[WIP] Checkpoint

include/xrpl/basics/Number.h

@@ -36,18 +36,37 @@ 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 log10,
+ * and rem is value divided by 10^log. 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 <typename 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;
 }
 
@@ -61,8 +80,6 @@ isPowerOfTen(T value)
 /** 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 mantissa_scale enum indicates whether the range is "small" or "large".
  * This intentionally restricts the number of MantissaRanges that can be
@@ -80,8 +97,8 @@ isPowerOfTen(T value)
  * "large" scale.
  *
  * The "large" scale is 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.
+ * by an STAmount - IOUs, XRP, and MPTs. It has a min value of 2^63/10+1
+ * (truncated), and a max value of 2^63-1.
  *
  * 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
@@ -93,28 +110,38 @@ struct MantissaRange
     enum mantissa_scale { small, large };
 
     explicit constexpr MantissaRange(mantissa_scale scale_)
-        : min(getMin(scale_))
-        , max(min * 10 - 1)
-        , log(logTen(min).value_or(-1))
+        : max(getMax(scale_))
+        , min(computeMin(max))
+        , log(computeLog(min))
         , scale(scale_)
     {
+        // Since this is constexpr, if any of these throw, it won't compile
+        if (min * 10 <= max)
+            throw std::out_of_range("min * 10 <= max");
+        if (max / 10 >= min)
+            throw std::out_of_range("max / 10 >= min");
+        if ((min - 1) * 10 > max)
+            throw std::out_of_range("(min - 1) * 10 > max");
+        // This is a little hacky
+        if ((max + 10) / 10 < min)
+            throw std::out_of_range("(max + 10) / 10 < min");
     }
 
-    rep min;
     rep max;
+    rep min;
     int log;
     mantissa_scale scale;
 
 private:
     static constexpr rep
-    getMin(mantissa_scale scale_)
+    getMax(mantissa_scale scale_)
     {
         switch (scale_)
         {
             case small:
-                return 1'000'000'000'000'000ULL;
+                return 9'999'999'999'999'999ULL;
             case large:
-                return 1'000'000'000'000'000'000ULL;
+                return std::numeric_limits<std::int64_t>::max();
             default:
                 // Since this can never be called outside a non-constexpr
                 // context, this throw assures that the build fails if an
@@ -122,6 +149,24 @@ private:
                 throw std::runtime_error("Unknown mantissa scale");
         }
     }
+
+    static constexpr rep
+    computeMin(rep max)
+    {
+        auto min = max + 1;
+        auto const r = min % 10;
+        min /= 10;
+        if (r != 0)
+            ++min;
+        return min;
+    }
+
+    static constexpr rep
+    computeLog(rep min)
+    {
+        auto const estimate = logTenEstimate(min);
+        return estimate.first + (estimate.second == 1 ? 0 : 1);
+    }
 };
 
 // Like std::integral, but only 64-bit integral types.
@@ -156,9 +201,7 @@ concept Integral64 =
  *   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. The max of the "large" range, 2^63-1, TODO: explain the large range.
  *
  * ---- External Interface ----
  *
@@ -172,7 +215,7 @@ concept Integral64 =
  *
  * Note:
  *   1. 2^63-1 is between 10^18 and 10^19-1, which are the limits of the "large"
- *      mantissa range.
+ *      mantissa range. TODO: update this explanation.
  *   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
@@ -232,6 +275,7 @@ class Number
     using rep = std::int64_t;
     using internalrep = MantissaRange::rep;
 
+    // TODO: Get rid of negative_ and convert mantissa back to rep
     bool negative_{false};
     internalrep mantissa_{0};
     int exponent_{std::numeric_limits<int>::lowest()};
@@ -241,9 +285,11 @@ public:
     constexpr static int minExponent = -32768;
     constexpr static int maxExponent = 32768;
 
+#if MAXREP
     constexpr static internalrep maxRep = std::numeric_limits<rep>::max();
     static_assert(maxRep == 9'223'372'036'854'775'807);
     static_assert(-maxRep == std::numeric_limits<rep>::min() + 1);
+#endif
 
