From: Lady <redacted>
Date: Sun, 17 Jul 2022 22:18:57 +0000 (-0700)
Subject: Add numeric functions and unit tests
X-Git-Tag: 0.1.0~6
X-Git-Url: https://git.ladys.computer/Pisces/commitdiff_plain/5af99cb7def7f5a9b19db6a8e214920dd233113d?ds=sidebyside;hp=29307967cb084aceaa9265fe22af4348c9e4376a

Add numeric functions and unit tests
---

diff --git a/numeric.js b/numeric.js
index 2c1a66f..78ea64c 100644
--- a/numeric.js
+++ b/numeric.js
@@ -7,5 +7,638 @@
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at <https://mozilla.org/MPL/2.0/>.
 
-/** 2^53 − 1. */
-export const MAX_SAFE_INTEGER = Number((1n << 53n) - 1n);
+import { sameValue, toPrimitive } from "./value.js";
+
+export const {
+  /**
+   * ln(10).
+   *
+   * ※ This is an alias for Math.LN10.
+   */
+  LN10,
+
+  /**
+   * ln(2).
+   *
+   * ※ This is an alias for Math.LN2.
+   */
+  LN2,
+
+  /**
+   * log10(ℇ).
+   *
+   * ※ This is an alias for Math.LOG10E.
+   */
+  LOG10E: LOG10ℇ,
+
+  /**
+   * log2(ℇ).
+   *
+   * ※ This is an alias for Math.LOG2E.
+   */
+  LOG2E: LOG2ℇ,
+
+  /**
+   * sqrt(.5).
+   *
+   * ※ This is an alias for Math.SQRT1_2.
+   */
+  SQRT1_2: RECIPROCAL_SQRT2,
+
+  /**
+   * sqrt(2).
+   *
+   * ※ This is an alias for Math.SQRT2.
+   */
+  SQRT2,
+
+  /**
+   * Returns the arccos of the provided value.
+   *
+   * ※ This is an alias for Math.acos.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  acos: arccos,
+
+  /**
+   * Returns the arccosh of the provided value.
+   *
+   * ※ This is an alias for Math.acosh.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  acosh: arccosh,
+
+  /**
+   * Returns the arcsin of the provided value.
+   *
+   * ※ This is an alias for Math.asin.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  asin: arcsin,
+
+  /**
+   * Returns the arcsinh of the provided value.
+   *
+   * ※ This is an alias for Math.asinh.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  asinh: arcsinh,
+
+  /**
+   * Returns the arctan of the provided value.
+   *
+   * ※ This is an alias for Math.atan.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  atan: arctan,
+
+  /**
+   * Returns the arctanh of the provided value.
+   *
+   * ※ This is an alias for Math.atanh.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  atanh: arctanh,
+
+  /**
+   * Returns the cube root of the provided value.
+   *
+   * ※ This is an alias for Math.cbrt.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  cbrt,
+
+  /**
+   * Returns the ceiling of the provided value.
+   *
+   * ※ This is an alias for Math.ceil.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  ceil,
+
+  /**
+   * Returns the cos of the provided value.
+   *
+   * ※ This is an alias for Math.cos.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  cos,
+
+  /**
+   * Returns the cosh of the provided value.
+   *
+   * ※ This is an alias for Math.cosh.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  cosh,
+
+  /**
+   * Returns the Euler number raised to the provided value.
+   *
+   * ※ This is an alias for Math.exp.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  exp,
+
+  /**
+   * Returns the Euler number raised to the provided value, minus one.
+   *
+   * ※ This is an alias for Math.expm1.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  expm1,
+
+  /**
+   * Returns the floor of the provided value.
+   *
+   * ※ This is an alias for Math.floor.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  floor,
+
+  /**
+   * Returns the square root of the sum of the squares of the provided
+   * arguments.
+   *
+   * ※ This is an alias for Math.hypot.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  hypot,
+
+  /**
+   * Returns the ln of the provided value.
+   *
+   * ※ This is an alias for Math.log.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  log: ln,
+
+  /**
+   * Returns the log10 of the provided value.
+   *
+   * ※ This is an alias for Math.log10.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  log10,
+
+  /**
+   * Returns the ln of one plus the provided value.
+   *
+   * ※ This is an alias for Math.log1p.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  log1p: ln1p,
+
+  /**
+   * Returns the log2 of the provided value.
+   *
+   * ※ This is an alias for Math.log2.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  log2,
+
+  /**
+   * Returns a pseudo·random value in the range [0, 1).
