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526 lines
19 KiB
526 lines
19 KiB
/** |
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* The **FixedNumber** class permits using values with decimal places, |
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* using fixed-pont math. |
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* |
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* Fixed-point math is still based on integers under-the-hood, but uses an |
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* internal offset to store fractional components below, and each operation |
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* corrects for this after each operation. |
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* |
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* @_section: api/utils/fixed-point-math:Fixed-Point Maths [about-fixed-point-math] |
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*/ |
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import { getBytes } from "./data.js"; |
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import { assert, assertArgument, assertPrivate } from "./errors.js"; |
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import { getBigInt, getNumber, fromTwos, mask, toBigInt } from "./maths.js"; |
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import { defineProperties } from "./properties.js"; |
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const BN_N1 = BigInt(-1); |
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const BN_0 = BigInt(0); |
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const BN_1 = BigInt(1); |
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const BN_5 = BigInt(5); |
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const _guard = {}; |
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// Constant to pull zeros from for multipliers |
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let Zeros = "0000"; |
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while (Zeros.length < 80) { |
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Zeros += Zeros; |
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} |
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// Returns a string "1" followed by decimal "0"s |
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function getTens(decimals) { |
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let result = Zeros; |
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while (result.length < decimals) { |
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result += result; |
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} |
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return BigInt("1" + result.substring(0, decimals)); |
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} |
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function checkValue(val, format, safeOp) { |
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const width = BigInt(format.width); |
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if (format.signed) { |
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const limit = (BN_1 << (width - BN_1)); |
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assert(safeOp == null || (val >= -limit && val < limit), "overflow", "NUMERIC_FAULT", { |
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operation: safeOp, fault: "overflow", value: val |
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}); |
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if (val > BN_0) { |
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val = fromTwos(mask(val, width), width); |
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} |
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else { |
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val = -fromTwos(mask(-val, width), width); |
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} |
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} |
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else { |
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const limit = (BN_1 << width); |
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assert(safeOp == null || (val >= 0 && val < limit), "overflow", "NUMERIC_FAULT", { |
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operation: safeOp, fault: "overflow", value: val |
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}); |
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val = (((val % limit) + limit) % limit) & (limit - BN_1); |
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} |
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return val; |
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} |
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function getFormat(value) { |
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if (typeof (value) === "number") { |
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value = `fixed128x${value}`; |
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} |
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let signed = true; |
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let width = 128; |
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let decimals = 18; |
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if (typeof (value) === "string") { |
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// Parse the format string |
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if (value === "fixed") { |
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// defaults... |
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} |
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else if (value === "ufixed") { |
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signed = false; |
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} |
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else { |
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const match = value.match(/^(u?)fixed([0-9]+)x([0-9]+)$/); |
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assertArgument(match, "invalid fixed format", "format", value); |
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signed = (match[1] !== "u"); |
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width = parseInt(match[2]); |
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decimals = parseInt(match[3]); |
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} |
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} |
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else if (value) { |
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// Extract the values from the object |
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const v = value; |
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const check = (key, type, defaultValue) => { |
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if (v[key] == null) { |
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return defaultValue; |
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} |
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assertArgument(typeof (v[key]) === type, "invalid fixed format (" + key + " not " + type + ")", "format." + key, v[key]); |
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return v[key]; |
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}; |
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signed = check("signed", "boolean", signed); |
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width = check("width", "number", width); |
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decimals = check("decimals", "number", decimals); |
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} |
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assertArgument((width % 8) === 0, "invalid FixedNumber width (not byte aligned)", "format.width", width); |
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assertArgument(decimals <= 80, "invalid FixedNumber decimals (too large)", "format.decimals", decimals); |
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const name = (signed ? "" : "u") + "fixed" + String(width) + "x" + String(decimals); |
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return { signed, width, decimals, name }; |
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} |
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function toString(val, decimals) { |
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let negative = ""; |
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if (val < BN_0) { |
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negative = "-"; |
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val *= BN_N1; |
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} |
