Intel(R) - Computational and Systems Biology at MIT

Coding Tips 8This is another chapter whose contents discusses programming with Intel® Math KernelLibrary (Intel® MKL). Whereas chapter 7 focuses on general language-specificprogramming options, this one presents coding tips that may be helpful to meet certainspecific needs. Currently the only tip advising how to achieve numerical stability is given.You can find other coding tips, relevant to performance and memory management, inchapter 6.Aligning Data for Numerical StabilityIf linear algebra routines (LAPACK, BLAS) are applied to inputs that are bit-for-bit identicalbut the arrays are differently aligned or the computations are performed either on differentplatforms or with different numbers of threads, the outputs may not be bit-for-bit identical,though they will deviate within the appropriate error bounds. The Intel MKL version mayalso affect numerical stability of the output, as the routines may be implementeddifferently in different versions. With a given Intel MKL version, the outputs will bebit-for-bit identical provided all the following conditions are met:• the outputs are obtained on the same platform;• the inputs are bit-for-bit identical;• the input arrays are aligned identically at 16-byte boundaries.Unlike the first two conditions, which are under users' control, the alignment of arrays, bydefault, is not. For instance, arrays dynamically allocated using malloc are aligned at8-byte boundaries, but not at 16-byte. If you need the numerically stable output, useMKL_malloc() to get the properly aligned workspace:8-1