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rippled/src/test/basics/Number_test.cpp
Ed Hennis 9b4587f9af Update formatting
2026-02-20 13:29:51 -05:00

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#include <xrpl/basics/Number.h>
#include <xrpl/beast/unit_test.h>
#include <xrpl/protocol/IOUAmount.h>
#include <xrpl/protocol/STAmount.h>
#include <xrpl/protocol/SystemParameters.h>
#include <sstream>
#include <tuple>
namespace xrpl {
class Number_test : public beast::unit_test::suite
{
public:
void
testZero()
{
testcase << "zero " << to_string(Number::getMantissaScale());
for (Number const& z : {Number{0, 0}, Number{0}})
{
BEAST_EXPECT(z.mantissa() == 0);
BEAST_EXPECT(z.exponent() == Number{}.exponent());
BEAST_EXPECT((z + z) == z);
BEAST_EXPECT((z - z) == z);
BEAST_EXPECT(z == -z);
}
}
void
test_limits()
{
auto const scale = Number::getMantissaScale();
auto const minMantissa = Number::minMantissa();
testcase << "test_limits " << to_string(scale) << ", " << minMantissa;
bool caught = false;
try
{
Number x = Number{false, minMantissa * 10, 32768, Number::normalized{}};
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
auto test = [this](auto const& x, auto const& y, int line) {
auto const result = x == y;
std::stringstream ss;
ss << x << " == " << y << " -> " << (result ? "true" : "false");
expect(result, ss.str(), __FILE__, line);
};
test(
Number{false, minMantissa * 10, 32767, Number::normalized{}},
Number{false, minMantissa, 32768, Number::normalized{}},
__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, 1'501, 32000, Number::normalized{}},
Number{false, minMantissa + 2, 32003, Number::normalized{}},
__LINE__);
// 9,223,372,036,854,775,808
test(
Number{std::numeric_limits<std::int64_t>::min()},
scale == MantissaRange::small
? Number{-9'223'372'036'854'776, 3}
: Number{true, 9'223'372'036'854'775'808ULL, 0, Number::normalized{}},
__LINE__);
test(
Number{std::numeric_limits<std::int64_t>::min() + 1},
scale == MantissaRange::small ? Number{-9'223'372'036'854'776, 3}
: Number{-9'223'372'036'854'775'807},
__LINE__);
test(
Number{std::numeric_limits<std::int64_t>::max()},
Number{
scale == MantissaRange::small ? 9'223'372'036'854'776
: std::numeric_limits<std::int64_t>::max(),
18 - Number::mantissaLog()},
__LINE__);
caught = false;
try
{
[[maybe_unused]]
Number q = Number{false, minMantissa, 32767, Number::normalized{}} * 100;
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
void
test_add()
{
auto const scale = Number::getMantissaScale();
testcase << "test_add " << to_string(scale);
using Case = std::tuple<Number, Number, Number>;
auto const cSmall = std::to_array<Case>(
{{Number{1'000'000'000'000'000, -15},
Number{6'555'555'555'555'555, -29},
Number{1'000'000'000'000'066, -15}},
{Number{-1'000'000'000'000'000, -15},
Number{-6'555'555'555'555'555, -29},
Number{-1'000'000'000'000'066, -15}},
{Number{-1'000'000'000'000'000, -15},
Number{6'555'555'555'555'555, -29},
Number{-9'999'999'999'999'344, -16}},
{Number{-6'555'555'555'555'555, -29},
Number{1'000'000'000'000'000, -15},
Number{9'999'999'999'999'344, -16}},
{Number{}, Number{5}, Number{5}},
{Number{5}, Number{}, Number{5}},
{Number{5'555'555'555'555'555, -32768},
Number{-5'555'555'555'555'554, -32768},
Number{0}},
{Number{-9'999'999'999'999'999, -31},
Number{1'000'000'000'000'000, -15},
Number{9'999'999'999'999'990, -16}}});
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{1'000'000'000'000'000, -15},
Number{6'555'555'555'555'555, -29},
Number{1'000'000'000'000'065'556, -18}},
{Number{-1'000'000'000'000'000, -15},
Number{-6'555'555'555'555'555, -29},
Number{-1'000'000'000'000'065'556, -18}},
{Number{-1'000'000'000'000'000, -15},
Number{6'555'555'555'555'555, -29},
Number{true, 9'999'999'999'999'344'444ULL, -19, Number::normalized{}}},
{Number{-6'555'555'555'555'555, -29},
Number{1'000'000'000'000'000, -15},
Number{false, 9'999'999'999'999'344'444ULL, -19, Number::normalized{}}},
{Number{}, Number{5}, Number{5}},
{Number{5}, Number{}, Number{5}},
{Number{5'555'555'555'555'555'000, -32768},
Number{-5'555'555'555'555'554'000, -32768},
Number{0}},
{Number{-9'999'999'999'999'999, -31},
Number{1'000'000'000'000'000, -15},
Number{9'999'999'999'999'990, -16}},
// Items from cSmall expanded for the larger mantissa
{Number{1'000'000'000'000'000'000, -18},
Number{6'555'555'555'555'555'555, -35},
Number{1'000'000'000'000'000'066, -18}},
{Number{-1'000'000'000'000'000'000, -18},
Number{-6'555'555'555'555'555'555, -35},
Number{-1'000'000'000'000'000'066, -18}},
{Number{-1'000'000'000'000'000'000, -18},
Number{6'555'555'555'555'555'555, -35},
Number{true, 9'999'999'999'999'999'344ULL, -19, Number::normalized{}}},
{Number{-6'555'555'555'555'555'555, -35},
Number{1'000'000'000'000'000'000, -18},
Number{false, 9'999'999'999'999'999'344ULL, -19, Number::normalized{}}},
{Number{}, Number{5}, Number{5}},
{Number{5'555'555'555'555'555'555, -32768},
Number{-5'555'555'555'555'555'554, -32768},
Number{0}},
{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::largestMantissa},
Number{6, -1},
Number{Number::largestMantissa / 10, 1}},
{Number{Number::largestMantissa - 1},
Number{1, 0},
Number{Number::largestMantissa}},
// Test extremes
{
// Each Number operand rounds up, so the actual mantissa is
// minMantissa
Number{false, 9'999'999'999'999'999'999ULL, 0, Number::normalized{}},
Number{false, 9'999'999'999'999'999'999ULL, 0, Number::normalized{}},
Number{2, 19},
},
{
// 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::largestMantissa, 0, Number::normalized{}},
Number{false, Number::largestMantissa, 0, Number::normalized{}},
Number{false, Number::largestMantissa * 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 test = [this](auto const& c) {
for (auto const& [x, y, z] : c)
{
auto const result = x + y;
std::stringstream ss;
ss << x << " + " << y << " = " << result << ". Expected: " << z;
BEAST_EXPECTS(result == z, ss.str());
}
};
if (scale == MantissaRange::small)
test(cSmall);
else
test(cLarge);
{
bool caught = false;
try
{
Number{false, Number::maxMantissa(), 32768, Number::normalized{}} +
Number{false, Number::minMantissa(), 32767, Number::normalized{}} * 5;
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
}
void
test_sub()
{
auto const scale = Number::getMantissaScale();
testcase << "test_sub " << to_string(scale);
using Case = std::tuple<Number, Number, Number>;
auto const cSmall = std::to_array<Case>(
{{Number{1'000'000'000'000'000, -15},
Number{6'555'555'555'555'555, -29},
Number{9'999'999'999'999'344, -16}},
{Number{6'555'555'555'555'555, -29},
Number{1'000'000'000'000'000, -15},
Number{-9'999'999'999'999'344, -16}},
{Number{1'000'000'000'000'000, -15}, Number{1'000'000'000'000'000, -15}, Number{0}},
{Number{1'000'000'000'000'000, -15},
Number{1'000'000'000'000'001, -15},
Number{-1'000'000'000'000'000, -30}},
{Number{1'000'000'000'000'001, -15},
Number{1'000'000'000'000'000, -15},
Number{1'000'000'000'000'000, -30}}});
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{1'000'000'000'000'000, -15},
Number{6'555'555'555'555'555, -29},
Number{false, 9'999'999'999'999'344'444ULL, -19, Number::normalized{}}},
{Number{6'555'555'555'555'555, -29},
Number{1'000'000'000'000'000, -15},
Number{true, 9'999'999'999'999'344'444ULL, -19, Number::normalized{}}},
{Number{1'000'000'000'000'000, -15}, Number{1'000'000'000'000'000, -15}, Number{0}},
{Number{1'000'000'000'000'000, -15},
Number{1'000'000'000'000'001, -15},
Number{-1'000'000'000'000'000, -30}},
{Number{1'000'000'000'000'001, -15},
Number{1'000'000'000'000'000, -15},
Number{1'000'000'000'000'000, -30}},
// Items from cSmall expanded for the larger mantissa
{Number{1'000'000'000'000'000'000, -18},
Number{6'555'555'555'555'555'555, -32},
Number{false, 9'999'999'999'999'344'444ULL, -19, Number::normalized{}}},
{Number{6'555'555'555'555'555'555, -32},
Number{1'000'000'000'000'000'000, -18},
Number{true, 9'999'999'999'999'344'444ULL, -19, Number::normalized{}}},
{Number{1'000'000'000'000'000'000, -18},
Number{1'000'000'000'000'000'000, -18},
Number{0}},
{Number{1'000'000'000'000'000'000, -18},
Number{1'000'000'000'000'000'001, -18},
Number{-1'000'000'000'000'000'000, -36}},
{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::largestMantissa},
Number{6, -1},
Number{Number::largestMantissa - 1}},
{Number{false, Number::largestMantissa + 1, 0, Number::normalized{}},
Number{1, 0},
Number{Number::largestMantissa / 10 + 1, 1}},
{Number{false, Number::largestMantissa + 1, 0, Number::normalized{}},
Number{3, 0},
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)
{
auto const result = x - y;
std::stringstream ss;
ss << x << " - " << y << " = " << result << ". Expected: " << z;
BEAST_EXPECTS(result == z, ss.str());
}
};
if (scale == MantissaRange::small)
test(cSmall);
else
test(cLarge);
}
void
test_mul()
{
auto const scale = Number::getMantissaScale();
testcase << "test_mul " << to_string(scale);
// 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, line] : c)
{
auto const result = x * y;
std::stringstream ss;
ss << x << " * " << y << " = " << result << ". Expected: " << z;
BEAST_EXPECTS(result == z, ss.str() + " line: " + std::to_string(line));
}
};
auto tests = [&](auto const& cSmall, auto const& cLarge) {
if (scale == MantissaRange::small)
test(cSmall);
else
test(cLarge);
};
auto const maxMantissa = Number::maxMantissa();
auto const maxInternalMantissa = static_cast<std::uint64_t>(static_cast<std::int64_t>(
power(10, Number::mantissaLog()))) *
10 -
1;
saveNumberRoundMode save{Number::setround(Number::to_nearest)};
{
auto const cSmall = std::to_array<Case>({
{Number{7}, Number{8}, Number{56}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{2000000000000000, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-2000000000000000, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{2000000000000000, -15},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
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},
__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}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{1999999999999999862, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-1999999999999999862, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{1999999999999999862, -18},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
Number{false, 9'999'999'999'999'999'579ULL, -18, Number::normalized{}},
__LINE__},
{Number{1000000000000000000, -32768},
Number{1000000000000000000, -32768},
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},
__LINE__},
{Number{-1414213562373095048, -18},
Number{1414213562373095048, -18},
Number{-1999999999999999998, -18},
__LINE__},
{Number{-1414213562373095048, -18},
Number{-1414213562373095049, -18},
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{85'070'591'730'234'615'85, 19},
__LINE__},
// Maximum int64 range
{Number{Number::largestMantissa, 0},
Number{Number::largestMantissa, 0},
Number{85'070'591'730'234'615'85, 19},
__LINE__},
});
tests(cSmall, cLarge);
}
Number::setround(Number::towards_zero);
testcase << "test_mul " << to_string(Number::getMantissaScale()) << " towards_zero";
{
auto const cSmall = std::to_array<Case>(
{{Number{7}, Number{8}, Number{56}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{1999999999999999, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-1999999999999999, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{1999999999999999, -15},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
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}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{1999999999999999861, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-1999999999999999861, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{1999999999999999861, -18},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
Number{false, 9999999999999999579ULL, -18, Number::normalized{}},
__LINE__},
{Number{1000000000000000000, -32768},
Number{1000000000000000000, -32768},
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},
__LINE__},
{Number{-1414213562373095048, -18},
Number{1414213562373095048, -18},
Number{-1999999999999999997, -18},
__LINE__},
{Number{-1414213562373095048, -18},
Number{-1414213562373095049, -18},
Number{1999999999999999999, -18},
__LINE__},
{Number{3214285714285714278, -18},
Number{3111111111111111119, -18},
