How to Emulate Double-Precision Arithmetic Using Single-Precision Floats?

Emulating Double-Precision Arithmetic with Floats

In certain scenarios, embedded hardware systems with limited floating-point support may encounter the need for double-precision functionality. This raises the question of how to achieve this using only single-precision floating-point operations.

To emulate a double-precision value, the approach is to utilize a struct containing a tuple of two single-precision floats, representing the high and low portions of the double. The comparison can be performed using lexicographic ordering.

However, the addition operation presents a challenge. The base for the addition should be carefully considered to ensure accuracy. It is recommended to use a multiple of FLT_MAX (the maximum value representable by a single-precision float) to avoid intermediate underflow or overflow.

To detect a carry, one can subtract the sum of the two floats from the expected value. If the result is less than or equal to zero, a carry has occurred.

The references below provide valuable insights into techniques for double-precision emulation using single-precision floats on GPU architectures:

• https://hal.archives-ouvertes.fr/hal-00021443
• http://andrewthall.org/papers/df64_qf128.pdf

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