1 files changed, 726 insertions, 0 deletions

diff --git a/src/common/fixed_point.h b/src/common/fixed_point.h
new file mode 100644
index 000000000..1d45e51b3
--- /dev/null
+++ b/src/common/fixed_point.h
@@ -0,0 +1,726 @@
+// From: https://github.com/eteran/cpp-utilities/blob/master/fixed/include/cpp-utilities/fixed.h
+// See also: http://stackoverflow.com/questions/79677/whats-the-best-way-to-do-fixed-point-math
+/*
+ * The MIT License (MIT)
+ *
+ * Copyright (c) 2015 Evan Teran
+ *
+ * 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 FIXED_H_
+#define FIXED_H_
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR14 constexpr
+#else
+#define CONSTEXPR14
+#endif
+
+#include <cstddef> // for size_t
+#include <cstdint>
+#include <exception>
+#include <ostream>
+#include <type_traits>
+
+namespace Common {
+
+template <size_t I, size_t F>
+class FixedPoint;
+
+namespace detail {
+
+// helper templates to make magic with types :)
+// these allow us to determine resonable types from
+// a desired size, they also let us infer the next largest type
+// from a type which is nice for the division op
+template <size_t T>
+struct type_from_size {
+    using value_type = void;
+    using unsigned_type = void;
+    using signed_type = void;
+    static constexpr bool is_specialized = false;
+};
+
+#if defined(__GNUC__) && defined(__x86_64__) && !defined(__STRICT_ANSI__)
+template <>
+struct type_from_size<128> {
+    static constexpr bool is_specialized = true;
+    static constexpr size_t size = 128;
+
+    using value_type = __int128;
+    using unsigned_type = unsigned __int128;
+    using signed_type = __int128;
+    using next_size = type_from_size<256>;
+};
+#endif
+
+template <>
+struct type_from_size<64> {
+    static constexpr bool is_specialized = true;
+    static constexpr size_t size = 64;
+
+    using value_type = int64_t;
+    using unsigned_type = std::make_unsigned<value_type>::type;
+    using signed_type = std::make_signed<value_type>::type;
+    using next_size = type_from_size<128>;
+};
+
+template <>
+struct type_from_size<32> {
+    static constexpr bool is_specialized = true;
+    static constexpr size_t size = 32;
+
+    using value_type = int32_t;
+    using unsigned_type = std::make_unsigned<value_type>::type;
+    using signed_type = std::make_signed<value_type>::type;
+    using next_size = type_from_size<64>;
+};
+
+template <>
+struct type_from_size<16> {
+    static constexpr bool is_specialized = true;
+    static constexpr size_t size = 16;
+
+    using value_type = int16_t;
+    using unsigned_type = std::make_unsigned<value_type>::type;
+    using signed_type = std::make_signed<value_type>::type;
+    using next_size = type_from_size<32>;
+};
+
+template <>
+struct type_from_size<8> {
+    static constexpr bool is_specialized = true;
+    static constexpr size_t size = 8;
+
+    using value_type = int8_t;
+    using unsigned_type = std::make_unsigned<value_type>::type;
+    using signed_type = std::make_signed<value_type>::type;
+    using next_size = type_from_size<16>;
+};
+
+// this is to assist in adding support for non-native base
+// types (for adding big-int support), this should be fine
+// unless your bit-int class doesn't nicely support casting
+template <class B, class N>
+constexpr B next_to_base(N rhs) {
+    return static_cast<B>(rhs);
+}
+
+struct divide_by_zero : std::exception {};
+
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> divide(
+    FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
+    typename std::enable_if<type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
+
+    using next_type = typename FixedPoint<I, F>::next_type;
+    using base_type = typename FixedPoint<I, F>::base_type;
+    constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
+
+    next_type t(numerator.to_raw());
+    t <<= fractional_bits;
+
+    FixedPoint<I, F> quotient;
+
+    quotient = FixedPoint<I, F>::from_base(next_to_base<base_type>(t / denominator.to_raw()));
+    remainder = FixedPoint<I, F>::from_base(next_to_base<base_type>(t % denominator.to_raw()));