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let str = val.toString(); |
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// No decimal point for whole values |
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if (decimals === 0) { |
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return (negative + str); |
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} |
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// Pad out to the whole component (including a whole digit) |
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while (str.length <= decimals) { |
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str = Zeros + str; |
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} |
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// Insert the decimal point |
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const index = str.length - decimals; |
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str = str.substring(0, index) + "." + str.substring(index); |
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// Trim the whole component (leaving at least one 0) |
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while (str[0] === "0" && str[1] !== ".") { |
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str = str.substring(1); |
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} |
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// Trim the decimal component (leaving at least one 0) |
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while (str[str.length - 1] === "0" && str[str.length - 2] !== ".") { |
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str = str.substring(0, str.length - 1); |
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} |
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return (negative + str); |
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} |
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/** |
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* A FixedNumber represents a value over its [[FixedFormat]] |
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* arithmetic field. |
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* |
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* A FixedNumber can be used to perform math, losslessly, on |
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* values which have decmial places. |
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* |
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* A FixedNumber has a fixed bit-width to store values in, and stores all |
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* values internally by multiplying the value by 10 raised to the power of |
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* %%decimals%%. |
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* |
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* If operations are performed that cause a value to grow too high (close to |
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* positive infinity) or too low (close to negative infinity), the value |
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* is said to //overflow//. |
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* |
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* For example, an 8-bit signed value, with 0 decimals may only be within |
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* the range ``-128`` to ``127``; so ``-128 - 1`` will overflow and become |
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* ``127``. Likewise, ``127 + 1`` will overflow and become ``-127``. |
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* |
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* Many operation have a normal and //unsafe// variant. The normal variant |
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* will throw a [[NumericFaultError]] on any overflow, while the //unsafe// |
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* variant will silently allow overflow, corrupting its value value. |
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* |
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* If operations are performed that cause a value to become too small |
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* (close to zero), the value loses precison and is said to //underflow//. |
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* |
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* For example, a value with 1 decimal place may store a number as small |
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* as ``0.1``, but the value of ``0.1 / 2`` is ``0.05``, which cannot fit |
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* into 1 decimal place, so underflow occurs which means precision is lost |
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* and the value becomes ``0``. |
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* |
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* Some operations have a normal and //signalling// variant. The normal |
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* variant will silently ignore underflow, while the //signalling// variant |
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* will thow a [[NumericFaultError]] on underflow. |
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*/ |
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export class FixedNumber { |
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/** |
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* The specific fixed-point arithmetic field for this value. |
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*/ |
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format; |
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#format; |
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// The actual value (accounting for decimals) |
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#val; |
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// A base-10 value to multiple values by to maintain the magnitude |
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#tens; |
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/** |
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* This is a property so console.log shows a human-meaningful value. |
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* |
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* @private |
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*/ |
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_value; |
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// Use this when changing this file to get some typing info, |
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// but then switch to any to mask the internal type |
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//constructor(guard: any, value: bigint, format: _FixedFormat) { |
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/** |
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* @private |
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*/ |
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constructor(guard, value, format) { |
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assertPrivate(guard, _guard, "FixedNumber"); |
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this.#val = value; |
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this.#format = format; |
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const _value = toString(value, format.decimals); |
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defineProperties(this, { format: format.name, _value }); |
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this.#tens = getTens(format.decimals); |
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} |
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/** |
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* If true, negative values are permitted, otherwise only |
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* positive values and zero are allowed. |
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*/ |
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get signed() { return this.#format.signed; } |
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/** |
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* The number of bits available to store the value. |
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*/ |
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get width() { return this.#format.width; } |
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/** |
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* The number of decimal places in the fixed-point arithment field. |
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*/ |
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get decimals() { return this.#format.decimals; } |
