feat(stdlib): Reimplement Number.sin, Number.cos, Number.tan (#2158)

Author: spotandjake

compiler/test/stdlib/number.test.gr

@@ -949,3 +949,111 @@ assert Number.linearMap(
   0.5
 ) ==
   150
+
+// Number.sin - 0 to pi/2
+assert Number.sin(0) == 0
+assert Number.isClose(Number.sin(Number.pi / 6), 1/2)
+assert Number.isClose(Number.sin(Number.pi / 4), Number.sqrt(2) / 2)
+assert Number.isClose(Number.sin(Number.pi / 3), Number.sqrt(3) / 2)
+assert Number.isClose(Number.sin(Number.pi / 2), 1)
+// Number.sin - pi/2 to 2pi
+assert Number.isClose(Number.sin(2 * Number.pi / 3), Number.sqrt(3) / 2)
+assert Number.isClose(Number.sin(3 * Number.pi / 4), Number.sqrt(2) / 2)
+assert Number.isClose(Number.sin(5 * Number.pi / 6), 1/2)
+// Note: This has an absolute error of 1e-15 because `Number.pi` is not exact
+assert Number.isClose(Number.sin(Number.pi), 0, absoluteTolerance=1e-15)
+// Number.sin - 2pi to 3pi/2
+assert Number.isClose(Number.sin(7 * Number.pi / 6), -1/2)
+assert Number.isClose(Number.sin(5 * Number.pi / 4), Number.sqrt(2) / -2)
+assert Number.isClose(Number.sin(4 * Number.pi / 3), Number.sqrt(3) / -2)
+assert Number.isClose(Number.sin(3 * Number.pi / 2), -1)
+// Number.sin - 3pi/2 to 0
+assert Number.isClose(Number.sin(5 * Number.pi / 3), Number.sqrt(3) / -2)
+assert Number.isClose(Number.sin(7 * Number.pi / 4), Number.sqrt(2) / -2)
+assert Number.isClose(Number.sin(11 * Number.pi / 6), -1/2)
+// Note: This has an absolute error of 1e-15 because `Number.pi` is not exact
+assert Number.isClose(Number.sin(2 * Number.pi), 0, absoluteTolerance=1e-15)
+// Number.sin - special cases
+assert Number.sin(1/2) == Number.sin(0.5)
+assert Number.sin(1/4) == Number.sin(0.25)
+assert Number.isClose(Number.sin(18_446_744_073_709_551_615), 0.0235985099) // 2^64-1
+assert Number.isClose(Number.sin(-18_446_744_073_709_551_615), -0.0235985099) // -2^64+1
+assert Number.isClose(Number.sin(18_446_744_073_709_551_616), 0.0235985099) // 2^64
+assert Number.isClose(Number.sin(-18_446_744_073_709_551_616), -0.0235985099) // -2^64
+assert Number.isClose( // Note: We lose a lot of precision here do to ieee754 representation
+  Number.sin(1.7976931348623157e+308),
+  0.0049619,
+  absoluteTolerance=1e7
+) // Max F64
+assert Number.isClose(
+  Number.sin(-1.7976931348623157e+308),
+  0.00496,
+  absoluteTolerance=1e7
+) // Max F64
+assert Number.isNaN(Number.sin(Infinity))
+assert Number.isNaN(Number.sin(-Infinity))
+assert Number.isNaN(Number.sin(NaN))
+
+// Number.cos - 0 to pi/2
+assert Number.cos(0) == 1
+assert Number.isClose(Number.cos(Number.pi / 6), Number.sqrt(3) / 2)
+assert Number.isClose(Number.cos(Number.pi / 4), Number.sqrt(2) / 2)
+assert Number.isClose(Number.cos(Number.pi / 3), 1/2)
+// Note: This has an absolute error of 1e-15 because `Number.pi` is not exact
+assert Number.isClose(Number.cos(Number.pi / 2), 0, absoluteTolerance=1e-15)
+// Number.cos - pi/2 to 2pi
+assert Number.isClose(Number.cos(2 * Number.pi / 3), -1/2)
+assert Number.isClose(Number.cos(3 * Number.pi / 4), Number.sqrt(2) / -2)