+
+    return quotient;
+}
+
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> divide(
+    FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
+    typename std::enable_if<!type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
+
+    using unsigned_type = typename FixedPoint<I, F>::unsigned_type;
+
+    constexpr int bits = FixedPoint<I, F>::total_bits;
+
+    if (denominator == 0) {
+        throw divide_by_zero();
+    } else {
+
+        int sign = 0;
+
+        FixedPoint<I, F> quotient;
+
+        if (numerator < 0) {
+            sign ^= 1;
+            numerator = -numerator;
+        }
+
+        if (denominator < 0) {
+            sign ^= 1;
+            denominator = -denominator;
+        }
+
+        unsigned_type n = numerator.to_raw();
+        unsigned_type d = denominator.to_raw();
+        unsigned_type x = 1;
+        unsigned_type answer = 0;
+
+        // egyptian division algorithm
+        while ((n >= d) && (((d >> (bits - 1)) & 1) == 0)) {
+            x <<= 1;
+            d <<= 1;
+        }
+
+        while (x != 0) {
+            if (n >= d) {
+                n -= d;
+                answer += x;
+            }
+
+            x >>= 1;
+            d >>= 1;
+        }
+
+        unsigned_type l1 = n;
+        unsigned_type l2 = denominator.to_raw();
+
+        // calculate the lower bits (needs to be unsigned)
+        while (l1 >> (bits - F) > 0) {
+            l1 >>= 1;
+            l2 >>= 1;
+        }
+        const unsigned_type lo = (l1 << F) / l2;
+
+        quotient = FixedPoint<I, F>::from_base((answer << F) | lo);
+        remainder = n;
+
+        if (sign) {
+            quotient = -quotient;
+        }
+
+        return quotient;
+    }
+}
+
+// this is the usual implementation of multiplication
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> multiply(
+    FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
+    typename std::enable_if<type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
+
+    using next_type = typename FixedPoint<I, F>::next_type;
+    using base_type = typename FixedPoint<I, F>::base_type;
+
+    constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
+
+    next_type t(static_cast<next_type>(lhs.to_raw()) * static_cast<next_type>(rhs.to_raw()));
+    t >>= fractional_bits;
+
+    return FixedPoint<I, F>::from_base(next_to_base<base_type>(t));
+}
+
+// this is the fall back version we use when we don't have a next size
+// it is slightly slower, but is more robust since it doesn't
+// require and upgraded type
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> multiply(
+    FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
+    typename std::enable_if<!type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
+
+    using base_type = typename FixedPoint<I, F>::base_type;
+
+    constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
+    constexpr base_type integer_mask = FixedPoint<I, F>::integer_mask;
+    constexpr base_type fractional_mask = FixedPoint<I, F>::fractional_mask;
+
+    // more costly but doesn't need a larger type
+    const base_type a_hi = (lhs.to_raw() & integer_mask) >> fractional_bits;
+    const base_type b_hi = (rhs.to_raw() & integer_mask) >> fractional_bits;
+    const base_type a_lo = (lhs.to_raw() & fractional_mask);
+    const base_type b_lo = (rhs.to_raw() & fractional_mask);
+
+    const base_type x1 = a_hi * b_hi;
+    const base_type x2 = a_hi * b_lo;
+    const base_type x3 = a_lo * b_hi;
+    const base_type x4 = a_lo * b_lo;
+
+    return FixedPoint<I, F>::from_base((x1 << fractional_bits) + (x3 + x2) +
+                                       (x4 >> fractional_bits));
+}
+} // namespace detail
+
+template <size_t I, size_t F>
+class FixedPoint {
+    static_assert(detail::type_from_size<I + F>::is_specialized, "invalid combination of sizes");
+
+public:
+    static constexpr size_t fractional_bits = F;
+    static constexpr size_t integer_bits = I;
+    static constexpr size_t total_bits = I + F;