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/** |
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* The value as an integer, based on the smallest unit the |
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* [[decimals]] allow. |
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*/ |
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get value() { return this.#val; } |
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#checkFormat(other) { |
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assertArgument(this.format === other.format, "incompatible format; use fixedNumber.toFormat", "other", other); |
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} |
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#checkValue(val, safeOp) { |
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/* |
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const width = BigInt(this.width); |
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if (this.signed) { |
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const limit = (BN_1 << (width - BN_1)); |
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assert(safeOp == null || (val >= -limit && val < limit), "overflow", "NUMERIC_FAULT", { |
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operation: <string>safeOp, fault: "overflow", value: val |
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}); |
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|
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if (val > BN_0) { |
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val = fromTwos(mask(val, width), width); |
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} else { |
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val = -fromTwos(mask(-val, width), width); |
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} |
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|
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} else { |
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const masked = mask(val, width); |
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assert(safeOp == null || (val >= 0 && val === masked), "overflow", "NUMERIC_FAULT", { |
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operation: <string>safeOp, fault: "overflow", value: val |
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}); |
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val = masked; |
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} |
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*/ |
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val = checkValue(val, this.#format, safeOp); |
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return new FixedNumber(_guard, val, this.#format); |
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} |
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#add(o, safeOp) { |
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this.#checkFormat(o); |
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return this.#checkValue(this.#val + o.#val, safeOp); |
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} |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% added |
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* to %%other%%, ignoring overflow. |
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*/ |
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addUnsafe(other) { return this.#add(other); } |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% added |
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* to %%other%%. A [[NumericFaultError]] is thrown if overflow |
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* occurs. |
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*/ |
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add(other) { return this.#add(other, "add"); } |
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#sub(o, safeOp) { |
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this.#checkFormat(o); |
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return this.#checkValue(this.#val - o.#val, safeOp); |
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} |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%other%% subtracted |
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* from %%this%%, ignoring overflow. |
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*/ |
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subUnsafe(other) { return this.#sub(other); } |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%other%% subtracted |
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* from %%this%%. A [[NumericFaultError]] is thrown if overflow |
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* occurs. |
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*/ |
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sub(other) { return this.#sub(other, "sub"); } |
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#mul(o, safeOp) { |
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this.#checkFormat(o); |
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return this.#checkValue((this.#val * o.#val) / this.#tens, safeOp); |
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} |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% multiplied |
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* by %%other%%, ignoring overflow and underflow (precision loss). |
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*/ |
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mulUnsafe(other) { return this.#mul(other); } |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% multiplied |
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* by %%other%%. A [[NumericFaultError]] is thrown if overflow |
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* occurs. |
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*/ |
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mul(other) { return this.#mul(other, "mul"); } |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% multiplied |
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* by %%other%%. A [[NumericFaultError]] is thrown if overflow |
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* occurs or if underflow (precision loss) occurs. |
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*/ |
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mulSignal(other) { |
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this.#checkFormat(other); |
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const value = this.#val * other.#val; |
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assert((value % this.#tens) === BN_0, "precision lost during signalling mul", "NUMERIC_FAULT", { |
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operation: "mulSignal", fault: "underflow", value: this |
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}); |
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return this.#checkValue(value / this.#tens, "mulSignal"); |
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} |
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#div(o, safeOp) { |
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assert(o.#val !== BN_0, "division by zero", "NUMERIC_FAULT", { |
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operation: "div", fault: "divide-by-zero", value: this |
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}); |
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this.#checkFormat(o); |
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return this.#checkValue((this.#val * this.#tens) / o.#val, safeOp); |
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} |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% divided |
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* by %%other%%, ignoring underflow (precision loss). A |
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* [[NumericFaultError]] is thrown if overflow occurs. |
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*/ |
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divUnsafe(other) { return this.#div(other); } |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% divided |
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* by %%other%%, ignoring underflow (precision loss). A |
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* [[NumericFaultError]] is thrown if overflow occurs. |
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*/ |
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div(other) { return this.#div(other, "div"); } |
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/** |
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* Returns a new [[FixedNumber]] with the result of %%this%% divided |
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* by %%other%%. A [[NumericFaultError]] is thrown if underflow |
