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Stan Math Library
5.4.0
Automatic Differentiation
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Stan Math Library
5.4.0
Automatic Differentiation
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| double stan::math::opencl_kernels::erfcx | ( | double | x | ) |
Return the scaled complementary error function exp(x * x) * erfc(x) of the kernel generator expression.
Mirrors stan/math/prim/fun/erfcx.hpp branch for branch and formula for formula; the two must be kept in step. The whole positive axis is covered without a library call. On the negative side exp is unavoidable, since erfcx grows like 2*exp(x*x); its argument is corrected with fma, because exp amplifies the rounding of x * x into roughly x * x * eps.
The correction must be written with fma and not with a Dekker split. The split relies on t - (t - x) not being simplified to x, which holds in floating point but not over the reals, and the OpenCL compiler does simplify it: the split form silently degrades to the uncorrected product on device while still being correct on the host. Do not reintroduce it.
| x | argument |