+
+    using base_type_info = detail::type_from_size<total_bits>;
+
+    using base_type = typename base_type_info::value_type;
+    using next_type = typename base_type_info::next_size::value_type;
+    using unsigned_type = typename base_type_info::unsigned_type;
+
+public:
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Woverflow"
+#endif
+    static constexpr base_type fractional_mask =
+        ~(static_cast<unsigned_type>(~base_type(0)) << fractional_bits);
+    static constexpr base_type integer_mask = ~fractional_mask;
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+
+public:
+    static constexpr base_type one = base_type(1) << fractional_bits;
+
+public: // constructors
+    FixedPoint() = default;
+    FixedPoint(const FixedPoint&) = default;
+    FixedPoint(FixedPoint&&) = default;
+    FixedPoint& operator=(const FixedPoint&) = default;
+
+    template <class Number>
+    constexpr FixedPoint(
+        Number n, typename std::enable_if<std::is_arithmetic<Number>::value>::type* = nullptr)
+        : data_(static_cast<base_type>(n * one)) {}
+
+public: // conversion
+    template <size_t I2, size_t F2>
+    CONSTEXPR14 explicit FixedPoint(FixedPoint<I2, F2> other) {
+        static_assert(I2 <= I && F2 <= F, "Scaling conversion can only upgrade types");
+        using T = FixedPoint<I2, F2>;
+
+        const base_type fractional = (other.data_ & T::fractional_mask);
+        const base_type integer = (other.data_ & T::integer_mask) >> T::fractional_bits;
+        data_ =
+            (integer << fractional_bits) | (fractional << (fractional_bits - T::fractional_bits));
+    }
+
+private:
+    // this makes it simpler to create a FixedPoint point object from
+    // a native type without scaling
+    // use "FixedPoint::from_base" in order to perform this.
+    struct NoScale {};
+
+    constexpr FixedPoint(base_type n, const NoScale&) : data_(n) {}
+
+public:
+    static constexpr FixedPoint from_base(base_type n) {
+        return FixedPoint(n, NoScale());
+    }
+
+public: // comparison operators
+    constexpr bool operator==(FixedPoint rhs) const {
+        return data_ == rhs.data_;
+    }
+
+    constexpr bool operator!=(FixedPoint rhs) const {
+        return data_ != rhs.data_;
+    }
+
+    constexpr bool operator<(FixedPoint rhs) const {
+        return data_ < rhs.data_;
+    }
+
+    constexpr bool operator>(FixedPoint rhs) const {
+        return data_ > rhs.data_;
+    }
+
+    constexpr bool operator<=(FixedPoint rhs) const {
+        return data_ <= rhs.data_;
+    }
+
+    constexpr bool operator>=(FixedPoint rhs) const {
+        return data_ >= rhs.data_;
+    }
+
+public: // unary operators
+    constexpr bool operator!() const {
+        return !data_;
+    }
+
+    constexpr FixedPoint operator~() const {
+        // NOTE(eteran): this will often appear to "just negate" the value
+        // that is not an error, it is because -x == (~x+1)
+        // and that "+1" is adding an infinitesimally small fraction to the
+        // complimented value
+        return FixedPoint::from_base(~data_);
+    }
+
+    constexpr FixedPoint operator-() const {
+        return FixedPoint::from_base(-data_);
+    }
+
+    constexpr FixedPoint operator+() const {
+        return FixedPoint::from_base(+data_);
+    }
+
+    CONSTEXPR14 FixedPoint& operator++() {
+        data_ += one;
+        return *this;
+    }
+
+    CONSTEXPR14 FixedPoint& operator--() {
+        data_ -= one;
+        return *this;
+    }
+
+    CONSTEXPR14 FixedPoint operator++(int) {
+        FixedPoint tmp(*this);
+        data_ += one;
+        return tmp;
+    }
+
+    CONSTEXPR14 FixedPoint operator--(int) {
+        FixedPoint tmp(*this);
+        data_ -= one;
+        return tmp;
+    }
+
+public: // basic math operators
+    CONSTEXPR14 FixedPoint& operator+=(FixedPoint n) {
+        data_ += n.data_;
+        return *this;
+    }
+
+    CONSTEXPR14 FixedPoint& operator-=(FixedPoint n) {
+        data_ -= n.data_;
+        return *this;
+    }
+
