X-Git-Url: https://git.ladys.computer/Pisces/blobdiff_plain/f3e417be2077db5839dcada4aa1395ae2e9337ba..refs/heads/current:/numeric.js?ds=inline

diff --git a/numeric.js b/numeric.js
index ce92585..079e56e 100644
--- a/numeric.js
+++ b/numeric.js
@@ -1,392 +1,34 @@
 // ♓🌟 Piscēs ∷ numeric.js
 // ====================================================================
 //
-// Copyright © 2022 Lady [@ Lady’s Computer].
+// Copyright © 2022–2023 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 { 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.
-   */
+import { call, createArrowFunction } from "./function.js";
+import { defineOwnDataProperty } from "./object.js";
+import {
+  stringCatenate,
+  stringPadEnd,
+  stringRepeat,
+  substring,
+  toString,
+} from "./string.js";
+import {
+  NAN,
   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;
-
-/** Positive zero. */
-export const POSITIVE_ZERO = 0;
-
-/** Negative zero. */
-export const NEGATIVE_ZERO = -0;
+  sameValue,
+  toPrimitive,
+  UNDEFINED,
+} from "./value.js";
 
 /**
  * Returns the magnitude (absolute value) of the provided value.
  *
- * ※ Unlike Math.abs, this function can take big·int arguments.
+ * ※ Unlike `Math.abs`, this function can take big·int arguments.
  */
 export const abs = ($) => {
   const n = toNumeric($);
@@ -403,21 +45,81 @@ export const abs = ($) => {
     : n;
 };
 
+/**
+ * Returns the arccos of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.acos`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const arccos = createArrowFunction(
+  Math.acos,
+  { name: "arccos" },
+);
+
+/**
+ * Returns the arccosh of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.acosh`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const arccosh = createArrowFunction(
+  Math.acosh,
+  { name: "arccosh" },
+);
+
+/**
+ * Returns the arcsin of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.asin`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const arcsin = createArrowFunction(
+  Math.asin,
+  { name: "arcsin" },
+);
+
+/**
+ * Returns the arcsinh of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.asinh`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const arcsinh = createArrowFunction(
+  Math.asinh,
+  { name: "arcsinh" },
+);
+
+/**
+ * Returns the arctan of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.atan`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const arctan = createArrowFunction(
+  Math.atan,
+  { name: "arctan" },
+);
+
 export const {
   /**
    * Returns the arctangent of the dividend of the provided values.
    *
-   * ※ Unlike Math.atan2, this function can take big·int arguments.
+   * ※ Unlike `Math.atan2`, this function can take big·int arguments.
    * However, the result will always be a number.
    */
-  atan2,
+  arctan2,
 
   /**
-   * Returns the number of leading zeroes in the 32‐bit representation of
-   * the provided value.
+   * 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.
+   * ※ Unlike `Math.clz32`, this function accepts either number or
+   * big·int values.
    */
   clz32,
 
@@ -425,41 +127,204 @@ export const {
    * Returns the 32‐bit float which best approximate the provided
    * value.
    *
-   * ※ Unlike Math.fround, this function can take big·int arguments.
+   * ※ 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)),
+    arctan2: (y, x) => atan2(toNumber(y), toNumber(x)),
     clz32: ($) => {
       const n = toNumeric($);
       return clz32(
-        typeof n === "bigint" ? toNumber(toUintN(32, n)) : n,
+        typeof n === "bigint"
+          ? toNumber(toUnsignedIntegralNumeric(32, n))
+          : n,
       );
     },
     toFloat32: ($) => fround(toNumber($)),
   };
 })();
 