     // May need to make unchecked private
     struct unchecked
@@ -477,15 +523,27 @@ private:
     static_assert(smallRange.min == 1'000'000'000'000'000LL);
     static_assert(smallRange.max == 9'999'999'999'999'999LL);
     static_assert(smallRange.log == 15);
+#if MAXREP
     static_assert(smallRange.min < maxRep);
     static_assert(smallRange.max < maxRep);
+#endif
     constexpr static MantissaRange largeRange{MantissaRange::large};
-    static_assert(isPowerOfTen(largeRange.min));
-    static_assert(largeRange.min == 1'000'000'000'000'000'000ULL);
-    static_assert(largeRange.max == internalrep(9'999'999'999'999'999'999ULL));
+    static_assert(!isPowerOfTen(largeRange.min));
+    static_assert(largeRange.min == 922337203685477581ULL);
+    static_assert(largeRange.max == internalrep(9223372036854775807ULL));
+    static_assert(largeRange.max == std::numeric_limits<rep>::max());
     static_assert(largeRange.log == 18);
+    // There are 2 values that will not fit in largeRange without some extra
+    // work
+    // * 9223372036854775808
+    // * 9223372036854775809
+    // They both end up < min, but with a leftover. If they round up, everything
+    // will be fine. If they don't, well need to bring them up into range.
+
+#if MAXREP
     static_assert(largeRange.min < maxRep);
     static_assert(largeRange.max > maxRep);
+#endif
 
     // The range for the mantissa when normalized.
     // Use reference_wrapper to avoid making copies, and prevent accidentally
@@ -536,6 +594,9 @@ private:
     externalToInternal(rep mantissa);
 
     class Guard;
+
+public:
+    constexpr static internalrep largestMantissa = largeRange.max;
 };
 
 inline constexpr Number::Number(
@@ -589,17 +650,8 @@ inline Number::Number(rep mantissa) : Number{mantissa, 0}
 inline constexpr Number::rep
 Number::mantissa() const noexcept
 {
-    auto m = mantissa_;
-    if (m > maxRep)
-    {
-        XRPL_ASSERT_PARTS(
-            !isnormal() || (m % 10 == 0 && m / 10 <= maxRep),
-            "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 sign * static_cast<Number::rep>(mantissa_);
 }
 
 /** Returns the exponent of the external view of the Number.
@@ -610,16 +662,7 @@ Number::mantissa() const noexcept
 inline constexpr int
 Number::exponent() const noexcept
 {
-    auto e = exponent_;
-    if (mantissa_ > maxRep)
-    {
-        XRPL_ASSERT_PARTS(
-            !isnormal() || (mantissa_ % 10 == 0 && mantissa_ / 10 <= maxRep),
-            "xrpl::Number::exponent",
-            "large normalized mantissa has no remainder");
-        ++e;
-    }
-    return e;
+    return exponent_;
 }
 
 inline constexpr Number
@@ -715,15 +758,13 @@ Number::min() noexcept
 inline Number
 Number::max() noexcept
 {
-    return Number{
-        false, std::min(range_.get().max, maxRep), maxExponent, unchecked{}};
+    return Number{false, range_.get().max, maxExponent, unchecked{}};
 }
 
 inline Number
 Number::lowest() noexcept
 {
-    return Number{
-        true, std::min(range_.get().max, maxRep), maxExponent, unchecked{}};
+    return Number{true, range_.get().max, maxExponent, unchecked{}};
 }
 
 inline bool
@@ -732,9 +773,8 @@ Number::isnormal() const noexcept
     MantissaRange const& range = range_;
     auto const abs_m = mantissa_;
     return *this == Number{} ||
-        (range.min <= abs_m && abs_m <= range.max &&
-         (abs_m <= maxRep || abs_m % 10 == 0) && minExponent <= exponent_ &&
-         exponent_ <= maxExponent);
+        (range.min <= abs_m && abs_m <= range.max &&  //
+         minExponent <= exponent_ && exponent_ <= maxExponent);
 }
 
 template <Integral64 T>

include/xrpl/protocol/Protocol.h

@@ -252,7 +252,7 @@ std::size_t constexpr maxMPTokenMetadataLength = 1024;
 
 /** The maximum amount of MPTokenIssuance */
 std::uint64_t constexpr maxMPTokenAmount = 0x7FFF'FFFF'FFFF'FFFFull;
-static_assert(Number::maxRep >= maxMPTokenAmount);
+static_assert(Number::largestMantissa >= maxMPTokenAmount);
 