+    CONSTEXPR14 FixedPoint& operator*=(FixedPoint n) {
+        return assign(detail::multiply(*this, n));
+    }
+
+    CONSTEXPR14 FixedPoint& operator/=(FixedPoint n) {
+        FixedPoint temp;
+        return assign(detail::divide(*this, n, temp));
+    }
+
+private:
+    CONSTEXPR14 FixedPoint& assign(FixedPoint rhs) {
+        data_ = rhs.data_;
+        return *this;
+    }
+
+public: // binary math operators, effects underlying bit pattern since these
+        // don't really typically make sense for non-integer values
+    CONSTEXPR14 FixedPoint& operator&=(FixedPoint n) {
+        data_ &= n.data_;
+        return *this;
+    }
+
+    CONSTEXPR14 FixedPoint& operator|=(FixedPoint n) {
+        data_ |= n.data_;
+        return *this;
+    }
+
+    CONSTEXPR14 FixedPoint& operator^=(FixedPoint n) {
+        data_ ^= n.data_;
+        return *this;
+    }
+
+    template <class Integer,
+              class = typename std::enable_if<std::is_integral<Integer>::value>::type>
+    CONSTEXPR14 FixedPoint& operator>>=(Integer n) {
+        data_ >>= n;
+        return *this;
+    }
+
+    template <class Integer,
+              class = typename std::enable_if<std::is_integral<Integer>::value>::type>
+    CONSTEXPR14 FixedPoint& operator<<=(Integer n) {
+        data_ <<= n;
+        return *this;
+    }
+
+public: // conversion to basic types
+    constexpr void round_up() {
+        data_ += (data_ & fractional_mask) >> 1;
+    }
+
+    constexpr int to_int() {
+        round_up();
+        return static_cast<int>((data_ & integer_mask) >> fractional_bits);
+    }
+
+    constexpr unsigned int to_uint() const {
+        round_up();
+        return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
+    }
+
+    constexpr int64_t to_long() {
+        round_up();
+        return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
+    }
+
+    constexpr int to_int_floor() const {
+        return static_cast<int>((data_ & integer_mask) >> fractional_bits);
+    }
+
+    constexpr int64_t to_long_floor() {
+        return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
+    }
+
+    constexpr unsigned int to_uint_floor() const {
+        return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
+    }
+
+    constexpr float to_float() const {
+        return static_cast<float>(data_) / FixedPoint::one;
+    }
+
+    constexpr double to_double() const {
+        return static_cast<double>(data_) / FixedPoint::one;
+    }
+
+    constexpr base_type to_raw() const {
+        return data_;
+    }
+
+    constexpr void clear_int() {
+        data_ &= fractional_mask;
+    }
+
+    constexpr base_type get_frac() const {
+        return data_ & fractional_mask;
+    }
+
+public:
+    CONSTEXPR14 void swap(FixedPoint& rhs) {
+        using std::swap;
+        swap(data_, rhs.data_);
+    }
+
+public:
+    base_type data_;
+};
+
+// if we have the same fractional portion, but differing integer portions, we trivially upgrade the
+// smaller type
+template <size_t I1, size_t I2, size_t F>
+CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
+operator+(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
+
+    using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
+
+    const T l = T::from_base(lhs.to_raw());
+    const T r = T::from_base(rhs.to_raw());
+    return l + r;
+}
+
+template <size_t I1, size_t I2, size_t F>
+CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
+operator-(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
+
+    using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
+
+    const T l = T::from_base(lhs.to_raw());
+    const T r = T::from_base(rhs.to_raw());
+    return l - r;
+}
+
+template <size_t I1, size_t I2, size_t F>
+CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
+operator*(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
+
+    using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
+
+    const T l = T::from_base(lhs.to_raw());
+    const T r = T::from_base(rhs.to_raw());
+    return l * r;
+}
+