+   *
+   * ※ This is an alias for Math.random.
+   */
+  random: rand,
+
+  /**
+   * Returns the round of the provided value.
+   *
+   * ※ This is an alias for Math.round.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  round,
+
+  /**
+   * Returns the sinh of the provided value.
+   *
+   * ※ This is an alias for Math.sinh.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  sinh,
+
+  /**
+   * Returns the square root of the provided value.
+   *
+   * ※ This is an alias for Math.sqrt.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  sqrt,
+
+  /**
+   * Returns the tan of the provided value.
+   *
+   * ※ This is an alias for Math.tan.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  tan,
+
+  /**
+   * Returns the tanh of the provided value.
+   *
+   * ※ This is an alias for Math.tanh.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  tanh,
+
+  /**
+   * Returns the trunc of the provided value.
+   *
+   * ※ This is an alias for Math.trunc.
+   *
+   * ☡ This function does not allow big·int arguments.
+   */
+  trunc,
+
+  /**
+   * The mathematical constant π.
+   *
+   * ※ This is an alias for Math.PI.
+   */
+  PI: Π,
+
+  /**
+   * The Euler number.
+   *
+   * ※ This is an alias for Math.E.
+   */
+  E: ℇ,
+} = Math;
+
+export const {
+  /**
+   * The largest number value less than infinity.
+   *
+   * ※ This is an alias for Number.MAX_VALUE.
+   */
+  MAX_VALUE: MAXIMUM_NUMBER,
+
+  /**
+   * 2**53 - 1.
+   *
+   * ※ This is an alias for Number.MAX_SAFE_INTEGER.
+   */
+  MAX_SAFE_INTEGER: MAXIMUM_SAFE_INTEGRAL_NUMBER,
+
+  /**
+   * The smallest number value greater than negative infinity.
+   *
+   * ※ This is an alias for Number.MIN_VALUE.
+   */
+  MIN_VALUE: MINIMUM_NUMBER,
+
+  /**
+   * -(2**53 - 1).
+   *
+   * ※ This is an alias for Number.MIN_SAFE_INTEGER.
+   */
+  MIN_SAFE_INTEGER: MINIMUM_SAFE_INTEGRAL_NUMBER,
+
+  /**
+   * Negative infinity.
+   *
+   * ※ This is an alias for Number.NEGATIVE_INFINITY.
+   */
+  NEGATIVE_INFINITY,
+
+  /**
+   * Nan.
+   *
+   * ※ This is an alias for Number.NaN.
+   */
+  NaN: NAN,
+
+  /**
+   * Positive infinity.
+   *
+   * ※ This is an alias for Number.POSITIVE_INFINITY.
+   */
+  POSITIVE_INFINITY,
+
+  /**
+   * The difference between 1 and the smallest number greater than 1.
+   *
+   * ※ This is an alias for Number.EPSILON.
+   */
+  EPSILON: Ε,
+
+  /**
+   * Returns whether the provided value is a finite number.
+   *
+   * ※ This is an alias for Number.isFinite.
+   */
+  isFinite: isFiniteNumber,
+
+  /**
+   * Returns whether the provided value is an integral number.
+   *
+   * ※ This is an alias for Number.isInteger.
+   */
+  isInteger: isIntegralNumber,
+
+  /**
+   * Returns whether the provided value is nan.
+   *
+   * ※ This is an alias for Number.isNaN.
+   */
+  isNaN: isNan,
+
+  /**
+   * Returns whether the provided value is a safe integral number.
+   *
+   * ※ This is an alias for Number.isSafeInteger.
+   */
+  isSafeInteger: isSafeIntegralNumber,
+} = Number;
+
+/**
+ * Returns the magnitude (absolute value) of the provided value.
+ *
+ * ※ Unlike Math.abs, this function can take big·int arguments.
+ */
+export const abs = ($) => {
+  const n = toNumeric($);
+  return typeof n === "bigint"
+    ? n < 0n ? -n : n
+    : isNan(n)
+    ? NAN
+    : sameValue(n, -0)
+    ? 0
+    : sameValue(n, NEGATIVE_INFINITY)
+    ? POSITIVE_INFINITY
+    : n < 0
+    ? -n
+    : n;
+};
+
+export const {
+  /**
+   * Returns the arctangent of the dividend of the provided values.
+   *
+   * ※ Unlike Math.atan2, this function can take big·int arguments.
+   * However, the result will always be a number.
+   */
+  atan2,
+
+  /**
+   * Returns the number of leading zeroes in the 32‐bit representation of
+   * the provided value.
