ulp (epsilon function)

Compute the ULP of a given IEEE-754 64-bit number: eps(x) (alias: ulp(x)). Get the closest representable number that comes before/after it on the float64 number line: nextFloat(x), prevFloat(x).

Install

npm install @lvlte/ulp

Usage

Import

// ESM
import { eps, nextFloat, prevFloat } from '@lvlte/ulp';

// CJS
const { eps, nextFloat, prevFloat } = require('@lvlte/ulp');

eps(x) / ulp(x) (alias)

console.log( eps() );                               // 2.220446049250313e-16
console.log( eps() === eps(1) );                    // true
console.log( eps() === Number.EPSILON );            // true

console.log( eps(Number.MAX_SAFE_INTEGER) );        // 1
console.log( eps(Number.MAX_SAFE_INTEGER + 1) );    // 2

console.log( eps(0) );                              // 5e-324
console.log( eps(0) === Number.MIN_VALUE );         // true

console.log( eps(Infinity) );                       // NaN

nextFloat(x) / prevFloat(x)

console.log( nextFloat(0) );                        // 5e-324
console.log( nextFloat(0) === Number.MIN_VALUE );   // true

console.log( nextFloat(1) );                        // 1.0000000000000002
console.log( nextFloat(1) === 1 + eps(1) );         // true

console.log( nextFloat(Number.MAX_SAFE_INTEGER) );  // 9007199254740992
console.log( nextFloat(9007199254740992) );         // 9007199254740994
console.log( nextFloat(Number.MAX_VALUE) );         // Infinity

console.log( prevFloat(0) );                        // -5e-324
console.log( prevFloat(1) );                        // 0.9999999999999999
console.log( prevFloat(9007199254740992) );         // 9007199254740991
console.log( prevFloat(Infinity) );                 // 1.7976931348623157e+308

Use case

• Use the proper tolerance to check whether two floating-point numbers should be considered equal.
• Use the proper tolerance to approximate a floating-point number as a rational number.