+/**
+ * Returns the arctanh of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.atanh`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const arctanh = createArrowFunction(
+  Math.atanh,
+  { name: "arctanh" },
+);
+
+/**
+ * Returns the cube root of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.cbrt`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const cbrt = createArrowFunction(Math.cbrt);
+
+/**
+ * Returns the ceiling of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.ceil`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const ceil = createArrowFunction(Math.ceil);
+
+/**
+ * Returns the cos of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.cos`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const cos = createArrowFunction(Math.cos);
+
+/**
+ * Returns the cosh of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.cosh`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const cosh = createArrowFunction(Math.cosh);
+
+/**
+ * Returns the Euler number raised to the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.exp`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const exp = createArrowFunction(Math.exp);
+
+/**
+ * Returns the Euler number raised to the provided value, minus one.
+ *
+ * ※ This function is effectively an alias for `Math.expm1`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const expm1 = createArrowFunction(Math.expm1);
+
+/**
+ * Returns the floor of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.floor`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const floor = createArrowFunction(Math.floor);
+
+/**
+ * Returns the square root of the sum of the squares of the provided
+ * arguments.
+ *
+ * ※ This function is effectively an alias for `Math.hypot`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const hypot = createArrowFunction(Math.hypot);
+
+/**
+ * Returns whether the provided value is a finite number.
+ *
+ * ※ This function is effectively an alias for `Number.isFinite`.
+ */
+export const isFiniteNumber = createArrowFunction(
+  Number.isFinite,
+  { name: "isFiniteNumber" },
+);
+
+/**
+ * Returns whether the provided value is an integral number.
+ *
+ * ※ This function is effectively an alias for `Number.isInteger`.
+ */
+export const isIntegralNumber = createArrowFunction(
+  Number.isInteger,
+  { name: "isIntegralNumber" },
+);
+
+/**
+ * Returns whether the provided value is nan.
+ *
+ * ※ This function is effectively an alias for `Number.isNaN`.
+ */
+export const isNan = createArrowFunction(
+  Number.isNaN,
+  { name: "isNan" },
+);
+
+/**
+ * Returns whether the provided value is a safe integral number.
+ *
+ * ※ This function is effectively an alias for `Number.isSafeInteger`.
+ */
+export const isSafeIntegralNumber = createArrowFunction(
+  Number.isSafeInteger,
+  { name: "isSafeIntegralNumber" },
+);
+
+/**
+ * Returns the ln of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.log`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const ln = createArrowFunction(Math.log, { name: "ln" });
+
+/**
+ * Returns the ln of one plus the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.log1p`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const ln1p = createArrowFunction(Math.log1p, { name: "ln1p" });
+
+/**
+ * Returns the log10 of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.log10`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const log10 = createArrowFunction(Math.log10);
+
+/**
+ * Returns the log2 of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.log2`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const log2 = createArrowFunction(Math.log2);
+
 /**
  * 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
+ * ※ 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 = (...$s) => {
-  let highest = undefined;
+export const max = Object.defineProperties((...$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) {
+    if (highest === UNDEFINED) {
       // The current number is the first one.
       if (isNan(number)) {
         // The current number is nan.
@@ -479,7 +344,7 @@ export const max = (...$s) => {
       } else if (sameValue(number, 0) && sameValue(highest, -0)) {
         // The current number is +0 and the highest number is -0.
         highest = 0;
-      } else if (highest === undefined || number > highest) {
+      } else if (number > highest) {
         // The current number is greater than the highest number.
         highest = number;
       } else {
@@ -490,25 +355,28 @@ export const max = (...$s) => {
     }
   }
   return highest ?? NEGATIVE_INFINITY;
-};
+}, {
+  name: defineOwnDataProperty(Object.create(null), "value", "max"),
+  length: defineOwnDataProperty(Object.create(null), "value", 2),
+});
 
 /**
  * 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
+ * ※ 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 = (...$s) => {
-  let lowest = undefined;
+export const min = Object.defineProperties((...$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) {
+    if (lowest === UNDEFINED) {
       // The current number is the first one.
       if (isNan(number)) {
         // The current number is nan.
@@ -540,7 +408,29 @@ export const min = (...$s) => {
     }
   }
   return lowest ?? POSITIVE_INFINITY;
-};
+}, {
+  name: defineOwnDataProperty(Object.create(null), "value", "min"),
+  length: defineOwnDataProperty(Object.create(null), "value", 2),
+});
+
+/**
+ * Returns a pseudo·random value in the range [0, 1).
+ *
+ * ※ This function is effectively an alias for `Math.random`.
+ */
+export const rand = createArrowFunction(
+  Math.random,
+  { name: "rand" },
+);
+
+/**
+ * Returns the round of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.round`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const round = createArrowFunction(Math.round);
 
 /**
  * Returns a unit value with the same sign as the provided value, or
@@ -548,17 +438,17 @@ export const min = (...$s) => {
  * signed) zero.
  *
  * For big·ints, the return value of this function is 0n if the
- * provided value is 0n, -1n if the provided value is negative, and +1n
+ * provided value is 0n, −1n if the provided value is negative, and +1n
  * otherwise.
  *
- * For numbers, the return value is nan, -0, or +0 if the provided
- * value is nan, -0, or +0, respectively, and -1 if the provided value
+ * For numbers, the return value is nan, −0, or +0 if the provided
+ * value is nan, −0, or +0, respectively, and −1 if the provided value
  * is negative and +1 if the provided value is positive otherwise. Note
- * that positive and negative infinity will return +1 and -1
+ * that positive and negative infinity will return +1 and −1
  * respectively.
  *
- * ※ Unlike Math.sign, this function accepts either number or big·int
- * values.
+ * ※ Unlike `Math.sign`, this function accepts either number or
+ * big·int values.
  */
 export const sgn = ($) => {
   const n = toNumeric($);
@@ -572,12 +462,57 @@ export const sgn = ($) => {
     : 1;
 };
 
