Add a working arbitrary integer solution to pi series

1-elementary/elementary_test.go

@@ -302,12 +302,27 @@ func TestAlternatingSeries(t *testing.T) {
 	}
 }
 
+func TestAlternatingSeriesBig(t *testing.T) { 
+	response := AlternatingSeriesBig()
+	correct := big.NewFloat(math.Pi)
+	if !withinBig(response, correct, big.NewFloat(.001)) {
+		t.Errorf("AlternatingSeries() = '%v'; want '%v'", response, correct)
+	}
+}
+
 func within(a, b, tolerance float64) bool {
 	difference := math.Abs(a - b)
 	belowTolerance := difference < tolerance
 	return belowTolerance
 }
 
+func withinBig(a, b, tolerance *big.Float) bool {
+	difference := a.Sub(a, b)
+	absDiff := new(big.Float).Abs(difference)
+	belowTolerance := absDiff.Cmp(tolerance) == -1
+	return belowTolerance
+}
+
 // captureOutput takes in a function to catch the output,
 //
 //	optionally taking in lines of input for stdin

1-elementary/exercise11sumSeriesBigInt.go

@@ -0,0 +1,39 @@
+package elementary
+
+import (
+	"math/big"
+)
+
+// Write a program that computes the sum of an alternating series
+//  where each element of the series is an expression of the form
+//  ((-1)^{k+1})/(2 * k-1)
+// for each value of k from 1 to a million, multiplied by 4.
+
+// AlternatingSeries computes the series in exercise 11 and prints the reuslt
+func AlternatingSeriesBig() *big.Float {
+	i := big.NewInt(1)
+	limit := big.NewInt(1000000)
+	sum := big.NewFloat(0)
+	for i.Cmp(limit) == -1 {
+		k := *i
+		k.Add(&k, big.NewInt(1))
+		numerator := big.NewInt(0)
+		numerator.Exp(big.NewInt(-1), &k, nil)
+
+		k.Sub(&k, big.NewInt(1)) // k = k - 1 because 1 was added above and it's reused
+
+		denominator := big.NewInt(0)
+		denominator.Mul(big.NewInt(2), &k)
+		denominator.Sub(denominator, big.NewInt(1))
+
+		value := big.NewFloat(0)
+		value.SetPrec(100000)
+		value.SetInt(numerator)
+		value.Quo(value, big.NewFloat(0).SetInt(denominator))
+
+		sum.Add(sum, value)
+		// fmt.Println("sum, value: ", sum, value)
+		i.Add(i, big.NewInt(1))
+	}
+	return sum.Mul(sum, big.NewFloat(4))
+}