On properties of floating-point roundoff noise
Alfred Fettweis · IEEE Transactions on Acoustics Speech and Signal Processing · 1974
The probability density and related properties of the relative error due to rounding after floating-point arithmetic operations can be computed from the distributions of the mantissa and its absolute error. Various results obtained, in particular, under different assumptions concerning the distribution of the mantissa are presented on a common basis and in such a way that they are independent of the number of digits in the mantissa, thus facilitating comparisons.