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{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::largestMantissa, 0},
Number{Number::largestMantissa, 0},
Number{85'070'591'730'234'615'84, 19},
__LINE__},
});
tests(cSmall, cLarge);
}
Number::setround(Number::downward);
testcase << "test_mul " << to_string(Number::getMantissaScale()) << " downward";
{
auto const cSmall = std::to_array<Case>(
{{Number{7}, Number{8}, Number{56}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{1999999999999999, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-2000000000000000, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{1999999999999999, -15},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
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}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{1999999999999999861, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-1999999999999999862, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{1999999999999999861, -18},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
Number{false, 9'999'999'999'999'999'579ULL, -18, Number::normalized{}},
__LINE__},
{Number{1000000000000000000, -32768},
Number{1000000000000000000, -32768},
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},
__LINE__},
{Number{-1414213562373095048, -18},
Number{1414213562373095048, -18},
Number{-1999999999999999998, -18},
__LINE__},
{Number{-1414213562373095048, -18},
Number{-1414213562373095049, -18},
Number{1999999999999999999, -18},
__LINE__},
{Number{3214285714285714278, -18},
Number{3111111111111111119, -18},
Number{10, 0},
__LINE__},
// Maximum internal mantissa range - rounds down to
// maxMantissa/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 mantissa range - same as int64
{Number{false, maxMantissa, 0, Number::normalized{}},
Number{false, maxMantissa, 0, 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::largestMantissa, 0},
Number{Number::largestMantissa, 0},
Number{85'070'591'730'234'615'84, 19},
__LINE__},
});
tests(cSmall, cLarge);
}
Number::setround(Number::upward);
testcase << "test_mul " << to_string(Number::getMantissaScale()) << " upward";
{
auto const cSmall = std::to_array<Case>(
{{Number{7}, Number{8}, Number{56}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{2000000000000000, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-1999999999999999, -15},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{2000000000000000, -15},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
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}, __LINE__},
{Number{1414213562373095, -15},
Number{1414213562373095, -15},
Number{1999999999999999862, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{1414213562373095, -15},
Number{-1999999999999999861, -18},
__LINE__},
{Number{-1414213562373095, -15},
Number{-1414213562373095, -15},
Number{1999999999999999862, -18},
__LINE__},
{Number{3214285714285706, -15},
Number{3111111111111119, -15},
Number{999999999999999958, -17},
__LINE__},
{Number{1000000000000000000, -32768},
Number{1000000000000000000, -32768},
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},
__LINE__},
{Number{-1414213562373095048, -18},
Number{1414213562373095048, -18},
Number{-1999999999999999997, -18},
__LINE__},
{Number{-1414213562373095048, -18},
Number{-1414213562373095049, -18},
Number{2, 0},
__LINE__},
{Number{3214285714285714278, -18},
Number{3111111111111111119, -18},
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{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::largestMantissa, 0},
Number{Number::largestMantissa, 0},
Number{85'070'591'730'234'615'85, 19},
__LINE__},
});
tests(cSmall, cLarge);
}
testcase << "test_mul " << to_string(Number::getMantissaScale()) << " overflow";
{
bool caught = false;
try
{
Number{false, maxMantissa, 32768, Number::normalized{}} *
Number{false, Number::minMantissa() * 5, 32767, Number::normalized{}};
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
}
void
test_div()
{
auto const scale = Number::getMantissaScale();
testcase << "test_div " << to_string(scale);
using Case = std::tuple<Number, Number, Number>;
auto test = [this](auto const& c) {
for (auto const& [x, y, z] : c)
{
auto const result = x / y;
std::stringstream ss;
ss << x << " / " << y << " = " << result << ". Expected: " << z;
BEAST_EXPECTS(result == z, ss.str());
}
};
auto const maxMantissa = Number::maxMantissa();
auto tests = [&](auto const& cSmall, auto const& cLarge) {
if (scale == MantissaRange::small)
test(cSmall);
else
test(cLarge);
};
saveNumberRoundMode save{Number::setround(Number::to_nearest)};
{
auto const cSmall = std::to_array<Case>(
{{Number{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'667, -16}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'667, -16}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428, -16}}});
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{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'666'667, -19}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'666'667, -19}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428'571, -19}},
// Items from cSmall expanded for the larger mantissa, except
// duplicates.
{Number{1414213562373095049, -13}, Number{1414213562373095049, -13}, Number{1}},
{Number{false, maxMantissa, 0, Number::normalized{}},
Number{1'000'000'000'000'000'000},
Number{false, maxMantissa, -18, Number::normalized{}}}});
tests(cSmall, cLarge);
}
testcase << "test_div " << to_string(Number::getMantissaScale()) << " towards_zero";
Number::setround(Number::towards_zero);
{
auto const cSmall = std::to_array<Case>(
{{Number{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'666, -16}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'666, -16}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428, -16}}});
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{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'666'666, -19}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'666'666, -19}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428'571, -19}},
// Items from cSmall expanded for the larger mantissa, except
// duplicates.
