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Round Log in a base, Log2, Log2P1 and Log10P1 to the digits asked for [patch] #183

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Round Log in a base, Log2, Log2P1 and Log10P1 to the digits asked for [patch] #183

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36 changes: 36 additions & 0 deletions PreciseNumber.Test/PreciseNumberExponentialTests.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -383,6 +383,42 @@ public void TestLog2P1AndLog10P1KeepTheDigitsOfASmallArgument()
"Log10P1(1E-30) is wrong");
}

[TestMethod]
public void TestLogInABaseRoundsATerminatingQuotientToTheDigitsAskedFor()
{
// ln 1e5 / ln 1e4 is exactly 1.25 once both logarithms are carried to the same working width,
// so an unrounded Divide hands back three digits for a one-digit request.
PreciseNumber oneDigit = PreciseNumber.Log(Parse("1E5"), Parse("1E4"), 1);
Assert.AreEqual(PreciseNumber.One, oneDigit, "Log(1E5, 1E4, 1) is wrong");
Assert.AreEqual(1, oneDigit.SignificantDigits, "Log(1E5, 1E4, 1) returned more digits than asked for");

PreciseNumber twoDigits = PreciseNumber.Log(Parse("1E5"), Parse("1E4"), 2);
Assert.AreEqual(2, twoDigits.SignificantDigits, "Log(1E5, 1E4, 2) returned more digits than asked for");
Assert.AreEqual(Parse("1.3"), twoDigits, "Log(1E5, 1E4, 2) is wrong");

Assert.AreEqual(Parse("1.25"), PreciseNumber.Log(Parse("1E5"), Parse("1E4"), 3), "Log(1E5, 1E4, 3) is wrong");
Assert.AreEqual(Parse("1.8"), PreciseNumber.Log(Parse("1E7"), Parse("1E4"), 2), "Log(1E7, 1E4, 2) is wrong");
}

[TestMethod]
public void TestDividedLogarithmsNeverReturnMoreDigitsThanAskedFor()
{
// Log2, Log2P1 and Log10P1 finish with the same division as a logarithm in a chosen base, so
// they share its rule: the result is rounded to the request whether or not the quotient
// terminates.
for (int digits = 1; digits <= 4; digits++)
{
for (int i = 1; i <= 64; i++)
{
PreciseNumber x = Parse(i.ToString(CultureInfo.InvariantCulture));
Assert.IsLessThanOrEqualTo(digits, PreciseNumber.Log2(x, digits).SignificantDigits, $"Log2({i}, {digits}) returned more digits than asked for");
Assert.IsLessThanOrEqualTo(digits, PreciseNumber.Log2P1(x, digits).SignificantDigits, $"Log2P1({i}, {digits}) returned more digits than asked for");
Assert.IsLessThanOrEqualTo(digits, PreciseNumber.Log10P1(x, digits).SignificantDigits, $"Log10P1({i}, {digits}) returned more digits than asked for");
Assert.IsLessThanOrEqualTo(digits, PreciseNumber.Log(x, Parse("1E4"), digits).SignificantDigits, $"Log({i}, 1E4, {digits}) returned more digits than asked for");
}
}
}

[TestMethod]
public void TestPrecisionFollowsTheWiderOperandRatherThanDouble()
{
Expand Down
8 changes: 4 additions & 4 deletions PreciseNumber/PreciseNumber.Exponentials.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -193,7 +193,7 @@ public static PreciseNumber Log(PreciseNumber x, PreciseNumber newBase, int sign
{
RequireSignificantDigits(significantDigits);
int working = significantDigits + ExponentialGuardDigits;
return Divide(Log(x, working), Log(newBase, working), significantDigits);
return DivideApproximation(Log(x, working), Log(newBase, working), working, significantDigits);
}

/// <summary>
Expand Down Expand Up @@ -224,7 +224,7 @@ public static PreciseNumber Log2(PreciseNumber x, int significantDigits)
{
RequireSignificantDigits(significantDigits);
int working = significantDigits + ExponentialGuardDigits;
return Divide(Log(x, working), Ln2To(working), significantDigits);
return DivideApproximation(Log(x, working), Ln2To(working), working, significantDigits);
}

/// <summary>
Expand Down Expand Up @@ -354,7 +354,7 @@ public static PreciseNumber Log2P1(PreciseNumber x, int significantDigits)
}

int working = significantDigits + ExponentialGuardDigits;
return Divide(LogP1(x, working), Ln2To(working), significantDigits);
return DivideApproximation(LogP1(x, working), Ln2To(working), working, significantDigits);
}

/// <summary>
Expand Down Expand Up @@ -386,7 +386,7 @@ public static PreciseNumber Log10P1(PreciseNumber x, int significantDigits)
}

int working = significantDigits + ExponentialGuardDigits;
return Divide(LogP1(x, working), Ln10To(working), significantDigits);
return DivideApproximation(LogP1(x, working), Ln10To(working), working, significantDigits);
}

/// <summary>
Expand Down
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