+template <size_t I1, size_t I2, size_t F>
+CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
+operator/(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
+
+    using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
+
+    const T l = T::from_base(lhs.to_raw());
+    const T r = T::from_base(rhs.to_raw());
+    return l / r;
+}
+
+template <size_t I, size_t F>
+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>
+CONSTEXPR14 FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
+    lhs += rhs;
+    return lhs;
+}
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
+    lhs -= rhs;
+    return lhs;
+}
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
+    lhs *= rhs;
+    return lhs;
+}
+template <size_t I, size_t F>
+CONSTEXPR14 FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
+    lhs /= rhs;
+    return lhs;
+}
+
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, Number rhs) {
+    lhs += FixedPoint<I, F>(rhs);
+    return lhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, Number rhs) {
+    lhs -= FixedPoint<I, F>(rhs);
+    return lhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, Number rhs) {
+    lhs *= FixedPoint<I, F>(rhs);
+    return lhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, Number rhs) {
+    lhs /= FixedPoint<I, F>(rhs);
+    return lhs;
+}
+
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 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, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 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, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 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, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+CONSTEXPR14 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, class Integer,
+          class = typename std::enable_if<std::is_integral<Integer>::value>::type>
+CONSTEXPR14 FixedPoint<I, F> operator<<(FixedPoint<I, F> lhs, Integer rhs) {
+    lhs <<= rhs;
+    return lhs;
+}
+template <size_t I, size_t F, class Integer,
+          class = typename std::enable_if<std::is_integral<Integer>::value>::type>
+CONSTEXPR14 FixedPoint<I, F> operator>>(FixedPoint<I, F> lhs, Integer rhs) {
+    lhs >>= rhs;
+    return lhs;
+}
+
+// comparison operators
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator>(FixedPoint<I, F> lhs, Number rhs) {
+    return lhs > FixedPoint<I, F>(rhs);
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator<(FixedPoint<I, F> lhs, Number rhs) {
+    return lhs < FixedPoint<I, F>(rhs);
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator>=(FixedPoint<I, F> lhs, Number rhs) {
+    return lhs >= FixedPoint<I, F>(rhs);
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator<=(FixedPoint<I, F> lhs, Number rhs) {
+    return lhs <= FixedPoint<I, F>(rhs);
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator==(FixedPoint<I, F> lhs, Number rhs) {
+    return lhs == FixedPoint<I, F>(rhs);
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator!=(FixedPoint<I, F> lhs, Number rhs) {
+    return lhs != FixedPoint<I, F>(rhs);
+}
+
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator>(Number lhs, FixedPoint<I, F> rhs) {
+    return FixedPoint<I, F>(lhs) > rhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator<(Number lhs, FixedPoint<I, F> rhs) {
+    return FixedPoint<I, F>(lhs) < rhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator>=(Number lhs, FixedPoint<I, F> rhs) {
+    return FixedPoint<I, F>(lhs) >= rhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator<=(Number lhs, FixedPoint<I, F> rhs) {
+    return FixedPoint<I, F>(lhs) <= rhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator==(Number lhs, FixedPoint<I, F> rhs) {
+    return FixedPoint<I, F>(lhs) == rhs;
+}
+template <size_t I, size_t F, class Number,
+          class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
+constexpr bool operator!=(Number lhs, FixedPoint<I, F> rhs) {
+    return FixedPoint<I, F>(lhs) != rhs;
+}
+
+} // namespace Common
+
+#undef CONSTEXPR14
+
+#endif