+   *
+   * ※ Unlike Math.clz32, this function accepts either number or big·int
+   * values.
+   */
+  clz32,
+
+  /**
+   * Returns the 32‐bit float which best approximate the provided
+   * value.
+   *
+   * ※ Unlike Math.fround, this function can take big·int arguments.
+   * However, the result will always be a number.
+   */
+  toFloat32,
+} = (() => {
+  const { atan2, fround, clz32 } = Math;
+  return {
+    atan2: (y, x) => atan2(toNumber(y), toNumber(x)),
+    clz32: ($) => {
+      const n = toNumeric($);
+      return clz32(
+        typeof n === "bigint" ? toNumber(toUintN(32, n)) : n,
+      );
+    },
+    toFloat32: ($) => fround(toNumber($)),
+  };
+})();
+
+/**
+ * Returns the highest value of the provided arguments, or negative
+ * infinity if no argument is provided.
+ *
+ * ※ Unlike Math.max, this function accepts either number or big·int
+ * values. All values must be of the same type, or this function will
+ * throw an error.
+ *
+ * ☡ If no argument is supplied, the result will be a number, not a
+ * big·int.
+ */
+export const max = (...$s) => {
+  let highest = undefined;
+  for (let i = 0; i < $s.length; ++i) {
+    // Iterate over all the numbers.
+    const number = toNumeric($s[i]);
+    if (highest === undefined) {
+      // The current number is the first one.
+      if (isNan(number)) {
+        // The current number is nan.
+        return NAN;
+      } else {
+        // The current number is not nan.
+        highest = number;
+      }
+    } else {
+      if (typeof highest !== typeof number) {
+        // The type of the current number and the lowest number don’t
+        // match.
+        throw new TypeError("Piscēs: Type mismatch.");
+      } else if (isNan(number)) {
+        // The current number is nan.
+        return NAN;
+      } else if (sameValue(number, 0) && sameValue(highest, -0)) {
+        // The current number is +0 and the highest number is -0.
+        highest = 0;
+      } else if (highest === undefined || number > highest) {
+        // The current number is greater than the highest number.
+        highest = number;
+      } else {
+        // The current number is less than or equal to the lowest
+        // number.
+        /* do nothing */
+      }
+    }
+  }
+  return highest ?? NEGATIVE_INFINITY;
+};
+
+/**
+ * Returns the lowest value of the provided arguments, or positive
+ * infinity if no argument is provided.
+ *
+ * ※ Unlike Math.min, this function accepts either number or big·int
+ * values. All values must be of the same type, or this function will
+ * throw an error.
+ *
+ * ☡ If no argument is supplied, the result will be a number, not a
+ * big·int.
+ */
+export const min = (...$s) => {
+  let lowest = undefined;
+  for (let i = 0; i < $s.length; ++i) {
+    // Iterate over all the numbers.
+    const number = toNumeric($s[i]);
+    if (lowest === undefined) {
+      // The current number is the first one.
+      if (isNan(number)) {
+        // The current number is nan.
+        return NAN;
+      } else {
+        // The current number is not nan.
+        lowest = number;
+      }
+    } else {
+      // The current number is not the first one.
+      if (typeof lowest !== typeof number) {
+        // The type of the current number and the lowest number don’t
+        // match.
+        throw new TypeError("Piscēs: Type mismatch.");
+      } else if (isNan(number)) {
+        // The current number is nan.
+        return NAN;
+      } else if (sameValue(number, -0) && sameValue(lowest, 0)) {
+        // The current number is -0 and the lowest number is +0.
+        lowest = -0;
+      } else if (number < lowest) {
+        // The current number is less than the lowest number.
+        lowest = number;
+      } else {
+        // The current number is greater than or equal to the lowest
+        // number.
+        /* do nothing */
+      }
+    }
+  }
+  return lowest ?? POSITIVE_INFINITY;
+};
+
+/**
+ * Returns a unit value with the same sign as the provided value, or
+ * the provided value itself if it is not a number or (potentially
+ * signed) zero.
+ *
+ * For big·ints, the return value of this function is 0n if the
+ * provided value is 0n, -1n if the provided value is negative, and +1n
+ * otherwise.
+ *
+ * For numbers, the return value is nan, -0, or +0 if the provided
+ * value is nan, -0, or +0, respectively, and -1 if the provided value
+ * is negative and +1 if the provided value is positive otherwise. Note
+ * that positive and negative infinity will return +1 and -1
+ * respectively.