{Number{1414213562373095049, -13}, Number{1414213562373095049, -13}, Number{1}},
{Number{false, maxMantissa, 0, Number::normalized{}},
Number{1'000'000'000'000'000'000},
Number{false, maxMantissa, -18, Number::normalized{}}}});
tests(cSmall, cLarge);
}
testcase << "test_div " << to_string(Number::getMantissaScale()) << " downward";
Number::setround(Number::downward);
{
auto const cSmall = std::to_array<Case>(
{{Number{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'666, -16}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'667, -16}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428, -16}}});
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{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'666'666, -19}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'666'667, -19}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428'571, -19}},
// Items from cSmall expanded for the larger mantissa, except
// duplicates.
{Number{1414213562373095049, -13}, Number{1414213562373095049, -13}, Number{1}},
{Number{false, maxMantissa, 0, Number::normalized{}},
Number{1'000'000'000'000'000'000},
Number{false, maxMantissa, -18, Number::normalized{}}}});
tests(cSmall, cLarge);
}
testcase << "test_div " << to_string(Number::getMantissaScale()) << " upward";
Number::setround(Number::upward);
{
auto const cSmall = std::to_array<Case>(
{{Number{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'667, -16}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'666, -16}},
{Number{1}, Number{7}, Number{1'428'571'428'571'429, -16}}});
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{1}, Number{2}, Number{5, -1}},
{Number{1}, Number{10}, Number{1, -1}},
{Number{1}, Number{-10}, Number{-1, -1}},
{Number{0}, Number{100}, Number{0}},
{Number{1414213562373095, -10}, Number{1414213562373095, -10}, Number{1}},
{Number{9'999'999'999'999'999},
Number{1'000'000'000'000'000},
Number{9'999'999'999'999'999, -15}},
{Number{2}, Number{3}, Number{6'666'666'666'666'666'667, -19}},
{Number{-2}, Number{3}, Number{-6'666'666'666'666'666'666, -19}},
{Number{1}, Number{7}, Number{1'428'571'428'571'428'572, -19}},
// Items from cSmall expanded for the larger mantissa, except
// duplicates.
{Number{1414213562373095049, -13}, Number{1414213562373095049, -13}, Number{1}},
{Number{false, maxMantissa, 0, Number::normalized{}},
Number{1'000'000'000'000'000'000},
Number{false, maxMantissa, -18, Number::normalized{}}}});
tests(cSmall, cLarge);
}
testcase << "test_div " << to_string(Number::getMantissaScale()) << " overflow";
bool caught = false;
try
{
Number{1000000000000000, -15} / Number{0};
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
void
test_root()
{
auto const scale = Number::getMantissaScale();
testcase << "test_root " << to_string(scale);
using Case = std::tuple<Number, unsigned, Number>;
auto test = [this](auto const& c) {
for (auto const& [x, y, z] : c)
{
auto const result = root(x, y);
std::stringstream ss;
ss << "root(" << x << ", " << y << ") = " << result << ". Expected: " << z;
BEAST_EXPECTS(result == z, ss.str());
}
};
/*
auto tests = [&](auto const& cSmall, auto const& cLarge) {
test(cSmall);
if (scale != MantissaRange::small)
test(cLarge);
};
*/
auto const maxInternalMantissa = static_cast<std::uint64_t>(static_cast<std::int64_t>(
power(10, Number::mantissaLog()))) *
10 -
1;
auto const cSmall = std::to_array<Case>(
{{Number{2}, 2, Number{1414213562373095049, -18}},
{Number{2'000'000}, 2, Number{1414213562373095049, -15}},
{Number{2, -30}, 2, Number{1414213562373095049, -33}},
{Number{-27}, 3, Number{-3}},
{Number{1}, 5, Number{1}},
{Number{-1}, 0, Number{1}},
{Number{5, -1}, 0, Number{0}},
{Number{0}, 5, Number{0}},
{Number{5625, -4}, 2, Number{75, -2}}});
auto const cLarge = std::to_array<Case>({
{Number{false, maxInternalMantissa - 9, -1, Number::normalized{}},
2,
Number{false, 999'999'999'999'999'999, -9, Number::normalized{}}},
{Number{false, maxInternalMantissa - 9, 0, Number::normalized{}},
2,
Number{false, 3'162'277'660'168'379'330, -9, Number::normalized{}}},
{Number{Number::largestMantissa},
2,
Number{false, 3'037'000'499'976049692, -9, Number::normalized{}}},
{Number{Number::largestMantissa},
4,
Number{false, 55'108'98747006743627, -14, Number::normalized{}}},
});
test(cSmall);
if (Number::getMantissaScale() != MantissaRange::small)
{
NumberRoundModeGuard mg(Number::towards_zero);
test(cLarge);
}
bool caught = false;
try
{
(void)root(Number{-2}, 0);
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
caught = false;
try
{
(void)root(Number{-2}, 4);
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
void
test_root2()
{
auto const scale = Number::getMantissaScale();
testcase << "test_root2 " << to_string(scale);
auto test = [this](auto const& c) {
for (auto const& x : c)
{
auto const expected = root(x, 2);
