X-Git-Url: https://git.ladys.computer/Pisces/blobdiff_plain/8c8953d378b20e194535e22214750367961b6963..refs/heads/current:/numeric.js

diff --git a/numeric.js b/numeric.js
index 2c1a66f..079e56e 100644
--- a/numeric.js
+++ b/numeric.js
@@ -1,11 +1,741 @@
 // ♓🌟 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/>.
 
-/** 2^53 − 1. */
-export const MAX_SAFE_INTEGER = Number((1n << 53n) - 1n);
+import { call, createArrowFunction } from "./function.js";
+import { defineOwnDataProperty } from "./object.js";
+import {
+  stringCatenate,
+  stringPadEnd,
+  stringRepeat,
+  substring,
+  toString,
+} from "./string.js";
+import {
+  NAN,
+  NEGATIVE_INFINITY,
+  POSITIVE_INFINITY,
+  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.
+ */
+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;
+};
+
+/**
+ * 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.
+   * However, the result will always be a number.
+   */
+  arctan2,
+
+  /**
+   * 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 {
+    arctan2: (y, x) => atan2(toNumber(y), toNumber(x)),
+    clz32: ($) => {
+      const n = toNumeric($);
+      return clz32(
+        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
+ * 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 = 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) {
+      // 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 (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;
+}, {
+  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
+ * 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 = 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) {
+      // 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;
+}, {
+  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
+ * 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 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`.
+ */
+export const { toBigInt } = (() => {
+  const makeBigInt = BigInt;
+  return { toBigInt: ($) => makeBigInt($) };
+})();
+
+export const {
+  /**
+   * Returns the result of converting the provided value to an
+   * exponential notation string.
+   *
+   * 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.
+   *
+   * ※ This method is safe to use with big·ints.
+   */
+  toExponentialNotation,
+
+  /**
+   * Returns the result of converting the provided value to a fixed
+   * decimal notation string with the provided number of fractional
+   * digits.
+   *
+   * ※ This method is safe to use with big·ints.
+   */
+  toFixedDecimalNotation,
+} = (() => {
+  const {
+    toExponential: numberToExponential,
+    toFixed: numberToFixed,
+  } = Number.prototype;
+  const { toString: bigintToString } = BigInt.prototype;
+  return {
+    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: ${f}.`,
+        );
+      } else {
+        if (typeof n === "number") {
+          return call(
+            numberToExponential,
+            n,
+            [fractionDigits === UNDEFINED ? fractionDigits : f],
+          );
+        } else {
+          const digits = call(bigintToString, n, [10]);
+          const { length } = digits;
+          if (fractionDigits === UNDEFINED) {
+            return length === 1
+              ? `${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+${length - 1}`;
+          }
+        }
+      }
+    },
+    toFixedDecimalNotation: ($, 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: ${f}.`,
+        );
+      } else {
+        const n = toNumeric($);
+        if (typeof n === "number") {
+          return call(numberToFixed, n, [f]);
+        } else {
+          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.
+ *
+ * ※ 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 toIntegralNumberOrInfinity = ($) => {
+  const integer = trunc(toNumber($));
+  if (isNan(integer) || integer == 0) {
+    // The provided value truncs to nan or (positive or negative) zero.
+    return 0;
+  } else if (integer == POSITIVE_INFINITY) {
+    // The provided value truncs to positive infinity.
+    return POSITIVE_INFINITY;
+  } else if (integer == NEGATIVE_INFINITY) {
+    // The provided value truncs to negative infinity.
+    return NEGATIVE_INFINITY;
+  } else {
+    // The provided value truncs to an integer.
+    return integer;
+  }
+};
+
+/**
+ * Returns the result of converting the provided value to a number.
+ *
+ * ※ This function 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;
+};
+
+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);