+ *
+ * ※ Unlike Math.sign, this function accepts either number or big·int
+ * values.
+ */
+export const sgn = ($) => {
+  const n = toNumeric($);
+  return typeof n === "bigint"
+    ? n === 0n ? 0n : n < 0n ? -1n : 1n
+    : isNan(n) || n === 0
+    ? n
+    : //deno-lint-ignore no-compare-neg-zero
+      n < -0
+      ? -1
+      : 1;
+};
+
+/**
+ * Returns the result of converting the provided value to a big·int.
+ *
+ * ※ This method is safe to use with numbers.
+ *
+ * ※ This is effectively an alias for BigInt.
+ */
+export const { toBigInt } = (() => {
+  const makeBigInt = BigInt;
+  return { toBigInt: ($) => makeBigInt($) };
+})();
+
+export const {
+  /**
+   * Returns the result of converting the provided value to fit within
+   * the provided number of bits as a signed integer.
+   *
+   * ※ Unlike BigInt.asIntN, this function accepts both big·int and
+   * number values.
+   *
+   * ☡ The first argument, the number of bits, must be a number.
+   */
+  toIntN,
+
+  /**
+   * Returns the result of converting the provided value to fit within
+   * the provided number of bits as an unsigned integer.
+   *
+   * ※ Unlike BigInt.asUintN, this function accepts both big·int and
+   * number values.
+   *
+   * ☡ The first argument, the number of bits, must be a number.
+   */
+  toUintN,
+} = (() => {
+  const { asIntN, asUintN } = BigInt;
+  return {
+    toIntN: (n, $) => {
+      const prim = toPrimitive($);
+      const big·int = toBigInt(prim);
+      const intN = asIntN(n, big·int);
+      return typeof prim === "bigint" ? intN : toNumber(intN);
+    },
+    toUintN: (n, $) => {
+      const prim = toPrimitive($);
+      const big·int = toBigInt(prim);
+      const uintN = asUintN(n, big·int);
+      return typeof prim === "bigint" ? uintN : toNumber(uintN);
+    },
+  };
+})();
+
+/**
+ * Returns the result of converting the provided value to a number.
+ *
+ * ※ This method is safe to use with big·ints.
+ *
+ * ※ This is effectively a nonconstructible version of the Number
+ * constructor.
+ */
+export const { toNumber } = (() => {
+  const makeNumber = Number;
+  return { toNumber: ($) => makeNumber($) };
+})();
+
+/**
+ * Returns the result of converting the provided value to a number or
+ * big·int.
+ *
+ * ※ If the result of converting the provided value to a primitive is
+ * not a big·int, this function will return a number.
+ */
+export const toNumeric = ($) => {
+  const primValue = toPrimitive($, "number");
+  return typeof primValue === "bigint" ? primValue : +primValue;
+};
diff --git a/numeric.test.js b/numeric.test.js
new file mode 100644
index 0000000..e82e04b
--- /dev/null
+++ b/numeric.test.js
@@ -0,0 +1,192 @@
+// ♓🌟 Piscēs ∷ numeric.test.js
+// ====================================================================
+//
+// Copyright © 2022 Lady [@ Lady’s Computer].
+//
+// This Source Code Form is subject to the terms of the Mozilla Public
+// License, v. 2.0. If a copy of the MPL was not distributed with this
+// file, You can obtain one at <https://mozilla.org/MPL/2.0/>.
