Fast evaluation of the inverse Poisson CDF

The function normcdfinv(u) in NVIDIA's CUDA maths library (and similar functions in various libraries for CPU execution) computes the inverse of the cumulative distribution function (CDF) for the Normal distribution. It can be used to convert uniformly distributed pseudo-random (or quasi-random) numbers into psuedo-random (or quasi-random) Normals.

Here I present an article, and associated software, on algorithms for a function poissinv(u) which performs the corresponding task for Poisson distributions, and can be used to generate Poisson random variates.

Paper and presentations:

• paper (PDF)
• presentation at IMACS Monte Carlo conference (PDF)
• presentation at NVIDIA's 2014 GTC conference (PDF)

• poissinv_cuda.h -- header file defining inline CUDA device functions
• poissinv_timing.cu -- test code to assess performance
• poissinv_check.cu -- test code to verify accuracy
• poissinv_quad.c -- quad-precision function used in validation (requires gcc's libquadmath library)
• Makefile_sm30 -- Makefile for Kepler GPUs

• poissinv.h -- header file defining scalar and vector functions
• poissinv_timing.c -- test code to assess performance
• poissinv_check.c -- test code to verify accuracy
• poissinv_quad.c -- quad-precision function used in validation (requires gcc's libquadmath library)
• Makefile

• asymp.m -- generates Normal asymptotic approximations
• approx.m -- generates approximations based on inverse of Temme approximation
• figs.m -- generates a number of figures for the paper
• temme.m -- implements and tests the accuracy of Temme's asymptotic approximation to the incomplete Gamma function
• as241.m -- implements and tests the accuracy of Algorithm AS241 to compute the inverse of the Normal CDF function

Licensing

EMail