ledger/tests/corelib/numerics/CommodityAmount.cc
2008-04-13 03:38:28 -04:00

699 lines
20 KiB
C++

#include "CommodityAmount.h"
#include "ledger.h"
using namespace ledger;
#define internalAmount(x) amount_t::exact(x)
CPPUNIT_TEST_SUITE_NAMED_REGISTRATION(CommodityAmountTestCase, "numerics");
void CommodityAmountTestCase::setUp()
{
amount_t::initialize();
// Cause the display precision for dollars to be initialized to 2.
amount_t x1("$1.00");
assertTrue(x1);
amount_t::full_strings = true; // makes error reports from UnitTests accurate
}
void CommodityAmountTestCase::tearDown()
{
amount_t::full_strings = false;
amount_t::shutdown();
}
void CommodityAmountTestCase::testConstructors()
{
amount_t x1("$123.45");
amount_t x2("-$123.45");
amount_t x3("$-123.45");
amount_t x4("DM 123.45");
amount_t x5("-DM 123.45");
amount_t x6("DM -123.45");
amount_t x7("123.45 euro");
amount_t x8("-123.45 euro");
amount_t x9("123.45€");
amount_t x10("-123.45€");
assertEqual(amount_t("$123.45"), x1);
assertEqual(amount_t("-$123.45"), x2);
assertEqual(amount_t("$-123.45"), x3);
assertEqual(amount_t("DM 123.45"), x4);
assertEqual(amount_t("-DM 123.45"), x5);
assertEqual(amount_t("DM -123.45"), x6);
assertEqual(amount_t("123.45 euro"), x7);
assertEqual(amount_t("-123.45 euro"), x8);
assertEqual(amount_t("123.45€"), x9);
assertEqual(amount_t("-123.45€"), x10);
assertEqual(string("$123.45"), x1.to_string());
assertEqual(string("$-123.45"), x2.to_string());
assertEqual(string("$-123.45"), x3.to_string());
assertEqual(string("DM 123.45"), x4.to_string());
assertEqual(string("DM -123.45"), x5.to_string());
assertEqual(string("DM -123.45"), x6.to_string());
assertEqual(string("123.45 euro"), x7.to_string());
assertEqual(string("-123.45 euro"), x8.to_string());
assertEqual(string("123.45€"), x9.to_string());
assertEqual(string("-123.45€"), x10.to_string());
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
assertValid(x8);
assertValid(x9);
assertValid(x10);
}
void CommodityAmountTestCase::testNegation()
{
amount_t x1("$123.45");
amount_t x2("-$123.45");
amount_t x3("$-123.45");
amount_t x4("DM 123.45");
amount_t x5("-DM 123.45");
amount_t x6("DM -123.45");
amount_t x7("123.45 euro");
amount_t x8("-123.45 euro");
amount_t x9("123.45€");
amount_t x10("-123.45€");
assertEqual(amount_t("$-123.45"), - x1);
assertEqual(amount_t("$123.45"), - x2);
assertEqual(amount_t("$123.45"), - x3);
assertEqual(amount_t("DM -123.45"), - x4);
assertEqual(amount_t("DM 123.45"), - x5);
assertEqual(amount_t("DM 123.45"), - x6);
assertEqual(amount_t("-123.45 euro"), - x7);
assertEqual(amount_t("123.45 euro"), - x8);
assertEqual(amount_t("-123.45€"), - x9);
assertEqual(amount_t("123.45€"), - x10);
assertEqual(amount_t("$-123.45"), x1.negate());
assertEqual(amount_t("$123.45"), x2.negate());
assertEqual(amount_t("$123.45"), x3.negate());
assertEqual(string("$-123.45"), (- x1).to_string());
assertEqual(string("$123.45"), (- x2).to_string());
assertEqual(string("$123.45"), (- x3).to_string());
assertEqual(string("DM -123.45"), (- x4).to_string());
assertEqual(string("DM 123.45"), (- x5).to_string());
assertEqual(string("DM 123.45"), (- x6).to_string());
assertEqual(string("-123.45 euro"), (- x7).to_string());