+assert Number.isClose(Number.cos(5 * Number.pi / 6), Number.sqrt(3) / -2)
+assert Number.isClose(Number.cos(Number.pi), -1)
+// Number.cos - 2pi to 3pi/2
+assert Number.isClose(Number.cos(7 * Number.pi / 6), Number.sqrt(3) / -2)
+assert Number.isClose(Number.cos(5 * Number.pi / 4), Number.sqrt(2) / -2)
+assert Number.isClose(Number.cos(4 * Number.pi / 3), -1/2)
+// Note: This has an absolute error of 1e-15 because `Number.pi` is not exact
+assert Number.isClose(Number.cos(3 * Number.pi / 2), 0, absoluteTolerance=1e-15)
+// Number.cos - 3pi/2 to 0
+assert Number.isClose(Number.cos(5 * Number.pi / 3), 1/2)
+assert Number.isClose(Number.cos(7 * Number.pi / 4), Number.sqrt(2) / 2)
+assert Number.isClose(Number.cos(11 * Number.pi / 6), Number.sqrt(3) / 2)
+assert Number.isClose(Number.cos(2 * Number.pi), 1)
+// Number.cos - special cases
+assert Number.cos(1/2) == Number.cos(0.5)
+assert Number.cos(1/4) == Number.cos(0.25)
+assert Number.isClose(Number.cos(18_446_744_073_709_551_615), -0.99972151638) // 2^64-1
+assert Number.isClose(Number.cos(-18_446_744_073_709_551_615), -0.99972151638) // -2^64+1
+assert Number.isClose(Number.cos(18_446_744_073_709_551_616), -0.99972151638) // 2^64
+assert Number.isClose(Number.cos(-18_446_744_073_709_551_616), -0.99972151638) // -2^64
+assert Number.isClose(Number.cos(1.7976931348623157e+308), -0.99998768942) // Max F64
+assert Number.isClose(Number.cos(-1.7976931348623157e+308), -0.99998768942) // Max F64
+assert Number.isNaN(Number.cos(Infinity))
+assert Number.isNaN(Number.cos(-Infinity))
+assert Number.isNaN(Number.cos(NaN))
+
+// Number.tan - base cases
+assert Number.tan(0) == 0
+assert Number.isClose(Number.tan(Number.pi / 6), 1 / Number.sqrt(3))
+assert Number.isClose(Number.tan(Number.pi / 4), 1)
+assert Number.isClose(Number.tan(Number.pi / 3), Number.sqrt(3))
+// Note: one might expect this to produce infinity but instead we produce 16331239353195370 because pi can not be represented accurately in iee754, This logic follows c
+assert Number.isClose(Number.tan(Number.pi / 2), 16331239353195370)
+// Number.tan - special cases
+assert Number.tan(1/2) == Number.tan(0.5)
+assert Number.tan(1/4) == Number.tan(0.25)
+assert Number.isClose(Number.tan(18_446_744_073_709_551_615), -0.02360508353) // 2^64-1
+assert Number.isClose(Number.tan(-18_446_744_073_709_551_615), 0.02360508353) // -2^64+1
+assert Number.isClose(Number.tan(18_446_744_073_709_551_616), -0.02360508353) // 2^64
+assert Number.isClose(Number.tan(-18_446_744_073_709_551_616), 0.02360508353) // -2^64
+assert Number.isClose( // Note: We lose a lot of precision here do to ieee754 representation
+  Number.tan(1.7976931348623157e+308),
+  -0.00496201587,
+  absoluteTolerance=1e7
+) // Max F64
+assert Number.isClose(
+  Number.tan(-1.7976931348623157e+308),
+  -0.00496201587,
+  absoluteTolerance=1e7
+) // Max F64
+assert Number.isNaN(Number.tan(Infinity))
+assert Number.isNaN(Number.tan(-Infinity))
+assert Number.isNaN(Number.tan(NaN))

