Changed references to epsilon in docs and tests

docs/core/configuration.md

@@ -8,7 +8,8 @@ import { create, all } from 'mathjs'
 
 // create a mathjs instance with configuration
 const config = {
-  epsilon: 1e-12,
+  relTol: 1e-12,
+  absTol: 1e.15,
   matrix: 'Matrix',
   number: 'number',
   precision: 64,
@@ -28,10 +29,14 @@ math.config({
 
 The following configuration options are available:
 
-- `epsilon`. The minimum relative difference used to test equality between two
+- `relTol`. The minimum relative difference used to test equality between two
   compared values. This value is used by all relational functions.
   Default value is `1e-12`.
 
+- `absTol`. The minimum absolute difference used to test equality between two
+  compared values. This value is used by all relational functions.
+  Default value is `1e-15`.
+
 - `matrix`. The default type of matrix output for functions.
   Available values are: `'Matrix'` (default) or `'Array'`.
   Where possible, the type of matrix output from functions is determined from

docs/datatypes/bignumbers.md

@@ -24,7 +24,8 @@ math.config({
   number: 'BigNumber',      // Default type of number:
                             // 'number' (default), 'BigNumber', or 'Fraction'
   precision: 64,            // Number of significant digits for BigNumbers
-  epsilon: 1e-60
+  relTol: 1e-60,
+  absTol: 1e-63
 })
 
 // use math
@@ -34,12 +35,12 @@ math.evaluate('0.1 + 0.2')  // BigNumber, 0.3
 The default precision for BigNumber is 64 digits, and can be configured with
 the option `precision`. 
 
-Note that we also change the configuration of `epsilon` 
-to be close to the precision limit of our BigNumbers. `epsilon` is used for 
+Note that we also change the configuration of `relTol` and `absTol` 
+to be close to the precision limit of our BigNumbers. `relTol` and `absTol` are used for 
 example in relational and rounding functions (`equal`, `larger`, `smaller`, 
 `round`, `floor`, etc) to determine when a value is nearly equal, 
-see [Equality](numbers.md#equality). If we would leave `epsilon` unchanged, 
-having the default value of `1e-12`, we could get inaccurate and misleading 
+see [Equality](numbers.md#equality). If we would leave `relTol` and `absTol`  unchanged, 
+having the default value of `1e-12` and `1e-15` respectively, we could get inaccurate and misleading 
 results since we're now working with a higher precision.
 
 

docs/datatypes/numbers.md

@@ -74,16 +74,13 @@ return exactly `0.3`.
 
 To solve this problem, the relational functions of math.js check whether the
 relative and absolute differences between the compared values is smaller than the configured
-option `epsilon`. In pseudo code (without exceptions for 0, Infinity and NaN):
+option `relTol` and `absTol`. In pseudo code (without exceptions for 0, Infinity and NaN):
 
-    relTol = epsilon
-    absTol = epsilon / 1000
     abs(a-b) <= max(relTol * max(abs(a), abs(b)), absTol)
 
 where:
 
- - `EPSILON` is the relative difference between x and y. Epsilon is configurable
-   and is `1e-12` by default. See [Configuration](../core/configuration.md).
+ - `relTol` is the relative tolerance between x and y and `absTol` the absolute tolerance. Relative tolerance and absolute tolerance are configurable and are `1e-12` and `1e-15` respectively by default. See [Configuration](../core/configuration.md).
  - `DBL_EPSILON` is the minimum positive floating point number such that
    `1.0 + DBL_EPSILON !== 1.0`. This is a constant with a value of approximately
    `2.2204460492503130808472633361816e-16`.

src/core/create.js

@@ -63,9 +63,12 @@ import { DEFAULT_CONFIG } from './config.js'
  *                             The object can contain nested objects,
  *                             all nested objects will be flattened.
  * @param {Object} [config]    Available options:
- *                            {number} epsilon
+ *                            {number} relTol
  *                              Minimum relative difference between two
  *                              compared values, used by all comparison functions.
+ *                            {number} absTol
+ *                              Minimum absolute difference between two
+ *                              compared values, used by all comparison functions.
  *                            {string} matrix
  *                              A string 'Matrix' (default) or 'Array'.
  *                            {string} number

src/core/function/config.js

@@ -29,9 +29,12 @@ export function configFactory (config, emit) {
    *     math.evaluate('0.4')                // outputs Fraction 2/5
    *
    * @param {Object} [options] Available options:
-   *                            {number} epsilon
+   *                            {number} relTol
    *                              Minimum relative difference between two
    *                              compared values, used by all comparison functions.
+   *                            {number} absTol
+   *                              Minimum absolute difference between two
+   *                              compared values, used by all comparison functions.
    *                            {string} matrix
    *                              A string 'Matrix' (default) or 'Array'.
    *                            {string} number