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* (precision loss) occurs. |
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*/ |
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divSignal(other) { |
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assert(other.#val !== BN_0, "division by zero", "NUMERIC_FAULT", { |
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operation: "div", fault: "divide-by-zero", value: this |
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}); |
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this.#checkFormat(other); |
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const value = (this.#val * this.#tens); |
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assert((value % other.#val) === BN_0, "precision lost during signalling div", "NUMERIC_FAULT", { |
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operation: "divSignal", fault: "underflow", value: this |
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}); |
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return this.#checkValue(value / other.#val, "divSignal"); |
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} |
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/** |
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* Returns a comparison result between %%this%% and %%other%%. |
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* |
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* This is suitable for use in sorting, where ``-1`` implies %%this%% |
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* is smaller, ``1`` implies %%this%% is larger and ``0`` implies |
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* both are equal. |
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*/ |
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cmp(other) { |
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let a = this.value, b = other.value; |
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// Coerce a and b to the same magnitude |
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const delta = this.decimals - other.decimals; |
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if (delta > 0) { |
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b *= getTens(delta); |
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} |
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else if (delta < 0) { |
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a *= getTens(-delta); |
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} |
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// Comnpare |
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if (a < b) { |
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return -1; |
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} |
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if (a > b) { |
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return 1; |
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} |
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return 0; |
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} |
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/** |
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* Returns true if %%other%% is equal to %%this%%. |
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*/ |
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eq(other) { return this.cmp(other) === 0; } |
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/** |
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* Returns true if %%other%% is less than to %%this%%. |
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*/ |
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lt(other) { return this.cmp(other) < 0; } |
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/** |
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* Returns true if %%other%% is less than or equal to %%this%%. |
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*/ |
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lte(other) { return this.cmp(other) <= 0; } |
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/** |
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* Returns true if %%other%% is greater than to %%this%%. |
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*/ |
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gt(other) { return this.cmp(other) > 0; } |
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/** |
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* Returns true if %%other%% is greater than or equal to %%this%%. |
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*/ |
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gte(other) { return this.cmp(other) >= 0; } |
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/** |
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* Returns a new [[FixedNumber]] which is the largest **integer** |
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* that is less than or equal to %%this%%. |
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* |
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* The decimal component of the result will always be ``0``. |
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*/ |
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floor() { |
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let val = this.#val; |
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if (this.#val < BN_0) { |
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val -= this.#tens - BN_1; |
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} |
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val = (this.#val / this.#tens) * this.#tens; |
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return this.#checkValue(val, "floor"); |
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} |
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/** |
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* Returns a new [[FixedNumber]] which is the smallest **integer** |
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* that is greater than or equal to %%this%%. |
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* |
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* The decimal component of the result will always be ``0``. |
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*/ |
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ceiling() { |
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let val = this.#val; |
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if (this.#val > BN_0) { |
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val += this.#tens - BN_1; |
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} |
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val = (this.#val / this.#tens) * this.#tens; |
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return this.#checkValue(val, "ceiling"); |
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} |
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/** |
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* Returns a new [[FixedNumber]] with the decimal component |
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* rounded up on ties at %%decimals%% places. |
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*/ |
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round(decimals) { |
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if (decimals == null) { |
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decimals = 0; |
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} |
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// Not enough precision to not already be rounded |
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if (decimals >= this.decimals) { |
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return this; |
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} |
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const delta = this.decimals - decimals; |
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const bump = BN_5 * getTens(delta - 1); |
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let value = this.value + bump; |
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const tens = getTens(delta); |
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value = (value / tens) * tens; |
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checkValue(value, this.#format, "round"); |
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return new FixedNumber(_guard, value, this.#format); |
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} |
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/** |
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* Returns true if %%this%% is equal to ``0``. |
