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[BE][Ez]: Make c10/special arrays constexpr (#146246)

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No reason to have array creation overhead for these constexpr arrays. This is better because it guarantees the array is not duplicated across templates or translation units unless necessary and allows the compiler to do static compile time bounds checking (even in loop based accesses)
Pull Request resolved: https://github.com/pytorch/pytorch/pull/146246
Approved by: https://github.com/dcci, https://github.com/malfet
This commit is contained in:
Aaron Gokaslan 2025-02-01 21:03:16 +00:00 committed by PyTorch MergeBot
parent d4ad7b91ad
commit 07dbd539b4
1 changed files with 32 additions and 30 deletions
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62
c10/metal/special_math.h
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@ -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<T>(::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<T>(
(::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,