 /** The maximum length of Data payload */
 std::size_t constexpr maxDataPayloadLength = 256;

include/xrpl/protocol/SystemParameters.h

@@ -43,7 +43,7 @@ systemName()
 /** Number of drops in the genesis account. */
 constexpr XRPAmount INITIAL_XRP{100'000'000'000 * DROPS_PER_XRP};
 static_assert(INITIAL_XRP.drops() == 100'000'000'000'000'000);
-static_assert(Number::maxRep >= INITIAL_XRP.drops());
+static_assert(Number::largestMantissa >= INITIAL_XRP.drops());
 
 /** Returns true if the amount does not exceed the initial XRP in existence. */
 inline bool

src/libxrpl/basics/Number.cpp

@@ -279,7 +279,7 @@ Number::Guard::doRoundUp(
         ++mantissa;
         // Ensure mantissa after incrementing fits within both the
         // min/maxMantissa range and is a valid "rep".
-        if (mantissa > maxMantissa || mantissa > maxRep)
+        if (mantissa > maxMantissa)
         {
             mantissa /= 10;
             ++exponent;
@@ -318,7 +318,7 @@ Number::Guard::doRound(rep& drops, std::string location)
     auto r = round();
     if (r == 1 || (r == 0 && (drops & 1) == 1))
     {
-        if (drops >= maxRep)
+        if (drops >= maxMantissa())
         {
             static_assert(sizeof(internalrep) == sizeof(rep));
             // This should be impossible, because it's impossible to represent
@@ -406,7 +406,6 @@ doNormalize(
 {
     auto constexpr minExponent = Number::minExponent;
     auto constexpr maxExponent = Number::maxExponent;
-    auto constexpr maxRep = Number::maxRep;
 
     using Guard = Number::Guard;
 
@@ -443,33 +442,8 @@ doNormalize(
         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 > maxRep)
-    {
-        if (exponent_ >= maxExponent)
-            throw std::overflow_error("Number::normalize 1.5");
-        g.push(m % 10);
-        m /= 10;
-        ++exponent_;
-    }
-    // Before modification, m should be within the min/max range. After
-    // modification, it must be less than maxRep. In other words, the original
-    // value should have been no more than maxRep * 10.
-    // (maxRep * 10 > maxMantissa)
     XRPL_ASSERT_PARTS(
-        m <= maxRep,
+        m <= maxMantissa,
         "xrpl::doNormalize",
         "intermediate mantissa fits in int64");
     mantissa_ = m;
@@ -616,7 +590,7 @@ Number::operator+=(Number const& y)
     if (xn == yn)
     {
         xm += ym;
-        if (xm > maxMantissa || xm > maxRep)
+        if (xm > maxMantissa)
         {
             g.push(xm % 10);
             xm /= 10;
@@ -637,7 +611,7 @@ Number::operator+=(Number const& y)
             xe = ye;
             xn = yn;
         }
-        while (xm < minMantissa && xm * 10 <= maxRep)
+        while (xm < minMantissa)
         {
             xm *= 10;
             xm -= g.pop();
@@ -719,7 +693,7 @@ Number::operator*=(Number const& y)
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
 
-    while (zm > maxMantissa || zm > maxRep)
+    while (zm > maxMantissa)
     {
         // The following is optimization for:
         // g.push(static_cast<unsigned>(zm % 10));
@@ -861,7 +835,7 @@ Number::operator rep() const
         }
         for (; offset > 0; --offset)
         {
-            if (drops > maxRep / 10)
+            if (drops > largeRange.max / 10)
                 throw std::overflow_error("Number::operator rep() overflow");
             drops *= 10;
         }