auto const result = root2(x);
std::stringstream ss;
ss << "root2(" << x << ") = " << result << ". Expected: " << expected;
BEAST_EXPECTS(result == expected, ss.str());
}
};
auto const maxInternalMantissa = power(10, Number::mantissaLog()) * 10 - 1;
auto const cSmall = std::to_array<Number>({
Number{2},
Number{2'000'000},
Number{2, -30},
Number{27},
Number{1},
Number{5, -1},
Number{0},
Number{5625, -4},
Number{Number::largestMantissa},
maxInternalMantissa,
Number{Number::minMantissa(), 0, Number::unchecked{}},
Number{Number::maxMantissa(), 0, Number::unchecked{}},
});
test(cSmall);
bool caught = false;
try
{
(void)root2(Number{-2});
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
void
test_power1()
{
testcase << "test_power1 " << to_string(Number::getMantissaScale());
using Case = std::tuple<Number, unsigned, Number>;
Case c[]{
{Number{64}, 0, Number{1}},
{Number{64}, 1, Number{64}},
{Number{64}, 2, Number{4096}},
{Number{-64}, 2, Number{4096}},
{Number{64}, 3, Number{262144}},
{Number{-64}, 3, Number{-262144}},
{Number{64}, 11, Number{false, 7378697629483820646ULL, 1, Number::normalized{}}},
{Number{-64}, 11, Number{true, 7378697629483820646ULL, 1, Number::normalized{}}}};
for (auto const& [x, y, z] : c)
BEAST_EXPECT((power(x, y) == z));
}
void
test_power2()
{
testcase << "test_power2 " << to_string(Number::getMantissaScale());
using Case = std::tuple<Number, unsigned, unsigned, Number>;
Case c[]{
{Number{1}, 3, 7, Number{1}},
{Number{-1}, 1, 0, Number{1}},
{Number{-1, -1}, 1, 0, Number{0}},
{Number{16}, 0, 5, Number{1}},
{Number{34}, 3, 3, Number{34}},
{Number{4}, 3, 2, Number{8}}};
for (auto const& [x, n, d, z] : c)
BEAST_EXPECT((power(x, n, d) == z));
bool caught = false;
try
{
(void)power(Number{7}, 0, 0);
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
caught = false;
try
{
(void)power(Number{7}, 1, 0);
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
caught = false;
try
{
(void)power(Number{-1, -1}, 3, 2);
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
void
testConversions()
{
testcase << "testConversions " << to_string(Number::getMantissaScale());
IOUAmount x{5, 6};
Number y = x;
BEAST_EXPECT((y == Number{5, 6}));
IOUAmount z{y};
BEAST_EXPECT(x == z);
XRPAmount xrp{500};
STAmount st = xrp;
Number n = st;
BEAST_EXPECT(XRPAmount{n} == xrp);
IOUAmount x0{0, 0};
Number y0 = x0;
BEAST_EXPECT((y0 == Number{0}));
IOUAmount z0{y0};
BEAST_EXPECT(x0 == z0);
XRPAmount xrp0{0};
Number n0 = xrp0;
BEAST_EXPECT(n0 == Number{0});
XRPAmount xrp1{n0};
BEAST_EXPECT(xrp1 == xrp0);
}
void
test_to_integer()
{
testcase << "test_to_integer " << to_string(Number::getMantissaScale());
using Case = std::tuple<Number, std::int64_t>;
saveNumberRoundMode save{Number::setround(Number::to_nearest)};
{
Case c[]{
{Number{0}, 0},
{Number{1}, 1},
{Number{2}, 2},
{Number{3}, 3},
{Number{-1}, -1},
{Number{-2}, -2},
{Number{-3}, -3},
{Number{10}, 10},
{Number{99}, 99},
{Number{1155}, 1155},
{Number{9'999'999'999'999'999, 0}, 9'999'999'999'999'999},
{Number{9'999'999'999'999'999, 1}, 99'999'999'999'999'990},
{Number{9'999'999'999'999'999, 2}, 999'999'999'999'999'900},
{Number{-9'999'999'999'999'999, 2}, -999'999'999'999'999'900},
{Number{15, -1}, 2},
{Number{14, -1}, 1},
{Number{16, -1}, 2},
{Number{25, -1}, 2},
{Number{6, -1}, 1},
{Number{5, -1}, 0},
{Number{4, -1}, 0},
{Number{-15, -1}, -2},
{Number{-14, -1}, -1},
{Number{-16, -1}, -2},
{Number{-25, -1}, -2},
{Number{-6, -1}, -1},
{Number{-5, -1}, 0},
{Number{-4, -1}, 0}};
for (auto const& [x, y] : c)
{
auto j = static_cast<std::int64_t>(x);
BEAST_EXPECT(j == y);
}
}
auto prev_mode = Number::setround(Number::towards_zero);
BEAST_EXPECT(prev_mode == Number::to_nearest);
{
Case c[]{
{Number{0}, 0},
{Number{1}, 1},
{Number{2}, 2},
{Number{3}, 3},
{Number{-1}, -1},
{Number{-2}, -2},
{Number{-3}, -3},
{Number{10}, 10},
{Number{99}, 99},
{Number{1155}, 1155},
{Number{9'999'999'999'999'999, 0}, 9'999'999'999'999'999},
{Number{9'999'999'999'999'999, 1}, 99'999'999'999'999'990},
{Number{9'999'999'999'999'999, 2}, 999'999'999'999'999'900},
{Number{-9'999'999'999'999'999, 2}, -999'999'999'999'999'900},
{Number{15, -1}, 1},
{Number{14, -1}, 1},
{Number{16, -1}, 1},
{Number{25, -1}, 2},
{Number{6, -1}, 0},
{Number{5, -1}, 0},
{Number{4, -1}, 0},
{Number{-15, -1}, -1},
{Number{-14, -1}, -1},
{Number{-16, -1}, -1},
{Number{-25, -1}, -2},
{Number{-6, -1}, 0},
{Number{-5, -1}, 0},
{Number{-4, -1}, 0}};
for (auto const& [x, y] : c)
{
auto j = static_cast<std::int64_t>(x);
BEAST_EXPECT(j == y);
}
}
prev_mode = Number::setround(Number::downward);
BEAST_EXPECT(prev_mode == Number::towards_zero);
{
Case c[]{
{Number{0}, 0},
{Number{1}, 1},
{Number{2}, 2},
{Number{3}, 3},
{Number{-1}, -1},
{Number{-2}, -2},
{Number{-3}, -3},
{Number{10}, 10},
{Number{99}, 99},
{Number{1155}, 1155},
{Number{9'999'999'999'999'999, 0}, 9'999'999'999'999'999},