src/function/arithmetic/round.js

@@ -75,14 +75,14 @@ export const createRound = /* #__PURE__ */ factory(name, dependencies, ({ typed,
    */
   return typed(name, {
     number: function (x) {
-      // Handle round off errors by first rounding to epsilon precision
+      // Handle round off errors by first rounding to relTol precision
       const xEpsilon = roundNumber(x, toExponent(config.relTol))
       const xSelected = nearlyEqual(x, xEpsilon, config.relTol, config.absTol) ? xEpsilon : x
       return roundNumber(xSelected)
     },
 
     'number, number': function (x, n) {
-      // Same as number: unless user specifies more decimals than epsilon
+      // Same as number: unless user specifies more decimals than relTol
       const epsilonExponent = toExponent(config.relTol)
       if (n >= epsilonExponent) { return roundNumber(x, n) }
 
@@ -115,7 +115,7 @@ export const createRound = /* #__PURE__ */ factory(name, dependencies, ({ typed,
     },
 
     BigNumber: function (x) {
-      // Handle round off errors by first rounding to epsilon precision
+      // Handle round off errors by first rounding to relTol precision
       const xEpsilon = new BigNumber(x).toDecimalPlaces(toExponent(config.relTol))
       const xSelected = bigNearlyEqual(x, xEpsilon, config.relTol, config.absTol) ? xEpsilon : x
       return xSelected.toDecimalPlaces(0)
@@ -124,7 +124,7 @@ export const createRound = /* #__PURE__ */ factory(name, dependencies, ({ typed,
     'BigNumber, BigNumber': function (x, n) {
       if (!n.isInteger()) { throw new TypeError(NO_INT) }
 
-      // Same as BigNumber: unless user specifies more decimals than epsilon
+      // Same as BigNumber: unless user specifies more decimals than relTol
       const epsilonExponent = toExponent(config.relTol)
       if (n >= epsilonExponent) { return x.toDecimalPlaces(n.toNumber()) }
 

src/function/relational/compare.js

@@ -30,7 +30,7 @@ export const createCompare = /* #__PURE__ */ factory(name, dependencies, ({ type
    * Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.
    *
    * x and y are considered equal when the relative difference between x and y
-   * is smaller than the configured epsilon. The function cannot be used to
+   * is smaller than the configured absTol and relTol. The function cannot be used to
    * compare values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/relational/compareNatural.js

@@ -19,7 +19,7 @@ export const createCompareNatural = /* #__PURE__ */ factory(name, dependencies,
    * the function compares in a natural way.
    *
    * For numeric values, x and y are considered equal when the relative
-   * difference between x and y is smaller than the configured epsilon.
+   * difference between x and y is smaller than the configured relTol and absTol.
    * The function cannot be used to compare values smaller than
    * approximately 2.22e-16.
    *

src/function/relational/equal.js

@@ -23,7 +23,7 @@ export const createEqual = /* #__PURE__ */ factory(name, dependencies, ({ typed,
    * Test whether two values are equal.
    *
    * The function tests whether the relative difference between x and y is
-   * smaller than the configured epsilon. The function cannot be used to
+   * smaller than the configured relTol and absTol. The function cannot be used to
    * compare values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/relational/larger.js

@@ -27,7 +27,7 @@ export const createLarger = /* #__PURE__ */ factory(name, dependencies, ({ typed
    * Test whether value x is larger than y.
    *
    * The function returns true when x is larger than y and the relative
-   * difference between x and y is larger than the configured epsilon. The
+   * difference between x and y is larger than the configured relTol and absTol. The
    * function cannot be used to compare values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/relational/largerEq.js

@@ -27,7 +27,7 @@ export const createLargerEq = /* #__PURE__ */ factory(name, dependencies, ({ typ
    * Test whether value x is larger or equal to y.
    *
    * The function returns true when x is larger than y or the relative
-   * difference between x and y is smaller than the configured epsilon. The
+   * difference between x and y is smaller than the configured relTol and absTol. The
    * function cannot be used to compare values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/relational/smaller.js

