clang-tidy: readability-math-missing-parentheses

* XRPLF/develop:
  ci: Check binaries separately from building them (7355)
  ci: [DEPENDABOT] bump eps1lon/actions-label-merge-conflict from 3.0.3 to 3.1.0 (7375)
  refactor: Use `STLedgerEntry` type aliases instead of `std::shared_ptr` (7282)
  fix: Adjust xrpld systemd service and update timer (7374)
  release: Bump version to 3.2.0-rc3 (7371)
  fix: Pin overpayment principal reduction to exact on-grid value (7360)

include/xrpl/basics/Number.h

@@ -3,6 +3,7 @@
 #include <xrpl/beast/utility/instrumentation.h>
 
 #include <array>
+#include <concepts>
 #include <cstdint>
 #include <functional>
 #include <limits>
@@ -13,6 +14,10 @@
 #include <string>
 #include <unordered_map>
 
+#ifdef _MSC_VER
+#include <boost/multiprecision/cpp_int.hpp>
+#endif  // !defined(_MSC_VER)
+
 namespace xrpl {
 
 class Number;
@@ -20,18 +25,39 @@ class Number;
 std::string
 to_string(Number const& amount);
 
+/** Returns a rough estimate of log10(value).
+ *
+ * The return value is a pair (log, rem), where log is the estimated
+ * base-10 logarithm (roughly floor(log10(value))), and rem is value with
+ * all trailing 0s removed (i.e., divided by the largest power of 10 that
+ * evenly divides value). If rem is 1, then value is an exact power of ten, and
+ * log is the exact log10(value).
+ *
+ * This function only works for positive values.
+ */
+template <std::unsigned_integral T>
+constexpr std::pair<int, T>
+logTenEstimate(T value)
+{
+    int log = 0;
+    T remainder = value;
+    while (value >= 10)
+    {
+        if (value % 10 == 0)
+            remainder = remainder / 10;
+        value /= 10;
+        ++log;
+    }
+    return {log, remainder};
+}
+
 template <typename T>
 constexpr std::optional<int>
 logTen(T value)
 {
-    int log = 0;
-    while (value >= 10 && value % 10 == 0)
-    {
-        value /= 10;
-        ++log;
-    }
-    if (value == 1)
-        return log;
+    auto const est = logTenEstimate(value);
+    if (est.second == 1)
+        return est.first;
     return std::nullopt;
 }
 
@@ -86,12 +112,9 @@ static_assert(
 /** MantissaRange defines a range for the mantissa of a normalized Number.
  *
  * The mantissa is in the range [min, max], where
- * * min is a power of 10, and
- * * max = min * 10 - 1.
  *
- * The MantissaScale enum indicates properties of the range: size, and some behavioral
- * options. This intentionally restricts the number of unique MantissaRanges that can
- * be instantiated: one for each scale.
+ * The MantissaScale enum indicates properties of the range: size, and some behavioral options.
+ * This intentionally prevents the creation of any MantissaRanges representing other values.
  *
  * The "Small" scale is based on the behavior of STAmount for IOUs. It has a min
  * value of 10^15, and a max value of 10^16-1. This was sufficient for
@@ -105,12 +128,14 @@ static_assert(
  * "large" scale.
  *
  * The "Large" scales are intended to represent all values that can be represented
- * by an STAmount - IOUs, XRP, and MPTs. It has a min value of 10^18, and a max
- * value of 10^19-1. "LargeLegacy" is like "Large", but preserves
- * a rounding error when a computation results in a mantissa of
- * Number::kMaxRep that needs to be rounded up, but rounds down
- * instead. It will maintain consistent behavior until the fixCleanup3_2_0
- * amendment is enabled.
+ * by an STAmount - IOUs, XRP, and MPTs.
+ *
+ * They have a min value of 2^63/10+1 (truncated), and a max value of 2^63-1.
+ *
+ * "LargeLegacy" is like "Large", but preserves a rounding error when
+ * a computation results in a mantissa of Number::kLargestMantissa that needs to
+ * be rounded up, but rounds down instead. It will maintain consistent
+ * behavior until the fixCleanup3_2_0 amendment is enabled.
  *
  * Note that if the mentioned amendments are eventually retired, this class
  * should be left in place, but the "Small" scale option should be removed. This
@@ -135,12 +160,39 @@ struct MantissaRange final
 
     explicit constexpr MantissaRange(MantissaScale sc) : scale(sc)
     {
+        // Keep the error messages terse. Since this is constexpr, if any of these throw, it won't
+        // compile, so there's no real need to worry about runtime exceptions here.
+        if (min * 10 <= max)
+            throw std::out_of_range("Invalid mantissa range: min * 10 <= max");
+        if (max / 10 >= min)
+            throw std::out_of_range("Invalid mantissa range: max / 10 >= min");
+        if ((min - 1) * 10 > max)
+            throw std::out_of_range("Invalid mantissa range: (min - 1) * 10 > max");
+        // This is a little hacky
+        if ((max + 10) / 10 < min)
+            throw std::out_of_range("Invalid mantissa range: (max + 10) / 10 < min");
+        if (internalMin != kPowerOfTen[log])
+            throw std::out_of_range("Invalid mantissa range: internalMin != kPowersOfTen[log]");
     }
 
+    // Explicitly delete copy and move operations
+    MantissaRange(MantissaRange const&) = delete;
+    MantissaRange(MantissaRange&&) = delete;
+    MantissaRange&
+    operator=(MantissaRange const&) = delete;
+    MantissaRange&
+    operator=(MantissaRange&&) = delete;
+
     MantissaScale const scale;
     int const log{getExponent(scale)};
-    rep const min{getMin(scale, log)};
-    rep const max{(min * 10) - 1};
+    rep const max{getMax(scale, log)};
+    rep const min{computeMin(max)};
+    /* Used to determine if mantissas are in range, but have fewer digits than max.
+     *
+     * Unlike min, internalMin is always an exact power of 10, so a mantissa in the internal
+     * representation will always have a consistent number of digits.
+     */
+    rep const internalMin{getInternalMin(scale, log)};
     CuspRoundingFix const cuspRoundingFixEnabled{isCuspFixEnabled(scale)};
 
     static MantissaRange const&
@@ -169,13 +221,39 @@ private:
         }
     }
 
-    // Keep this function for future use with different ways to compute
-    // the ranges.
     static constexpr rep
-    getMin(MantissaScale scale, int exponent)
+    getMax(MantissaScale scale, int log)
+    {
+        switch (scale)
+        {
+            case MantissaScale::Small:
+                return kPowerOfTen[log + 1] - 1;
+            case MantissaScale::LargeLegacy:
+            case MantissaScale::Large:
+                return std::numeric_limits<std::int64_t>::max();
+            default:
+                // If called in a constexpr context, this throw assures that the build fails if an
+                // invalid scale is used.
+                throw std::runtime_error("Unknown mantissa scale");
+                // LCOV_EXCL_STOP
+        }
+    }
+
+    static constexpr rep
+    computeMin(rep max)
+    {
+        return (max / 10) + 1;
+    }
+
+    static constexpr rep
+    getInternalMin(MantissaScale scale, int exponent)
     {
         if (exponent < 0 || exponent >= kPowerOfTen.size())
+        {
+            // If called in a constexpr context, this throw assures that the build fails if an
+            // invalid exponent is used.
             throw std::runtime_error("Invalid exponent");  // LCOV_EXCL_LINE
+        }
         return kPowerOfTen[exponent];
     }
 
@@ -204,13 +282,26 @@ private:
 template <class T>
 concept Integral64 = std::is_same_v<T, std::int64_t> || std::is_same_v<T, std::uint64_t>;
 
+namespace detail {
+#ifdef _MSC_VER
+using uint128_t = boost::multiprecision::uint128_t;
+using int128_t = boost::multiprecision::int128_t;
+#else   // !defined(_MSC_VER)
+using uint128_t = __uint128_t;
+using int128_t = __int128_t;
+#endif  // !defined(_MSC_VER)
+
+template <class T>
+concept UnsignedMantissa = std::is_unsigned_v<T> || std::is_same_v<T, uint128_t>;
+}  // namespace detail
+
 /** Number is a floating point type that can represent a wide range of values.
  *
  * It can represent all values that can be represented by an STAmount -
  * regardless of asset type - XRPAmount, MPTAmount, and IOUAmount, with at least
  * as much precision as those types require.
  *
- * ---- Internal Representation ----
+ * ---- Internal Operational Representation ----
  *
  * Internally, Number is represented with three values:
  *   1. a bool sign flag,
@@ -219,40 +310,45 @@ concept Integral64 = std::is_same_v<T, std::int64_t> || std::is_same_v<T, std::u
  *
  * The internal mantissa is an unsigned integer in the range defined by the
  * current MantissaRange. The exponent is an integer in the range
- * [minExponent, maxExponent].
+ * [kMinExponent, kMaxExponent].
  *
  * See the description of MantissaRange for more details on the ranges.
  *
  * A non-zero mantissa is (almost) always normalized, meaning it and the
  * exponent are grown or shrunk until the mantissa is in the range
- * [MantissaRange.min, MantissaRange.max].
+ * [MantissaRange.internalMin, MantissaRange.internalMin * 10 - 1].
+ *
+ * This internal representation is only used during some operations to ensure
+ * that the mantissa is a known, predictable size. The class itself stores the
+ * values using the external representation described below.
  *
  * Note:
  *   1. Normalization can be disabled by using the "unchecked" ctor tag. This
  *      should only be used at specific conversion points, some constexpr
  *      values, and in unit tests.
- *   2. The max of the "large" range, 10^19-1, is the largest 10^X-1 value that
- *      fits in an unsigned 64-bit number. (10^19-1 < 2^64-1 and
- *      10^20-1 > 2^64-1). This avoids under- and overflows.
+ *   2. Unlike MantissaRange.min, internalMin is always an exact power of 10,
+ *      so a mantissa in the internal representation will always have a
+ *      consistent number of digits.
+ *   3. The functions toInternal() and fromInternal() are used to convert
+ *      between the two representations.
  *
  * ---- External Interface ----
  *
  * The external interface of Number consists of a std::int64_t mantissa, which
  * is restricted to 63-bits, and an int exponent, which must be in the range
- * [minExponent, maxExponent]. The range of the mantissa depends on which
+ * [kMinExponent, kMaxExponent]. The range of the mantissa depends on which
  * MantissaRange is currently active. For the "short" range, the mantissa will
  * be between 10^15 and 10^16-1. For the "large" range, the mantissa will be
  * between -(2^63-1) and 2^63-1. As noted above, the "large" range is needed to
  * represent the full range of valid XRP and MPT integer values accurately.
  *
  * Note:
- *   1. 2^63-1 is between 10^18 and 10^19-1, which are the limits of the "large"
- *      mantissa range.
+ *   1. The "large" mantissa range is (2^63/10+1) to 2^63-1. 2^63-1 is between
+ *      10^18 and 10^19-1, and (2^63/10+1) is between 10^17 and 10^18-1. Thus,
+ *      the mantissa may have 18 or 19 digits. This value will be modified to
+ *      always have 19 digits before some operations to ensure consistency.
  *   2. The functions mantissa() and exponent() return the external view of the
- *      Number value, specifically using a signed 63-bit mantissa. This may
- *      require altering the internal representation to fit into that range
- *      before the value is returned. The interface guarantees consistency of
- *      the two values.
+ *      Number value, specifically using a signed 63-bit mantissa.
  *   3. Number cannot represent -2^63 (std::numeric_limits<std::int64_t>::min())
  *      as an exact integer, but it doesn't need to, because all asset values
  *      on-ledger are non-negative. This is due to implementation details of
@@ -307,8 +403,7 @@ class Number final
     using rep = std::int64_t;
     using internalrep = MantissaRange::rep;
 
-    bool negative_{false};
-    internalrep mantissa_{0};
+    rep mantissa_{0};
     int exponent_{std::numeric_limits<int>::lowest()};
 
 public:
@@ -316,10 +411,6 @@ public:
     static constexpr int kMinExponent = -32768;
     static constexpr int kMaxExponent = 32768;
 