assertEqual(string("123.45 euro"), (- x8).to_string());
assertEqual(string("-123.45€"), (- x9).to_string());
assertEqual(string("123.45€"), (- x10).to_string());
assertEqual(amount_t("$-123.45"), x1.negate());
assertEqual(amount_t("$123.45"), x2.negate());
assertEqual(amount_t("$123.45"), x3.negate());
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
assertValid(x8);
assertValid(x9);
assertValid(x10);
}
void CommodityAmountTestCase::testAssignment()
{
amount_t x1 = "$123.45";
amount_t x2 = "-$123.45";
amount_t x3 = "$-123.45";
amount_t x4 = "DM 123.45";
amount_t x5 = "-DM 123.45";
amount_t x6 = "DM -123.45";
amount_t x7 = "123.45 euro";
amount_t x8 = "-123.45 euro";
amount_t x9 = "123.45€";
amount_t x10 = "-123.45€";
assertEqual(amount_t("$123.45"), x1);
assertEqual(amount_t("-$123.45"), x2);
assertEqual(amount_t("$-123.45"), x3);
assertEqual(amount_t("DM 123.45"), x4);
assertEqual(amount_t("-DM 123.45"), x5);
assertEqual(amount_t("DM -123.45"), x6);
assertEqual(amount_t("123.45 euro"), x7);
assertEqual(amount_t("-123.45 euro"), x8);
assertEqual(amount_t("123.45€"), x9);
assertEqual(amount_t("-123.45€"), x10);
assertEqual(string("$123.45"), x1.to_string());
assertEqual(string("$-123.45"), x2.to_string());
assertEqual(string("$-123.45"), x3.to_string());
assertEqual(string("DM 123.45"), x4.to_string());
assertEqual(string("DM -123.45"), x5.to_string());
assertEqual(string("DM -123.45"), x6.to_string());
assertEqual(string("123.45 euro"), x7.to_string());
assertEqual(string("-123.45 euro"), x8.to_string());
assertEqual(string("123.45€"), x9.to_string());
assertEqual(string("-123.45€"), x10.to_string());
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
assertValid(x8);
assertValid(x9);
assertValid(x10);
}
void CommodityAmountTestCase::testEquality()
{
amount_t x0;
amount_t x1 = "$123.45";
amount_t x2 = "-$123.45";
amount_t x3 = "$-123.45";
amount_t x4 = "DM 123.45";
amount_t x5 = "-DM 123.45";
amount_t x6 = "DM -123.45";
amount_t x7 = "123.45 euro";
amount_t x8 = "-123.45 euro";
amount_t x9 = "123.45€";
amount_t x10 = "-123.45€";
assertTrue(x0.null());
assertTrue(x0.zero());
assertTrue(x0.realzero());
assertTrue(x0.sign() == 0);
assertTrue(x0.compare(x1) < 0);
assertTrue(x0.compare(x2) > 0);
assertTrue(x0.compare(x0) == 0);
assertTrue(x1 != x2);
assertTrue(x1 != x4);
assertTrue(x1 != x7);
assertTrue(x1 != x9);
assertTrue(x2 == x3);
assertTrue(x4 != x5);
assertTrue(x5 == x6);
assertTrue(x7 == - x8);
assertTrue(x9 == - x10);
assertValid(x0);
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
assertValid(x8);
assertValid(x9);
assertValid(x10);
}
void CommodityAmountTestCase::testAddition()
{
amount_t x0;
amount_t x1("$123.45");
amount_t x2(internalAmount("$123.456789"));
amount_t x3("DM 123.45");
amount_t x4("123.45 euro");
amount_t x5("123.45€");
amount_t x6("123.45");
assertEqual(amount_t("$246.90"), x1 + x1);
assertNotEqual(amount_t("$246.91"), x1 + x2);
assertEqual(internalAmount("$246.906789"), x1 + x2);
// Converting to string drops internal precision
assertEqual(string("$246.90"), (x1 + x1).to_string());
assertEqual(string("$246.91"), (x1 + x2).to_string());
assertThrow(x1 + x0, amount_error *);
assertThrow(x1 + x3, amount_error *);
