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GPU Computing Gems Jade Edition by Wen-mei W. Hwu

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Chapter 10

Approximating the erfinv Function

Mike Giles

The inverse error function erfinv is a standard component of mathematical libraries, and particularly useful in statistical applications for converting uniform random numbers into Normal random numbers. This chapter presents a new approximation of the erfinv function, which is significantly more efficient for GPU execution due to the greatly reduced warp divergence.

10.1 Introduction

Like cos x, sin x, ex and log x, the error function

image

and its inverse erfinv(x) are a standard part of libraries such as Intel’s MKL, AMD’s ACML and NVIDIA’s CUDA math library.

The inverse error function is a particularly ...

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