diff --git a/c10/metal/special_math.h b/c10/metal/special_math.h index 7f6dc5b76f2..309f57907e6 100644 --- a/c10/metal/special_math.h +++ b/c10/metal/special_math.h @@ -94,21 +94,22 @@ T i0(T _x) { * * lim(x->0){ exp(-x) I0(x) } = 1. */ - const float A[] = {-4.41534164647933937950E-18, 3.33079451882223809783E-17, - -2.43127984654795469359E-16, 1.71539128555513303061E-15, - -1.16853328779934516808E-14, 7.67618549860493561688E-14, - -4.85644678311192946090E-13, 2.95505266312963983461E-12, - -1.72682629144155570723E-11, 9.67580903537323691224E-11, - -5.18979560163526290666E-10, 2.65982372468238665035E-9, - -1.30002500998624804212E-8, 6.04699502254191894932E-8, - -2.67079385394061173391E-7, 1.11738753912010371815E-6, - -4.41673835845875056359E-6, 1.64484480707288970893E-5, - -5.75419501008210370398E-5, 1.88502885095841655729E-4, - -5.76375574538582365885E-4, 1.63947561694133579842E-3, - -4.32430999505057594430E-3, 1.05464603945949983183E-2, - -2.37374148058994688156E-2, 4.93052842396707084878E-2, - -9.49010970480476444210E-2, 1.71620901522208775349E-1, - -3.04682672343198398683E-1, 6.76795274409476084995E-1}; + constexpr float A[] = { + -4.41534164647933937950E-18, 3.33079451882223809783E-17, + -2.43127984654795469359E-16, 1.71539128555513303061E-15, + -1.16853328779934516808E-14, 7.67618549860493561688E-14, + -4.85644678311192946090E-13, 2.95505266312963983461E-12, + -1.72682629144155570723E-11, 9.67580903537323691224E-11, + -5.18979560163526290666E-10, 2.65982372468238665035E-9, + -1.30002500998624804212E-8, 6.04699502254191894932E-8, + -2.67079385394061173391E-7, 1.11738753912010371815E-6, + -4.41673835845875056359E-6, 1.64484480707288970893E-5, + -5.75419501008210370398E-5, 1.88502885095841655729E-4, + -5.76375574538582365885E-4, 1.63947561694133579842E-3, + -4.32430999505057594430E-3, 1.05464603945949983183E-2, + -2.37374148058994688156E-2, 4.93052842396707084878E-2, + -9.49010970480476444210E-2, 1.71620901522208775349E-1, + -3.04682672343198398683E-1, 6.76795274409476084995E-1}; auto y = (x / 2.0) - 2.0; return static_cast(::metal::exp(x) * chbevl(y, A, 30)); @@ -120,19 +121,20 @@ T i0(T _x) { * * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi). */ - const float B[] = {-7.23318048787475395456E-18, -4.83050448594418207126E-18, - 4.46562142029675999901E-17, 3.46122286769746109310E-17, - -2.82762398051658348494E-16, -3.42548561967721913462E-16, - 1.77256013305652638360E-15, 3.81168066935262242075E-15, - -9.55484669882830764870E-15, -4.15056934728722208663E-14, - 1.54008621752140982691E-14, 3.85277838274214270114E-13, - 7.18012445138366623367E-13, -1.79417853150680611778E-12, - -1.32158118404477131188E-11, -3.14991652796324136454E-11, - 1.18891471078464383424E-11, 4.94060238822496958910E-10, - 3.39623202570838634515E-9, 2.26666899049817806459E-8, - 2.04891858946906374183E-7, 2.89137052083475648297E-6, - 6.88975834691682398426E-5, 3.36911647825569408990E-3, - 8.04490411014108831608E-1}; + constexpr float B[] = { + -7.23318048787475395456E-18, -4.83050448594418207126E-18, + 4.46562142029675999901E-17, 3.46122286769746109310E-17, + -2.82762398051658348494E-16, -3.42548561967721913462E-16, + 1.77256013305652638360E-15, 3.81168066935262242075E-15, + -9.55484669882830764870E-15, -4.15056934728722208663E-14, + 1.54008621752140982691E-14, 3.85277838274214270114E-13, + 7.18012445138366623367E-13, -1.79417853150680611778E-12, + -1.32158118404477131188E-11, -3.14991652796324136454E-11, + 1.18891471078464383424E-11, 4.94060238822496958910E-10, + 3.39623202570838634515E-9, 2.26666899049817806459E-8, + 2.04891858946906374183E-7, 2.89137052083475648297E-6, + 6.88975834691682398426E-5, 3.36911647825569408990E-3, + 8.04490411014108831608E-1}; return static_cast( (::metal::exp(x) * chbevl(32.0 / x - 2.0, B, 25)) / ::metal::sqrt(x)); @@ -148,7 +150,7 @@ T i1(T _x) { if (x <= 8.0) { // Chebyshev coefficients for exp(-x) i1(x) in the internal [0, 8] // lim(x->0){ exp(-x) i1(x) / x } = 1/2 - const float coefficients[] = { + constexpr float coefficients[] = { 2.77791411276104639959E-18, -2.11142121435816608115E-17, 1.55363195773620046921E-16, -1.10559694773538630805E-15, 7.60068429473540693410E-15, -5.04218550472791168711E-14, @@ -172,7 +174,7 @@ T i1(T _x) { // Chebyshev coefficients for exp(-x) sqrt(x) i1(x) // in the inverted interval [8, infinity] // lim(x->inf){ exp(-x) sqrt(x) i1(x) } = 1/sqrt(2pi) - const float coefficients[] = { + constexpr float coefficients[] = { 7.51729631084210481353E-18, 4.41434832307170791151E-18, -4.65030536848935832153E-17, -3.20952592199342395980E-17, 2.96262899764595013876E-16, 3.30820231092092828324E-16,