assertThrow(x1 + x4, amount_error *);
assertThrow(x1 + x5, amount_error *);
assertThrow(x1 + x6, amount_error *);
assertThrow(x1 + 123.45, amount_error *);
assertThrow(x1 + 123L, amount_error *);
assertEqual(amount_t("DM 246.90"), x3 + x3);
assertEqual(amount_t("246.90 euro"), x4 + x4);
assertEqual(amount_t("246.90€"), x5 + x5);
assertEqual(string("DM 246.90"), (x3 + x3).to_string());
assertEqual(string("246.90 euro"), (x4 + x4).to_string());
assertEqual(string("246.90€"), (x5 + x5).to_string());
x1 += amount_t("$456.45");
assertEqual(amount_t("$579.90"), x1);
x1 += amount_t("$456.45");
assertEqual(amount_t("$1036.35"), x1);
x1 += amount_t("$456");
assertEqual(amount_t("$1492.35"), x1);
amount_t x7(internalAmount("$123456789123456789.123456789123456789"));
assertEqual(internalAmount("$246913578246913578.246913578246913578"), x7 + x7);
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
}
void CommodityAmountTestCase::testSubtraction()
{
amount_t x0;
amount_t x1("$123.45");
amount_t x2(internalAmount("$123.456789"));
amount_t x3("DM 123.45");
amount_t x4("123.45 euro");
amount_t x5("123.45€");
amount_t x6("123.45");
assertNotEqual(amount_t(), x1 - x1);
assertEqual(amount_t("$0"), x1 - x1);
assertEqual(amount_t("$23.45"), x1 - amount_t("$100.00"));
assertEqual(amount_t("$-23.45"), amount_t("$100.00") - x1);
assertNotEqual(amount_t("$-0.01"), x1 - x2);
assertEqual(internalAmount("$-0.006789"), x1 - x2);
// Converting to string drops internal precision. If an amount is
// zero, it drops the commodity as well.
assertEqual(string("$0.00"), (x1 - x1).to_string());
assertEqual(string("$-0.01"), (x1 - x2).to_string());
assertThrow(x1 - x0, amount_error *);
assertThrow(x1 - x3, amount_error *);
assertThrow(x1 - x4, amount_error *);
assertThrow(x1 - x5, amount_error *);
assertThrow(x1 - x6, amount_error *);
assertThrow(x1 - 123.45, amount_error *);
assertThrow(x1 - 123L, amount_error *);
assertEqual(amount_t("DM 0.00"), x3 - x3);
assertEqual(amount_t("DM 23.45"), x3 - amount_t("DM 100.00"));
assertEqual(amount_t("DM -23.45"), amount_t("DM 100.00") - x3);
assertEqual(amount_t("0.00 euro"), x4 - x4);
assertEqual(amount_t("23.45 euro"), x4 - amount_t("100.00 euro"));
assertEqual(amount_t("-23.45 euro"), amount_t("100.00 euro") - x4);
assertEqual(amount_t("0.00€"), x5 - x5);
assertEqual(amount_t("23.45€"), x5 - amount_t("100.00€"));
assertEqual(amount_t("-23.45€"), amount_t("100.00€") - x5);
assertEqual(string("DM 0.00"), (x3 - x3).to_string());
assertEqual(string("DM 23.45"), (x3 - amount_t("DM 100.00")).to_string());
assertEqual(string("DM -23.45"), (amount_t("DM 100.00") - x3).to_string());
assertEqual(string("0.00 euro"), (x4 - x4).to_string());
assertEqual(string("23.45 euro"), (x4 - amount_t("100.00 euro")).to_string());
assertEqual(string("-23.45 euro"), (amount_t("100.00 euro") - x4).to_string());
assertEqual(string("0.00€"), (x5 - x5).to_string());
assertEqual(string("23.45€"), (x5 - amount_t("100.00€")).to_string());
assertEqual(string("-23.45€"), (amount_t("100.00€") - x5).to_string());
x1 -= amount_t("$456.45");
assertEqual(amount_t("$-333.00"), x1);
x1 -= amount_t("$456.45");
assertEqual(amount_t("$-789.45"), x1);
x1 -= amount_t("$456");