@@ -27,7 +27,7 @@ export const createSmaller = /* #__PURE__ */ factory(name, dependencies, ({ type
    * Test whether value x is smaller than y.
    *
    * The function returns true when x is smaller than y and the relative
-   * difference between x and y is smaller than the configured epsilon. The
+   * difference between x and y is smaller than the configured relTol and absTol. The
    * function cannot be used to compare values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/relational/smallerEq.js

@@ -27,7 +27,7 @@ export const createSmallerEq = /* #__PURE__ */ factory(name, dependencies, ({ ty
    * Test whether value x is smaller or equal to y.
    *
    * The function returns true when x is smaller than y or the relative
-   * difference between x and y is smaller than the configured epsilon. The
+   * difference between x and y is smaller than the configured relTol and absTol. The
    * function cannot be used to compare values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/relational/unequal.js

@@ -24,7 +24,7 @@ export const createUnequal = /* #__PURE__ */ factory(name, dependencies, ({ type
    * Test whether two values are unequal.
    *
    * The function tests whether the relative difference between x and y is
-   * larger than the configured epsilon. The function cannot be used to compare
+   * larger than the configured relTol and absTol. The function cannot be used to compare
    * values smaller than approximately 2.22e-16.
    *
    * For matrices, the function is evaluated element wise.

src/function/special/zeta.js

@@ -37,7 +37,7 @@ export const createZeta = /* #__PURE__ */ factory(name, dependencies, ({ typed,
       s,
       value => new BigNumber(value),
       () => {
-        // epsilon is for example 1e-12. Extract the positive exponent 12 from that
+        // relTol is for example 1e-12. Extract the positive exponent 12 from that
         return Math.abs(Math.log10(config.relTol))
       }
     ),

src/utils/complex.js

@@ -1,13 +1,13 @@
 import { nearlyEqual } from './number.js'
 
 /**
- * Test whether two complex values are equal provided a given epsilon.
+ * Test whether two complex values are equal provided a given relTol and absTol.
  * Does not use or change the global Complex.EPSILON setting
- * @param {Complex} x
- * @param {Complex} y
- * @param {number} relTol
- * @param {number} absTol
- * @returns {boolean}
+ * @param {Complex} x - The first complex number for comparison.
+ * @param {Complex} y - The second complex number for comparison.
+ * @param {number} relTol - The relative tolerance for comparison.
+ * @param {number} absTol - The absolute tolerance for comparison.
+ * @returns {boolean} - Returns true if the two complex numbers are equal within the given tolerances, otherwise returns false.
  */
 export function complexEquals (x, y, relTol, absTol) {
   return nearlyEqual(x.re, y.re, relTol, absTol) && nearlyEqual(x.im, y.im, relTol, absTol)

test/node-tests/defaultInstance.test.js

@@ -12,7 +12,8 @@ describe('defaultInstance', function () {
       number: 'number',
       precision: 64,
       predictable: false,
-      epsilon: 1e-12,
+      relTol: 1e-12,
+      absTol: 1e-15,
       randomSeed: null
     })
   })
@@ -29,7 +30,8 @@ describe('defaultInstance', function () {
       number: 'BigNumber',
       precision: 64,
       predictable: false,
-      epsilon: 1e-12,
+      relTol: 1e-12,
+      absTol: 1e-15,
       randomSeed: null
     })
   })
@@ -72,7 +74,8 @@ describe('defaultInstance', function () {
       number: 'BigNumber',
       precision: 4,
       predictable: true,
-      epsilon: 1e-12,
+      relTol: 1e-12,
+      absTol: 1e-15,
       randomSeed: null
     })
 
@@ -92,7 +95,8 @@ describe('defaultInstance', function () {
       number: 'number',
       precision: 64,
       predictable: false,
-      epsilon: 1e-12,
+      relTol: 1e-12,
+      absTol: 1e-15,
       randomSeed: null
     })
 

test/unit-tests/constants.test.js

@@ -23,7 +23,7 @@ import {
 
 describe('constants', function () {
   describe('number', function () {
-    const config = { number: 'number', precision: 64, epsilon: 1e-12 }
+    const config = { number: 'number', precision: 64, relTol: 1e-12 }
     const BigNumber = createBigNumberClass({ config })
     const Complex = createComplexClass({ config })
     const dependencies = {
@@ -86,7 +86,7 @@ describe('constants', function () {
   })
 
   describe('bignumbers', function () {
-    const config = { number: 'BigNumber', precision: 64, epsilon: 1e-12 }
+    const config = { number: 'BigNumber', precision: 64, relTol: 1e-12 }
     const BigNumber = createBigNumberClass({ config })
     const Complex = createComplexClass({ config })
     const dependencies = {

test/unit-tests/function/arithmetic/round.test.js

@@ -180,7 +180,7 @@ describe('round', function () {
     })
 
     it('uses updated config.relTol value', function () {
-      math2.config({ epsilon: 1e-13 })
+      math2.config({ relTol: 1e-13 })
       assert.strictEqual(math2.round((0.000000000001459), 12), 1e-12)
       assert.deepStrictEqual(math2.round(bignumber(1.49e-12), bignumber(12)), bignumber(1e-12))
     })

test/unit-tests/function/relational/compare.test.js

@@ -173,7 +173,7 @@ describe('compare', function () {
     })
   })
 