stdlib/number.gr

@@ -48,6 +48,8 @@ from "runtime/atoi/parse" include Parse as Atoi
 from "runtime/atof/parse" include Parse as Atof
 from "runtime/unsafe/tags" include Tags
 from "runtime/exception" include Exception
+from "runtime/math/trig" include Trig
+use Trig.{ sin, cos, tan }
 
 use Atoi.{ type ParseIntError }
 
@@ -1072,3 +1074,69 @@ provide let linearMap = (inputRange, outputRange, current) => {
     clamp(outputRange, mapped)
   }
 }
+
+/**
+ * Computes the sine of a number (in radians).
+ *
+ * @param radians: The input in radians
+ * @returns The computed sine
+ *
+ * @example Number.sin(0) == 0
+ *
+ * @since v0.7.0
+ */
+@unsafe
+provide let sin = (radians: Number) => {
+  use WasmF64.{ (==) }
+  let xval = coerceNumberToWasmF64(radians)
+  let value = sin(xval)
+  return if (!isFloat(radians) && value == WasmF64.trunc(value)) {
+    WasmI32.toGrain(reducedInteger(WasmI64.truncF64S(value))): Number
+  } else {
+    WasmI32.toGrain(newFloat64(value)): Number
+  }
+}
+
+/**
+ * Computes the cosine of a number (in radians).
+ *
+ * @param radians: The input in radians
+ * @returns The computed cosine
+ *
+ * @example Number.cos(0) == 1
+ *
+ * @since v0.7.0
+ */
+@unsafe
+provide let cos = (radians: Number) => {
+  use WasmF64.{ (==) }
+  let xval = coerceNumberToWasmF64(radians)
+  let value = cos(xval)
+  return if (!isFloat(radians) && value == WasmF64.trunc(value)) {
+    WasmI32.toGrain(reducedInteger(WasmI64.truncF64S(value))): Number
+  } else {
+    WasmI32.toGrain(newFloat64(value)): Number
+  }
+}
+
+/**
+ * Computes the tangent of a number (in radians).
+ *
+ * @param radians: The input in radians
+ * @returns The computed tangent
+ *
+ * @example Number.tan(0) == 0
+ *
+ * @since v0.7.0
+ */
+@unsafe
+provide let tan = (radians: Number) => {
+  use WasmF64.{ (==) }
+  let xval = coerceNumberToWasmF64(radians)
+  let value = tan(xval)
+  return if (!isFloat(radians) && value == WasmF64.trunc(value)) {
+    WasmI32.toGrain(reducedInteger(WasmI64.truncF64S(value))): Number
+  } else {
+    WasmI32.toGrain(newFloat64(value)): Number
+  }
+}

stdlib/number.md

@@ -1566,3 +1566,96 @@ Throws:
 * When `outputRange` is not finite
 * When `outputRange` includes NaN
 
+### Number.**sin**
+
+<details disabled>
+<summary tabindex="-1">Added in <code>next</code></summary>
+No other changes yet.
+</details>
+
+```grain
+sin : (radians: Number) => Number
+```
+
+Computes the sine of a number (in radians).
+
+Parameters:
+
+|param|type|description|
+|-----|----|-----------|
+|`radians`|`Number`|The input in radians|
+
+Returns:
+
+|type|description|
+|----|-----------|
+|`Number`|The computed sine|
+
+Examples:
+
+```grain
+Number.sin(0) == 0
+```
+
+### Number.**cos**
+
+<details disabled>
+<summary tabindex="-1">Added in <code>next</code></summary>
+No other changes yet.
+</details>
+
+```grain
+cos : (radians: Number) => Number
+```
+
+Computes the cosine of a number (in radians).
+
+Parameters:
+
+|param|type|description|
+|-----|----|-----------|
+|`radians`|`Number`|The input in radians|
+
+Returns:
+
+|type|description|
+|----|-----------|
+|`Number`|The computed cosine|
+
+Examples:
+
+```grain
+Number.cos(0) == 1
+```
+
+### Number.**tan**
+
+<details disabled>
+<summary tabindex="-1">Added in <code>next</code></summary>
+No other changes yet.
+</details>
+
+```grain
+tan : (radians: Number) => Number
+```
+
+Computes the tangent of a number (in radians).
+
+Parameters:
+
+|param|type|description|
+|-----|----|-----------|
+|`radians`|`Number`|The input in radians|
+
+Returns:
+
+|type|description|
+|----|-----------|
+|`Number`|The computed tangent|
+
+Examples:
+
+```grain
+Number.tan(0) == 0
+```
+