{Number{9'999'999'999'999'999, 1}, 99'999'999'999'999'990},
{Number{9'999'999'999'999'999, 2}, 999'999'999'999'999'900},
{Number{-9'999'999'999'999'999, 2}, -999'999'999'999'999'900},
{Number{15, -1}, 1},
{Number{14, -1}, 1},
{Number{16, -1}, 1},
{Number{25, -1}, 2},
{Number{6, -1}, 0},
{Number{5, -1}, 0},
{Number{4, -1}, 0},
{Number{-15, -1}, -2},
{Number{-14, -1}, -2},
{Number{-16, -1}, -2},
{Number{-25, -1}, -3},
{Number{-6, -1}, -1},
{Number{-5, -1}, -1},
{Number{-4, -1}, -1}};
for (auto const& [x, y] : c)
{
auto j = static_cast<std::int64_t>(x);
BEAST_EXPECT(j == y);
}
}
prev_mode = Number::setround(Number::upward);
BEAST_EXPECT(prev_mode == Number::downward);
{
Case c[]{
{Number{0}, 0},
{Number{1}, 1},
{Number{2}, 2},
{Number{3}, 3},
{Number{-1}, -1},
{Number{-2}, -2},
{Number{-3}, -3},
{Number{10}, 10},
{Number{99}, 99},
{Number{1155}, 1155},
{Number{9'999'999'999'999'999, 0}, 9'999'999'999'999'999},
{Number{9'999'999'999'999'999, 1}, 99'999'999'999'999'990},
{Number{9'999'999'999'999'999, 2}, 999'999'999'999'999'900},
{Number{-9'999'999'999'999'999, 2}, -999'999'999'999'999'900},
{Number{15, -1}, 2},
{Number{14, -1}, 2},
{Number{16, -1}, 2},
{Number{25, -1}, 3},
{Number{6, -1}, 1},
{Number{5, -1}, 1},
{Number{4, -1}, 1},
{Number{-15, -1}, -1},
{Number{-14, -1}, -1},
{Number{-16, -1}, -1},
{Number{-25, -1}, -2},
{Number{-6, -1}, 0},
{Number{-5, -1}, 0},
{Number{-4, -1}, 0}};
for (auto const& [x, y] : c)
{
auto j = static_cast<std::int64_t>(x);
BEAST_EXPECT(j == y);
}
}
bool caught = false;
try
{
(void)static_cast<std::int64_t>(Number{9223372036854776, 3});
}
catch (std::overflow_error const&)
{
caught = true;
}
BEAST_EXPECT(caught);
}
void
test_squelch()
{
testcase << "test_squelch " << to_string(Number::getMantissaScale());
Number limit{1, -6};
BEAST_EXPECT((squelch(Number{2, -6}, limit) == Number{2, -6}));
BEAST_EXPECT((squelch(Number{1, -6}, limit) == Number{1, -6}));
BEAST_EXPECT((squelch(Number{9, -7}, limit) == Number{0}));
BEAST_EXPECT((squelch(Number{-2, -6}, limit) == Number{-2, -6}));
BEAST_EXPECT((squelch(Number{-1, -6}, limit) == Number{-1, -6}));
BEAST_EXPECT((squelch(Number{-9, -7}, limit) == Number{0}));
}
void
testToString()
{
auto const scale = Number::getMantissaScale();
testcase << "testToString " << to_string(scale);
auto test = [this](Number const& n, std::string const& expected) {
auto const result = to_string(n);
std::stringstream ss;
ss << "to_string(" << result << "). Expected: " << expected;
BEAST_EXPECTS(result == expected, ss.str());
};
test(Number(-2, 0), "-2");
test(Number(0, 0), "0");
test(Number(2, 0), "2");
test(Number(25, -3), "0.025");
test(Number(-25, -3), "-0.025");
test(Number(25, 1), "250");
test(Number(-25, 1), "-250");
test(Number(2, 20), "2e20");
test(Number(-2, -20), "-2e-20");
// Test the edges
// ((exponent < -(25)) || (exponent > -(5)))))
// or ((exponent < -(28)) || (exponent > -(8)))))
test(Number(2, -10), "0.0000000002");
test(Number(2, -11), "2e-11");
test(Number(-2, 10), "-20000000000");
test(Number(-2, 11), "-2e11");
switch (scale)
{
case MantissaRange::small:
test(Number::min(), "1e-32753");
test(Number::max(), "9999999999999999e32768");
test(Number::lowest(), "-9999999999999999e32768");
{
NumberRoundModeGuard mg(Number::towards_zero);
auto const maxMantissa = Number::maxMantissa();
BEAST_EXPECT(maxMantissa == 9'999'999'999'999'999);
test(
Number{false, maxMantissa * 1000 + 999, -3, Number::normalized()},
"9999999999999999");
test(
Number{true, maxMantissa * 1000 + 999, -3, Number::normalized()},
"-9999999999999999");
test(Number{std::numeric_limits<std::int64_t>::max(), -3}, "9223372036854775");
test(
-(Number{std::numeric_limits<std::int64_t>::max(), -3}),
"-9223372036854775");
test(
Number{std::numeric_limits<std::int64_t>::min(), 0}, "-9223372036854775e3");
test(
-(Number{std::numeric_limits<std::int64_t>::min(), 0}),
"9223372036854775e3");
}
break;
case MantissaRange::large:
// Test the edges
// ((exponent < -(28)) || (exponent > -(8)))))
test(Number::min(), "922337203685477581e-32768");
test(Number::max(), "9223372036854775807e32768");
test(Number::lowest(), "-9223372036854775807e32768");
{
NumberRoundModeGuard mg(Number::towards_zero);
auto const maxMantissa = Number::maxMantissa();
BEAST_EXPECT(maxMantissa == 9'223'372'036'854'775'807ULL);
test(
Number{false, maxMantissa, 0, Number::normalized{}}, "9223372036854775807");
test(
Number{true, maxMantissa, 0, Number::normalized{}}, "-9223372036854775807");
test(
Number{std::numeric_limits<std::int64_t>::max(), 0}, "9223372036854775807");
test(
-(Number{std::numeric_limits<std::int64_t>::max(), 0}),
"-9223372036854775807");
// Because the absolute value of min is larger than max, it
// will be scaled down to fit under max. Since we're
// rounding towards zero, the 8 at the end is dropped.
