Revert to using the approximate exponential in the gravity long-range truncation.

src/approx_math.h

@@ -49,4 +49,16 @@ __attribute__((always_inline)) INLINE static float good_approx_expf(float x) {
                              x * ((1.f / 120.f) + (1.f / 720.f) * x)))));
 }
 
+/**
+ * @brief Approximate version of exp(x) using a 6th order Taylor expansion
+ */
+__attribute__((always_inline)) INLINE static double good_approx_exp(double x) {
+  return 1. +
+         x * (1. +
+              x * (0.5 +
+                   x * ((1. / 6.) +
+                        x * ((1. / 24.) +
+                             x * ((1. / 120.) + (1. / 720.) * x)))));
+}
+
 #endif /* SWIFT_APPROX_MATH_H */

src/kernel_long_gravity.h

@@ -49,7 +49,7 @@ __attribute__((always_inline)) INLINE static void kernel_long_grav_pot_eval(
 #else
 
   const float x = 2.f * u;
-  const float exp_x = expf(x);
+  const float exp_x = good_approx_expf(x);
   const float alpha = 1.f / (1.f + exp_x);
 
   /* We want 2 - 2 exp(x) * alpha */
@@ -83,7 +83,7 @@ __attribute__((always_inline)) INLINE static void kernel_long_grav_force_eval(
 #else
 
   const float arg = 2.f * u;
-  const float exp_arg = expf(arg);
+  const float exp_arg = good_approx_expf(arg);
   const float term = 1.f / (1.f + exp_arg);
 
   *W = arg * exp_arg * term * term - exp_arg * term + 1.f;
@@ -111,4 +111,4 @@ __attribute__((always_inline)) INLINE static void fourier_kernel_long_grav_eval(
 #endif
 }
 
-#endif  // SWIFT_KERNEL_LONG_GRAVITY_H
+#endif /* SWIFT_KERNEL_LONG_GRAVITY_H */

tests/testPotentialSelf.c

@@ -41,15 +41,18 @@ const double eps = 0.02;
  * @param s String used to identify this check in messages
  */
 void check_value(double a, double b, const char *s) {
-  if (fabs(a - b) / fabs(a + b) > 2e-6 && fabs(a - b) > 1.e-6)
+  if (fabs(a - b) / fabs(a + b) > 1e-6 && fabs(a - b) > 1.e-6)
     error("Values are inconsistent: %12.15e %12.15e (%s)!", a, b, s);
 }
 
 /* Definitions of the potential and force that match
    exactly the theory document */
-double S(double x) { return exp(x) / (1. + exp(x)); }
+double S(double x) { return good_approx_exp(x) / (1. + good_approx_exp(x)); }
 
-double S_prime(double x) { return exp(x) / ((1. + exp(x)) * (1. + exp(x))); }
+double S_prime(double x) {
+  return good_approx_exp(x) /
+         ((1. + good_approx_exp(x)) * (1. + good_approx_exp(x)));
+}
 
 double potential(double mass, double r, double H, double rlr) {