assertEqual(amount_t("$-1245.45"), x1);
amount_t x7(internalAmount("$123456789123456789.123456789123456789"));
amount_t x8(internalAmount("$2354974984698.98459845984598"));
assertEqual(internalAmount("$123454434148472090.138858329277476789"), x7 - x8);
assertEqual(string("$123454434148472090.138858329277476789"), (x7 - x8).to_string());
assertEqual(string("$123454434148472090.14"),
(amount_t("$1.00") * (x7 - x8)).to_string());
assertEqual(internalAmount("$-123454434148472090.138858329277476789"), x8 - x7);
assertEqual(string("$-123454434148472090.138858329277476789"), (x8 - x7).to_string());
assertEqual(string("$-123454434148472090.14"),
(amount_t("$1.00") * (x8 - x7)).to_string());
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
assertValid(x8);
}
void CommodityAmountTestCase::testMultiplication()
{
amount_t x1("$123.12");
amount_t y1("$456.45");
amount_t x2(internalAmount("$123.456789"));
amount_t x3("DM 123.45");
amount_t x4("123.45 euro");
amount_t x5("123.45€");
assertEqual(amount_t("$0.00"), x1 * 0L);
assertEqual(amount_t("$0.00"), 0L * x1);
assertEqual(x1, x1 * 1L);
assertEqual(x1, 1L * x1);
assertEqual(- x1, x1 * -1L);
assertEqual(- x1, -1L * x1);
assertEqual(internalAmount("$56198.124"), x1 * y1);
assertEqual(string("$56198.12"), (x1 * y1).to_string());
assertEqual(internalAmount("$56198.124"), y1 * x1);
assertEqual(string("$56198.12"), (y1 * x1).to_string());
// Internal amounts retain their precision, even when being
// converted to strings
assertEqual(internalAmount("$15199.99986168"), x1 * x2);
assertEqual(internalAmount("$15199.99986168"), x2 * x1);
assertEqual(string("$15200.00"), (x1 * x2).to_string());
assertEqual(string("$15199.99986168"), (x2 * x1).to_string());
assertThrow(x1 * x3, amount_error *);
assertThrow(x1 * x4, amount_error *);
assertThrow(x1 * x5, amount_error *);
x1 *= amount_t("123.12");
assertEqual(internalAmount("$15158.5344"), x1);
assertEqual(string("$15158.53"), x1.to_string());
x1 *= 123.12;
assertEqual(internalAmount("$1866318.755328"), x1);
assertEqual(string("$1866318.76"), x1.to_string());
x1 *= 123L;
assertEqual(internalAmount("$229557206.905344"), x1);
assertEqual(string("$229557206.91"), x1.to_string());
amount_t x7(internalAmount("$123456789123456789.123456789123456789"));
assertEqual(internalAmount("$15241578780673678546105778311537878.046486820281054720515622620750190521"),
x7 * x7);
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x7);
}
void CommodityAmountTestCase::testDivision()
{
amount_t x1("$123.12");
amount_t y1("$456.45");
amount_t x2(internalAmount("$123.456789"));
amount_t x3("DM 123.45");
amount_t x4("123.45 euro");
amount_t x5("123.45€");
assertThrow(x1 / 0L, amount_error *);
assertEqual(amount_t("$0.00"), 0L / x1);
assertEqual(x1, x1 / 1L);
assertEqual(internalAmount("$0.00812216"), 1L / x1);
assertEqual(- x1, x1 / -1L);
assertEqual(internalAmount("$-0.00812216"), -1L / x1);
assertEqual(internalAmount("$0.26973382"), x1 / y1);
assertEqual(string("$0.27"), (x1 / y1).to_string());
assertEqual(internalAmount("$3.70735867"), y1 / x1);
assertEqual(string("$3.71"), (y1 / x1).to_string());
// Internal amounts retain their precision, even when being
// converted to strings
assertEqual(internalAmount("$0.99727201"), x1 / x2);
