fix: #1485 improve conversion of numbers with a round-off errors into…

… a BigNumber

src/core/function/typed.js

@@ -36,6 +36,9 @@
  * @returns {function} The created typed-function.
  */
 
+import typedFunction from 'typed-function'
+import { convertNumberToBigNumber } from '../../utils/bignumber/convertNumberToBigNumber.js'
+import { factory } from '../../utils/factory.js'
 import {
   isAccessorNode,
   isArray,
@@ -68,18 +71,15 @@ import {
   isParenthesisNode,
   isRange,
   isRangeNode,
-  isRelationalNode,
   isRegExp,
+  isRelationalNode,
   isResultSet,
   isSparseMatrix,
   isString,
   isSymbolNode,
   isUndefined,
   isUnit
 } from '../../utils/is.js'
-import typedFunction from 'typed-function'
-import { digits } from '../../utils/number.js'
-import { factory } from '../../utils/factory.js'
 import { isMap } from '../../utils/map.js'
 
 // returns a new instance of typed-function
@@ -173,13 +173,7 @@ export const createTyped = /* #__PURE__ */ factory('typed', dependencies, functi
           throwNoBignumber(x)
         }
 
-        // note: conversion from number to BigNumber can fail if x has >15 digits
-        if (digits(x) > 15) {
-          throw new TypeError('Cannot implicitly convert a number with >15 significant digits to BigNumber ' +
-            '(value: ' + x + '). ' +
-            'Use function bignumber(x) to convert to BigNumber.')
-        }
-        return new BigNumber(x)
+        return convertNumberToBigNumber(x, BigNumber)
       }
     }, {
       from: 'number',

src/utils/bignumber/convertNumberToBigNumber.js

@@ -0,0 +1,43 @@
+import { digits } from '../number.js'
+
+/**
+ * Convert a number into a BigNumber when it is safe to do so: only when the number
+ * is has max 15 digits, since a JS number can only represent about ~16 digits.
+ * This function will correct round-off errors introduced by the JS floating-point
+ * operations. For example, it will change 0.1+0.2 = 0.30000000000000004 into 0.3.
+ *
+ * The function throws an Error when the number cannot be converted safely into a BigNumber.
+ *
+ * @param {number} x
+ * @param {function} BigNumber The bignumber constructor
+ * @returns {BigNumber}
+ */
+export function convertNumberToBigNumber (x, BigNumber) {
+  const d = digits(x)
+  if (d.length <= 15) {
+    return new BigNumber(x)
+  }
+
+  // recognize round-off errors like 0.1 + 0.2 = 0.30000000000000004, which should be 0.3
+  // we test whether the first 15 digits end with at least 6 zeros, and a non-zero last digit
+  // note that a number can optionally end with an exponent
+  const xStr = x.toString()
+  const matchTrailingZeros = xStr.match(/(?<start>.+)(?<zeros>0{6,}[1-9][0-9]*)(?<end>$|[+-eE])/)
+  if (matchTrailingZeros) {
+    const { start, end } = matchTrailingZeros.groups
+    return new BigNumber(start + end)
+  }
+
+  // recognize round-off errors like 40 - 38.6 = 1.3999999999999986, which should be 1.4
+  // we test whether the first 15 digits end with at least 6 nines, and a non-nine and non-zero last digit
+  // note that a number can optionally end with an exponent
+  const matchTrailingNines = xStr.match(/(?<start>.+)(?<digitBeforeNines>[0-8])(?<nines>9{6,}[1-8][0-9]*)(?<end>$|[+-eE])/)
+  if (matchTrailingNines) {
+    const { start, digitBeforeNines, end } = matchTrailingNines.groups
+    return new BigNumber(start + String(parseInt(digitBeforeNines) + 1) + end)
+  }
+
+  throw new TypeError('Cannot implicitly convert a number with >15 significant digits to BigNumber ' +
+    '(value: ' + x + '). ' +
+    'Use function bignumber(x) to convert to BigNumber.')
+}

src/utils/number.js

@@ -572,22 +572,22 @@ function zeros (length) {
 }
 
 /**
- * Count the number of significant digits of a number.
+ * Extract all significant digits of a number.
  *
  * For example:
- *   2.34 returns 3
- *   0.0034 returns 2
- *   120.5e+30 returns 4
+ *   2.34 returns '234'
+ *   0.0034 returns '34'
+ *   120.5e+30 returns '1205'
  *
  * @param {number} value
- * @return {number} digits   Number of significant digits
+ * @return {string} Returns a string with all digits
  */
 export function digits (value) {
   return value
     .toExponential()
+    .replace(/^-/, '') // remove sign
     .replace(/e.*$/, '') // remove exponential notation
     .replace(/^0\.?0*|\./, '') // remove decimal point and leading zeros
-    .length
 }
 