-    static constexpr internalrep kMaxRep = std::numeric_limits<rep>::max();
-    static_assert(kMaxRep == 9'223'372'036'854'775'807);
-    static_assert(-kMaxRep == std::numeric_limits<rep>::min() + 1);
-
     // May need to make unchecked private
     struct Unchecked
     {
@@ -397,8 +488,7 @@ public:
     friend constexpr bool
     operator==(Number const& x, Number const& y) noexcept
     {
-        return x.negative_ == y.negative_ && x.mantissa_ == y.mantissa_ &&
-            x.exponent_ == y.exponent_;
+        return x.mantissa_ == y.mantissa_ && x.exponent_ == y.exponent_;
     }
 
     friend constexpr bool
@@ -412,8 +502,8 @@ public:
     {
         // If the two amounts have different signs (zero is treated as positive)
         // then the comparison is true iff the left is negative.
-        bool const lneg = x.negative_;
-        bool const rneg = y.negative_;
+        bool const lneg = x.mantissa_ < 0;
+        bool const rneg = y.mantissa_ < 0;
 
         if (lneg != rneg)
             return lneg;
@@ -441,9 +531,11 @@ public:
     [[nodiscard]] constexpr int
     signum() const noexcept
     {
-        if (negative_)
+        if (mantissa_ < 0)
+        {
             return -1;
-        return (mantissa_ != 0u) ? 1 : 0;
+        }
+        return (mantissa_ != 0 ? 1 : 0);
     }
 
     [[nodiscard]] Number
@@ -482,6 +574,9 @@ public:
     friend Number
     root2(Number f);
 
+    friend Number
+    power(Number const& f, unsigned n, unsigned d);
+
     // Thread local rounding control.  Default is to_nearest
     enum class RoundingMode { ToNearest, TowardsZero, Downward, Upward };
 
@@ -535,6 +630,18 @@ public:
     normalizeToRange() const;
 
 private:
+    /** May use ranges that don't fit the restrictions of the "real"
+     * normalizeToRange().
+     *
+     */
+    template <Integral64 T>
+    [[nodiscard]]
+    std::pair<T, int>
+    normalizeToRangeImpl(T minMantissa, T maxMantissa, MantissaRange::CuspRoundingFix fix) const;
+
+    // Number_test needs to use normalizeToRangeImpl
+    friend class Number_test;
+
     static thread_local RoundingMode mode;
     // The available ranges for mantissa
 
@@ -543,6 +650,14 @@ private:
     // changing the values inside the range.
     static thread_local std::reference_wrapper<MantissaRange const> kRange;
 
+    // And one is needed because it needs to choose between oneSmall and
+    // oneLarge based on the current range
+    static Number
+    one(MantissaRange const& range);
+
+    static Number
+    root(MantissaRange const& range, Number f, unsigned d);
+
     void
     normalize(MantissaRange const& range);
 
@@ -573,6 +688,10 @@ private:
         MantissaRange::CuspRoundingFix cuspRoundingFixEnabled,
         bool dropped);
 
+    [[nodiscard]]
+    bool
+    isnormal(MantissaRange const& range) const noexcept;
+
     [[nodiscard]] bool
     isnormal() const noexcept;
 
@@ -582,18 +701,66 @@ private:
     [[nodiscard]] Number
     shiftExponent(int exponentDelta) const;
 
-    // Safely convert rep (int64) mantissa to internalrep (uint64). If the rep
-    // is negative, returns the positive value. This takes a little extra work
-    // because converting std::numeric_limits<std::int64_t>::min() flirts with
-    // UB, and can vary across compilers.
+    // Safely return the absolute value of a rep (int64) mantissa as an internalrep (uint64).
     static internalrep
     externalToInternal(rep mantissa);
 
+    /** Breaks down the number into components, potentially de-normalizing it.
+     *
+     * Ensures that the mantissa always has kRange.log + 1 digits.
+     *
+     */
+    template <detail::UnsignedMantissa Rep = internalrep>
+    std::tuple<bool, Rep, int>
+    toInternal(MantissaRange const& range) const;
+
+    /** Breaks down the number into components, potentially de-normalizing it.
+     *
+     * Ensures that the mantissa always has kRange.log + 1 digits.
+     *
+     */
+    template <detail::UnsignedMantissa Rep = internalrep>
+    std::tuple<bool, Rep, int>
+    toInternal() const;
+
+    /** Rebuilds the number from components.
+     *
+     * If "expectNormal" is true, the values are expected to be normalized - all
+     * in their valid ranges.
+     *
+     * If "expectNormal" is false, the values are expected to be "near
+     * normalized", meaning that the mantissa has to be modified at most once to
+     * bring it back into range.
+     *
+     */
+    template <bool ExpectNormal = true, detail::UnsignedMantissa Rep = internalrep>
+    void
+    fromInternal(bool negative, Rep mantissa, int exponent, MantissaRange const* pRange);
+
+    /** Rebuilds the number from components.
+     *
+     * If "expectNormal" is true, the values are expected to be normalized - all
+     * in their valid ranges.
+     *
+     * If "expectNormal" is false, the values are expected to be "near
+     * normalized", meaning that the mantissa has to be modified at most once to
+     * bring it back into range.
+     *
+     */
+    template <bool ExpectNormal = true, detail::UnsignedMantissa Rep = internalrep>
+    void
+    fromInternal(bool negative, Rep mantissa, int exponent);
+
     class Guard;
+
+public:
+    constexpr static internalrep kLargestMantissa =
+        MantissaRange{MantissaRange::MantissaScale::Large}.max;
 };
 
 constexpr Number::Number(bool negative, internalrep mantissa, int exponent, Unchecked) noexcept
-    : negative_(negative), mantissa_{mantissa}, exponent_{exponent}
+    : mantissa_{negative ? -static_cast<rep>(mantissa) : static_cast<rep>(mantissa)}
+    , exponent_{exponent}
 {
 }
 
@@ -604,12 +771,6 @@ constexpr Number::Number(internalrep mantissa, int exponent, Unchecked) noexcept
 
 static constexpr Number kNumZero{};
 
-inline Number::Number(bool negative, internalrep mantissa, int exponent, Normalized)
-    : Number(negative, mantissa, exponent, Unchecked{})
-{
-    normalize(kRange);
-}
-
 inline Number::Number(internalrep mantissa, int exponent, Normalized)
     : Number(false, mantissa, exponent, Normalized{})
 {
@@ -632,17 +793,7 @@ inline Number::Number(rep mantissa) : Number{mantissa, 0}
 constexpr Number::rep
 Number::mantissa() const noexcept
 {
-    auto m = mantissa_;
-    if (m > kMaxRep)
-    {
-        XRPL_ASSERT_PARTS(
-            !isnormal() || (m % 10 == 0 && m / 10 <= kMaxRep),
-            "xrpl::Number::mantissa",
-            "large normalized mantissa has no remainder");
-        m /= 10;
-    }
-    auto const sign = negative_ ? -1 : 1;
-    return sign * static_cast<Number::rep>(m);
+    return mantissa_;
 }
 
 /** Returns the exponent of the external view of the Number.
@@ -653,16 +804,7 @@ Number::mantissa() const noexcept
 constexpr int
 Number::exponent() const noexcept
 {
-    auto e = exponent_;
-    if (mantissa_ > kMaxRep)
-    {
-        XRPL_ASSERT_PARTS(
-            !isnormal() || (mantissa_ % 10 == 0 && mantissa_ / 10 <= kMaxRep),
-            "xrpl::Number::exponent",
-            "large normalized mantissa has no remainder");
-        ++e;
-    }
-    return e;
+    return exponent_;
 }
 
 constexpr Number
@@ -677,7 +819,7 @@ Number::operator-() const noexcept
     if (mantissa_ == 0)
         return Number{};
     auto x = *this;
-    x.negative_ = !x.negative_;
+    x.mantissa_ = -x.mantissa_;
     return x;
 }
 
@@ -758,23 +900,29 @@ Number::min() noexcept
 inline Number
 Number::max() noexcept
 {
-    return Number{false, std::min(kRange.get().max, kMaxRep), kMaxExponent, Unchecked{}};
+    return Number{false, kRange.get().max, kMaxExponent, Unchecked{}};
 }
 
 inline Number
 Number::lowest() noexcept
 {
-    return Number{true, std::min(kRange.get().max, kMaxRep), kMaxExponent, Unchecked{}};
+    return Number{true, kRange.get().max, kMaxExponent, Unchecked{}};
+}
+
+inline bool
+Number::isnormal(MantissaRange const& range) const noexcept
+{
+    auto const absM = externalToInternal(mantissa_);
+
+    return *this == Number{} ||
+        (range.min <= absM && absM <= range.max &&  //
+         kMinExponent <= exponent_ && exponent_ <= kMaxExponent);
 }
 
 inline bool
 Number::isnormal() const noexcept
 {
-    MantissaRange const& range = kRange;
-    auto const absM = mantissa_;
-    return *this == Number{} ||
-        (range.min <= absM && absM <= range.max && (absM <= kMaxRep || absM % 10 == 0) &&
-         kMinExponent <= exponent_ && exponent_ <= kMaxExponent);
+    return isnormal(kRange);
 }
 
 template <auto MinMantissa, auto MaxMantissa, Integral64 T>
@@ -788,12 +936,28 @@ Number::normalizeToRange() const
     auto constexpr kMAX = static_cast<T>(MaxMantissa);
     static_assert(kMIN > 0);
     static_assert(kMIN % 10 == 0);
-    static_assert(isPowerOfTen(kMIN));
+    static_assert(isPowerOfTen(static_cast<std::make_unsigned_t<T>>(kMIN)));
     static_assert(kMAX % 10 == 9);
     static_assert((kMAX + 1) / 10 == kMIN);
 
-    bool negative = negative_;
-    internalrep mantissa = mantissa_;
+    // Don't need to worry about the cuspRounding fix because rounding up will never take the
+    // mantissa over maxMantissa with a ones digit value other than 0. 0 can safely be truncated.
+    return normalizeToRangeImpl(kMIN, kMAX, MantissaRange::CuspRoundingFix::Disabled);
+}
+
+/** Only intended to be used in tests
+ *
+ * May use ranges that don't fit the restrictions of the "real"
+ * normalizeToRange().
+ *
+ */
+template <Integral64 T>
+[[nodiscard]]
+std::pair<T, int>
+Number::normalizeToRangeImpl(T minMantissa, T maxMantissa, MantissaRange::CuspRoundingFix fix) const
+{
+    bool negative = mantissa_ < 0;
+    internalrep mantissa = externalToInternal(mantissa_);
     int exponent = exponent_;
 
     if constexpr (std::is_unsigned_v<T>)
@@ -802,14 +966,21 @@ Number::normalizeToRange() const
             !negative,
             "xrpl::Number::normalizeToRange",
             "Number is non-negative for unsigned range.");
+        // To avoid logical errors in release builds, throw if the Number is
+        // negative for an unsigned range.
+        if (negative)
+        {
+            throw std::runtime_error(
+                "Number::normalizeToRange: Number is negative for "
+                "unsigned range.");
+        }
     }
-    // Don't need to worry about the cuspRounding fix because rounding up will never take the
-    // mantissa over maxMantissa with a ones digit value other than 0. 0 can safely be truncated.
-    Number::normalize(
-        negative, mantissa, exponent, kMIN, kMAX, MantissaRange::CuspRoundingFix::Disabled);
+    Number::normalize(negative, mantissa, exponent, minMantissa, maxMantissa, fix);
 
-    auto const sign = negative ? -1 : 1;
-    return std::make_pair(static_cast<T>(sign * mantissa), exponent);
+    // Cast mantissa to signed type first (if T is a signed type) to avoid
+    // unsigned integer overflow when multiplying by negative sign
+    T signedMantissa = negative ? -static_cast<T>(mantissa) : static_cast<T>(mantissa);
+    return std::make_pair(signedMantissa, exponent);
 }
 
 constexpr Number

include/xrpl/protocol/Protocol.h

@@ -231,8 +231,8 @@ constexpr std::size_t kMaxPermissionedDomainCredentialsArraySize = 10;
 constexpr std::size_t kMaxMpTokenMetadataLength = 1024;
 