+
+import {
+  assertStrictEquals,
+  assertThrows,
+  describe,
+  it,
+} from "./dev-deps.js";
+import {
+  abs,
+  atan2,
+  clz32,
+  max,
+  min,
+  sgn,
+  toBigInt,
+  toFloat32,
+  toIntN,
+  toNumber,
+  toNumeric,
+  toUintN,
+} from "./numeric.js";
+
+describe("abs", () => {
+  it("[[Call]] returns the absolute value", () => {
+    assertStrictEquals(abs(-1), 1);
+  });
+
+  it("[[Call]] works with big·ints", () => {
+    const bn = BigInt(Number.MAX_SAFE_INTEGER) + 2n;
+    assertStrictEquals(abs(-bn), bn);
+  });
+});
+
+describe("atan2", () => {
+  it("[[Call]] returns the atan2", () => {
+    assertStrictEquals(atan2(6, 9), Math.atan2(6, 9));
+  });
+
+  it("[[Call]] works with big·ints", () => {
+    assertStrictEquals(atan2(6n, 9n), Math.atan2(6, 9));
+  });
+});
+
+describe("clz32", () => {
+  it("[[Call]] returns the clz32", () => {
+    assertStrictEquals(clz32(1 << 28), 3);
+  });
+
+  it("[[Call]] works with big·ints", () => {
+    assertStrictEquals(clz32(1n << 28n), 3);
+  });
+});
+
+describe("max", () => {
+  it("[[Call]] returns the largest number", () => {
+    assertStrictEquals(max(1, -6, 92, -Infinity, 0), 92);
+  });
+
+  it("[[Call]] returns the largest big·int", () => {
+    assertStrictEquals(max(1n, -6n, 92n, 0n), 92n);
+  });
+
+  it("[[Call]] returns nan if any argument is nan", () => {
+    assertStrictEquals(max(0, NaN, 1), NaN);
+  });
+
+  it("[[Call]] returns -Infinity when called with no arguments", () => {
+    assertStrictEquals(max(), -Infinity);
+  });
+
+  it("[[Call]] throws if both big·int and number arguments are provided", () => {
+    assertThrows(() => max(-Infinity, 0n));
+  });
+});
+
+describe("min", () => {
+  it("[[Call]] returns the largest number", () => {
+    assertStrictEquals(min(1, -6, 92, Infinity, 0), -6);
+  });
+
+  it("[[Call]] returns the largest big·int", () => {
+    assertStrictEquals(min(1n, -6n, 92n, 0n), -6n);
+  });
+
+  it("[[Call]] returns nan if any argument is nan", () => {
+    assertStrictEquals(min(0, NaN, 1), NaN);
+  });
+
+  it("[[Call]] returns Infinity when called with no arguments", () => {
+    assertStrictEquals(min(), Infinity);
+  });
+
+  it("[[Call]] throws if both big·int and number arguments are provided", () => {
+    assertThrows(() => min(Infinity, 0n));
+  });
+});
+
+describe("sgn", () => {
+  it("[[Call]] returns the sign", () => {
+    assertStrictEquals(sgn(Infinity), 1);
+    assertStrictEquals(sgn(-Infinity), -1);
+    assertStrictEquals(sgn(0), 0);
+    assertStrictEquals(sgn(-0), -0);
+    assertStrictEquals(sgn(NaN), NaN);
+  });
+
+  it("[[Call]] works with big·ints", () => {
+    assertStrictEquals(sgn(0n), 0n);
+    assertStrictEquals(sgn(92n), 1n);
+    assertStrictEquals(sgn(-92n), -1n);
+  });
+});
+
+describe("toBigInt", () => {
+  it("[[Call]] converts to a big·int", () => {
+    assertStrictEquals(toBigInt(2), 2n);
+  });
+});
+
+describe("toFloat32", () => {
+  it("[[Call]] returns the 32‐bit floating‐point representation", () => {
+    assertStrictEquals(
+      toFloat32(562949953421313),
+      Math.fround(562949953421313),
+    );
+  });
+
+  it("[[Call]] works with big·ints", () => {
+    assertStrictEquals(
+      toFloat32(562949953421313n),
+      Math.fround(562949953421313),
+    );
+  });
+});
+
+describe("toIntN", () => {
+  it("[[Call]] converts to an int·n", () => {
+    assertStrictEquals(toIntN(2, 7n), -1n);
+  });
+
+  it("[[Call]] works with numbers", () => {
+    assertStrictEquals(toIntN(2, 7), -1);
+  });
+});
+
+describe("toNumber", () => {
+  it("[[Call]] converts to a number", () => {
+    assertStrictEquals(toNumber(2n), 2);
+  });
+});
+
+describe("toNumeric", () => {
+  it("[[Call]] returns a big·int argument", () => {
+    assertStrictEquals(toNumeric(231n), 231n);
+  });
+
+  it("[[Call]] converts to a numeric", () => {
+    assertStrictEquals(toNumeric("231"), 231);
+  });
+
+  it("[[Call]] prefers `valueOf`", () => {
+    assertStrictEquals(
+      toNumeric({
+        toString() {
+          return 0;
+        },
+        valueOf() {
+          return 231n;
+        },
+      }),
+      231n,
+    );
+  });
+});
+
+describe("toUintN", () => {
+  it("[[Call]] converts to an int·n", () => {
+    assertStrictEquals(toUintN(2, 7n), 3n);
+  });
+
+  it("[[Call]] works with numbers", () => {
+    assertStrictEquals(toUintN(2, 7), 3);
+  });
+});