src/test/basics/Number_test.cpp

@@ -217,12 +217,12 @@ public:
                      9'999'999'999'999'999'990ULL,
                      -19,
                      Number::normalized{}}},
-                {Number{Number::maxRep},
+                {Number{Number::largestMantissa},
                  Number{6, -1},
-                 Number{Number::maxRep / 10, 1}},
-                {Number{Number::maxRep - 1},
+                 Number{Number::largestMantissa / 10, 1}},
+                {Number{Number::largestMantissa - 1},
                  Number{1, 0},
-                 Number{Number::maxRep}},
+                 Number{Number::largestMantissa}},
                 // Test extremes
                 {
                     // Each Number operand rounds up, so the actual mantissa is
@@ -240,11 +240,11 @@ public:
                     Number{2, 19},
                 },
                 {
-                    // Does not round. Mantissas are going to be > maxRep, 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
-                    // maxRep.
+                    // 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,
                         9'999'999'999'999'999'990ULL,
@@ -371,16 +371,24 @@ 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::maxRep},
+                {Number{Number::largestMantissa},
                  Number{6, -1},
-                 Number{Number::maxRep - 1}},
-                {Number{false, Number::maxRep + 1, 0, Number::normalized{}},
+                 Number{Number::largestMantissa - 1}},
+                {Number{
+                     false,
+                     Number::largestMantissa + 1,
+                     0,
+                     Number::normalized{}},
                  Number{1, 0},
-                 Number{Number::maxRep / 10 + 1, 1}},
-                {Number{false, Number::maxRep + 1, 0, Number::normalized{}},
+                 Number{Number::largestMantissa / 10 + 1, 1}},
+                {Number{
+                     false,
+                     Number::largestMantissa + 1,
+                     0,
+                     Number::normalized{}},
                  Number{3, 0},
-                 Number{Number::maxRep}},
-                {power(2, 63), Number{3, 0}, Number{Number::maxRep}},
+                 Number{Number::largestMantissa}},
+                {power(2, 63), Number{3, 0}, Number{Number::largestMantissa}},
             });
         auto test = [this](auto const& c) {
             for (auto const& [x, y, z] : c)
@@ -489,8 +497,8 @@ public:
                  Number{false, maxMantissa, 0, Number::normalized{}},
                  Number{1, 38}},
                 // Maximum int64 range
-                {Number{Number::maxRep, 0},
-                 Number{Number::maxRep, 0},
+                {Number{Number::largestMantissa, 0},
+                 Number{Number::largestMantissa, 0},
                  Number{85'070'591'730'234'615'85, 19}},
             });
             tests(cSmall, cLarge);
@@ -567,8 +575,8 @@ public:
                          Number::normalized{}}},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::maxRep, 0},
-                     Number{Number::maxRep, 0},
+                    {Number{Number::largestMantissa, 0},
+                     Number{Number::largestMantissa, 0},
                      Number{85'070'591'730'234'615'84, 19}},
                 });
             tests(cSmall, cLarge);
@@ -645,8 +653,8 @@ public:
                          Number::normalized{}}},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::maxRep, 0},
-                     Number{Number::maxRep, 0},
+                    {Number{Number::largestMantissa, 0},
+                     Number{Number::largestMantissa, 0},
                      Number{85'070'591'730'234'615'84, 19}},
                 });
             tests(cSmall, cLarge);
@@ -715,8 +723,8 @@ public:
                      Number{1, 38}},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::maxRep, 0},
-                     Number{Number::maxRep, 0},
+                    {Number{Number::largestMantissa, 0},
+                     Number{Number::largestMantissa, 0},
                      Number{85'070'591'730'234'615'85, 19}},
                 });
             tests(cSmall, cLarge);
@@ -1008,10 +1016,10 @@ public:
              2,
              Number{
                  false, 3'162'277'660'168'379'330, -9, Number::normalized{}}},
-            {Number{Number::maxRep},
+            {Number{Number::largestMantissa},
              2,
              Number{false, 3'037'000'499'976049692, -9, Number::normalized{}}},
-            {Number{Number::maxRep},
+            {Number{Number::largestMantissa},
              4,
              Number{false, 55'108'98747006743627, -14, Number::normalized{}}},
         });
@@ -1070,7 +1078,7 @@ public:
             Number{5, -1},
             Number{0},
             Number{5625, -4},
-            Number{Number::maxRep},
+            Number{Number::largestMantissa},
         });
         test(cSmall);
         bool caught = false;
@@ -1690,7 +1698,7 @@ public:
             Number const initalXrp{INITIAL_XRP};
             BEAST_EXPECT(initalXrp.exponent() > 0);
 
-            Number const maxInt64{Number::maxRep};
+            Number const maxInt64{Number::largestMantissa};
             BEAST_EXPECT(maxInt64.exponent() > 0);
             // 85'070'591'730'234'615'865'843'651'857'942'052'864 - 38 digits
             BEAST_EXPECT(
@@ -1710,7 +1718,7 @@ public:
             Number const initalXrp{INITIAL_XRP};
             BEAST_EXPECT(initalXrp.exponent() <= 0);
 
-            Number const maxInt64{Number::maxRep};
+            Number const maxInt64{Number::largestMantissa};
             BEAST_EXPECT(maxInt64.exponent() <= 0);
             // 85'070'591'730'234'615'847'396'907'784'232'501'249 - 38 digits
             BEAST_EXPECT(