 /** The maximum amount of MPTokenIssuance */
-constexpr std::uint64_t kMaxMpTokenAmount = 0x7FFF'FFFF'FFFF'FFFFull;
-static_assert(Number::kMaxRep >= kMaxMpTokenAmount);
+std::uint64_t constexpr kMaxMpTokenAmount = 0x7FFF'FFFF'FFFF'FFFFull;
+static_assert(Number::kLargestMantissa >= kMaxMpTokenAmount);
 
 /** The maximum length of Data payload */
 constexpr std::size_t kMaxDataPayloadLength = 256;

include/xrpl/protocol/STAmount.h

@@ -559,6 +559,8 @@ STAmount::fromNumber(A const& a, Number const& number)
         return STAmount{asset, intValue, 0, negative};
     }
 
+    XRPL_ASSERT_PARTS(
+        working.signum() >= 0, "xrpl::STAmount::fromNumber", "non-negative Number to normalize");
     auto const [mantissa, exponent] = working.normalizeToRange<kMinValue, kMaxValue>();
 
     return STAmount{asset, mantissa, exponent, negative};

include/xrpl/protocol/SystemParameters.h

@@ -23,7 +23,7 @@ systemName()
 /** Number of drops in the genesis account. */
 constexpr XRPAmount kInitialXrp{100'000'000'000 * kDropsPerXrp};
 static_assert(kInitialXrp.drops() == 100'000'000'000'000'000);
-static_assert(Number::kMaxRep >= kInitialXrp.drops());
+static_assert(Number::kLargestMantissa >= kInitialXrp.drops());
 
 /** Returns true if the amount does not exceed the initial XRP in existence. */
 inline bool

src/libxrpl/basics/Number.cpp

@@ -8,24 +8,22 @@
 #include <cstdint>
 #include <functional>
 #include <iterator>
-#include <limits>
 #include <numeric>
 #include <set>
 #include <stdexcept>
 #include <string>
+#include <string_view>
+#include <tuple>
 #include <type_traits>
 #include <unordered_map>
 #include <utility>
 
 #ifdef _MSC_VER
 #pragma message("Using boost::multiprecision::uint128_t and int128_t")
-#include <boost/multiprecision/cpp_int.hpp>
-using uint128_t = boost::multiprecision::uint128_t;
-using int128_t = boost::multiprecision::int128_t;
-#else   // !defined(_MSC_VER)
-using uint128_t = __uint128_t;
-using int128_t = __int128_t;
-#endif  // !defined(_MSC_VER)
+#endif
+
+using uint128_t = xrpl::detail::uint128_t;
+using int128_t = xrpl::detail::int128_t;
 
 namespace xrpl {
 
@@ -60,33 +58,39 @@ MantissaRange::getRanges()
             [[maybe_unused]]
             constexpr static MantissaRange kRange{MantissaRange::MantissaScale::Small};
             static_assert(isPowerOfTen(kRange.min));
+            static_assert(isPowerOfTen(kRange.internalMin));
             static_assert(kRange.min == 1'000'000'000'000'000LL);
+            static_assert(kRange.internalMin == kRange.min);
             static_assert(kRange.max == 9'999'999'999'999'999LL);
             static_assert(kRange.log == 15);
-            static_assert(kRange.min < Number::kMaxRep);
-            static_assert(kRange.max < Number::kMaxRep);
+            static_assert(kRange.min < Number::kLargestMantissa);
+            static_assert(kRange.max < Number::kLargestMantissa);
             static_assert(kRange.cuspRoundingFixEnabled == CuspRoundingFix::Disabled);
         }
         {
             [[maybe_unused]]
             constexpr static MantissaRange kRange{MantissaRange::MantissaScale::LargeLegacy};
-            static_assert(isPowerOfTen(kRange.min));
-            static_assert(kRange.min == 1'000'000'000'000'000'000ULL);
-            static_assert(kRange.max == rep(9'999'999'999'999'999'999ULL));
+            static_assert(!isPowerOfTen(kRange.min));
+            static_assert(isPowerOfTen(kRange.internalMin));
+            static_assert(kRange.min == 922'337'203'685'477'581ULL);
+            static_assert(kRange.internalMin == 1'000'000'000'000'000'000ULL);
+            static_assert(kRange.max == rep(9'223'372'036'854'775'807ULL));
             static_assert(kRange.log == 18);
-            static_assert(kRange.min < Number::kMaxRep);
-            static_assert(kRange.max > Number::kMaxRep);
+            static_assert(kRange.min < Number::kLargestMantissa);
+            static_assert(kRange.max == Number::kLargestMantissa);
             static_assert(kRange.cuspRoundingFixEnabled == CuspRoundingFix::Disabled);
         }
         {
             [[maybe_unused]]
             constexpr static MantissaRange kRange{MantissaRange::MantissaScale::Large};
-            static_assert(isPowerOfTen(kRange.min));
-            static_assert(kRange.min == 1'000'000'000'000'000'000ULL);
-            static_assert(kRange.max == rep(9'999'999'999'999'999'999ULL));
+            static_assert(!isPowerOfTen(kRange.min));
+            static_assert(isPowerOfTen(kRange.internalMin));
+            static_assert(kRange.min == 922'337'203'685'477'581ULL);
+            static_assert(kRange.internalMin == 1'000'000'000'000'000'000ULL);
+            static_assert(kRange.max == rep(9'223'372'036'854'775'807ULL));
             static_assert(kRange.log == 18);
-            static_assert(kRange.min < Number::kMaxRep);
-            static_assert(kRange.max > Number::kMaxRep);
+            static_assert(kRange.min < Number::kLargestMantissa);
+            static_assert(kRange.max == Number::kLargestMantissa);
             static_assert(kRange.cuspRoundingFixEnabled == CuspRoundingFix::Enabled);
         }
         return map;
@@ -161,9 +165,6 @@ divu10(uint128_t& u)
 // precision to an operation.  This enables the final result
 // to be correctly rounded to the internal precision of Number.
 
-template <class T>
-concept UnsignedMantissa = std::is_unsigned_v<T> || std::is_same_v<T, uint128_t>;
-
 class Number::Guard
 {
     std::uint64_t digits_{0};    // 16 decimal guard digits
@@ -213,7 +214,7 @@ public:
     round() const noexcept;
 
     // Modify the result to the correctly rounded value
-    template <UnsignedMantissa T>
+    template <detail::UnsignedMantissa T>
     void
     doRoundUp(
         bool& negative,
@@ -222,22 +223,22 @@ public:
         internalrep const& minMantissa,
         internalrep const& maxMantissa,
         MantissaRange::CuspRoundingFix cuspRoundingFixEnabled,
-        std::string location);
+        std::string_view location);
 
     // Modify the result to the correctly rounded value
-    template <UnsignedMantissa T>
+    template <detail::UnsignedMantissa T>
     void
     doRoundDown(bool& negative, T& mantissa, int& exponent, internalrep const& minMantissa);
 
     // Modify the result to the correctly rounded value
     void
-    doRound(rep& drops, std::string location) const;
+    doRound(internalrep& drops, std::string_view location) const;
 
 private:
     void
     doPush(unsigned d) noexcept;
 
-    template <UnsignedMantissa T>
+    template <detail::UnsignedMantissa T>
     void
     bringIntoRange(bool& negative, T& mantissa, int& exponent, internalrep const& minMantissa);
 };
@@ -351,7 +352,7 @@ Number::Guard::round() const noexcept
     return 0;
 }
 
-template <UnsignedMantissa T>
+template <detail::UnsignedMantissa T>
 void
 Number::Guard::bringIntoRange(
     bool& negative,
@@ -370,13 +371,11 @@ Number::Guard::bringIntoRange(
     {
         static constexpr Number kZero = Number{};
 
-        negative = kZero.negative_;
-        mantissa = kZero.mantissa_;
-        exponent = kZero.exponent_;
+        std::tie(negative, mantissa, exponent) = kZero.toInternal();
     }
 }
 
-template <UnsignedMantissa T>
+template <detail::UnsignedMantissa T>
 void
 Number::Guard::doRoundUp(
     bool& negative,
@@ -385,13 +384,13 @@ Number::Guard::doRoundUp(
     internalrep const& minMantissa,
     internalrep const& maxMantissa,
     MantissaRange::CuspRoundingFix cuspRoundingFixEnabled,
-    std::string location)
+    std::string_view location)
 {
     auto r = round();
     if (r == 1 || (r == 0 && (mantissa & 1) == 1))
     {
         auto const safeToIncrement = [&maxMantissa](auto const& mantissa) {
-            return mantissa < maxMantissa && mantissa < kMaxRep;
+            return mantissa < maxMantissa && mantissa < kLargestMantissa;
         };
         if (cuspRoundingFixEnabled == MantissaRange::CuspRoundingFix::Enabled)
         {
@@ -407,8 +406,8 @@ Number::Guard::doRoundUp(
                 // Incrementing the mantissa will require dividing, which will require rounding. So
                 // _don't_ increment the mantissa. Instead, divide and round recursively. It should
                 // be impossible to recurse more than once, because once the mantissa is divided by
-                // 10, it will be _well_ under maxMantissa and kMaxRep, so adding 1 will have no
-                // chance of bringing it back over.
+                // 10, it will be _well_ under maxMantissa and kLargestMantissa, so adding 1 will
+                // have no chance of bringing it back over.
                 doDropDigit(mantissa, exponent);
                 XRPL_ASSERT_PARTS(
                     safeToIncrement(mantissa),
@@ -432,7 +431,7 @@ Number::Guard::doRoundUp(
             ++mantissa;
             // Ensure mantissa after incrementing fits within both the
             // min/maxMantissa range and is a valid "rep".
-            if (mantissa > maxMantissa || mantissa > kMaxRep)
+            if (mantissa > maxMantissa || mantissa > kLargestMantissa)
             {
                 // Don't use doDropDigit here
                 mantissa /= 10;
@@ -445,7 +444,7 @@ Number::Guard::doRoundUp(
         Throw<std::overflow_error>(std::string(location));
 }
 
-template <UnsignedMantissa T>
+template <detail::UnsignedMantissa T>
 void
 Number::Guard::doRoundDown(
     bool& negative,
@@ -468,26 +467,25 @@ Number::Guard::doRoundDown(
 
 // Modify the result to the correctly rounded value
 void
-Number::Guard::doRound(rep& drops, std::string location) const
+Number::Guard::doRound(internalrep& drops, std::string_view location) const
 {
     auto r = round();
     if (r == 1 || (r == 0 && (drops & 1) == 1))
     {
-        if (drops >= kMaxRep)
+        auto const& range = kRange.get();
+        if (drops >= range.max)
         {
             static_assert(sizeof(internalrep) == sizeof(rep));
             // This should be impossible, because it's impossible to represent
-            // "kMaxRep + 0.6" in Number, regardless of the scale. There aren't
-            // enough digits available. You'd either get a mantissa of "kMaxRep"
-            // or "(kMaxRep + 1) / 10", neither of which will round up when
+            // "kLargestMantissa + 0.6" in Number, regardless of the scale. There aren't
+            // enough digits available. You'd either get a mantissa of "kLargestMantissa"
+            // or "kLargestMantissa / 10 + 1", neither of which will round up when
             // converting to rep, though the latter might overflow _before_
             // rounding.
             Throw<std::overflow_error>(std::string(location));  // LCOV_EXCL_LINE
         }
         ++drops;
     }
-    if (isNegative())
-        drops = -drops;
 }
 
 // Number
@@ -502,10 +500,6 @@ Number::externalToInternal(rep mantissa)
     // If the mantissa is already positive, just return it
     if (mantissa >= 0)
         return mantissa;
-    // If the mantissa is negative, but fits within the positive range of rep,
-    // return it negated
-    if (mantissa >= -std::numeric_limits<rep>::max())
-        return -mantissa;
 
