Fixed-point arithmetic is a well-known alternative to floating-point arithmetic on embedded systems. It is used to reduce some computation costs in terms of speed and power consumption on certain platforms, e.g. medical devices, cars, and robots. In this article, we present POPiX, a novel fixed-point program synthesis tool based on static analysis. The originality of our method is to solve a system of constraints generated from the program source code. Thus, the solution of our constraints gives the new fixed-point formats while accomplishing the accuracy required by the user. Basically, POPiX takes as input an imperative program running in floating-point arithmetic and synthesizes a new program coupled to a fixed-point library relying on integers only. We evaluate POPiX on a collection of floating-point benchmarks coming from FPBench. Results demonstrate the efficiency of our analysis by achieving memory savings up to 75% with energy savings up to 3.5x.