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*/ |
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isZero() { return (this.#val === BN_0); } |
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/** |
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* Returns true if %%this%% is less than ``0``. |
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*/ |
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isNegative() { return (this.#val < BN_0); } |
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/** |
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* Returns the string representation of %%this%%. |
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*/ |
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toString() { return this._value; } |
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/** |
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* Returns a float approximation. |
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* |
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* Due to IEEE 754 precission (or lack thereof), this function |
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* can only return an approximation and most values will contain |
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* rounding errors. |
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*/ |
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toUnsafeFloat() { return parseFloat(this.toString()); } |
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/** |
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* Return a new [[FixedNumber]] with the same value but has had |
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* its field set to %%format%%. |
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* |
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* This will throw if the value cannot fit into %%format%%. |
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*/ |
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toFormat(format) { |
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return FixedNumber.fromString(this.toString(), format); |
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} |
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/** |
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* Creates a new [[FixedNumber]] for %%value%% divided by |
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* %%decimal%% places with %%format%%. |
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* |
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* This will throw a [[NumericFaultError]] if %%value%% (once adjusted |
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* for %%decimals%%) cannot fit in %%format%%, either due to overflow |
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* or underflow (precision loss). |
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*/ |
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static fromValue(_value, _decimals, _format) { |
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const decimals = (_decimals == null) ? 0 : getNumber(_decimals); |
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const format = getFormat(_format); |
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let value = getBigInt(_value, "value"); |
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const delta = decimals - format.decimals; |
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if (delta > 0) { |
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const tens = getTens(delta); |
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assert((value % tens) === BN_0, "value loses precision for format", "NUMERIC_FAULT", { |
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operation: "fromValue", fault: "underflow", value: _value |
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}); |
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value /= tens; |
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} |
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else if (delta < 0) { |
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value *= getTens(-delta); |
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} |
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checkValue(value, format, "fromValue"); |
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return new FixedNumber(_guard, value, format); |
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} |
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/** |
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* Creates a new [[FixedNumber]] for %%value%% with %%format%%. |
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* |
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* This will throw a [[NumericFaultError]] if %%value%% cannot fit |
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* in %%format%%, either due to overflow or underflow (precision loss). |
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*/ |
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static fromString(_value, _format) { |
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const match = _value.match(/^(-?)([0-9]*)\.?([0-9]*)$/); |
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assertArgument(match && (match[2].length + match[3].length) > 0, "invalid FixedNumber string value", "value", _value); |
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const format = getFormat(_format); |
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let whole = (match[2] || "0"), decimal = (match[3] || ""); |
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// Pad out the decimals |
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while (decimal.length < format.decimals) { |
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decimal += Zeros; |
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} |
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// Check precision is safe |
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assert(decimal.substring(format.decimals).match(/^0*$/), "too many decimals for format", "NUMERIC_FAULT", { |
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operation: "fromString", fault: "underflow", value: _value |
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}); |
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// Remove extra padding |
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decimal = decimal.substring(0, format.decimals); |
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const value = BigInt(match[1] + whole + decimal); |
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checkValue(value, format, "fromString"); |
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return new FixedNumber(_guard, value, format); |
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} |
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/** |
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* Creates a new [[FixedNumber]] with the big-endian representation |
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* %%value%% with %%format%%. |
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* |
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* This will throw a [[NumericFaultError]] if %%value%% cannot fit |
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* in %%format%% due to overflow. |
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*/ |
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static fromBytes(_value, _format) { |
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let value = toBigInt(getBytes(_value, "value")); |
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const format = getFormat(_format); |
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if (format.signed) { |
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value = fromTwos(value, format.width); |
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} |
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checkValue(value, format, "fromBytes"); |
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return new FixedNumber(_guard, value, format); |
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} |
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} |
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//const f1 = FixedNumber.fromString("12.56", "fixed16x2"); |
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//const f2 = FixedNumber.fromString("0.3", "fixed16x2"); |
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//console.log(f1.divSignal(f2)); |
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//const BUMP = FixedNumber.from("0.5"); |
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//# sourceMappingURL=fixednumber.js.map
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