assertEqual(internalAmount("$1.00273545321637426901"), x2 / x1);
assertEqual(string("$1.00"), (x1 / x2).to_string());
assertEqual(string("$1.00273545321637426901"), (x2 / x1).to_string());
assertThrow(x1 / x3, amount_error *);
assertThrow(x1 / x4, amount_error *);
assertThrow(x1 / x5, amount_error *);
x1 /= amount_t("123.12");
assertEqual(internalAmount("$1.00"), x1);
assertEqual(string("$1.00"), x1.to_string());
x1 /= 123.12;
assertEqual(internalAmount("$0.00812216"), x1);
assertEqual(string("$0.01"), x1.to_string());
x1 /= 123L;
assertEqual(internalAmount("$0.00006603"), x1);
assertEqual(string("$0.00"), x1.to_string());
amount_t x6(internalAmount("$237235987235987.98723987235978"));
amount_t x7(internalAmount("$123456789123456789.123456789123456789"));
assertEqual(amount_t("$1"), x7 / x7);
assertEqual(internalAmount("$0.0019216115121765559608381226612019501046413574469262"),
x6 / x7);
assertEqual(internalAmount("$520.39654928343335571379527154924040947271699678158689736256"),
x7 / x6);
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
assertValid(x7);
}
void CommodityAmountTestCase::testConversion()
{
amount_t x1("$1234.56");
assertEqual(true, bool(x1));
assertEqual(1234L, long(x1));
assertEqual(1234.56, double(x1));
assertEqual(string("$1234.56"), x1.to_string());
assertEqual(string("1234.56"), x1.quantity_string());
assertValid(x1);
}
void CommodityAmountTestCase::testRound()
{
amount_t x1(internalAmount("$1234.567890"));
assertEqual(internalAmount("$1234.56789"), x1.round(6));
assertEqual(internalAmount("$1234.56789"), x1.round(5));
assertEqual(internalAmount("$1234.5679"), x1.round(4));
assertEqual(internalAmount("$1234.568"), x1.round(3));
assertEqual(amount_t("$1234.57"), x1.round(2));
assertEqual(amount_t("$1234.6"), x1.round(1));
assertEqual(amount_t("$1235"), x1.round(0));
amount_t x2(internalAmount("$9876.543210"));
assertEqual(internalAmount("$9876.543210"), x2.round(6));
assertEqual(internalAmount("$9876.54321"), x2.round(5));
assertEqual(internalAmount("$9876.5432"), x2.round(4));
assertEqual(internalAmount("$9876.543"), x2.round(3));
assertEqual(amount_t("$9876.54"), x2.round(2));
assertEqual(amount_t("$9876.5"), x2.round(1));
assertEqual(amount_t("$9877"), x2.round(0));
amount_t x3(internalAmount("$-1234.567890"));
assertEqual(internalAmount("$-1234.56789"), x3.round(6));
assertEqual(internalAmount("$-1234.56789"), x3.round(5));
assertEqual(internalAmount("$-1234.5679"), x3.round(4));
assertEqual(internalAmount("$-1234.568"), x3.round(3));
assertEqual(amount_t("$-1234.57"), x3.round(2));
assertEqual(amount_t("$-1234.6"), x3.round(1));
assertEqual(amount_t("$-1235"), x3.round(0));
amount_t x4(internalAmount("$-9876.543210"));
assertEqual(internalAmount("$-9876.543210"), x4.round(6));
assertEqual(internalAmount("$-9876.54321"), x4.round(5));
assertEqual(internalAmount("$-9876.5432"), x4.round(4));
assertEqual(internalAmount("$-9876.543"), x4.round(3));
assertEqual(amount_t("$-9876.54"), x4.round(2));
assertEqual(amount_t("$-9876.5"), x4.round(1));
assertEqual(amount_t("$-9877"), x4.round(0));
amount_t x5("$123.45");
x5 *= 100.12;
assertEqual(internalAmount("$12359.814"), x5);
assertEqual(string("$12359.81"), x5.to_string());
