Cache intermediate results in Z-R conversions

conversion.go

@@ -10,30 +10,43 @@ func IsNaN(f float32) (is bool) {
 	return f != f
 }
 
-// Z-R relationship mathematically expressed as Z = a * R^b
+// Z-R relationship
 type ZR struct {
-	A float64
-	B float64
+	// intermediate caching
+	c1 float64 // 10*b
+	c2 float64 // a^(-1/b)
+	c3 float64 // 10^(1/(10*b))
+	c4 float64 // 10 * log10(a)
 }
 
 // Common Z-R relationships
 var (
-	Aniol80          = ZR{256, 1.42} // operational use in germany, described in [6]
-	Doelling98       = ZR{316, 1.50} // operational use in switzerland
-	JossWaldvogel70  = ZR{300, 1.50}
-	MarshallPalmer55 = ZR{200, 1.60} // operational use in austria
+	Aniol80          = NewZR(256, 1.42) // operational use in germany, described in [6]
+	Doelling98       = NewZR(316, 1.50) // operational use in switzerland
+	JossWaldvogel70  = NewZR(300, 1.50)
+	MarshallPalmer55 = NewZR(200, 1.60) // operational use in austria
 )
 
+// New Z-R returns a Z-R relationship mathematically expressed as Z = a * R^b
+func NewZR(A, B float64) ZR {
+	c1 := 10.0 * B
+	c2 := math.Pow(A, -1.0/B)
+	c3 := math.Pow(10.0, 1/c1)
+	c4 := 10.0 * math.Log10(A)
+
+	return ZR{c1, c2, c3, c4}
+}
+
 // PrecipitationRate returns the estimated precipitation rate in mm/h for the given
 // reflectivity factor and Z-R relationship.
 func PrecipitationRate(relation ZR, dBZ float32) (rate float64) {
-	return math.Pow(math.Pow(10, float64(dBZ)/10)/relation.A, 1/relation.B)
+	return relation.c2 * math.Pow(relation.c3, float64(dBZ))
 }
 
 // Reflectivity returns the estimated reflectivity factor for the given precipitation
 // rate (mm/h) and Z-R relationship.
 func Reflectivity(relation ZR, rate float64) (dBZ float32) {
-	return float32(10 * math.Log10(relation.A*math.Pow(float64(rate), relation.B)))
+	return float32(relation.c4 + relation.c1 * math.Log10(rate))
 }
 
 // toDBZ converts the given radar video processor values (rvp-6) to radar reflectivity