     // If the mantissa doesn't fit within the positive range, convert to
     // int128_t, negate that, and cast it back down to the internalrep
@@ -515,11 +509,135 @@ Number::externalToInternal(rep mantissa)
     return static_cast<internalrep>(-temp);
 }
 
+/** Breaks down the number into components, potentially de-normalizing it.
+ *
+ * Ensures that the mantissa always has kRange.log + 1 digits.
+ *
+ */
+template <detail::UnsignedMantissa Rep>
+std::tuple<bool, Rep, int>
+Number::toInternal(MantissaRange const& range) const
+{
+    auto exponent = exponent_;
+    bool const negative = mantissa_ < 0;
+    // It should be impossible for mantissa_ to be INT64_MIN, but use externalToInternal just in
+    // case.
+    Rep mantissa = static_cast<Rep>(externalToInternal(mantissa_));
+
+    auto const internalMin = range.internalMin;
+    auto const minMantissa = range.min;
+
+    if (mantissa != 0 && mantissa >= minMantissa && mantissa < internalMin)
+    {
+        // Ensure the mantissa has the correct number of digits
+        mantissa *= 10;
+        --exponent;
+        XRPL_ASSERT_PARTS(
+            mantissa >= internalMin && mantissa < internalMin * 10,
+            "xrpl::Number::toInternal()",
+            "Number is within reference range and has 'log' digits");
+    }
+
+    return {negative, mantissa, exponent};
+}
+
+/** Breaks down the number into components, potentially de-normalizing it.
+ *
+ * Ensures that the mantissa always has exactly kRange.log + 1 digits.
+ *
+ */
+template <detail::UnsignedMantissa Rep>
+std::tuple<bool, Rep, int>
+Number::toInternal() const
+{
+    return toInternal(kRange);
+}
+
+/** Rebuilds the number from components.
+ *
+ * If "expectNormal" is true, the values are expected to be normalized - all
+ * in their valid ranges.
+ *
+ * If "expectNormal" is false, the values are expected to be "near
+ * normalized", meaning that the mantissa has to be modified at most once to
+ * bring it back into range.
+ *
+ */
+template <bool ExpectNormal, detail::UnsignedMantissa Rep>
+void
+Number::fromInternal(bool negative, Rep mantissa, int exponent, MantissaRange const* pRange)
+{
+    if constexpr (std::is_same_v<std::bool_constant<ExpectNormal>, std::false_type>)
+    {
+        if (!pRange)
+            throw std::runtime_error("Missing range to Number::fromInternal!");
+        auto const& range = *pRange;
+
+        auto const maxMantissa = range.max;
+        auto const minMantissa = range.min;
+
+        XRPL_ASSERT_PARTS(
+            mantissa >= minMantissa, "xrpl::Number::fromInternal", "mantissa large enough");
+
+        if (mantissa > maxMantissa || mantissa < minMantissa)
+        {
+            normalize(negative, mantissa, exponent, range.min, maxMantissa);
+        }
+
+        XRPL_ASSERT_PARTS(
+            mantissa >= minMantissa && mantissa <= maxMantissa,
+            "xrpl::Number::fromInternal",
+            "mantissa in range");
+    }
+
+    // mantissa is unsigned, but it might not be uint64
+    mantissa_ = static_cast<rep>(static_cast<internalrep>(mantissa));
+    if (negative)
+        mantissa_ = -mantissa_;
+    exponent_ = exponent;
+
+    XRPL_ASSERT_PARTS(
+        (pRange && isnormal(*pRange)) || isnormal(),
+        "xrpl::Number::fromInternal",
+        "Number is normalized");
+}
+
+/** Rebuilds the number from components.
+ *
+ * If "expectNormal" is true, the values are expected to be normalized - all in
+ * their valid ranges.
+ *
+ * If "expectNormal" is false, the values are expected to be "near normalized",
+ * meaning that the mantissa has to be modified at most once to bring it back
+ * into range.
+ *
+ */
+template <bool ExpectNormal, detail::UnsignedMantissa Rep>
+void
+Number::fromInternal(bool negative, Rep mantissa, int exponent)
+{
+    MantissaRange const* pRange = nullptr;
+    if constexpr (std::is_same_v<std::bool_constant<ExpectNormal>, std::false_type>)
+    {
+        pRange = &Number::kRange.get();
+    }
+
+    fromInternal(negative, mantissa, exponent, pRange);
+}
+
+Number
+Number::one(MantissaRange const& range)
+{
+    XRPL_ASSERT(isPowerOfTen(range.internalMin), "Number::one : valid range internalMin");
+    auto const result = Number{false, range.internalMin, -range.log, Number::Unchecked{}};
+    XRPL_ASSERT(result == 1, "Number::one : One == 1");
+    return result;
+}
+
 Number
 Number::one()
 {
-    auto const& range = kRange.get();
-    return Number{false, range.min, -range.log, Number::Unchecked{}};
+    return one(kRange);
 }
 
 template <class T>
@@ -533,20 +651,19 @@ doNormalize(
     MantissaRange::CuspRoundingFix cuspRoundingFixEnabled,
     bool dropped)
 {
-    static constexpr auto kMinExponent = Number::kMinExponent;
-    static constexpr auto kMaxExponent = Number::kMaxExponent;
-    static constexpr auto kMaxRep = Number::kMaxRep;
+    auto constexpr kMinExponent = Number::kMinExponent;
+    auto constexpr kMaxExponent = Number::kMaxExponent;
 
     using Guard = Number::Guard;
 
-    static constexpr Number kZero = Number{};
-    if (mantissa == 0)
+    constexpr Number kZero = Number{};
+    auto const& range = Number::kRange.get();
+    if (mantissa == 0 || (mantissa < minMantissa && exponent <= kMinExponent))
     {
-        mantissa = kZero.mantissa_;
-        exponent = kZero.exponent_;
-        negative = kZero.negative_;
+        std::tie(negative, mantissa, exponent) = kZero.toInternal(range);
         return;
     }
+
     auto m = mantissa;
     while ((m < minMantissa) && (exponent > kMinExponent))
     {
@@ -564,38 +681,13 @@ doNormalize(
             throw std::overflow_error("Number::normalize 1");
         g.doDropDigit(m, exponent);
     }
-    if ((exponent < kMinExponent) || (m < minMantissa))
+    if ((exponent < kMinExponent) || (m == 0))
     {
-        mantissa = kZero.mantissa_;
-        exponent = kZero.exponent_;
-        negative = kZero.negative_;
+        std::tie(negative, mantissa, exponent) = kZero.toInternal(range);
         return;
     }
 
-    // When using the largeRange, "m" needs fit within an int64, even if
-    // the final mantissa is going to end up larger to fit within the
-    // MantissaRange. Cut it down here so that the rounding will be done while
-    // it's smaller.
-    //
-    // Example: 9,900,000,000,000,123,456 > 9,223,372,036,854,775,807,
-    //      so "m" will be modified to 990,000,000,000,012,345. Then that value
-    //      will be rounded to 990,000,000,000,012,345 or
-    //      990,000,000,000,012,346, depending on the rounding mode. Finally,
-    //      mantissa will be "m*10" so it fits within the range, and end up as
-    //      9,900,000,000,000,123,450 or 9,900,000,000,000,123,460.
-    // mantissa() will return mantissa / 10, and exponent() will return
-    // exponent + 1.
-    if (m > kMaxRep)
-    {
-        if (exponent >= kMaxExponent)
-            throw std::overflow_error("Number::normalize 1.5");
-        g.doDropDigit(m, exponent);
-    }
-    // Before modification, m should be within the min/max range. After
-    // modification, it must be less than kMaxRep. In other words, the original
-    // value should have been no more than kMaxRep * 10.
-    // (kMaxRep * 10 > maxMantissa)
-    XRPL_ASSERT_PARTS(m <= kMaxRep, "xrpl::doNormalize", "intermediate mantissa fits in int64");
+    XRPL_ASSERT_PARTS(m <= maxMantissa, "xrpl::doNormalize", "intermediate mantissa fits in int64");
     mantissa = m;
 
     g.doRoundUp(
@@ -606,10 +698,15 @@ doNormalize(
         maxMantissa,
         cuspRoundingFixEnabled,
         "Number::normalize 2");
+
     XRPL_ASSERT_PARTS(
         mantissa >= minMantissa && mantissa <= maxMantissa,
         "xrpl::doNormalize",
         "final mantissa fits in range");
+    XRPL_ASSERT_PARTS(
+        exponent >= kMinExponent && exponent <= kMaxExponent,
+        "xrpl::doNormalize",
+        "final exponent fits in range");
 }
 
 template <>
@@ -665,7 +762,11 @@ Number::normalize<unsigned long>(
 void
 Number::normalize(MantissaRange const& range)
 {
-    normalize(negative_, mantissa_, exponent_, range.min, range.max, range.cuspRoundingFixEnabled);
+    auto [negative, mantissa, exponent] = toInternal(range);
+
+    normalize(negative, mantissa, exponent, range.min, range.max, range.cuspRoundingFixEnabled);
+
+    fromInternal(negative, mantissa, exponent, &range);
 }
 
 // Copy the number, but set a new exponent. Because the mantissa doesn't change,
@@ -675,22 +776,34 @@ Number
 Number::shiftExponent(int exponentDelta) const
 {
     XRPL_ASSERT_PARTS(isnormal(), "xrpl::Number::shiftExponent", "normalized");
-    auto const newExponent = exponent_ + exponentDelta;
-    if (newExponent >= kMaxExponent)
+
+    Number result = *this;
+
+    result.exponent_ += exponentDelta;
+
+    if (result.exponent_ >= kMaxExponent)
         throw std::overflow_error("Number::shiftExponent");
-    if (newExponent < kMinExponent)
+    if (result.exponent_ < kMinExponent)
     {
         return Number{};
     }
-    Number const result{negative_, mantissa_, newExponent, Unchecked{}};
-    XRPL_ASSERT_PARTS(result.isnormal(), "xrpl::Number::shiftExponent", "result is normalized");
+
     return result;
 }
 
+Number::Number(bool negative, internalrep mantissa, int exponent, Normalized)
+{
+    auto const& range = kRange.get();
+    normalize(negative, mantissa, exponent, range.min, range.max, range.cuspRoundingFixEnabled);
+    fromInternal(negative, mantissa, exponent, &range);
+}
+
 Number&
 Number::operator+=(Number const& y)
 {
-    static constexpr Number kZero = Number{};
+    auto const& range = kRange.get();
+
+    constexpr Number kZero = Number{};
     if (y == kZero)
         return *this;
     if (*this == kZero)
@@ -704,7 +817,8 @@ Number::operator+=(Number const& y)
         return *this;
     }
 
-    XRPL_ASSERT(isnormal() && y.isnormal(), "xrpl::Number::operator+=(Number) : is normal");
+    XRPL_ASSERT(
+        isnormal(range) && y.isnormal(range), "xrpl::Number::operator+=(Number) : is normal");
     // *n = negative
     // *s = sign
     // *m = mantissa
@@ -712,13 +826,10 @@ Number::operator+=(Number const& y)
 
     // Need to use uint128_t, because large mantissas can overflow when added
     // together.
-    bool xn = negative_;
-    uint128_t xm = mantissa_;
-    auto xe = exponent_;
+    auto [xn, xm, xe] = toInternal<uint128_t>(range);
+
+    auto [yn, ym, ye] = y.toInternal<uint128_t>(range);
 
-    bool const yn = y.negative_;
-    uint128_t ym = y.mantissa_;
-    auto ye = y.exponent_;
     Guard g;
     if (xe < ye)
     {
@@ -739,7 +850,6 @@ Number::operator+=(Number const& y)
         } while (xe > ye);
     }
 