stdlib/runtime/math/kernel/cos.gr

@@ -0,0 +1,70 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+module Cosine
+
+from "runtime/unsafe/wasmf64" include WasmF64
+
+/*
+ * Source: https://git.musl-libc.org/cgit/musl/tree/src/math/__cos.c
+ *
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ *
+ * Algorithm
+ *      1. Since cos(-x) = cos(x), we need only to consider positive x.
+ *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+ *      3. cos(x) is approximated by a polynomial of degree 14 on
+ *         [0,pi/4]
+ *                                       4            14
+ *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+ *         where the remez error is
+ *
+ *      |              2     4     6     8     10    12     14 |     -58
+ *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
+ *      |                                                      |
+ *
+ *                     4     6     8     10    12     14
+ *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
+ *             cos(x) ~ 1 - x*x/2 + r
+ *         since cos(x+y) ~ cos(x) - sin(x)*y
+ *                        ~ cos(x) - x*y,
+ *         a correction term is necessary in cos(x) and hence
+ *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
+ *         For better accuracy, rearrange to
+ *              cos(x+y) ~ w + (tmp + (r-x*y))
+ *         where w = 1 - x*x/2 and tmp is a tiny correction term
+ *         (1 - x*x/2 == w + tmp exactly in infinite precision).
+ *         The exactness of w + tmp in infinite precision depends on w
+ *         and tmp having the same precision as x.  If they have extra
+ *         precision due to compiler bugs, then the extra precision is
+ *         only good provided it is retained in all terms of the final
+ *         expression for cos().  Retention happens in all cases tested
+ *         under FreeBSD, so don't pessimize things by forcibly clipping
+ *         any extra precision in w.
+ */
+@unsafe
+provide let cos = (x: WasmF64, y: WasmF64) => {
+  use WasmF64.{ (+), (-), (*) }
+  let c1 = 4.16666666666666019037e-02W /* 0x3FA55555, 0x5555554C */
+  let c2 = -1.38888888888741095749e-03W /* 0xBF56C16C, 0x16C15177 */
+  let c3 = 2.48015872894767294178e-05W /* 0x3EFA01A0, 0x19CB1590 */
+  let c4 = -2.75573143513906633035e-07W /* 0xBE927E4F, 0x809C52AD */
+  let c5 = 2.08757232129817482790e-09W /* 0x3E21EE9E, 0xBDB4B1C4 */
+  let c6 = -1.13596475577881948265e-11W /* 0xBDA8FAE9, 0xBE8838D4 */
+
+  let z = x * x
+  let w = z * z
+  let r = z * (c1 + z * (c2 + z * c3)) + w * w * (c4 + z * (c5 + z * c6))
+  let hz = 0.5W * z
+  let w = 1.0W - hz
+  w + (1.0W - w - hz + (z * r - x * y))
+}

stdlib/runtime/math/kernel/cos.md

@@ -0,0 +1,14 @@
+---
+title: Cosine
+---
+
+## Values
+
+Functions and constants included in the Cosine module.
+
+### Cosine.**cos**
+
+```grain
+cos : (x: WasmF64, y: WasmF64) => WasmF64
+```
+