+/**
+ * Returns the sin of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.sin`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const sin = createArrowFunction(Math.sin);
+
+/**
+ * Returns the sinh of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.sinh`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const sinh = createArrowFunction(Math.sinh);
+
+/**
+ * Returns the square root of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.sqrt`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const sqrt = createArrowFunction(Math.sqrt);
+
+/**
+ * Returns the tan of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.tan`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const tan = createArrowFunction(Math.tan);
+
+/**
+ * Returns the tanh of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.tanh`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const tanh = createArrowFunction(Math.tanh);
+
 /**
  * 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.
+ * ※ This is effectively an alias for `BigInt`.
  */
 export const { toBigInt } = (() => {
   const makeBigInt = BigInt;
@@ -586,74 +521,114 @@ export const { toBigInt } = (() => {
 
 export const {
   /**
-   * Returns the result of converting the provided value to fit within
-   * the provided number of bits as a signed integer.
+   * Returns the result of converting the provided value to an
+   * exponential notation string.
    *
-   * ※ Unlike BigInt.asIntN, this function accepts both big·int and
-   * number values.
+   * If a second argument is provided, it gives the number of
+   * fractional digits to use in the mantissa. Otherwise, the smallest
+   * number which does not result in a reduction in precision is used.
    *
-   * ☡ The first argument, the number of bits, must be a number.
+   * ※ This method is safe to use with big·ints.
    */
-  toIntN,
+  toExponentialNotation,
 
   /**
-   * Returns the result of converting the provided value to fit within
-   * the provided number of bits as an unsigned integer.
+   * Returns the result of converting the provided value to a fixed
+   * decimal notation string with the provided number of fractional
+   * digits.
    *
-   * ※ Unlike BigInt.asUintN, this function accepts both big·int and
-   * number values.
-   *
-   * ☡ The first argument, the number of bits, must be a number.
+   * ※ This method is safe to use with big·ints.
    */
-  toUintN,
+  toFixedDecimalNotation,
 } = (() => {
-  const { asIntN, asUintN } = BigInt;
+  const {
+    toExponential: numberToExponential,
+    toFixed: numberToFixed,
+  } = Number.prototype;
+  const { toString: bigintToString } = BigInt.prototype;
   return {
-    toIntN: (n, $) => {
-      const prim = toPrimitive($);
-      if (typeof prim === "bigint") {
-        // The primitive value is a big·int.
-        return asIntN(n, prim);
+    toExponentialNotation: ($, fractionDigits) => {
+      const n = toNumeric($);
+      const f = toIntegralNumberOrInfinity(fractionDigits);
+      if (!isFiniteNumber(f) || f < 0 || f > 100) {
+        throw new RangeError(
+          `Piscēs: The number of fractional digits must be a finite number between 0 and 100 inclusive; got: ${f}.`,
+        );
       } else {
-        // The primitive value is not a big·int.
-        const int = trunc(prim);
-        if (!isFiniteNumber(int) || int == 0) {
-          // The truncated value is zero or not finite.
-          return 0;
+        if (typeof n === "number") {
+          return call(
+            numberToExponential,
+            n,
+            [fractionDigits === UNDEFINED ? fractionDigits : f],
+          );
         } else {
-          // The truncated value is finite.
-          return toNumber(asIntN(n, toBigInt(int)));
+          const digits = call(bigintToString, n, [10]);
+          const { length } = digits;
+          if (fractionDigits === UNDEFINED) {
+            return length === 1
+              ? `${digits[0]}e+0`
+              : `${digits[0]}.${substring(digits, 1)}e+${length - 1}`;
+          } else if (f === 0) {
+            return `${digits[0]}e+0`;
+          } else {
+            const fractionalPart = toString(
+              round(
+                +stringCatenate(
+                  stringPadEnd(substring(digits, 1, f + 1), f, "0"),
+                  ".",
+                  digits[f + 1] || "0",
+                ),
+              ),
+            );
+            return `${digits[0]}.${fractionalPart}e+${length - 1}`;
+          }
         }
       }
     },
-    toUintN: (n, $) => {
-      const prim = toPrimitive($);
-      if (typeof prim === "bigint") {
-        // The primitive value is a big·int.
-        return asUintN(n, prim);
+    toFixedDecimalNotation: ($, fractionDigits) => {
+      const f = toIntegralNumberOrInfinity(fractionDigits);
+      if (!isFiniteNumber(f) || f < 0 || f > 100) {
+        throw new RangeError(
+          `Piscēs: The number of fractional digits must be a finite number between 0 and 100 inclusive; got: ${f}.`,
+        );
       } else {
-        // The primitive value is not a big·int.
-        const int = trunc(prim);
-        if (!isFiniteNumber(int) || int == 0) {
-          // The truncated value is zero or not finite.
-          return 0;
+        const n = toNumeric($);
+        if (typeof n === "number") {
+          return call(numberToFixed, n, [f]);
         } else {
-          // The truncated value is finite.
-          return toNumber(asUintN(n, toBigInt(int)));
+          const digits = call(bigintToString, n, [10]);
+          return f === 0
+            ? digits
+            : `${digits}.${stringRepeat("0", f)}`;
         }
       }
     },
   };
 })();
 
