where s is the sign bit, p is the precision of significand, E is the exponent, and bits b i can take values 0 or 1. Although the second revision of the standard generalizes base, or radix, here we consider only binary formats. The number is called normal if b 0 is 1 and subnormal otherwise. Subnormal numbers fill the gap between the smallest positive normal number and zero. The attributes of single-and double-precision floating-point numbers are summarized in Table . Typical implementations of most ab initio methods use double precision arithmetic. The single precision format uses half the number of bits of double precision, thereby allowing to store twice as many values. Another benefit is proportionally faster memory access and disk input/output (in terms of the number of elements per second). This is important in practice because memory speed improves at a slower rate than CPUs. Furthermore, CPU caches can accommodate twice as many floating point numbers potentially leading to less frequent cache misses. In terms of computational time, single precision gives a twofold speedup on CPUs for most modern architectures and the gains on GPUs can be much larger. Thus, single-precision implementation of quantum-chemistry methods can extend the scope of systems amenable to these treatments, decrease time-to-solution, and reduce energy footprint. Using too much energy and power per calculation is recognized as one of the biggest challenges in high performance computing and using reduced precision or even entirely different representation of real numbers have been advocated. Although double precision is de facto a standard in quantum chemistry and other scientific calculations, many algorithms can be re-designed to work in mixed precision, as was recently done in such diverse areas as lattice quantum chromodynamics, 14 molecular dynamics, and general linear algebra algorithms with iterative refinements. In quantum chemistry mixed-precision algorithms have been explored in the context of integral calculations within Hartree-Fock (HF) and density functional theory (DFT). The main conclusion from these studies was that pure single precision is not sufficient for integral and HF/DFT calculations and one should only deploy it in a mixed-precision fashion, i.e., such that some operations are performed in single precision and some -in double precision. The utility of single precision has not yet been thoroughly investigated in post-HF calculations. Previous studies focused on non-iterative methods, such as MP2 and triples correction for CCSD. Single-precision MP2 was tested within resolution-of-the-identity (RI) and Cholesky decomposition (CD) schemes. These studies have shown that commonly used RI bases and CD thresholds (10 -2 -10 -3 ) yield much larger errors in total energies than errors due to using single-precision arithmetics. Numerical analysis of the (T) correction for CCSD has shown that this calculation is stable with respect to numerical noise, justifying single-precision implementation. Despite these encouraging findings, the extent of applicability of single precision in many-body theories is not fully understood. There are several open questions: