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fix: ExpHullAbrham drops significant figures for results below 1 #429

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fix: ExpHullAbrham drops significant figures for results below 1 #429

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11 changes: 4 additions & 7 deletions decimal.go
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Original file line number Diff line number Diff line change
Expand Up @@ -1037,14 +1037,11 @@ func (d Decimal) ExpHullAbrham(overallPrecision uint32) (Decimal, error) {
res = res.Mul(sum)
}

// Round to overallPrecision significant figures. This holds whether res is
// >=1 or <1; the old <1 branch rounded to a fixed number of decimal places,
// dropping leading zeros (so e.g. exp(-50).ExpHullAbrham(10) returned 0).
resNumDigits := int32(res.NumDigits())

var roundDigits int32
if resNumDigits > abs(res.exp) {
roundDigits = int32(currentPrecision) - resNumDigits - res.exp
} else {
roundDigits = int32(currentPrecision)
}
roundDigits := int32(currentPrecision) - resNumDigits - res.exp

res = res.Round(roundDigits)

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57 changes: 47 additions & 10 deletions decimal_test.go
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Original file line number Diff line number Diff line change
Expand Up @@ -2980,17 +2980,17 @@ func TestDecimal_ExpHullAbrham(t *testing.T) {
{"-0.569297", 20, "0.56592314285957604443"},
{"-1.0", 1, "0.4"},
{"-1.0", 5, "0.36788"},
{"-3.0", 1, "0"},
{"-3.0", 1, "0.05"},
{"-3.0", 2, "0.05"},
{"-3.0", 10, "0.0497870684"},
{"-5.26", 2, "0.01"},
{"-5.26", 10, "0.0051953047"},
{"-5.2663117716", 2, "0.01"},
{"-5.2663117716", 10, "0.0051626164"},
{"-26.1", 2, "0"},
{"-26.1", 15, "0.000000000004623"},
{"-50.1591", 10, "0"},
{"-50.1591", 30, "0.000000000000000000000164505208"},
{"-3.0", 10, "0.04978706837"},
{"-5.26", 2, "0.0052"},
{"-5.26", 10, "0.005195304719"},
{"-5.2663117716", 2, "0.0052"},
{"-5.2663117716", 10, "0.005162616411"},
{"-26.1", 2, "0.0000000000046"},
{"-26.1", 15, "0.00000000000462289492466867"},
{"-50.1591", 10, "0.0000000000000000000001645052084"},
{"-50.1591", 30, "0.000000000000000000000164505208424152908216198963722"},
} {
d, _ := NewFromString(testCase.Dec)
expected, _ := NewFromString(testCase.ExpectedDec)
Expand All @@ -3007,6 +3007,43 @@ func TestDecimal_ExpHullAbrham(t *testing.T) {
}
}

// ExpHullAbrham is documented to return overallPrecision significant figures.
// It used to round the result to overallPrecision decimal places whenever the
// result was < 1, discarding the leading-zero positions, so every sufficiently
// negative argument lost significant figures (exp(-50).ExpHullAbrham(10)
// returned 0). Check the delivered precision against exp(x) computed to 40
// digits with mpmath, across the negative half-line.
func TestDecimal_ExpHullAbrham_significantFigures(t *testing.T) {
trueExp := map[string]string{
"-2.5": "8.20849986238987951695286744671598078378041e-2",
"-5": "6.73794699908546709663604842314842424884959e-3",
"-10": "4.53999297624848515355915155605506102379181e-5",
"-20": "2.06115362243855782796594038015582097637581e-9",
"-30": "9.35762296884017460491583222337870674495832e-14",
"-50": "1.92874984796391778301734281652701257475283e-22",
}
for _, x := range []string{"-2.5", "-5", "-10", "-20", "-30", "-50"} {
d := RequireFromString(x)
want := RequireFromString(trueExp[x])
for _, prec := range []uint32{10, 20, 30} {
got, err := d.ExpHullAbrham(prec)
if err != nil {
t.Fatalf("exp(%s).ExpHullAbrham(%d): %v", x, prec, err)
}
if got.IsZero() {
t.Errorf("exp(%s).ExpHullAbrham(%d) = 0, want ~%s", x, prec, want)
continue
}
relErr := got.Sub(want).Abs().DivRound(want, 45)
tol := New(1, -int32(prec)+1) // one unit in the prec-th significant figure
if relErr.Cmp(tol) > 0 {
t.Errorf("exp(%s).ExpHullAbrham(%d) = %s: relative error %s > %s, fewer than %d significant figures",
x, prec, got, relErr, tol, prec)
}
}
}
}

func TestDecimal_ExpTaylor(t *testing.T) {
for _, testCase := range []struct {
Dec string
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