Let's talk about the problem of loss of precision in JavaScript

With the development of computer science and programming languages, we are increasingly aware of the importance of numerical accuracy. In JavaScript, numeric types include integers and floating point numbers. However, the way floating point numbers are represented in computers creates a vexing problem: loss of precision.

In JavaScript, floating point numbers are approximations, not exact values. Because computers represent numerical values ​​in binary, many decimal fractions cannot be accurately represented as binary fractions. This causes the floating point values ​​on the computer to deviate slightly from the decimal values ​​one would expect.

For example, using JavaScript to calculate the decimal 1.1 minus 0.1, the expected result is 1.0. But the actual result is 0.9999999999999999, which is due to the approximate way 1.1 is represented in binary. This error due to problems with the representation of floating point numbers is called "rounding error".

JavaScript uses the IEEE 754 standard to represent and process floating point numbers. In this standard, a floating-point number consists of three parts: the sign bit, the exponent bit, and the mantissa bit. The exponent bit represents the power of the floating point number, and the mantissa bit represents the significant digit of the floating point number. JavaScript uses "double-precision floating point numbers", that is, the mantissa is 52 bits. This makes JavaScript's floating point numbers more limited in range and precision.

For example, when using JavaScript to calculate 2 to the 51st power, the result is 2 to the 51st power, but when calculating 2 to the 52nd power, the result will be inaccurate because the highest bit in the 52-bit binary number is 1, causing the floating-point representation to be approximately 2 raised to the 51st power plus 1.

In order to solve the problem of losing precision, we can use some techniques and tools. One approach is to use integers instead of floating point numbers for calculations and then convert the results to floating point numbers. For example, calculate an amount after converting it to an integer, and then divide the result by 100. This approach reduces rounding errors.

Another approach is to use special JavaScript libraries such as decimal.js and big.js. These libraries provide high-precision calculations to handle larger and more precise numbers in JavaScript.

When writing JavaScript code, we also need to always pay attention to the issue of numerical precision. For example, avoid comparing floating point numbers directly and instead compare differences between them, usually by setting a small tolerance.

Generally speaking, the problem of JavaScript losing precision is a problem that needs to be dealt with carefully. Knowing how to reduce rounding errors, as well as using high-precision arithmetic libraries or other techniques, can help us write more robust and accurate code.

The above is the detailed content of Let's talk about the problem of loss of precision in JavaScript. For more information, please follow other related articles on the PHP Chinese website!