Many digital filters and signal-processing transforms can be expressed as a Sum of Products with Constants (SPC). This paper addresses the automatic construction of low-precision, but high accuracy SPC architectures: these architectures are specified as last-bit accurate with respect to a mathematical definition. In other words, they behave as if the computation was performed with infinite accuracy, then rounded only once to the low-precision output format. This eases the task of porting double-precision code (e.g. Matlab) to low-precision hardware or FPGA.