 /**

test/unit-tests/utils/bignumber/convertNumberToBigNumber.test.js

@@ -0,0 +1,35 @@
+import assert from 'assert'
+import BigNumber from 'decimal.js'
+import { convertNumberToBigNumber } from '../../../../src/utils/bignumber/convertNumberToBigNumber.js'
+
+describe('convertNumberToBigNumber', function () {
+  it('should convert numbers to BigNumbers when it is safe to do', function () {
+    assert.deepStrictEqual(convertNumberToBigNumber(2.4, BigNumber), new BigNumber('2.4'))
+    assert.deepStrictEqual(convertNumberToBigNumber(2, BigNumber), new BigNumber('2'))
+    assert.deepStrictEqual(convertNumberToBigNumber(-4, BigNumber), new BigNumber('-4'))
+    assert.deepStrictEqual(convertNumberToBigNumber(0.1234567, BigNumber), new BigNumber('0.1234567'))
+    assert.deepStrictEqual(convertNumberToBigNumber(0.12345678901234, BigNumber), new BigNumber('0.12345678901234'))
+    assert.deepStrictEqual(convertNumberToBigNumber(0.00000000000004, BigNumber), new BigNumber('0.00000000000004'))
+    assert.deepStrictEqual(convertNumberToBigNumber(1.2e-24, BigNumber), new BigNumber('1.2e-24'))
+  })
+
+  it('should convert numbers with round-off errors to BigNumbers when it is safe to do', function () {
+    // a round-off error above the actual value
+    assert.deepStrictEqual(convertNumberToBigNumber(0.1 + 0.2, BigNumber).toString(), '0.3') // 0.30000000000000004
+    assert.deepStrictEqual(convertNumberToBigNumber(0.1 + 0.24545, BigNumber).toString(), '0.34545') // 0.34545000000000003
+
+    // a round-off error below the actual value
+    assert.deepStrictEqual(convertNumberToBigNumber(40 - 38.6, BigNumber).toString(), '1.4') // 1.3999999999999986
+    assert.deepStrictEqual(convertNumberToBigNumber(159.119 - 159, BigNumber).toString(), '0.119') // 0.11899999999999977
+    assert.deepStrictEqual(convertNumberToBigNumber(159.11934444 - 159, BigNumber).toString(), '0.11934444') // 0.11934443999999189
+  })
+
+  it('should throw an error when converting an number to BigNumber when it is NOT safe to do', function () {
+    const errorRegex = /Cannot implicitly convert a number with >15 significant digits to BigNumber/
+
+    assert.throws(() => convertNumberToBigNumber(Math.PI, BigNumber), errorRegex)
+    assert.throws(() => convertNumberToBigNumber(1 / 3, BigNumber), errorRegex)
+    assert.throws(() => convertNumberToBigNumber(1 / 7, BigNumber), errorRegex)
+    assert.throws(() => convertNumberToBigNumber(0.1234567890123456, BigNumber), errorRegex)
+  })
+})

test/unit-tests/utils/number.test.js

@@ -44,16 +44,17 @@ describe('number', function () {
   })
 
   it('should count the number of significant digits of a number', function () {
-    assert.strictEqual(digits(0), 0)
-    assert.strictEqual(digits(2), 1)
-    assert.strictEqual(digits(1234), 4)
-    assert.strictEqual(digits(2.34), 3)
-    assert.strictEqual(digits(3000), 1)
-    assert.strictEqual(digits(0.0034), 2)
-    assert.strictEqual(digits(120.5e50), 4)
-    assert.strictEqual(digits(1120.5e+50), 5)
-    assert.strictEqual(digits(120.52e-50), 5)
-    assert.strictEqual(digits(Math.PI), 16)
+    assert.strictEqual(digits(0), '')
+    assert.strictEqual(digits(2), '2')
+    assert.strictEqual(digits(1234), '1234')
+    assert.strictEqual(digits(2.34), '234')
+    assert.strictEqual(digits(3000), '3')
+    assert.strictEqual(digits(0.0034), '34')
+    assert.strictEqual(digits(120.5e50), '1205')
+    assert.strictEqual(digits(1120.5e+50), '11205')
+    assert.strictEqual(digits(120.52e-50), '12052')
+    assert.strictEqual(digits(-1234), '1234')
+    assert.strictEqual(digits(Math.PI), '3141592653589793')
   })
 
   it('should format a number using toFixed', function () {