GPU渲染中的哈希函数性能与质量对比分析

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"Hash Functions for GPU Rendering - 2020 (Jarzynski2020Hash)" 是一篇关于在计算机科学领域，特别是在图形渲染中使用哈希函数的文章。作者Mark Jarzynski和Marc Olano来自UMBC，他们在2020年《计算机图形技术杂志》（Journal of Computer Graphics Techniques）第9卷第3期中详细探讨了哈希函数在GPU渲染中的应用。哈希函数在GPU渲染中的重要性在于它们能够生成确定性的随机数，这对于许多图形应用来说是至关重要的。这些随机数的质量和生成速度直接影响到渲染效果和效率。文章通过TestU01测试套件对一系列现有的哈希函数进行了评估，以衡量它们作为随机数生成器的性能。TestU01是一组专门用于检验随机数生成器统计性质的软件工具。文章中，作者对比了不同类型的哈希函数，包括： 1. 线性同余生成器(LCG, Linear Congruential Generator)：图1(a)显示了其明显的缺陷，如可见的条纹、线性模式和重复模式。 2. 三角函数(trig)：同样表现出明显的错误，如图1(b)所示。 3. iqint3 和 xxhash32：这两个函数的表现相对较好，尽管图1(c)和(d)没有充分展示xxhash32的显著优势。 4. tea3 和 tea4：这两个函数具有2D输出，如图1(e)和(f)所示。 5. hashwithoutsine33 和 pcg3d：它们提供3D输出，分别在图1(g)和(h)中以颜色表示。通过对这些函数进行GPU执行速度的基准测试，作者分析了哈希函数在性能与质量之间的权衡。他们关注的范围从高性能/低质量到高质星/低性能，寻找在各种需求下最佳的哈希函数。文章的目的是为GPU渲染中的哈希函数选择提供指导，帮助开发者在保证渲染质量和效率之间找到最优解。通过这样的研究，可以优化图形渲染过程，提高计算效率，同时确保生成的随机数序列足够随机，避免在视觉上出现可识别的模式，从而提升最终的图像质量。

Journal of Computer Graphics Techniques

Hash Functions for GPU Rendering

Vol. 9, No. 3, 2020

http://jcgt.org

A less rigorous test often used for graphics purposes draws the random values as

grayscale (or extracted single bits) into a 2D image [Zafar et al. 2010; Reed 2013].

This can show visual repetition and patterns, though not deeper statistical anomalies

detected by the more sophisticated tests (See Figure 1).

When performing a multidimensional optimization, the Pareto frontier contains

solutions where improving one dimension will make the other(s) worse. For hashes

where we care about both performance and quality, if a hash is on the Pareto frontier,

the only faster hashes will have worse quality, and the only higher-quality hashes

will be slower. For hashes off of the frontier, there is another hash in the set that will

improve at least one of the criteria without making the other criteria worse. Therefore,

we are primarily interested in identifying hashes that deﬁne the speed/quality Pareto

frontier.

The list of base hash functions we compare is given in Table 1. We also compare

several derived hashes created by applying the transformations in Sections 4.1–5.

3. Methodology

3.1. Testing Quality

Following O’Neill [2014a], we use the total number of TestU01 [L’Ecuyer and Simard

2007] BigCrush tests that failed as a measure of hash quality. BigCrush consists of

160 individual tests: a result of 0 means that the hash passed every test, and a result

of 160 means that the hash failed every test. The PractRand [Doty-Humphrey 2019]

provides more thorough testing for high-quality random number generators, but since

it runs with incrementally increasing test sizes and stops at the ﬁrst failure, it appears

to provide less useful discrimination at lower quality levels.

To accelerate testing, we parallelized each BigCrush test on our high perfor-

mance computing facility cluster. To ensure consistency between CPU code used

for randomness testing, and GPU code used for timing, we created C++ classes and

functions to allow the HLSL hash code to be compiled as valid C++ code without

change. The input for each hashing algorithm was initialized to be an unsigned

integer with a value of 0, incremented each time that the hashing algorithm was

called.

TestU01 expects a sequential stream of integers as the output of any random num-

ber generator to be tested. For hashes that had a vector as the output, each value was

serialized. For example, a hash with three-dimensional output would produce X, then

Y, then Z for one index before incrementing the index. Since the randomness tests

include testing for translational repetition, this method will catch problems in any

single channel as well as between channels. We did try testing each component inde-

pendently, but the results did not signiﬁcantly differ from rotating through the output

dimensions.

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