, size_t F>
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constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator+(
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FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
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using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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const T l = T::from_base(lhs.to_raw());
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const T r = T::from_base(rhs.to_raw());
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return l + r;
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}
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template <size_t I1, size_t I2, size_t F>
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constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator-(
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FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
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using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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const T l = T::from_base(lhs.to_raw());
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const T r = T::from_base(rhs.to_raw());
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return l - r;
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}
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template <size_t I1, size_t I2, size_t F>
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constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator*(
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FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
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using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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const T l = T::from_base(lhs.to_raw());
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const T r = T::from_base(rhs.to_raw());
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return l * r;
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}
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template <size_t I1, size_t I2, size_t F>
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constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator/(
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FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
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using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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const T l = T::from_base(lhs.to_raw());
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const T r = T::from_base(rhs.to_raw());
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return l / r;
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}
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template <size_t I, size_t F>
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std::ostream& operator<<(std::ostream& os, FixedPoint<I, F> f) {
|
|
os << f.to_double();
|
|
return os;
|
|
}
|
|
|
|
// basic math operators
|
|
template <size_t I, size_t F>
|
|
constexpr FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
|
|
lhs += rhs;
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F>
|
|
constexpr FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
|
|
lhs -= rhs;
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F>
|
|
constexpr FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
|
|
lhs *= rhs;
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F>
|
|
constexpr FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
|
|
lhs /= rhs;
|
|
return lhs;
|
|
}
|
|
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, Number rhs) {
|
|
lhs += FixedPoint<I, F>(rhs);
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, Number rhs) {
|
|
lhs -= FixedPoint<I, F>(rhs);
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, Number rhs) {
|
|
lhs *= FixedPoint<I, F>(rhs);
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, Number rhs) {
|
|
lhs /= FixedPoint<I, F>(rhs);
|
|
return lhs;
|
|
}
|
|
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator+(Number lhs, FixedPoint<I, F> rhs) {
|
|
FixedPoint<I, F> tmp(lhs);
|
|
tmp += rhs;
|
|
return tmp;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator-(Number lhs, FixedPoint<I, F> rhs) {
|
|
FixedPoint<I, F> tmp(lhs);
|
|
tmp -= rhs;
|
|
return tmp;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator*(Number lhs, FixedPoint<I, F> rhs) {
|
|
FixedPoint<I, F> tmp(lhs);
|
|
tmp *= rhs;
|
|
return tmp;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr FixedPoint<I, F> operator/(Number lhs, FixedPoint<I, F> rhs) {
|
|
FixedPoint<I, F> tmp(lhs);
|
|
tmp /= rhs;
|
|
return tmp;
|
|
}
|
|
|
|
// shift operators
|
|
template <size_t I, size_t F, IsIntegral Integer>
|
|
constexpr FixedPoint<I, F> operator<<(FixedPoint<I, F> lhs, Integer rhs) {
|
|
lhs <<= rhs;
|
|
return lhs;
|
|
}
|
|
template <size_t I, size_t F, IsIntegral Integer>
|
|
constexpr FixedPoint<I, F> operator>>(FixedPoint<I, F> lhs, Integer rhs) {
|
|
lhs >>= rhs;
|
|
return lhs;
|
|
}
|
|
|
|
// comparison operators
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator>(FixedPoint<I, F> lhs, Number rhs) {
|
|
return lhs > FixedPoint<I, F>(rhs);
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator<(FixedPoint<I, F> lhs, Number rhs) {
|
|
return lhs < FixedPoint<I, F>(rhs);
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator>=(FixedPoint<I, F> lhs, Number rhs) {
|
|
return lhs >= FixedPoint<I, F>(rhs);
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator<=(FixedPoint<I, F> lhs, Number rhs) {
|
|
return lhs <= FixedPoint<I, F>(rhs);
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator==(FixedPoint<I, F> lhs, Number rhs) {
|
|
return lhs == FixedPoint<I, F>(rhs);
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator!=(FixedPoint<I, F> lhs, Number rhs) {
|
|
return lhs != FixedPoint<I, F>(rhs);
|
|
}
|
|
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator>(Number lhs, FixedPoint<I, F> rhs) {
|
|
return FixedPoint<I, F>(lhs) > rhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator<(Number lhs, FixedPoint<I, F> rhs) {
|
|
return FixedPoint<I, F>(lhs) < rhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator>=(Number lhs, FixedPoint<I, F> rhs) {
|
|
return FixedPoint<I, F>(lhs) >= rhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator<=(Number lhs, FixedPoint<I, F> rhs) {
|
|
return FixedPoint<I, F>(lhs) <= rhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator==(Number lhs, FixedPoint<I, F> rhs) {
|
|
return FixedPoint<I, F>(lhs) == rhs;
|
|
}
|
|
template <size_t I, size_t F, IsArithmetic Number>
|
|
constexpr bool operator!=(Number lhs, FixedPoint<I, F> rhs) {
|
|
return FixedPoint<I, F>(lhs) != rhs;
|
|
}
|
|
|
|
} // namespace Common
|