test(
Number{std::numeric_limits<std::int64_t>::min(), 0},
"-9223372036854775800");
test(
-(Number{std::numeric_limits<std::int64_t>::min(), 0}),
"9223372036854775800");
}
test(
Number{std::numeric_limits<std::int64_t>::max(), 0} + 1, "9223372036854775810");
test(
-(Number{std::numeric_limits<std::int64_t>::max(), 0} + 1),
"-9223372036854775810");
break;
default:
BEAST_EXPECT(false);
}
}
void
test_relationals()
{
testcase << "test_relationals " << to_string(Number::getMantissaScale());
BEAST_EXPECT(!(Number{100} < Number{10}));
BEAST_EXPECT(Number{100} > Number{10});
BEAST_EXPECT(Number{100} >= Number{10});
BEAST_EXPECT(!(Number{100} <= Number{10}));
}
void
test_stream()
{
testcase << "test_stream " << to_string(Number::getMantissaScale());
Number x{100};
std::ostringstream os;
os << x;
BEAST_EXPECT(os.str() == to_string(x));
}
void
test_inc_dec()
{
testcase << "test_inc_dec " << to_string(Number::getMantissaScale());
Number x{100};
Number y = +x;
BEAST_EXPECT(x == y);
BEAST_EXPECT(x++ == y);
BEAST_EXPECT(x == Number{101});
BEAST_EXPECT(x-- == Number{101});
BEAST_EXPECT(x == y);
}
void
test_toSTAmount()
{
NumberSO stNumberSO{true};
Issue const issue;
Number const n{7'518'783'80596, -5};
saveNumberRoundMode const save{Number::setround(Number::to_nearest)};
auto res2 = STAmount{issue, n};
BEAST_EXPECT(res2 == STAmount{7518784});
Number::setround(Number::towards_zero);
res2 = STAmount{issue, n};
BEAST_EXPECT(res2 == STAmount{7518783});
Number::setround(Number::downward);
res2 = STAmount{issue, n};
BEAST_EXPECT(res2 == STAmount{7518783});
Number::setround(Number::upward);
res2 = STAmount{issue, n};
BEAST_EXPECT(res2 == STAmount{7518784});
}
void
test_truncate()
{
BEAST_EXPECT(Number(25, +1).truncate() == Number(250, 0));
BEAST_EXPECT(Number(25, 0).truncate() == Number(25, 0));
BEAST_EXPECT(Number(25, -1).truncate() == Number(2, 0));
BEAST_EXPECT(Number(25, -2).truncate() == Number(0, 0));
BEAST_EXPECT(Number(99, -2).truncate() == Number(0, 0));
BEAST_EXPECT(Number(-25, +1).truncate() == Number(-250, 0));
BEAST_EXPECT(Number(-25, 0).truncate() == Number(-25, 0));
BEAST_EXPECT(Number(-25, -1).truncate() == Number(-2, 0));
BEAST_EXPECT(Number(-25, -2).truncate() == Number(0, 0));
BEAST_EXPECT(Number(-99, -2).truncate() == Number(0, 0));
BEAST_EXPECT(Number(0, 0).truncate() == Number(0, 0));
BEAST_EXPECT(Number(0, 30000).truncate() == Number(0, 0));
BEAST_EXPECT(Number(0, -30000).truncate() == Number(0, 0));
BEAST_EXPECT(Number(100, -30000).truncate() == Number(0, 0));
BEAST_EXPECT(Number(100, -30000).truncate() == Number(0, 0));
BEAST_EXPECT(Number(-100, -30000).truncate() == Number(0, 0));
BEAST_EXPECT(Number(-100, -30000).truncate() == Number(0, 0));
}
void
testRounding()
{
// Test that rounding works as expected.
testcase("Rounding");
using NumberRoundings = std::map<Number::rounding_mode, std::int64_t>;
std::map<Number, NumberRoundings> const expected{
// Positive numbers
{Number{13, -1},
{{Number::to_nearest, 1},
{Number::towards_zero, 1},
{Number::downward, 1},
{Number::upward, 2}}},
{Number{23, -1},
{{Number::to_nearest, 2},
{Number::towards_zero, 2},
{Number::downward, 2},
{Number::upward, 3}}},
{Number{15, -1},
{{Number::to_nearest, 2},
{Number::towards_zero, 1},
{Number::downward, 1},
{Number::upward, 2}}},
{Number{25, -1},
{{Number::to_nearest, 2},
{Number::towards_zero, 2},
{Number::downward, 2},
{Number::upward, 3}}},
{Number{152, -2},
{{Number::to_nearest, 2},
{Number::towards_zero, 1},
{Number::downward, 1},
{Number::upward, 2}}},
{Number{252, -2},
{{Number::to_nearest, 3},
{Number::towards_zero, 2},
{Number::downward, 2},
{Number::upward, 3}}},
{Number{17, -1},
{{Number::to_nearest, 2},
{Number::towards_zero, 1},
{Number::downward, 1},
{Number::upward, 2}}},
{Number{27, -1},
{{Number::to_nearest, 3},
{Number::towards_zero, 2},
{Number::downward, 2},
{Number::upward, 3}}},
// Negative numbers
{Number{-13, -1},
{{Number::to_nearest, -1},
{Number::towards_zero, -1},
{Number::downward, -2},
{Number::upward, -1}}},
{Number{-23, -1},
{{Number::to_nearest, -2},
{Number::towards_zero, -2},
{Number::downward, -3},
{Number::upward, -2}}},
{Number{-15, -1},
{{Number::to_nearest, -2},
{Number::towards_zero, -1},
{Number::downward, -2},
{Number::upward, -1}}},
{Number{-25, -1},
{{Number::to_nearest, -2},
{Number::towards_zero, -2},
{Number::downward, -3},
{Number::upward, -2}}},
{Number{-152, -2},
{{Number::to_nearest, -2},
{Number::towards_zero, -1},
{Number::downward, -2},
{Number::upward, -1}}},
{Number{-252, -2},
{{Number::to_nearest, -3},
{Number::towards_zero, -2},
{Number::downward, -3},
{Number::upward, -2}}},
{Number{-17, -1},
{{Number::to_nearest, -2},
{Number::towards_zero, -1},
{Number::downward, -2},
{Number::upward, -1}}},
{Number{-27, -1},
{{Number::to_nearest, -3},
{Number::towards_zero, -2},
