Double-precision floating-point format

Double-precision floating-point format is a computer data format that allows for the representation of real numbers with a specified precision, or number of significant digits. The acronym “DPFP” stands for double-precision floating-point. This format is commonly used in scientific and engineering applications where many decimal places of precision are required and, compared to single-precision floating-point format, offers more bits of precision (54 bits).

The double-precision representation of a real number consists of three parts: the sign (s), the exponent (e), and the mantissa (m). The sign (s) indicates whether the real number is negative (s=1) or positive (s=0). The exponent (e) is a binary number that indicates the power to which the base number 2 must be raised or divided to obtain the desired number. Finally, the mantissa (m) is a binary fraction representing the digits of the real number to the right of the decimal point.

In order to store a double-precision value in computer memory, 64 bits are allocated as 8 bytes. This follows a specific format known as the IEEE 754 standard for floating-point numbers, which is used to ensure compatibility across different architectures. The first bit of the 8-byte memory is used to represent the sign bit (s). The next 11 bits represent the exponent (e) and the remaining 52 bits represent the mantissa (m).

Since 2018, double-precision floating-point format is being used in graphics processing units (GPU) as a way to achieve more accuracy and improved performance in scientific and engineering applications, and in general-purpose computing on graphics processing units (GPGPU). Moreover, double-precision floating-point operations can be performed on modern CPUs as well as GPUs, taking advantage of parallelism — a technique that allows for simultaneous calculation of multiple parts of a problem — to speed up the process.

With the development of large-scale deep-learning neural networks, the use of double-precision floats in GPU architectures has become increasingly important, since it allows for the capture and simulation of finer details in images, sound clips and other types of data.