Update accuracy comments and tighten bounds for FastPow

PiperOrigin-RevId: 909544721

Author: Nikhil0250

hwy/contrib/math/fast_math-inl.h

@@ -1882,7 +1882,7 @@ HWY_INLINE V FastLog1p(const D d, V x) {
  * Valid Lane Types: float32, float64
  * Valid Range: float32: base in (0, +FLT_MAX], exp * log(base) in [-25.0,
  * +25.0] float64: base in (0, +DBL_MAX], exp * log(base) in [-25.0, +25.0] Max
- * Relative Error for Valid Range: float32 : 0.27%, float64 : 0.22%
+ * Relative Error for Valid Range: float32 : 0.03%, float64 : 0.03%
  * @return base^exp
  */
 // If false, subnormals are treated as zero.

hwy/contrib/math/math_test.cc

@@ -581,7 +581,7 @@ struct TestFastPow {
               max_error_base = static_cast<double>(base);
               max_error_exp = static_cast<double>(exp_val);
             }
-            if (rel > 0.006) {
+            if (rel > 0.0003) {
               static int print_count = 0;
               if (print_count < 10) {
                 fprintf(stderr,
@@ -590,7 +590,7 @@ struct TestFastPow {
                         hwy::TypeName(T(), Lanes(d)).c_str(),
                         static_cast<double>(base), static_cast<double>(exp_val),
                         static_cast<double>(expected),
-                        static_cast<double>(actual), rel, 0.006);
+                        static_cast<double>(actual), rel, 0.0003);
                 print_count++;
               }
             }
@@ -601,7 +601,7 @@ struct TestFastPow {
     fprintf(stderr, "%s: FastPow max_rel_error %E at base=%E exp=%E\n",
             hwy::TypeName(T(), Lanes(d)).c_str(), max_actual_rel_error,
             max_error_base, max_error_exp);
-    HWY_ASSERT(max_actual_rel_error <= 0.006);
+    HWY_ASSERT(max_actual_rel_error <= 0.0003);
   }
 };