Add _fe_half and use in _gej_add_ge

- Trades 1 _half for 3 _mul_int and 2 _normalize_weak
- Updated formula and comments in _gej_add_ge
- Added internal benchmark for _fe_half

src/bench_internal.c

@@ -140,6 +140,15 @@ void bench_scalar_inverse_var(void* arg, int iters) {
     CHECK(j <= iters);
 }
 
+void bench_field_half(void* arg, int iters) {
+    int i;
+    bench_inv *data = (bench_inv*)arg;
+
+    for (i = 0; i < iters; i++) {
+        secp256k1_fe_half(&data->fe[0]);
+    }
+}
+
 void bench_field_normalize(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
@@ -354,6 +363,7 @@ int main(int argc, char **argv) {
     if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, iters);
     if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, iters);
 
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "half")) run_benchmark("field_half", bench_field_half, bench_setup, NULL, &data, 10, iters*100);
     if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, iters*100);
     if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, iters*100);
     if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, iters*10);