Improve accuracy of pi and roots

Author: printfn

core/src/num/bigrat.rs

@@ -967,7 +967,7 @@ impl BigRat {
 		int: &I,
 	) -> FResult<Self> {
 		let mut high_bound = low_bound.clone().add(1.into(), int)?;
-		for _ in 0..30 {
+		for _ in 0..50 {
 			let guess = low_bound
 				.clone()
 				.add(high_bound.clone(), int)?

core/src/num/real.rs

@@ -96,9 +96,41 @@ impl Real {
 		match self.pattern {
 			Pattern::Simple(s) => Ok(s),
 			Pattern::Pi(n) => {
-				let num = BigRat::from(3_141_592_653_589_793_238);
-				let den = BigRat::from(1_000_000_000_000_000_000);
-				let pi = num.div(&den, int)?;
+				let required_accuracy_dp = 20;
+				let mut pi = BigRat::from(0);
+				for k in 0..=(required_accuracy_dp / 14) {
+					let mut term = BigRat::from(1);
+					if k % 2 == 1 {
+						term = -term;
+					}
+					let k = BigRat::from(k);
+					term = term.mul(&BigRat::from(6).mul(&k, int)?.factorial(int)?, int)?;
+					term = term.mul(
+						&BigRat::from(545_140_134)
+							.mul(&k, int)?
+							.add(BigRat::from(13_591_409), int)?,
+						int,
+					)?;
+					term = term.div(&BigRat::from(3).mul(&k, int)?.factorial(int)?, int)?;
+					term = term.div(
+						&k.clone().factorial(int)?.pow(BigRat::from(3), int)?.value,
+						int,
+					)?;
+					term = term.div(
+						&BigRat::from(640_320)
+							.pow(
+								BigRat::from(3)
+									.mul(&k, int)?
+									.add(BigRat::from(3).div(&BigRat::from(2), int)?, int)?,
+								int,
+							)?
+							.value,
+						int,
+					)?;
+					pi = pi.add(term, int)?;
+				}
+				pi = pi.mul(&BigRat::from(12), int)?;
+				pi = pi.pow(-BigRat::from(1), int)?.value;
 				Ok(n.mul(&pi, int)?)
 			}
 		}

core/tests/integration_tests.rs

@@ -573,7 +573,7 @@ fn large_simple_subtraction_2() {
 
 #[test]
 fn sqrt_half() {
-	test_eval("sqrt (1/2)", "approx. 0.7071067814");
+	test_eval("sqrt (1/2)", "approx. 0.7071067811");
 }
 
 #[test]
@@ -588,7 +588,7 @@ fn sqrt_1() {
 
 #[test]
 fn sqrt_2() {
-	test_eval("sqrt 2", "approx. 1.4142135619");
+	test_eval("sqrt 2", "approx. 1.4142135623");
 }
 
 #[test]
@@ -1202,7 +1202,7 @@ fn powers_15() {
 
 #[test]
 fn powers_16() {
-	test_eval("4^(1/4)", "approx. 1.4142135619");
+	test_eval("4^(1/4)", "approx. 1.4142135623");
 }
 
 #[test]
@@ -1214,7 +1214,7 @@ fn powers_17() {
 fn powers_18() {
 	test_eval(
 		"5.2*10^15*300^(3/2)",
-		"approx. 27019992598076723515.9873962402",
+		"approx. 27019992598074485776.9266786817",
 	);
 }
 
@@ -2501,7 +2501,7 @@ fn abs_2_i() {
 
 #[test]
 fn abs_1_plus_i() {
-	test_eval("abs (1 + i)", "approx. 1.4142135619");
+	test_eval("abs (1 + i)", "approx. 1.4142135623");
 }
 
 #[test]
@@ -5398,7 +5398,7 @@ fn day_of_week_type_name() {
 
 #[test]
 fn phi() {
-	test_eval("phi", "approx. 1.6180339886");
+	test_eval("phi", "approx. 1.6180339887");
 }
 
 #[test]