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Two regression corpus cases for pytorch #199850: torch.erf in bfloat16 and float16 on CPU returns 0 at and
below 1.8e-7 and loses relative accuracy below 1e-3 (13404 bfloat16 ulps, 5 float16 ulps at worst), found with
the half precision rows of ulpwise survey --functions erf --backends torch --dtypes f16,bf16.
Two regression corpus cases for pytorch #199867: torch.special.logit in float16 and bfloat16 on CPU rounds 1 - x
and x / (1 - x) to the input dtype before the log, so logit(0.499756) in float16 is -0.000488 for an exact -0.000977
(512 ulp, 64 bfloat16 ulp at worst), found with ulpwise survey --functions logit --backends torch --dtypes f16,bf16.
studies/accuracy-survey-2026-10-half: the second accuracy survey, torch 2.14.0+cpu in float16 and bfloat16 for the
45 functions with half precision CPU kernels. 33 float16 and 34 bfloat16 rows of 45 are correctly rounded; erf
(pytorch #199850) and logit (pytorch #199867) lose their digits before the rounding step, polygamma(2, x) in
float16 is off at every half integer in (-1024, -256) because the Hurwitz zeta sum accumulates in float for the
reduced types, and the activation tails and the rsqrt and i0e vector versus scalar disagreements of September
show again.
ulpwise survey: the polygamma_1 and polygamma_2 references at a non positive integer are now the signed
infinity of the pole, +inf for an odd order (the limit from both sides) and -inf for an even one (the sign of (-1) ** (n + 1) * n! * zeta(n + 1, x), which is what scipy, torch and jax return), instead of a domain error
that expected nan. The f16 and bf16 grids reach the integers from 2048 and 256 up, so every negative point
past there was a pole and counted as a nonfinite mismatch: on torch 2.14 the two functions had 354 of 3546
float16 points and 492 of 4016 bfloat16 points each, polygamma_2 has 0 now in every dtype and polygamma_1
keeps 491 bfloat16, 4 float32 and 2 float16 points where torch returns a large finite value instead of inf
at a negative integer (pytorch #198663).