assertEqual(string("$12359.814"), x5.to_fullstring());
assertEqual(string("$12359.814"), x5.unround().to_string());
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
}
void CommodityAmountTestCase::testDisplayRound()
{
amount_t x1("$0.85");
amount_t x2("$0.1");
x1 *= 0.19;
assertNotEqual(amount_t("$0.16"), x1);
assertEqual(internalAmount("$0.1615"), x1);
assertEqual(string("$0.16"), x1.to_string());
assertEqual(amount_t("$0.10"), x2);
assertNotEqual(internalAmount("$0.101"), x2);
assertEqual(string("$0.10"), x2.to_string());
x1 *= 7L;
assertNotEqual(amount_t("$1.13"), x1);
assertEqual(internalAmount("$1.1305"), x1);
assertEqual(string("$1.13"), x1.to_string());
}
void CommodityAmountTestCase::testTruth()
{
amount_t x1("$1234");
amount_t x2("$1234.56");
if (x1)
CPPUNIT_ASSERT(true);
else
CPPUNIT_ASSERT(false);
if (x2)
CPPUNIT_ASSERT(true);
else
CPPUNIT_ASSERT(false);
assertValid(x1);
assertValid(x2);
}
void CommodityAmountTestCase::testForZero()
{
amount_t x1(internalAmount("$0.000000000000000000001"));
assertFalse(x1);
assertTrue(x1.zero());
assertFalse(x1.realzero());
assertValid(x1);
}
void CommodityAmountTestCase::testComparisons()
{
amount_t x0;
amount_t x1("$-123");
amount_t x2("$123.00");
amount_t x3(internalAmount("$-123.4544"));
amount_t x4(internalAmount("$123.4544"));
amount_t x5("$-123.45");
amount_t x6("$123.45");
assertTrue(x0 > x1);
assertTrue(x0 < x2);
assertTrue(x0 > x3);
assertTrue(x0 < x4);
assertTrue(x0 > x5);
assertTrue(x0 < x6);
assertTrue(x1 > x3);
assertTrue(x3 <= x5);
assertTrue(x3 < x5);
assertTrue(x3 <= x5);
assertFalse(x3 == x5);
assertTrue(x3 < x1);
assertTrue(x3 < x4);
assertValid(x0);
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
assertValid(x5);
assertValid(x6);
}
void CommodityAmountTestCase::testSign()
{
amount_t x0;
amount_t x1(internalAmount("$0.0000000000000000000000000000000000001"));
amount_t x2(internalAmount("$-0.0000000000000000000000000000000000001"));
amount_t x3("$1");
amount_t x4("$-1");
assertFalse(x0.sign());
assertTrue(x1.sign() != 0);
assertTrue(x2.sign() != 0);
assertTrue(x3.sign() > 0);
assertTrue(x4.sign() < 0);
assertValid(x0);
assertValid(x1);
assertValid(x2);
assertValid(x3);
assertValid(x4);
}
void CommodityAmountTestCase::testAbs()
{
amount_t x0;
amount_t x1("$-1234.56");
amount_t x2("$1234.56");
assertEqual(amount_t(), x0.abs());
assertEqual(amount_t("$1234.56"), x1.abs());
assertEqual(amount_t("$1234.56"), x2.abs());
assertValid(x0);
assertValid(x1);
assertValid(x2);
}
void CommodityAmountTestCase::testPrinting()
{
amount_t x0;
amount_t x1(internalAmount("$982340823.386238098235098235098235098"));
amount_t x2("$982340823.38");
{
std::ostringstream bufstr;
bufstr << x0;
assertEqual(std::string("0"), bufstr.str());
}
{
std::ostringstream bufstr;
bufstr << x1;
assertEqual(std::string("$982340823.386238098235098235098235098"),
bufstr.str());
}
{
std::ostringstream bufstr;
bufstr << (x1 * x2).to_string();
assertEqual(std::string("$964993493285024293.18099172508158508135413499124"),
bufstr.str());
}
{
std::ostringstream bufstr;
bufstr << (x2 * x1).to_string();
assertEqual(std::string("$964993493285024293.18"), bufstr.str());
}
assertValid(x0);
assertValid(x1);
assertValid(x2);
}