Add more tests for pow and fix a corner case for huge exponent where the result is always zero or infinite unless x is one.

Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h

@@ -929,6 +929,11 @@ Packet generic_pow(const Packet& x, const Packet& y) {
   Packet y_is_pos = pandnot(ptrue(y), por(y_is_zero, y_is_neg));
   Packet y_is_nan = pandnot(ptrue(y), pcmp_eq(y, y));
   Packet abs_y_is_inf = pcmp_eq(pabs(y), cst_pos_inf);
+  // |y| is so large that (1+eps)^y over- or underflows.
+  EIGEN_CONSTEXPR Scalar huge_exponent =
+      (std::numeric_limits<Scalar>::digits * Scalar(EIGEN_LOG2E)) /
+      std::numeric_limits<Scalar>::epsilon();
+  Packet abs_y_is_huge = pcmp_lt(pset1<Packet>(huge_exponent), pabs(y));
 
   // Predicates for whether y is integer and/or even.
   Packet y_is_int = pcmp_eq(pfloor(y), y);
@@ -937,14 +942,16 @@ Packet generic_pow(const Packet& x, const Packet& y) {
 
   // Predicates encoding special cases for the value of pow(x,y)
   Packet invalid_negative_x = pandnot(pandnot(pandnot(x_is_neg, abs_x_is_inf), y_is_int), abs_y_is_inf);
+  Packet pow_is_one = por(por(x_is_one, y_is_zero),
+                          pand(x_is_neg_one,
+                               por(abs_y_is_inf, pandnot(y_is_even, invalid_negative_x))));
   Packet pow_is_nan = por(invalid_negative_x, por(x_is_nan, y_is_nan));
-  Packet pow_is_one = por(por(y_is_zero, x_is_one), pand(x_is_neg_one, abs_y_is_inf));
   Packet pow_is_zero = por(por(por(pand(x_is_zero, y_is_pos), pand(abs_x_is_inf, y_is_neg)),
-                               pand(pand(abs_x_is_lt_one, abs_y_is_inf), y_is_pos)),
+                               pand(pand(abs_x_is_lt_one, abs_y_is_huge), y_is_pos)),
-                           pand(pand(abs_x_is_gt_one, abs_y_is_inf), y_is_neg));
+                           pand(pand(abs_x_is_gt_one, abs_y_is_huge), y_is_neg));
   Packet pow_is_inf = por(por(por(pand(x_is_zero, y_is_neg), pand(abs_x_is_inf, y_is_pos)),
-                              pand(pand(abs_x_is_lt_one, abs_y_is_inf), y_is_neg)),
+                              pand(pand(abs_x_is_lt_one, abs_y_is_huge), y_is_neg)),
-                          pand(pand(abs_x_is_gt_one, abs_y_is_inf), y_is_pos));
+                          pand(pand(abs_x_is_gt_one, abs_y_is_huge), y_is_pos));
 
   // General computation of pow(x,y) for positive x or negative x and integer y.
   Packet negate_pow_abs = pandnot(x_is_neg, y_is_even);

test/array_cwise.cpp

@@ -15,18 +15,31 @@ template<typename Scalar>
 void pow_test() {
   const Scalar zero = Scalar(0);
   const Scalar one = Scalar(1);
+  const Scalar two = Scalar(2);
+  const Scalar three = Scalar(3);
   const Scalar sqrt_half = Scalar(std::sqrt(0.5));
   const Scalar sqrt2 = Scalar(std::sqrt(2));
   const Scalar inf = std::numeric_limits<Scalar>::infinity();
   const Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
-  const static Scalar abs_vals[] = {zero, sqrt_half, one, sqrt2, inf, nan};
+  const Scalar min = (std::numeric_limits<Scalar>::min)();
-  const int abs_cases = 6;
+  const Scalar max = (std::numeric_limits<Scalar>::max)();
+  const static Scalar abs_vals[] = {zero,
+                                    sqrt_half,
+                                    one,
+                                    sqrt2,
+                                    two,
+                                    three,
+                                    min,
+                                    max,
+                                    inf,
+                                    nan};
+
+  const int abs_cases = 10;
   const int num_cases = 2*abs_cases * 2*abs_cases;
   // Repeat the same value to make sure we hit the vectorized path.
   const int num_repeats = 32;
   Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases);
   Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases);
-  Array<Scalar, Dynamic, Dynamic> expected(num_repeats, num_cases);
   int count = 0;
   for (int i = 0; i < abs_cases; ++i) {
     const Scalar abs_x = abs_vals[i];
@@ -39,7 +52,6 @@ void pow_test() {
           for (int repeat = 0; repeat < num_repeats; ++repeat) {
             x(repeat, count) = x_case;
             y(repeat, count) = y_case;
-            expected(repeat, count) = numext::pow(x_case, y_case);
           }
           ++count;
         }
@@ -52,8 +64,11 @@ void pow_test() {
   bool all_pass = true;
   for (int i = 0; i < 1; ++i) {
     for (int j = 0; j < num_cases; ++j) {
+      // TODO(rmlarsen): Skip tests that trigger a known bug in pldexp for now.
+      if (std::abs(x(i,j)) == max || std::abs(x(i,j)) == min) continue;
+
+      Scalar e = numext::pow(x(i,j), y(i,j));
       Scalar a = actual(i, j);
-      Scalar e = expected(i, j);
       bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e));
       all_pass &= !fail;
       if (fail) {