Single-Precision, Double-Precision, & Multi-Precision Computing: Main Differences

Understanding which precision format to utilize for a calculation is crucial, but it can sometimes feel like a balancing act: The accuracy of double-precision computing seems to compete against the performance value of its single-precision counterpart. Both ensure accuracy and push the limitations of numerical values, but each technique offers a unique purpose and operational cost.

Here, we’ll take a close look at each format, how they differ from one other, and how mixing different levels of precision can help you maintain efficiency without forfeiting accuracy. 

In order to understand the difference between single- and double-precision computing, it’s important to understand the role of precision in computer science. Imagine performing a calculation using an irrational number (such as pi) and including only two digits to the right of the decimal point (3.14). You would get a more accurate result if you were to do the calculation including ten digits to the right of the decimal point (3.1415926535).

For computers, this level of accuracy is called precision, and it’s measured in binary digits (bits) instead of decimal places. The more bits used, the higher the precision.

Representing large numbers in computer binary requires a standard to ensure there aren’t huge discrepancies in calculations. Thus, the Institute of Electrical and Electronics Engineers (IEEE) developed the IEEE Standard for Floating-Point Arithmetic (IEEE 754). 

There are three components of IEEE 754:

1. The base - 0 represents a positive number; 1 represents a negative number. 

2. The biased exponent - The exponent is used to represent both positive and negative exponents. Thus, a bias must be added to the actual exponent to get the stored exponent. 

3. The mantissa - Also known as the significand, the mantissa represents the precision bits of the number.

Using these components, IEEE 754 represents floating-point numbers in two ways: single-precision format and double-precision format. While there are still a variety of ways in which to represent floating-point numbers, IEEE 754 is the most common because it is generally the most efficient representation of numerical values. 

The simplest way to distinguish between single- and double-precision computing is to look at how many bits represent the floating-point number. For single precision, 32 bits are used to represent the floating-point number. For double precision, 64 bits are used to represent the floating-point number. 

The first number represents the base. The next set of numbers (eight for single precision and eleven for double precision) represents the biased exponent. The final set of numbers (23 for single precision and 52 for double precision) represents the mantissa.

In addition to single- and double-precision computing, which are considered multi-precision, there is also mixed-precision computing.

Mixed-precision computing, sometimes called transprecision, is commonly used in the field of machine learning. It performs calculations by starting with half-precision (16 bit) values for rapid matrix math. Then, as the numbers are computed, they’re stored by the machine at a higher precision. 

The advantage of mixed-precision computing is that it offers accumulated answers that are similar in accuracy to those run in double-precision computing—without requiring the same level of power, runtime, and memory.

While accuracy in computing is certainly essential, it’s important to understand how you can benefit from using a variety of precision levels. To ensure operational efficiency without foregoing precise calculations, you need flexible capabilities that support different floating-point formats.