// ♓🌟 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 { call } from "./function.js";
+import {
+ stringCatenate,
+ stringPadEnd,
+ stringRepeat,
+ substring,
+ toString,
+} from "./string.js";
import { sameValue, toPrimitive } from "./value.js";
export const {
/**
* ln(10).
*
- * ※ This is an alias for Math.LN10.
+ * ※ This is an alias for `Math.LN10`.
*/
LN10,
/**
* ln(2).
*
- * ※ This is an alias for Math.LN2.
+ * ※ This is an alias for `Math.LN2`.
*/
LN2,
/**
* log10(ℇ).
*
- * ※ This is an alias for Math.LOG10E.
+ * ※ This is an alias for `Math.LOG10E`.
*/
LOG10E: LOG10ℇ,
/**
* log2(ℇ).
*
- * ※ This is an alias for Math.LOG2E.
+ * ※ This is an alias for `Math.LOG2E`.
*/
LOG2E: LOG2ℇ,
/**
- * sqrt(.5).
+ * sqrt(½).
*
- * ※ This is an alias for Math.SQRT1_2.
+ * ※ This is an alias for `Math.SQRT1_2`.
*/
SQRT1_2: RECIPROCAL_SQRT2,
/**
* sqrt(2).
*
- * ※ This is an alias for Math.SQRT2.
+ * ※ This is an alias for `Math.SQRT2`.
*/
SQRT2,
/**
* Returns the arccos of the provided value.
*
- * ※ This is an alias for Math.acos.
+ * ※ This is an alias for `Math.acos`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the arccosh of the provided value.
*
- * ※ This is an alias for Math.acosh.
+ * ※ This is an alias for `Math.acosh`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the arcsin of the provided value.
*
- * ※ This is an alias for Math.asin.
+ * ※ This is an alias for `Math.asin`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the arcsinh of the provided value.
*
- * ※ This is an alias for Math.asinh.
+ * ※ This is an alias for `Math.asinh`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the arctan of the provided value.
*
- * ※ This is an alias for Math.atan.
+ * ※ This is an alias for `Math.atan`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the arctanh of the provided value.
*
- * ※ This is an alias for Math.atanh.
+ * ※ This is an alias for `Math.atanh`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the cube root of the provided value.
*
- * ※ This is an alias for Math.cbrt.
+ * ※ This is an alias for `Math.cbrt`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the ceiling of the provided value.
*
- * ※ This is an alias for Math.ceil.
+ * ※ This is an alias for `Math.ceil`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the cos of the provided value.
*
- * ※ This is an alias for Math.cos.
+ * ※ This is an alias for `Math.cos`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the cosh of the provided value.
*
- * ※ This is an alias for Math.cosh.
+ * ※ This is an alias for `Math.cosh`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the Euler number raised to the provided value.
*
- * ※ This is an alias for Math.exp.
+ * ※ This is an alias for `Math.exp`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the Euler number raised to the provided value, minus one.
*
- * ※ This is an alias for Math.expm1.
+ * ※ This is an alias for `Math.expm1`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the floor of the provided value.
*
- * ※ This is an alias for Math.floor.
+ * ※ This is an alias for `Math.floor`.
*
* ☡ This function does not allow big·int arguments.
*/
* Returns the square root of the sum of the squares of the provided
* arguments.
*
- * ※ This is an alias for Math.hypot.
+ * ※ This is an alias for `Math.hypot`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the ln of the provided value.
*
- * ※ This is an alias for Math.log.
+ * ※ This is an alias for `Math.log`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the log10 of the provided value.
*
- * ※ This is an alias for Math.log10.
+ * ※ This is an alias for `Math.log10`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the ln of one plus the provided value.
*
- * ※ This is an alias for Math.log1p.
+ * ※ This is an alias for `Math.log1p`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the log2 of the provided value.
*
- * ※ This is an alias for Math.log2.
+ * ※ This is an alias for `Math.log2`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns a pseudo·random value in the range [0, 1).
*
- * ※ This is an alias for Math.random.
+ * ※ This is an alias for `Math.random`.
*/
random: rand,
/**
* Returns the round of the provided value.
*
- * ※ This is an alias for Math.round.
+ * ※ This is an alias for `Math.round`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the sinh of the provided value.
*
- * ※ This is an alias for Math.sinh.
+ * ※ This is an alias for `Math.sinh`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the square root of the provided value.
*
- * ※ This is an alias for Math.sqrt.
+ * ※ This is an alias for `Math.sqrt`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the tan of the provided value.
*
- * ※ This is an alias for Math.tan.
+ * ※ This is an alias for `Math.tan`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the tanh of the provided value.
*
- * ※ This is an alias for Math.tanh.
+ * ※ This is an alias for `Math.tanh`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* Returns the trunc of the provided value.
*
- * ※ This is an alias for Math.trunc.
+ * ※ This is an alias for `Math.trunc`.
*
* ☡ This function does not allow big·int arguments.
*/
/**
* The mathematical constant π.
*
- * ※ This is an alias for Math.PI.
+ * ※ This is an alias for `Math.PI`.
*/
PI: Π,
/**
* The Euler number.
*
- * ※ This is an alias for Math.E.
+ * ※ This is an alias for `Math.E`.
*/
E: ℇ,
} = Math;
/**
* The largest number value less than infinity.
*
- * ※ This is an alias for Number.MAX_VALUE.
+ * ※ This is an alias for `Number.MAX_VALUE`.
*/
MAX_VALUE: MAXIMUM_NUMBER,
/**
* 2**53 - 1.
*
- * ※ This is an alias for Number.MAX_SAFE_INTEGER.
+ * ※ 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.
+ * ※ This is an alias for `Number.MIN_VALUE`.
*/
MIN_VALUE: MINIMUM_NUMBER,
/**
* -(2**53 - 1).
*
- * ※ This is an alias for Number.MIN_SAFE_INTEGER.
+ * ※ 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.
+ * ※ This is an alias for `Number.NEGATIVE_INFINITY`.
*/
NEGATIVE_INFINITY,
/**
* Nan.
*
- * ※ This is an alias for Number.NaN.
+ * ※ This is an alias for `Number.NaN`.
*/
NaN: NAN,
/**
* Positive infinity.
*
- * ※ This is an alias for Number.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.
+ * ※ 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.
+ * ※ 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.
+ * ※ This is an alias for `Number.isInteger`.
*/
isInteger: isIntegralNumber,
/**
* Returns whether the provided value is nan.
*
- * ※ This is an alias for Number.isNaN.
+ * ※ 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.
+ * ※ 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.
+ * ※ Unlike `Math.abs`, this function can take big·int arguments.
*/
export const abs = ($) => {
const n = toNumeric($);
/**
* 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,
/**
- * 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,
* 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,
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 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.
*
* 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.
*
* 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 = ($) => {
const n = toNumeric($);
*
* ※ 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;
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;
/**
* 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 } = (() => {
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)));
+ }
+ }
+ },
+ };
+})();
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