erfinv: Sharing erfinv scalar functor to align precision with other P…

…yTorch backends. (#634)

Use existing `calc_erfinv` implementation from `<ATen/native/Math.h>`
reduces the discrepancy between CPU MKL and XPU implementations of the
erfinv for specific test cases in float64

src/ATen/native/xpu/sycl/UnarySpecialOpsKernels.cpp

@@ -79,67 +79,16 @@ void erfc_kernel(TensorIteratorBase& iter) {
 
 template <typename scalar_t>
 struct ErfinvFunctor {
-  using opmath_type = at::opmath_type<scalar_t>;
-
   scalar_t operator()(scalar_t in) const {
-    scalar_t out;
-    opmath_type z, num, dem;
-
-    auto x = static_cast<opmath_type>(in);
-    if (std::fabs(x) > 1.0f) {
-      out = static_cast<scalar_t>(NAN);
-      return out;
-    }
-    if (std::fabs(x) == 1.0f) {
-      out = static_cast<scalar_t>(
-          (std::copysign(1.0, static_cast<double>(x))) *
-          (std::numeric_limits<double>::infinity()));
-      return out;
-    }
-    if (std::fabs(x) <= 0.7f) {
-      z = x * x;
-      num = (((a_[3] * z + a_[2]) * z + a_[1]) * z + a_[0]);
-      dem =
-          ((((b_[3] * z + b_[2]) * z + b_[1]) * z + b_[0]) * z +
-           static_cast<opmath_type>(1.0));
-      out = x * num / dem;
-    } else {
-      z = static_cast<opmath_type>(
-          std::sqrt(-std::log((1.0 - std::fabs(x)) / 2.0)));
-      num = ((c_[3] * z + c_[2]) * z + c_[1]) * z + c_[0];
-      dem = (d_[1] * z + d_[0]) * z + static_cast<opmath_type>(1.0);
-      out = static_cast<scalar_t>(
-          static_cast<opmath_type>(std::copysign(1.0, static_cast<double>(x))) *
-          num / dem);
-    }
-    out = out -
-        static_cast<scalar_t>(
-              (std::erf(static_cast<double>(out)) - x) /
-              ((2.0 / std::sqrt(PI_f64_)) * std::exp(-x * x)));
-    out = out -
-        static_cast<scalar_t>(
-              (std::erf(static_cast<double>(out)) - x) /
-              ((2.0 / std::sqrt(PI_f64_)) * std::exp(-x * x)));
-    return out;
+    return calc_erfinv(in);
   }
+};
 
-  static constexpr double PI_f64_ = 3.14159265358979323846;
-  static constexpr std::array<opmath_type, 4> a_ = {
-      0.886226899,
-      -1.645349621,
-      0.914624893,
-      -0.140543331};
-  static constexpr std::array<opmath_type, 4> b_ = {
-      -2.118377725,
-      1.442710462,
-      -0.329097515,
-      0.012229801};
-  static constexpr std::array<opmath_type, 4> c_ = {
-      -1.970840454,
-      -1.624906493,
-      3.429567803,
-      1.641345311};
-  static constexpr std::array<opmath_type, 2> d_ = {3.543889200, 1.637067800};
+template <>
+struct ErfinvFunctor<c10::Half> {
+  c10::Half operator()(c10::Half in) const {
+    return calc_erfinv(float(in));
+  }
 };
 
 void erfinv_kernel(TensorIteratorBase& iter) {

test/xpu/run_test_with_skip.py

@@ -1551,26 +1551,6 @@ def launch_test(test_case, skip_list=None, exe_list=None):
     # Relative difference: 6.156719153309558e-06 (up to 1e-06 allowed)
     "test_log1p_complex_xpu_complex64",
 
-    # CPU MKL::erfinv vs XPU impl. At most 6.e-06
-    # Greatest absolute difference: 5.250126961175994e-06 at index (0,) (up to 1e-07 allowed)
-    # Greatest relative difference: 1.680894105274219e-06 at index (0,) (up to 1e-07 allowed)
-    "test_reference_numerics_large__refs_erfinv_xpu_float64",
-    # Greatest absolute difference: 5.250126961175994e-06 at index (0,) (up to 1e-07 allowed)
-    # Greatest relative difference: 1.680894105274219e-06 at index (0,) (up to 1e-07 allowed)
-    "test_reference_numerics_large_erfinv_xpu_float64",
-    # Greatest absolute difference: 4.829411781148707e-06 at index (690, 855) (up to 1e-07 allowed)
-    # Greatest relative difference: 1.5588752485769885e-06 at index (690, 855) (up to 1e-07 allowed)
-    "test_reference_numerics_normal__refs_erfinv_xpu_float64",
-    # Greatest absolute difference: 4.829411781148707e-06 at index (690, 855) (up to 1e-07 allowed)
-    # Greatest relative difference: 1.5588752485769885e-06 at index (690, 855) (up to 1e-07 allowed)
-    "test_reference_numerics_normal_erfinv_xpu_float64",
-    # Greatest absolute difference: 5.250126961175994e-06 at index (96,) (up to 1e-07 allowed)
-    # Greatest relative difference: 1.680894105274219e-06 at index (96,) (up to 1e-07 allowed)
-    "test_reference_numerics_small__refs_erfinv_xpu_float64",
-    # Greatest absolute difference: 5.250126961175994e-06 at index (96,) (up to 1e-07 allowed)
-    # Greatest relative difference: 1.680894105274219e-06 at index (96,) (up to 1e-07 allowed)
-    "test_reference_numerics_small_erfinv_xpu_float64",
-
     # Issue: https://github.com/intel/torch-xpu-ops/issues/622
     # Mismatched elements: 8 / 943593 (0.0%)
     # Greatest absolute difference: inf at index (9, 860) (up to 0.001 allowed)