-    auto const& range = kRange.get();
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
     auto const cuspRoundingFixEnabled = range.cuspRoundingFixEnabled;
@@ -747,7 +857,7 @@ Number::operator+=(Number const& y)
     if (xn == yn)
     {
         xm += ym;
-        if (xm > maxMantissa || xm > kMaxRep)
+        if (xm > maxMantissa)
         {
             g.doDropDigit(xm, xe);
         }
@@ -772,7 +882,7 @@ Number::operator+=(Number const& y)
             xe = ye;
             xn = yn;
         }
-        while (xm < minMantissa && xm * 10 <= kMaxRep)
+        while (xm < minMantissa)
         {
             xm *= 10;
             xm -= g.pop();
@@ -781,17 +891,17 @@ Number::operator+=(Number const& y)
         g.doRoundDown(xn, xm, xe, minMantissa);
     }
 
-    negative_ = xn;
-    mantissa_ = static_cast<internalrep>(xm);
-    exponent_ = xe;
-    normalize(range);
+    normalize(xn, xm, xe, minMantissa, maxMantissa, cuspRoundingFixEnabled);
+    fromInternal(xn, xm, xe, &range);
     return *this;
 }
 
 Number&
 Number::operator*=(Number const& y)
 {
-    static constexpr Number kZero = Number{};
+    auto const& range = kRange.get();
+
+    constexpr Number kZero = Number{};
     if (*this == kZero)
         return *this;
     if (y == kZero)
@@ -804,15 +914,11 @@ Number::operator*=(Number const& y)
     // *m = mantissa
     // *e = exponent
 
-    bool const xn = negative_;
+    auto [xn, xm, xe] = toInternal(range);
     int const xs = xn ? -1 : 1;
-    internalrep xm = mantissa_;
-    auto xe = exponent_;
 
-    bool const yn = y.negative_;
+    auto [yn, ym, ye] = y.toInternal(range);
     int const ys = yn ? -1 : 1;
-    internalrep const ym = y.mantissa_;
-    auto ye = y.exponent_;
 
     auto zm = uint128_t(xm) * uint128_t(ym);
     auto ze = xe + ye;
@@ -822,12 +928,11 @@ Number::operator*=(Number const& y)
     if (zn)
         g.setNegative();
 
-    auto const& range = kRange.get();
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
     auto const cuspRoundingFixEnabled = range.cuspRoundingFixEnabled;
 
-    while (zm > maxMantissa || zm > kMaxRep)
+    while (zm > maxMantissa)
     {
         g.doDropDigit(zm, ze);
     }
@@ -842,18 +947,18 @@ Number::operator*=(Number const& y)
         maxMantissa,
         cuspRoundingFixEnabled,
         "Number::multiplication overflow : exponent is " + std::to_string(xe));
-    negative_ = zn;
-    mantissa_ = xm;
-    exponent_ = xe;
 
-    normalize(range);
+    normalize(zn, xm, xe, minMantissa, maxMantissa, cuspRoundingFixEnabled);
+    fromInternal(zn, xm, xe, &range);
     return *this;
 }
 
 Number&
 Number::operator/=(Number const& y)
 {
-    static constexpr Number kZero = Number{};
+    auto const& range = kRange.get();
+
+    constexpr Number kZero = Number{};
     if (y == kZero)
         throw std::overflow_error("Number: divide by 0");
     if (*this == kZero)
@@ -867,19 +972,14 @@ Number::operator/=(Number const& y)
     // *m = mantissa
     // *e = exponent
 
-    bool const np = negative_;
-    int const ns = (np ? -1 : 1);
-    auto nm = mantissa_;
-    auto ne = exponent_;
-
-    bool const dp = y.negative_;
-    int const ds = (dp ? -1 : 1);
-    // Create the denominator as 128-bit unsigned, since that's what we
+    // Create the mantissas as 128-bit unsigned, since that's what we
     // need to work with.
-    uint128_t const dm = static_cast<uint128_t>(y.mantissa_);
-    auto const de = y.exponent_;
+    auto const [np, nm, ne] = toInternal<uint128_t>(range);
+    int const ns = (np ? -1 : 1);
+
+    auto const [dp, dm, de] = y.toInternal<uint128_t>(range);
+    int const ds = (dp ? -1 : 1);
 
-    auto const& range = kRange.get();
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
     auto const cuspRoundingFixEnabled = range.cuspRoundingFixEnabled;
@@ -1022,10 +1122,8 @@ Number::operator/=(Number const& y)
         }
     }
     doNormalize(zp, zm, ze, minMantissa, maxMantissa, cuspRoundingFixEnabled, dropped);
-    negative_ = zp;
-    mantissa_ = static_cast<internalrep>(zm);
-    exponent_ = ze;
-    XRPL_ASSERT_PARTS(isnormal(), "xrpl::Number::operator/=", "result is normalized");
+    fromInternal(zp, zm, ze, &range);
+    XRPL_ASSERT_PARTS(isnormal(range), "xrpl::Number::operator/=", "result is normalized");
 
     return *this;
 }
@@ -1033,27 +1131,35 @@ Number::operator/=(Number const& y)
 Number::
 operator rep() const
 {
-    rep drops = mantissa();
+    auto const m = mantissa();
+    // drops will always be non-negative
+    internalrep drops = externalToInternal(m);
+
+    if (drops == 0)
+        return drops;
+
     int offset = exponent();
     Guard g;
-    if (drops != 0)
+
+    if (m < 0)
     {
-        if (negative_)
-        {
-            g.setNegative();
-            drops = -drops;
-        }
-        while (offset < 0)
-        {
-            g.doDropDigit(drops, offset);
-        }
-        for (; offset > 0; --offset)
-        {
-            if (drops > kMaxRep / 10)
-                throw std::overflow_error("Number::operator rep() overflow");
-            drops *= 10;
-        }
-        g.doRound(drops, "Number::operator rep() rounding overflow");
+        g.setNegative();
+    }
+    while (offset < 0)
+    {
+        g.doDropDigit(drops, offset);
+    }
+    for (; offset > 0; --offset)
+    {
+        if (drops > kLargestMantissa / 10)
+            throw std::overflow_error("Number::operator rep() overflow");
+        drops *= 10;
+    }
+    g.doRound(drops, "Number::operator rep() rounding overflow");
+
+    if (g.isNegative())
+    {
+        return -drops;
     }
     return drops;
 }
@@ -1079,19 +1185,22 @@ Number::truncate() const noexcept
 std::string
 to_string(Number const& amount)
 {
+    auto const& range = Number::kRange.get();
+
     // keep full internal accuracy, but make more human friendly if possible
     static constexpr Number kZero = Number{};
     if (amount == kZero)
         return "0";
 
-    auto exponent = amount.exponent_;
-    auto mantissa = amount.mantissa_;
-    bool const negative = amount.negative_;
+    // The mantissa must have a set number of decimal places for this to work
+    auto [negative, mantissa, exponent] = amount.toInternal(range);
 
     // Use scientific notation for exponents that are too small or too large
-    auto const rangeLog = Number::mantissaLog();
-    if (((exponent != 0) && ((exponent < -(rangeLog + 10)) || (exponent > -(rangeLog - 10)))))
+    auto const rangeLog = range.log;
+    if (((exponent != 0 && amount.exponent() != 0) &&
+         ((exponent < -(rangeLog + 10)) || (exponent > -(rangeLog - 10)))))
     {
+        // Remove trailing zeroes from the mantissa.
         while (mantissa != 0 && mantissa % 10 == 0 && exponent < Number::kMaxExponent)
         {
             mantissa /= 10;
@@ -1099,8 +1208,11 @@ to_string(Number const& amount)
         }
         std::string ret = negative ? "-" : "";
         ret.append(std::to_string(mantissa));
-        ret.append(1, 'e');
-        ret.append(std::to_string(exponent));
+        if (exponent != 0)
+        {
+            ret.append(1, 'e');
+            ret.append(std::to_string(exponent));
+        }
         return ret;
     }
 
@@ -1188,20 +1300,11 @@ power(Number const& f, unsigned n)
     return r;
 }
 
-// Returns f^(1/d)
-// Uses Newton–Raphson iterations until the result stops changing
-// to find the non-negative root of the polynomial g(x) = x^d - f
-
-// This function, and power(Number f, unsigned n, unsigned d)
-// treat corner cases such as 0 roots as advised by Annex F of
-// the C standard, which itself is consistent with the IEEE
-// floating point standards.
-
 Number
-root(Number f, unsigned d)
+Number::root(MantissaRange const& range, Number f, unsigned d)
 {
-    static constexpr Number kZero = Number{};
-    auto const one = Number::one();
+    constexpr Number kZero = Number{};
+    auto const one = Number::one(range);
 
     if (f == one || d == 1)
         return f;
@@ -1218,21 +1321,28 @@ root(Number f, unsigned d)
     if (f == kZero)
         return f;
 
-    // Scale f into the range (0, 1) such that f's exponent is a multiple of d
-    auto e = f.exponent_ + Number::mantissaLog() + 1;
-    auto const di = static_cast<int>(d);
-    auto ex = [e = e, di = di]()  // Euclidean remainder of e/d
-    {
-        int const k = (e >= 0 ? e : e - (di - 1)) / di;
-        int const k2 = e - (k * di);
-        if (k2 == 0)
-            return 0;
-        return di - k2;
-    }();
-    e += ex;
-    f = f.shiftExponent(-e);  // f /= 10^e;
+    auto const [e, di] = [&]() {
+        auto const exponent = std::get<2>(f.toInternal(range));
 
-    XRPL_ASSERT_PARTS(f.isnormal(), "xrpl::root(Number, unsigned)", "f is normalized");
+        // Scale f into the range (0, 1) such that the scale change (e) is a
+        // multiple of the root (d)
+        auto e = exponent + range.log + 1;
+        auto const di = static_cast<int>(d);
+        auto ex = [e = e, di = di]()  // Euclidean remainder of e/d
+        {
+            int const k = (e >= 0 ? e : e - (di - 1)) / di;
+            int const k2 = e - (k * di);
+            if (k2 == 0)
+                return 0;
+            return di - k2;
+        }();
+        e += ex;
+        f = f.shiftExponent(-e);  // f /= 10^e;
+        return std::make_tuple(e, di);
+    }();
+
+    XRPL_ASSERT_PARTS(e % di == 0, "xrpl::root(Number, unsigned)", "e is divisible by d");
+    XRPL_ASSERT_PARTS(f.isnormal(range), "xrpl::root(Number, unsigned)", "f is normalized");
     bool neg = false;
     if (f < kZero)
     {
@@ -1265,15 +1375,33 @@ root(Number f, unsigned d)
 
     //  return r * 10^(e/d) to reverse scaling
     auto const result = r.shiftExponent(e / di);
-    XRPL_ASSERT_PARTS(result.isnormal(), "xrpl::root(Number, unsigned)", "result is normalized");
+    XRPL_ASSERT_PARTS(
+        result.isnormal(range), "xrpl::root(Number, unsigned)", "result is normalized");
     return result;
 }
 
+// Returns f^(1/d)
+// Uses Newton–Raphson iterations until the result stops changing
+// to find the non-negative root of the polynomial g(x) = x^d - f
+
+// This function, and power(Number f, unsigned n, unsigned d)
+// treat corner cases such as 0 roots as advised by Annex F of
+// the C standard, which itself is consistent with the IEEE
+// floating point standards.
+
+Number
+root(Number f, unsigned d)
+{
+    auto const& range = Number::kRange.get();
+    return Number::root(range, f, d);
+}
+
 Number
 root2(Number f)
 {
-    static constexpr Number kZero = Number{};
-    auto const one = Number::one();
+    auto const& range = Number::kRange.get();
+    constexpr Number kZero = Number{};
+    auto const one = Number::one(range);
 
     if (f == one)
         return f;
@@ -1282,12 +1410,18 @@ root2(Number f)
     if (f == kZero)
         return f;
 
