lib/decimal: reduce rounding error when converting from decimal to float with negative exponent

While at it, slightly increase the conversion performance by moving fast path to the top of the loop.

lib/decimal/decimal.go

@@ -93,16 +93,25 @@ func AppendDecimalToFloat(dst []float64, va []int64, e int16) []float64 {
 	// Extend dst capacity in order to eliminate memory allocations below.
 	dst = ExtendFloat64sCapacity(dst, len(va))
 
+	// increase conversion precision for negative exponents by dividing by e10
+	isMul := true
+	if e < 0 {
+		e = -e
+		isMul = false
+	}
 	e10 := math.Pow10(int(e))
 	for _, v := range va {
 		// Manually inline ToFloat here for better performance
-		var f float64
+		f := float64(v)
+		if isMul {
+			f *= e10
+		} else {
+			f /= e10
+		}
 		if v == vInfPos {
 			f = infPos
 		} else if v == vInfNeg {
 			f = infNeg
-		} else {
-			f = float64(v) * e10
 		}
 		dst = append(dst, f)
 	}
@@ -254,13 +263,26 @@ func maxUpExponent(v int64) int16 {
 
 // ToFloat returns f=v*10^e.
 func ToFloat(v int64, e int16) float64 {
+	// increase conversion precision for negative exponents by dividing by e10
+	isMul := true
+	if e < 0 {
+		e = -e
+		isMul = false
+	}
+	e10 := math.Pow10(int(e))
+	f := float64(v)
+	if isMul {
+		f *= e10
+	} else {
+		f /= e10
+	}
 	if v == vInfPos {
 		return infPos
 	}
 	if v == vInfNeg {
 		return infNeg
 	}
-	return float64(v) * math.Pow10(int(e))
+	return f
 }
 
 const (

lib/decimal/decimal_test.go

@@ -43,6 +43,9 @@ func TestPositiveFloatToDecimal(t *testing.T) {
 	f(1234567890123456789e-14, 1234567890123, -8)
 	f(1234567890123456789e-17, 12345678901234, -12)
 	f(1234567890123456789e-20, 1234567890123, -14)
+
+	f(0.000874957, 874957, -9)
+	f(0.001130435, 1130435, -9)
 }
 
 func TestAppendDecimalToFloat(t *testing.T) {
@@ -52,6 +55,7 @@ func TestAppendDecimalToFloat(t *testing.T) {
 	testAppendDecimalToFloat(t, []int64{0}, -10, []float64{0})
 	testAppendDecimalToFloat(t, []int64{-1, -10, 0, 100}, 2, []float64{-1e2, -1e3, 0, 1e4})
 	testAppendDecimalToFloat(t, []int64{-1, -10, 0, 100}, -2, []float64{-1e-2, -1e-1, 0, 1})
+	testAppendDecimalToFloat(t, []int64{874957, 1130435}, -9, []float64{0.000874957, 0.001130435})
 }
 
 func testAppendDecimalToFloat(t *testing.T, va []int64, e int16, fExpected []float64) {
@@ -323,6 +327,8 @@ func TestFloatToDecimalRoundtrip(t *testing.T) {
 	f(12.34567890125)
 	f(-1234567.8901256789)
 	f(15e18)
+	f(0.000874957)
+	f(0.001130435)
 
 	f(math.Inf(1))
 	f(math.Inf(-1))

lib/decimal/decimal_timing_test.go

@@ -8,9 +8,12 @@ import (
 )
 
 func BenchmarkAppendDecimalToFloat(b *testing.B) {
-	b.Run("VarNums", func(b *testing.B) {
+	b.Run("RealFloat", func(b *testing.B) {
 		benchmarkAppendDecimalToFloat(b, testVA)
 	})
+	b.Run("Integers", func(b *testing.B) {
+		benchmarkAppendDecimalToFloat(b, testIntegers)
+	})
 	b.Run("Zeros", func(b *testing.B) {
 		benchmarkAppendDecimalToFloat(b, testZeros)
 	})
@@ -83,7 +86,7 @@ func benchmarkAppendFloatToDecimal(b *testing.B, fa []float64) {
 var testFAReal = func() []float64 {
 	fa := make([]float64, 8*1024)
 	for i := 0; i < len(fa); i++ {
-		fa[i] = rand.NormFloat64() * 1e6
+		fa[i] = rand.NormFloat64() * 1e-6
 	}
 	return fa
 }()
@@ -101,6 +104,11 @@ var testVA = func() []int64 {
 	return va
 }()
 
+var testIntegers = func() []int64 {
+	va, _ := AppendFloatToDecimal(nil, testFAInteger)
+	return va
+}()
+
 func BenchmarkFromFloat(b *testing.B) {
 	for _, f := range []float64{0, 1234, 12334345, 12343.4344, 123.45678901e12, 12.3454435e30} {
 		b.Run(fmt.Sprintf("%g", f), func(b *testing.B) {