{Number::downward, -3},
{Number::upward, -2}}},
};
for (auto const& [num, roundings] : expected)
{
for (auto const& [mode, val] : roundings)
{
NumberRoundModeGuard g{mode};
auto const res = static_cast<std::int64_t>(num);
BEAST_EXPECTS(
res == val,
to_string(num) + " with mode " + std::to_string(mode) + " expected " +
std::to_string(val) + " got " + std::to_string(res));
}
}
}
void
testInt64()
{
auto const scale = Number::getMantissaScale();
testcase << "std::int64_t " << to_string(scale);
// Control case
BEAST_EXPECT(Number::maxMantissa() > 10);
Number ten{10};
BEAST_EXPECT(ten.exponent() <= 0);
if (scale == MantissaRange::small)
{
BEAST_EXPECT(std::numeric_limits<std::int64_t>::max() > INITIAL_XRP.drops());
BEAST_EXPECT(Number::maxMantissa() < INITIAL_XRP.drops());
Number const initalXrp{INITIAL_XRP};
BEAST_EXPECT(initalXrp.exponent() > 0);
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((power(maxInt64, 2) == Number{85'070'591'730'234'62, 22}));
Number const max = Number{false, Number::maxMantissa(), 0, Number::normalized{}};
BEAST_EXPECT(max.exponent() <= 0);
// 99'999'999'999'999'980'000'000'000'000'001 - 32 digits
BEAST_EXPECT((power(max, 2) == Number{99'999'999'999'999'98, 16}));
}
else
{
BEAST_EXPECT(std::numeric_limits<std::int64_t>::max() > INITIAL_XRP.drops());
BEAST_EXPECT(Number::maxMantissa() > INITIAL_XRP.drops());
Number const initalXrp{INITIAL_XRP};
BEAST_EXPECT(initalXrp.exponent() <= 0);
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((power(maxInt64, 2) == Number{85'070'591'730'234'615'85, 19}));
NumberRoundModeGuard mg(Number::towards_zero);
{
auto const maxInternalMantissa =
static_cast<std::uint64_t>(
static_cast<std::int64_t>(power(10, Number::mantissaLog()))) *
10 -
1;
// 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.normalizeToRange(rangeMin, rangeMax);
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 iRangeMin = 100;
std::int64_t constexpr iRangeMax = 999;
std::uint64_t constexpr uRangeMin = 100;
std::uint64_t constexpr uRangeMax = 999;
constexpr static MantissaRange largeRange{MantissaRange::large};
std::int64_t constexpr iBigMin = largeRange.min;
std::int64_t constexpr iBigMax = largeRange.max;
auto const testSuite = [&](Number const& n,
auto const expectedSmallMantissa,
auto const expectedSmallExponent,
auto const expectedLargeMantissa,
auto const expectedLargeExponent,
auto const line) {
test(n, iRangeMin, iRangeMax, expectedSmallMantissa, expectedSmallExponent, line);
test(n, iBigMin, iBigMax, 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, uRangeMin, uRangeMax, expectedSmallMantissa, expectedSmallExponent, line);
test(
n,
largeRange.min,
largeRange.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::largestMantissa, 0, Number::normalized{}};
if (scale == MantissaRange::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::largestMantissa, 0, __LINE__);
}
{
// Biggest valid mantissa + 1
Number const n{Number::largestMantissa + 1, 0, Number::normalized{}};
if (scale == MantissaRange::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, 922'337'203'685'477'581, 1, __LINE__);
}
{
// Biggest valid mantissa + 2
Number const n{Number::largestMantissa + 2, 0, Number::normalized{}};
if (scale == MantissaRange::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, 922'337'203'685'477'581, 1, __LINE__);
}
{
// Biggest valid mantissa + 3
Number const n{Number::largestMantissa + 3, 0, Number::normalized{}};
if (scale == MantissaRange::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, 922'337'203'685'477'581, 1, __LINE__);
}
{
// int64 min
Number const n{std::numeric_limits<std::int64_t>::min(), 0};
if (scale == MantissaRange::small)
testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
else
testSuite(n, -922, 16, -922'337'203'685'477'581, 1, __LINE__);
}
{
// int64 min + 1
Number const n{std::numeric_limits<std::int64_t>::min() + 1, 0};
if (scale == MantissaRange::small)
testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
else
testSuite(n, -922, 16, -9'223'372'036'854'775'807, 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::small)
testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
else
testSuite(n, -922, 16, -922'337'203'685'477'581, 1, __LINE__);
}
}
void
run() override
{
for (auto const scale : {MantissaRange::small, MantissaRange::large})
{
NumberMantissaScaleGuard sg(scale);
testZero();
test_limits();
testToString();
test_add();
test_sub();
test_mul();
test_div();
test_root();
test_root2();
test_power1();
test_power2();
testConversions();
test_to_integer();
test_squelch();
test_relationals();
test_stream();
test_inc_dec();
test_toSTAmount();
test_truncate();
testRounding();
testInt64();
testNormalizeToRange();
}
}
};
BEAST_DEFINE_TESTSUITE(Number, basics, xrpl);
} // namespace xrpl
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