-    // Scale f into the range (0, 1) such that f's exponent is a multiple of d
-    auto e = f.exponent_ + Number::mantissaLog() + 1;
-    if (e % 2 != 0)
-        ++e;
-    f = f.shiftExponent(-e);  // f /= 10^e;
-    XRPL_ASSERT_PARTS(f.isnormal(), "xrpl::root2(Number)", "f is normalized");
+    auto const e = [&]() {
+        auto const exponent = std::get<2>(f.toInternal(range));
+
+        // Scale f into the range (0, 1) such that f's exponent is a
+        // multiple of d
+        auto e = exponent + range.log + 1;
+        if (e % 2 != 0)
+            ++e;
+        f = f.shiftExponent(-e);  // f /= 10^e;
+        return e;
+    }();
+    XRPL_ASSERT_PARTS(f.isnormal(range), "xrpl::root2(Number)", "f is normalized");
 
     // Quadratic least squares curve fit of f^(1/d) in the range [0, 1]
     auto const D = 105;  // NOLINT(readability-identifier-naming)
@@ -1309,7 +1443,7 @@ root2(Number f)
 
     //  return r * 10^(e/2) to reverse scaling
     auto const result = r.shiftExponent(e / 2);
-    XRPL_ASSERT_PARTS(result.isnormal(), "xrpl::root2(Number)", "result is normalized");
+    XRPL_ASSERT_PARTS(result.isnormal(range), "xrpl::root2(Number)", "result is normalized");
 
     return result;
 }
@@ -1319,8 +1453,10 @@ root2(Number f)
 Number
 power(Number const& f, unsigned n, unsigned d)
 {
-    static constexpr Number kZero = Number{};
-    auto const one = Number::one();
+    auto const& range = Number::kRange.get();
+
+    constexpr Number kZero = Number{};
+    auto const one = Number::one(range);
 
     if (f == one)
         return f;
@@ -1342,7 +1478,7 @@ power(Number const& f, unsigned n, unsigned d)
     d /= g;
     if ((n % 2) == 1 && (d % 2) == 0 && f < kZero)
         throw std::overflow_error("Number::power nan");
-    return root(power(f, n), d);
+    return Number::root(range, power(f, n), d);
 }
 
 }  // namespace xrpl

src/test/basics/Number_test.cpp

@@ -12,6 +12,7 @@
 
 #include <array>
 #include <cctype>
+#include <chrono>
 #include <cstdint>
 #include <iomanip>
 #include <limits>
@@ -98,9 +99,10 @@ public:
     testLimits()
     {
         auto const scale = Number::getMantissaScale();
-        testcase << "test_limits " << to_string(scale);
-        bool caught = false;
         auto const minMantissa = Number::minMantissa();
+
+        testcase << "test_limits " << to_string(scale) << ", " << minMantissa;
+        bool caught = false;
         try
         {
             [[maybe_unused]] Number const x =
@@ -125,8 +127,9 @@ public:
             __LINE__);
         test(Number{false, minMantissa, -32769, Number::Normalized{}}, Number{}, __LINE__);
         test(
+            // Use 1501 to force rounding up
             Number{false, minMantissa, 32000, Number::Normalized{}} * 1'000 +
-                Number{false, 1'500, 32000, Number::Normalized{}},
+                Number{false, 1'501, 32000, Number::Normalized{}},
             Number{false, minMantissa + 2, 32003, Number::Normalized{}},
             __LINE__);
         // 9,223,372,036,854,775,808
@@ -236,7 +239,9 @@ public:
                 {Number{true, 9'999'999'999'999'999'999ULL, -37, Number::Normalized{}},
                  Number{1'000'000'000'000'000'000, -18},
                  Number{false, 9'999'999'999'999'999'990ULL, -19, Number::Normalized{}}},
-                {Number{Number::kMaxRep - 1}, Number{1, 0}, Number{Number::kMaxRep}},
+                {Number{Number::kLargestMantissa - 1},
+                 Number{1, 0},
+                 Number{Number::kLargestMantissa}},
                 // Test extremes
                 {
                     // Each Number operand rounds up, so the actual mantissa is
@@ -246,21 +251,32 @@ public:
                     Number{2, 19},
                 },
                 {
-                    // Does not round. Mantissas are going to be > kMaxRep, so if
-                    // added together as uint64_t's, the result will overflow.
-                    // With addition using uint128_t, there's no problem. After
-                    // normalizing, the resulting mantissa ends up less than
-                    // kMaxRep.
+                    // Does not round. Mantissas are going to be >
+                    // largestMantissa, so if added together as uint64_t's, the
+                    // result will overflow. With addition using uint128_t,
+                    // there's no problem. After normalizing, the resulting
+                    // mantissa ends up less than largestMantissa.
+                    Number{false, Number::kLargestMantissa, 0, Number::Normalized{}},
+                    Number{false, Number::kLargestMantissa, 0, Number::Normalized{}},
+                    Number{false, Number::kLargestMantissa * 2, 0, Number::Normalized{}},
+                },
+                {
+                    // These mantissas round down, so adding them together won't
+                    // have any consequences.
                     Number{false, 9'999'999'999'999'999'990ULL, 0, Number::Normalized{}},
                     Number{false, 9'999'999'999'999'999'990ULL, 0, Number::Normalized{}},
                     Number{false, 1'999'999'999'999'999'998ULL, 1, Number::Normalized{}},
                 },
             });
         auto const cLargeLegacy = std::to_array<Case>({
-            {Number{Number::kMaxRep}, Number{6, -1}, Number{Number::kMaxRep / 10, 1}},
+            {Number{Number::kLargestMantissa},
+             Number{6, -1},
+             Number{Number::kLargestMantissa / 10, 1}},
         });
         auto const cLargeCorrected = std::to_array<Case>({
-            {Number{Number::kMaxRep}, Number{6, -1}, Number{(Number::kMaxRep / 10) + 1, 1}},
+            {Number{Number::kLargestMantissa},
+             Number{6, -1},
+             Number{(Number::kLargestMantissa / 10) + 1, 1}},
         });
         auto test = [this](auto const& c) {
             for (auto const& [x, y, z] : c)
@@ -357,14 +373,16 @@ public:
                 {Number{1'000'000'000'000'000'001, -18},
                  Number{1'000'000'000'000'000'000, -18},
                  Number{1'000'000'000'000'000'000, -36}},
-                {Number{Number::kMaxRep}, Number{6, -1}, Number{Number::kMaxRep - 1}},
-                {Number{false, Number::kMaxRep + 1, 0, Number::Normalized{}},
+                {Number{Number::kLargestMantissa},
+                 Number{6, -1},
+                 Number{Number::kLargestMantissa - 1}},
+                {Number{false, Number::kLargestMantissa + 1, 0, Number::Normalized{}},
                  Number{1, 0},
-                 Number{(Number::kMaxRep / 10) + 1, 1}},
-                {Number{false, Number::kMaxRep + 1, 0, Number::Normalized{}},
+                 Number{(Number::kLargestMantissa / 10) + 1, 1}},
+                {Number{false, Number::kLargestMantissa + 1, 0, Number::Normalized{}},
                  Number{3, 0},
-                 Number{Number::kMaxRep}},
-                {power(2, 63), Number{3, 0}, Number{Number::kMaxRep}},
+                 Number{Number::kLargestMantissa}},
+                {power(2, 63), Number{3, 0}, Number{Number::kLargestMantissa}},
             });
         auto test = [this](auto const& c) {
             for (auto const& [x, y, z] : c)
@@ -385,20 +403,30 @@ public:
         }
     }
 
+    static std::uint64_t
+    getMaxInternalMantissa()
+    {
+        return (static_cast<std::uint64_t>(
+                    static_cast<std::int64_t>(power(10, Number::mantissaLog()))) *
+                10) -
+            1;
+    }
+
     void
     testMul()
     {
         auto const scale = Number::getMantissaScale();
         testcase << "test_mul " << to_string(scale);
 
-        using Case = std::tuple<Number, Number, Number>;
+        // Case: Factor 1, Factor 2, Expected product, Line number
+        using Case = std::tuple<Number, Number, Number, int>;
         auto test = [this](auto const& c) {
-            for (auto const& [x, y, z] : c)
+            for (auto const& [x, y, z, line] : c)
             {
                 auto const result = x * y;
                 std::stringstream ss;
                 ss << x << " * " << y << " = " << result << ". Expected: " << z;
-                BEAST_EXPECTS(result == z, ss.str());
+                BEAST_EXPECTS(result == z, ss.str() + " line: " + std::to_string(line));
             }
         };
         auto tests = [&](auto const& cSmall, auto const& cLarge) {
@@ -412,70 +440,97 @@ public:
             }
         };
         auto const maxMantissa = Number::maxMantissa();
+        auto const maxInternalMantissa = getMaxInternalMantissa();
 