+/**
+ * Returns the result of converting the provided number to an integral
+ * number.
+ *
+ * ※ This function will never return negative zero.
+ */
+export const toIntegralNumber = ($) => {
+  const n = toIntegralNumberOrInfinity($);
+  return !isFiniteNumber(n) || n == 0 ? 0 : n;
+};
+
 /**
  * Returns the result of converting the provided number to an integer
  * or infinity.
  *
- * ☡ This function does not allow big·int arguments.
+ * ※ Unlike the ToIntegerOrInfinity function defined in the Ecmascript
+ * specification, this function is safe to use with big·ints. However,
+ * the result will always be a number.
+ *
+ * ※ This function will never return negative zero.
  */
-export const toIntegerOrInfinity = ($) => {
-  const integer = trunc($);
+export const toIntegralNumberOrInfinity = ($) => {
+  const integer = trunc(toNumber($));
   if (isNan(integer) || integer == 0) {
     // The provided value truncs to nan or (positive or negative) zero.
     return 0;
@@ -672,9 +647,9 @@ export const toIntegerOrInfinity = ($) => {
 /**
  * Returns the result of converting the provided value to a number.
  *
- * ※ This method is safe to use with big·ints.
+ * ※ This function is safe to use with big·ints.
  *
- * ※ This is effectively a nonconstructible version of the Number
+ * ※ This is effectively a nonconstructible version of the `Number`
  * constructor.
  */
 export const { toNumber } = (() => {
@@ -693,3 +668,74 @@ export const toNumeric = ($) => {
   const primValue = toPrimitive($, "number");
   return typeof primValue === "bigint" ? primValue : +primValue;
 };
+
+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.
+   */
+  toSignedIntegralNumeric,
+
+  /**
+   * 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.
+   */
+  toUnsignedIntegralNumeric,
+} = (() => {
+  const { asIntN, asUintN } = BigInt;
+  return {
+    toSignedIntegralNumeric: (n, $) => {
+      const prim = toPrimitive($);
+      if (typeof prim === "bigint") {
+        // The primitive value is a big·int.
+        return asIntN(n, prim);
+      } else {
+        // The primitive value is not a big·int.
+        const int = trunc(prim);
+        if (!isFiniteNumber(int) || int == 0) {
+          // The truncated value is zero or not finite.
+          return 0;
+        } else {
+          // The truncated value is finite.
+          return toNumber(asIntN(n, toBigInt(int)));
+        }
+      }
+    },
+    toUnsignedIntegralNumeric: (n, $) => {
+      const prim = toPrimitive($);
+      if (typeof prim === "bigint") {
+        // The primitive value is a big·int.
+        return asUintN(n, prim);
+      } else {
+        // The primitive value is not a big·int.
+        const int = trunc(prim);
+        if (!isFiniteNumber(int) || int == 0) {
+          // The truncated value is zero or not finite.
+          return 0;
+        } else {
+          // The truncated value is finite.
+          return toNumber(asUintN(n, toBigInt(int)));
+        }
+      }
+    },
+  };
+})();
+
+/**
+ * Returns the trunc of the provided value.
+ *
+ * ※ This function is effectively an alias for `Math.trunc`.
+ *
+ * ☡ This function does not allow big·int arguments.
+ */
+export const trunc = createArrowFunction(Math.trunc);