feat(stdlib): Implement Number.sin and Number.cos (#1343)

compiler/test/stdlib/number.test.gr

@@ -216,3 +216,14 @@ assert Number.sign(BI.toNumber(1t)) == 1
 assert 1 / Number.sign(0.0) == Float64.toNumber(Float64.infinity)
 // TODO(#693): Replace with -Infinity literal when it exists
 assert 1 / Number.sign(-0.0) == Number.neg(Float64.toNumber(Float64.infinity))
+
+// Number.sin
+assert Number.sin(0.0) == 0
+assert Number.sin(1) > 0.84147 && Number.sin(1) < 0.84148
+assert Number.sin(-1) < -0.84147 && Number.sin(-1) > -0.84148
+assert Number.sin(20) > 0.91294 && Number.sin(20) < 0.91295
+
+// Number.cos
+assert Number.cos(1) > 0.5403 && Number.cos(1) < 0.5404
+assert Number.cos(-1) > 0.5403 && Number.cos(-1) < 0.5404
+assert Number.cos(15) < -0.7596 && Number.cos(15) > -0.7597

stdlib/number.gr

@@ -346,3 +346,55 @@ export let isInfinite = (x: Number) => {
  * @since v0.4.5
  */
 export parseInt
+
+/**
+ * Computes how many times pi has to be subtracted to achieve the required bounds for sin.
+ */
+let reduceToPiBound = (radians: Number) => {
+  floor(radians / pi)
+}
+
+/**
+ * Computes the sine of a number using Chebyshev polynomials. Requires the input to be bounded to (-pi, pi). More information on the algorithm can be found here: http://mooooo.ooo/chebyshev-sine-approximation/.
+ */
+let chebyshevSine = (radians: Number) => {
+  let pi_minor = -0.00000008742278
+  let x2 = radians * radians
+  let p11 = 0.00000000013291342
+  let p9 = p11 * x2 + -0.000000023317787
+  let p7 = p9 * x2 + 0.0000025222919
+  let p5 = p7 * x2 + -0.00017350505
+  let p3 = p5 * x2 + 0.0066208798
+  let p1 = p3 * x2 + -0.10132118
+  (radians - pi - pi_minor) * (radians + pi + pi_minor) * p1 * radians
+}
+
+/**
+ * Computes the sine of a number (in radians) using Chebyshev polynomials.
+ *
+ * @param radians: The input in radians
+ * @returns The computed sine
+ *
+ * @since v0.5.2
+ */
+export let sin = (radians: Number) => {
+  let quot = reduceToPiBound(radians)
+  let bounded = radians - pi * quot
+  if (quot % 2 == 0) {
+    chebyshevSine(bounded)
+  } else {
+    neg(chebyshevSine(bounded))
+  }
+}
+
+/**
+ * Computes the cosine of a number (in radians) using Chebyshev polynomials.
+ *
+ * @param radians: The input in radians
+ * @returns The computed cosine
+ *
+ * @since v0.5.2
+ */
+export let cos = (radians: Number) => {
+  sin(pi / 2 + radians)
+}

stdlib/number.md

@@ -535,3 +535,53 @@ Returns:
 |----|-----------|
 |`Result<Number, String>`|`Ok(value)` containing the parsed number on a successful parse or `Err(msg)` containing an error message string otherwise|
 
+### Number.**sin**
+
+<details disabled>
+<summary tabindex="-1">Added in <code>next</code></summary>
+No other changes yet.
+</details>
+
+```grain
+sin : Number -> Number
+```
+
+Computes the sine of a number (in radians) using Chebyshev polynomials.
+
+Parameters:
+
+|param|type|description|
+|-----|----|-----------|
+|`radians`|`Number`|The input in radians|
+
+Returns:
+
+|type|description|
+|----|-----------|
+|`Number`|The computed sine|
+
+### Number.**cos**
+
+<details disabled>
+<summary tabindex="-1">Added in <code>next</code></summary>
+No other changes yet.
+</details>
+
+```grain
+cos : Number -> Number
+```
+
+Computes the cosine of a number (in radians) using Chebyshev polynomials.
+
+Parameters:
+
+|param|type|description|
+|-----|----|-----------|
+|`radians`|`Number`|The input in radians|
+
+Returns:
+
+|type|description|
+|----|-----------|
+|`Number`|The computed cosine|
+