         SaveNumberRoundMode const save{Number::setround(Number::RoundingMode::ToNearest)};
         {
             auto const cSmall = std::to_array<Case>({
-                {Number{7}, Number{8}, Number{56}},
+                {Number{7}, Number{8}, Number{56}, __LINE__},
                 {Number{1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{2000000000000000, -15}},
+                 Number{2000000000000000, -15},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{-2000000000000000, -15}},
+                 Number{-2000000000000000, -15},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{-1414213562373095, -15},
-                 Number{2000000000000000, -15}},
+                 Number{2000000000000000, -15},
+                 __LINE__},
                 {Number{3214285714285706, -15},
                  Number{3111111111111119, -15},
-                 Number{1000000000000000, -14}},
-                {Number{1000000000000000, -32768}, Number{1000000000000000, -32768}, Number{0}},
+                 Number{1000000000000000, -14},
+                 __LINE__},
+                {Number{1000000000000000, -32768},
+                 Number{1000000000000000, -32768},
+                 Number{0},
+                 __LINE__},
                 // Maximum mantissa range
                 {Number{9'999'999'999'999'999, 0},
                  Number{9'999'999'999'999'999, 0},
-                 Number{9'999'999'999'999'998, 16}},
+                 Number{9'999'999'999'999'998, 16},
+                 __LINE__},
             });
             auto const cLarge = std::to_array<Case>({
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
-                {Number{7}, Number{8}, Number{56}},
+                {Number{7}, Number{8}, Number{56}, __LINE__},
                 {Number{1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{1999999999999999862, -18}},
+                 Number{1999999999999999862, -18},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{-1999999999999999862, -18}},
+                 Number{-1999999999999999862, -18},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{-1414213562373095, -15},
-                 Number{1999999999999999862, -18}},
+                 Number{1999999999999999862, -18},
+                 __LINE__},
                 {Number{3214285714285706, -15},
                  Number{3111111111111119, -15},
-                 Number{false, 9'999'999'999'999'999'579ULL, -18, Number::Normalized{}}},
+                 Number{false, 9'999'999'999'999'999'579ULL, -18, Number::Normalized{}},
+                 __LINE__},
                 {Number{1000000000000000000, -32768},
                  Number{1000000000000000000, -32768},
-                 Number{0}},
+                 Number{0},
+                 __LINE__},
                 // Items from cSmall expanded for the larger mantissa,
                 // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                 // with higher precision
                 {Number{1414213562373095049, -18},
                  Number{1414213562373095049, -18},
-                 Number{2000000000000000001, -18}},
+                 Number{2000000000000000001, -18},
+                 __LINE__},
                 {Number{-1414213562373095048, -18},
                  Number{1414213562373095048, -18},
-                 Number{-1999999999999999998, -18}},
+                 Number{-1999999999999999998, -18},
+                 __LINE__},
                 {Number{-1414213562373095048, -18},
                  Number{-1414213562373095049, -18},
-                 Number{1999999999999999999, -18}},
-                {Number{3214285714285714278, -18}, Number{3111111111111111119, -18}, Number{10, 0}},
-                // Maximum mantissa range - rounds up to 1e19
+                 Number{1999999999999999999, -18},
+                 __LINE__},
+                {Number{3214285714285714278, -18},
+                 Number{3111111111111111119, -18},
+                 Number{10, 0},
+                 __LINE__},
+                // Maximum internal mantissa range - rounds up to 1e19
+                {Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                 Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                 Number{1, 38},
+                 __LINE__},
+                // Maximum actual mantissa range - same as int64 range
                 {Number{false, maxMantissa, 0, Number::Normalized{}},
                  Number{false, maxMantissa, 0, Number::Normalized{}},
-                 Number{1, 38}},
+                 Number{85'070'591'730'234'615'85, 19},
+                 __LINE__},
                 // Maximum int64 range
-                {Number{Number::kMaxRep, 0},
-                 Number{Number::kMaxRep, 0},
-                 Number{85'070'591'730'234'615'85, 19}},
+                {Number{Number::kLargestMantissa, 0},
+                 Number{Number::kLargestMantissa, 0},
+                 Number{85'070'591'730'234'615'85, 19},
+                 __LINE__},
             });
             tests(cSmall, cLarge);
         }
@@ -483,66 +538,90 @@ public:
         testcase << "test_mul " << to_string(Number::getMantissaScale()) << " towards_zero";
         {
             auto const cSmall = std::to_array<Case>(
-                {{Number{7}, Number{8}, Number{56}},
+                {{Number{7}, Number{8}, Number{56}, __LINE__},
                  {Number{1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{-1999999999999999, -15}},
+                  Number{-1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{-1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{3214285714285706, -15},
                   Number{3111111111111119, -15},
-                  Number{9999999999999999, -15}},
-                 {Number{1000000000000000, -32768}, Number{1000000000000000, -32768}, Number{0}}});
+                  Number{9999999999999999, -15},
+                  __LINE__},
+                 {Number{1000000000000000, -32768},
+                  Number{1000000000000000, -32768},
+                  Number{0},
+                  __LINE__}});
             auto const cLarge = std::to_array<Case>(
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
                 {
-                    {Number{7}, Number{8}, Number{56}},
+                    {Number{7}, Number{8}, Number{56}, __LINE__},
                     {Number{1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{-1999999999999999861, -18}},
+                     Number{-1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{-1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{3214285714285706, -15},
                      Number{3111111111111119, -15},
-                     Number{false, 9999999999999999579ULL, -18, Number::Normalized{}}},
+                     Number{false, 9999999999999999579ULL, -18, Number::Normalized{}},
+                     __LINE__},
                     {Number{1000000000000000000, -32768},
                      Number{1000000000000000000, -32768},
-                     Number{0}},
+                     Number{0},
+                     __LINE__},
                     // Items from cSmall expanded for the larger mantissa,
                     // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                     // with higher precision
                     {Number{1414213562373095049, -18},
                      Number{1414213562373095049, -18},
-                     Number{2, 0}},
+                     Number{2, 0},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{1414213562373095048, -18},
-                     Number{-1999999999999999997, -18}},
+                     Number{-1999999999999999997, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{-1414213562373095049, -18},
-                     Number{1999999999999999999, -18}},
+                     Number{1999999999999999999, -18},
+                     __LINE__},
                     {Number{3214285714285714278, -18},
                      Number{3111111111111111119, -18},
-                     Number{10, 0}},
-                    // Maximum mantissa range - rounds down to maxMantissa/10e1
+                     Number{10, 0},
+                     __LINE__},
+                    // Maximum internal mantissa range - rounds down to
+                    // maxMantissa/10e1
                     // 99'999'999'999'999'999'800'000'000'000'000'000'100
+                    {Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                     Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                     Number{false, (maxInternalMantissa / 10) - 1, 20, Number::Normalized{}},
+                     __LINE__},
+                    // Maximum actual mantissa range - same as int64
                     {Number{false, maxMantissa, 0, Number::Normalized{}},
                      Number{false, maxMantissa, 0, Number::Normalized{}},
-                     Number{false, (maxMantissa / 10) - 1, 20, Number::Normalized{}}},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::kMaxRep, 0},
-                     Number{Number::kMaxRep, 0},
-                     Number{85'070'591'730'234'615'84, 19}},
+                    {Number{Number::kLargestMantissa, 0},
+                     Number{Number::kLargestMantissa, 0},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                 });
             tests(cSmall, cLarge);
         }
@@ -550,66 +629,90 @@ public:
         testcase << "test_mul " << to_string(Number::getMantissaScale()) << " downward";
         {
             auto const cSmall = std::to_array<Case>(
-                {{Number{7}, Number{8}, Number{56}},
+                {{Number{7}, Number{8}, Number{56}, __LINE__},
                  {Number{1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{-2000000000000000, -15}},
+                  Number{-2000000000000000, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{-1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{3214285714285706, -15},
                   Number{3111111111111119, -15},
-                  Number{9999999999999999, -15}},
-                 {Number{1000000000000000, -32768}, Number{1000000000000000, -32768}, Number{0}}});
+                  Number{9999999999999999, -15},
+                  __LINE__},
+                 {Number{1000000000000000, -32768},
+                  Number{1000000000000000, -32768},
+                  Number{0},
+                  __LINE__}});
             auto const cLarge = std::to_array<Case>(
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
                 {
-                    {Number{7}, Number{8}, Number{56}},
+                    {Number{7}, Number{8}, Number{56}, __LINE__},
                     {Number{1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{-1999999999999999862, -18}},
+                     Number{-1999999999999999862, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{-1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{3214285714285706, -15},
                      Number{3111111111111119, -15},
-                     Number{false, 9'999'999'999'999'999'579ULL, -18, Number::Normalized{}}},
+                     Number{false, 9'999'999'999'999'999'579ULL, -18, Number::Normalized{}},
+                     __LINE__},
                     {Number{1000000000000000000, -32768},
                      Number{1000000000000000000, -32768},
-                     Number{0}},
+                     Number{0},
+                     __LINE__},
                     // Items from cSmall expanded for the larger mantissa,
                     // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                     // with higher precision
                     {Number{1414213562373095049, -18},
                      Number{1414213562373095049, -18},
-                     Number{2, 0}},
+                     Number{2, 0},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{1414213562373095048, -18},
-                     Number{-1999999999999999998, -18}},
+                     Number{-1999999999999999998, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{-1414213562373095049, -18},
-                     Number{1999999999999999999, -18}},
+                     Number{1999999999999999999, -18},
+                     __LINE__},
                     {Number{3214285714285714278, -18},
                      Number{3111111111111111119, -18},
-                     Number{10, 0}},
-                    // Maximum mantissa range - rounds down to maxMantissa/10e1
+                     Number{10, 0},
+                     __LINE__},
+                    // Maximum internal mantissa range - rounds down to
+                    // maxInternalMantissa/10-1
                     // 99'999'999'999'999'999'800'000'000'000'000'000'100
+                    {Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                     Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                     Number{false, (maxInternalMantissa / 10) - 1, 20, Number::Normalized{}},
+                     __LINE__},
+                    // Maximum external mantissa range - same as INT64_MAX (2^63-1)
                     {Number{false, maxMantissa, 0, Number::Normalized{}},
                      Number{false, maxMantissa, 0, Number::Normalized{}},
-                     Number{false, (maxMantissa / 10) - 1, 20, Number::Normalized{}}},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::kMaxRep, 0},
-                     Number{Number::kMaxRep, 0},
-                     Number{85'070'591'730'234'615'84, 19}},
+                    {Number{Number::kLargestMantissa, 0},
+                     Number{Number::kLargestMantissa, 0},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                 });
             tests(cSmall, cLarge);
         }
@@ -617,66 +720,89 @@ public:
         testcase << "test_mul " << to_string(Number::getMantissaScale()) << " upward";
         {
             auto const cSmall = std::to_array<Case>(
-                {{Number{7}, Number{8}, Number{56}},
+                {{Number{7}, Number{8}, Number{56}, __LINE__},
                  {Number{1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{2000000000000000, -15}},
+                  Number{2000000000000000, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{-1999999999999999, -15}},
+                  Number{-1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{-1414213562373095, -15},
-                  Number{2000000000000000, -15}},
+                  Number{2000000000000000, -15},
+                  __LINE__},
                  {Number{3214285714285706, -15},
                   Number{3111111111111119, -15},
-                  Number{1000000000000000, -14}},
-                 {Number{1000000000000000, -32768}, Number{1000000000000000, -32768}, Number{0}}});
+                  Number{1000000000000000, -14},
+                  __LINE__},
+                 {Number{1000000000000000, -32768},
+                  Number{1000000000000000, -32768},
+                  Number{0},
+                  __LINE__}});
             auto const cLarge = std::to_array<Case>(
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
                 {
-                    {Number{7}, Number{8}, Number{56}},
+                    {Number{7}, Number{8}, Number{56}, __LINE__},
                     {Number{1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{1999999999999999862, -18}},
+                     Number{1999999999999999862, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{-1999999999999999861, -18}},
+                     Number{-1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{-1414213562373095, -15},
-                     Number{1999999999999999862, -18}},
+                     Number{1999999999999999862, -18},
+                     __LINE__},
                     {Number{3214285714285706, -15},
                      Number{3111111111111119, -15},
-                     Number{999999999999999958, -17}},
+                     Number{999999999999999958, -17},
+                     __LINE__},
                     {Number{1000000000000000000, -32768},
                      Number{1000000000000000000, -32768},
-                     Number{0}},
+                     Number{0},
+                     __LINE__},
                     // Items from cSmall expanded for the larger mantissa,
                     // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                     // with higher precision
                     {Number{1414213562373095049, -18},
                      Number{1414213562373095049, -18},
-                     Number{2000000000000000001, -18}},
+                     Number{2000000000000000001, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{1414213562373095048, -18},
-                     Number{-1999999999999999997, -18}},
+                     Number{-1999999999999999997, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{-1414213562373095049, -18},
-                     Number{2, 0}},
+                     Number{2, 0},
+                     __LINE__},
                     {Number{3214285714285714278, -18},
                      Number{3111111111111111119, -18},
-                     Number{1000000000000000001, -17}},
-                    // Maximum mantissa range - rounds up to minMantissa*10
-                    // 1e19*1e19=1e38
+                     Number{1000000000000000001, -17},
+                     __LINE__},
+                    // Maximum internal mantissa range - rounds up to
+                    // minMantissa*10 1e19*1e19=1e38
+                    {Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                     Number{false, maxInternalMantissa, 0, Number::Normalized{}},
+                     Number{1, 38},
+                     __LINE__},
+                    // Maximum mantissa range - same as int64
                     {Number{false, maxMantissa, 0, Number::Normalized{}},
                      Number{false, maxMantissa, 0, Number::Normalized{}},
-                     Number{1, 38}},
+                     Number{85'070'591'730'234'615'85, 19},
+                     __LINE__},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::kMaxRep, 0},
-                     Number{Number::kMaxRep, 0},
-                     Number{85'070'591'730'234'615'85, 19}},
+                    {Number{Number::kLargestMantissa, 0},
+                     Number{Number::kLargestMantissa, 0},
+                     Number{85'070'591'730'234'615'85, 19},
+                     __LINE__},
                 });
             tests(cSmall, cLarge);
         }
@@ -911,6 +1037,8 @@ public:
         };
         */
 
+        auto const maxInternalMantissa = getMaxInternalMantissa();
+
         auto const cSmall = std::to_array<Case>(
             {{Number{2}, 2, Number{1414213562373095049, -18}},
              {Number{2'000'000}, 2, Number{1414213562373095049, -15}},
@@ -922,16 +1050,16 @@ public:
              {Number{0}, 5, Number{0}},
              {Number{5625, -4}, 2, Number{75, -2}}});
         auto const cLarge = std::to_array<Case>({
-            {Number{false, Number::maxMantissa() - 9, -1, Number::Normalized{}},
+            {Number{false, maxInternalMantissa - 9, -1, Number::Normalized{}},
              2,
              Number{false, 999'999'999'999'999'999, -9, Number::Normalized{}}},
-            {Number{false, Number::maxMantissa() - 9, 0, Number::Normalized{}},
+            {Number{false, maxInternalMantissa - 9, 0, Number::Normalized{}},
              2,
              Number{false, 3'162'277'660'168'379'330, -9, Number::Normalized{}}},
-            {Number{Number::kMaxRep},
+            {Number{Number::kLargestMantissa},
              2,
              Number{false, 3'037'000'499'976049692, -9, Number::Normalized{}}},
-            {Number{Number::kMaxRep},
+            {Number{Number::kLargestMantissa},
              4,
              Number{false, 55'108'98747006743627, -14, Number::Normalized{}}},
         });
@@ -980,6 +1108,8 @@ public:
             }
         };
 