-  it('should apply configuration option epsilon', function () {
+  it('should apply configuration option relTol', function () {
     const mymath = math.create()
     assert.strictEqual(mymath.compare(1, 0.991), 1)
     assert.strictEqual(mymath.compare(mymath.bignumber(1), mymath.bignumber(0.991)).valueOf(), '1')

test/unit-tests/function/relational/compareNatural.test.js

@@ -219,7 +219,7 @@ describe('compareNatural', function () {
     assert.strictEqual(compareNatural({ a: 2, b: { c: 3 } }, { a: 2, b: { c: 4 } }), -1)
   })
 
-  it('should apply configuration option epsilon', function () {
+  it('should apply configuration option relTol', function () {
     const mymath = math.create()
 
     assert.strictEqual(mymath.compareNatural(1, 0.991), 1)

test/unit-tests/function/relational/equal.test.js

@@ -146,7 +146,7 @@ describe('equal', function () {
     assert.throws(function () { equal('A', 'B') }, /Cannot convert "A" to a number/)
   })
 
-  it('should apply configuration option epsilon', function () {
+  it('should apply configuration option relTol', function () {
     const mymath = math.create()
     assert.strictEqual(mymath.equal(1, 0.991), false)
     assert.strictEqual(mymath.equal(mymath.bignumber(1), mymath.bignumber(0.991)), false)

test/unit-tests/function/relational/larger.test.js

@@ -90,7 +90,7 @@ describe('larger', function () {
     assert.strictEqual(larger(unit('101cm'), unit('1m')), true)
   })
 
-  it('should apply configuration option epsilon', function () {
+  it('should apply configuration option relTol', function () {
     const mymath = math.create()
     assert.strictEqual(mymath.larger(1, 0.991), true)
     assert.strictEqual(mymath.larger(mymath.bignumber(1), mymath.bignumber(0.991)), true)

test/unit-tests/function/relational/largerEq.test.js

@@ -92,7 +92,7 @@ describe('largerEq', function () {
     assert.strictEqual(largerEq(unit('101cm'), unit('1m')), true)
   })
 
-  it('should apply configuration option epsilon', function () {
+  it('should apply configuration option relTol', function () {
     const mymath = math.create()
     assert.strictEqual(mymath.largerEq(1, 1.01), false)
     assert.strictEqual(mymath.largerEq(mymath.bignumber(1), mymath.bignumber(1.01)), false)

test/unit-tests/function/relational/smaller.test.js

@@ -97,7 +97,7 @@ describe('smaller', function () {
     assert.strictEqual(smaller(unit('101cm'), unit('1m')), false)
   })
 
-  it('should apply configuration option epsilon', function () {
+  it('should apply configuration option relTol', function () {
     const mymath = math.create()
     assert.strictEqual(mymath.smaller(0.991, 1), true)
     assert.strictEqual(mymath.smaller(mymath.bignumber(0.991), mymath.bignumber(1)), true)

test/unit-tests/type/unit/physicalConstants.test.js

@@ -60,7 +60,7 @@ const { BigNumber, Unit } = math
 describe('physical constants', function () {
   it('should return the correct value and unit for physical constants', function () {
     // Note: to keep these unit tests readable and compact, the toString() of the units is compared
-    const config = { number: 'number', precision: 64, epsilon: 1e-12 }
+    const config = { number: 'number', precision: 64, relTol: 1e-12 }
     const dependencies = { config, BigNumber, Unit }
 
     // Universal constants
@@ -137,7 +137,7 @@ describe('physical constants', function () {
   })
 
   it('should create BigNumber unit values if configured', function () {
-    const config = { number: 'BigNumber', precision: 64, epsilon: 1e-12 }
+    const config = { number: 'BigNumber', precision: 64, relTol: 1e-12 }
     const dependencies = { config, BigNumber, Unit }
     const molarMass = createMolarMass(dependencies)