+        Number const maxInternalMantissa{getMaxInternalMantissa(), 0, Number::Normalized{}};
+
         auto const cSmall = std::to_array<Number>({
             Number{2},
             Number{2'000'000},
@@ -989,7 +1119,10 @@ public:
             Number{5, -1},
             Number{0},
             Number{5625, -4},
-            Number{Number::kMaxRep},
+            Number{Number::kLargestMantissa},
+            maxInternalMantissa,
+            Number{Number::minMantissa(), 0, Number::Unchecked{}},
+            Number{Number::maxMantissa(), 0, Number::Unchecked{}},
         });
         test(cSmall);
         bool caught = false;
@@ -1341,18 +1474,18 @@ public:
             case MantissaRange::MantissaScale::Large:
                 // Test the edges
                 // ((exponent < -(28)) || (exponent > -(8)))))
-                test(Number::min(), "1e-32750");
+                test(Number::min(), "922337203685477581e-32768");
                 test(Number::max(), "9223372036854775807e32768");
                 test(Number::lowest(), "-9223372036854775807e32768");
                 {
                     NumberRoundModeGuard const mg(Number::RoundingMode::TowardsZero);
 
                     auto const maxMantissa = Number::maxMantissa();
-                    BEAST_EXPECT(maxMantissa == 9'999'999'999'999'999'999ULL);
+                    BEAST_EXPECT(maxMantissa == 9'223'372'036'854'775'807ULL);
                     test(
-                        Number{false, maxMantissa, 0, Number::Normalized{}}, "9999999999999999990");
+                        Number{false, maxMantissa, 0, Number::Normalized{}}, "9223372036854775807");
                     test(
-                        Number{true, maxMantissa, 0, Number::Normalized{}}, "-9999999999999999990");
+                        Number{true, maxMantissa, 0, Number::Normalized{}}, "-9223372036854775807");
 
                     test(
                         Number{std::numeric_limits<std::int64_t>::max(), 0}, "9223372036854775807");
@@ -1588,7 +1721,7 @@ public:
             Number const initalXrp{kInitialXrp};
             BEAST_EXPECT(initalXrp.exponent() > 0);
 
-            Number const maxInt64{Number::kMaxRep};
+            Number const maxInt64{Number::kLargestMantissa};
             BEAST_EXPECT(maxInt64.exponent() > 0);
             // 85'070'591'730'234'615'865'843'651'857'942'052'864 - 38 digits
             BEAST_EXPECT((power(maxInt64, 2) == Number{85'070'591'730'234'62, 22}));
@@ -1605,21 +1738,242 @@ public:
             Number const initalXrp{kInitialXrp};
             BEAST_EXPECT(initalXrp.exponent() <= 0);
 
-            Number const maxInt64{Number::kMaxRep};
+            Number const maxInt64{Number::kLargestMantissa};
             BEAST_EXPECT(maxInt64.exponent() <= 0);
             // 85'070'591'730'234'615'847'396'907'784'232'501'249 - 38 digits
             BEAST_EXPECT((power(maxInt64, 2) == Number{85'070'591'730'234'615'85, 19}));
 
             NumberRoundModeGuard const mg(Number::RoundingMode::TowardsZero);
 
-            auto const maxMantissa = Number::maxMantissa();
-            Number const max = Number{false, maxMantissa, 0, Number::Normalized{}};
-            BEAST_EXPECT(max.mantissa() == maxMantissa / 10);
-            BEAST_EXPECT(max.exponent() == 1);
-            // 99'999'999'999'999'999'800'000'000'000'000'000'100 - also 38
-            // digits
-            BEAST_EXPECT(
-                (power(max, 2) == Number{false, (maxMantissa / 10) - 1, 20, Number::Normalized{}}));
+            {
+                auto const maxInternalMantissa = getMaxInternalMantissa();
+
+                // Rounds down to fit under 2^63
+                Number const max = Number{false, maxInternalMantissa, 0, Number::Normalized{}};
+                // No alterations by the accessors
+                BEAST_EXPECT(max.mantissa() == maxInternalMantissa / 10);
+                BEAST_EXPECT(max.exponent() == 1);
+                // 99'999'999'999'999'999'800'000'000'000'000'000'100 - also 38
+                // digits
+                BEAST_EXPECT(
+                    (power(max, 2) ==
+                     Number{false, (maxInternalMantissa / 10) - 1, 20, Number::Normalized{}}));
+            }
+
+            {
+                auto const maxMantissa = Number::maxMantissa();
+                Number const max = Number{false, maxMantissa, 0, Number::Normalized{}};
+                // No alterations by the accessors
+                BEAST_EXPECT(max.mantissa() == maxMantissa);
+                BEAST_EXPECT(max.exponent() == 0);
+                // 85'070'591'730'234'615'847'396'907'784'232'501'249 - also 38
+                // digits
+                BEAST_EXPECT(
+                    (power(max, 2) ==
+                     Number{false, 85'070'591'730'234'615'84, 19, Number::Normalized{}}));
+            }
+        }
+    }
+
+    void
+    testNormalizeToRange()
+    {
+        // Test edge-cases of normalizeToRange
+        auto const scale = Number::getMantissaScale();
+        testcase << "normalizeToRange " << to_string(scale);
+
+        auto test = [this](
+                        Number const& n,
+                        auto const rangeMin,
+                        auto const rangeMax,
+                        auto const expectedMantissa,
+                        auto const expectedExponent,
+                        auto const line) {
+            auto const normalized =
+                n.normalizeToRangeImpl(rangeMin, rangeMax, MantissaRange::CuspRoundingFix::Enabled);
+            BEAST_EXPECTS(
+                normalized.first == expectedMantissa,
+                "Number " + to_string(n) + " scaled to " + std::to_string(rangeMax) +
+                    ". Expected mantissa:" + std::to_string(expectedMantissa) +
+                    ", got: " + std::to_string(normalized.first) + " @ " + std::to_string(line));
+            BEAST_EXPECTS(
+                normalized.second == expectedExponent,
+                "Number " + to_string(n) + " scaled to " + std::to_string(rangeMax) +
+                    ". Expected exponent:" + std::to_string(expectedExponent) +
+                    ", got: " + std::to_string(normalized.second) + " @ " + std::to_string(line));
+        };
+
+        std::int64_t constexpr kIRangeMin = 100;
+        std::int64_t constexpr kIRangeMax = 999;
+
+        std::uint64_t constexpr kURangeMin = 100;
+        std::uint64_t constexpr kURangeMax = 999;
+
+        constexpr static MantissaRange kLargeRange{MantissaRange::MantissaScale::Large};
+
+        std::int64_t constexpr kIBigMin = kLargeRange.min;
+        std::int64_t constexpr kIBigMax = kLargeRange.max;
+
+        auto const testSuite = [&](Number const& n,
+                                   auto const expectedSmallMantissa,
+                                   auto const expectedSmallExponent,
+                                   auto const expectedLargeMantissa,
+                                   auto const expectedLargeExponent,
+                                   auto const line) {
+            test(n, kIRangeMin, kIRangeMax, expectedSmallMantissa, expectedSmallExponent, line);
+            test(n, kIBigMin, kIBigMax, expectedLargeMantissa, expectedLargeExponent, line);
+
+            // Only test non-negative. testing a negative number with an
+            // unsigned range will assert, and asserts can't be tested.
+            if (n.signum() >= 0)
+            {
+                test(n, kURangeMin, kURangeMax, expectedSmallMantissa, expectedSmallExponent, line);
+                test(
+                    n,
+                    kLargeRange.min,
+                    kLargeRange.max,
+                    expectedLargeMantissa,
+                    expectedLargeExponent,
+                    line);
+            }
+        };
+
+        {
+            // zero
+            Number const n{0};
+
+            testSuite(
+                n,
+                0,
+                std::numeric_limits<int>::lowest(),
+                0,
+                std::numeric_limits<int>::lowest(),
+                __LINE__);
+        }
+        {
+            // Small positive number
+            Number const n{2};
+
+            testSuite(n, 200, -2, 2'000'000'000'000'000'000, -18, __LINE__);
+        }
+        {
+            // Negative number
+            Number const n{-2};
+
+            testSuite(n, -200, -2, -2'000'000'000'000'000'000, -18, __LINE__);
+        }
+        {
+            // Biggest valid mantissa
+            Number const n{Number::kLargestMantissa, 0, Number::Normalized{}};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, 922, 16, Number::kLargestMantissa, 0, __LINE__);
+            }
+        }
+        {
+            // Biggest valid mantissa + 1
+            Number const n{Number::kLargestMantissa + 1, 0, Number::Normalized{}};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, 922, 16, (Number::kLargestMantissa / 10) + 1, 1, __LINE__);
+            }
+        }
+        {
+            // Biggest valid mantissa + 2
+            Number const n{Number::kLargestMantissa + 2, 0, Number::Normalized{}};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, 922, 16, (Number::kLargestMantissa / 10) + 1, 1, __LINE__);
+            }
+        }
+        {
+            // Biggest valid mantissa + 3
+            Number const n{Number::kLargestMantissa + 3, 0, Number::Normalized{}};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, 922, 16, (Number::kLargestMantissa / 10) + 1, 1, __LINE__);
+            }
+        }
+        {
+            // int64 min
+            Number const n{std::numeric_limits<std::int64_t>::min(), 0};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, -922, 16, -((Number::kLargestMantissa / 10) + 1), 1, __LINE__);
+            }
+        }
+        {
+            // int64 min + 1
+            Number const n{std::numeric_limits<std::int64_t>::min() + 1, 0};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, -922, 16, -Number::kLargestMantissa, 0, __LINE__);
+            }
+        }
+        {
+            // int64 min - 1
+            // Need to cast to uint, even though we're dealing with a negative
+            // number to avoid overflow and UB
+            Number const n{
+                true,
+                -static_cast<std::uint64_t>(std::numeric_limits<std::int64_t>::min()) + 1,
+                0,
+                Number::Normalized{}};
+
+            if (scale == MantissaRange::MantissaScale::Small)
+            {
+                testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
+            }
+            else
+            {
+                testSuite(n, -922, 16, -((Number::kLargestMantissa / 10) + 1), 1, __LINE__);
+            }
         }
     }
 
@@ -1628,7 +1982,7 @@ public:
     {
         auto const scale = Number::getMantissaScale();
         {
-            testcase << "upward rounding produces a value below exact at kMaxRep cusp "
+            testcase << "upward rounding produces a value below exact at kLargestMantissa cusp"
                      << to_string(scale);
 
             NumberRoundModeGuard const rg{Number::RoundingMode::Upward};
@@ -1898,12 +2252,37 @@ public:
             testTruncate();
             testRounding();
             testInt64();
+            testNormalizeToRange();
 
             testUpwardRoundsDown();
         }
     }
 };
 
+class NumberPerf_test : public Number_test
+{
+    void
+    run() override
+    {
+        // This suite will give the most accurate results when run
+        // single threaded, suppressing non-log output.
+        // "--unittest=NumberPerf --quiet --unittest-log"
+        using clock_type = std::chrono::steady_clock;
+
+        int const limit = 100000;
+        auto const start = clock_type::now();
+        for (int i = 0; i < limit; ++i)
+        {
+            Number_test::run();
+        }
+        auto const duration =
+            std::chrono::duration_cast<std::chrono::milliseconds>(clock_type::now() - start);
+
+        log << "Number test repeated " << limit << " times took " << duration << "\n";
+    }
+};
+
 BEAST_DEFINE_TESTSUITE(Number, basics, xrpl);
+BEAST_DEFINE_TESTSUITE_MANUAL(NumberPerf, tx, xrpl);
 
 }  // namespace xrpl