Make WINDOW_G configurable

This makes WINDOW_G a configurable value in the range of [3..24].
The upper limit of 24 is a defensive choice. The code is probably
correct for values up to 33 but those larger values yield in huge
tables (>= 256MiB), which are i) unlikely to be really beneficial
in practice and ii) increasingly difficult to test.

configure.ac

@@ -186,6 +186,16 @@ AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
 AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto]
 [Specify assembly optimizations to use. Default is auto (experimental: arm)])],[req_asm=$withval], [req_asm=auto])
 
+# Default is window size 16 (or window size 15 with endomorphism) which needs 1.375 MiB. */
+AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto],
+[window size for ecmult precomputation for verification, specified as integer in range [3..24].]
+[Larger values result in possibly better performance at the cost of an exponentially larger precomputed table.]
+[The table will store 2^(SIZE-2) * 64 bytes of data but can be larger in memory due]
+[to platform-specific padding and alignment. "auto" is a reasonable setting for desktop machines]
+[(currently 15 if the endomorphism optimization is disabled and 16 if it is enabled). [default=auto]]
+)],
+[req_ecmult_window=$withval], [req_ecmult_window=auto])
+
 AC_CHECK_TYPES([__int128])
 
 AC_MSG_CHECKING([for __builtin_expect])
@@ -413,6 +423,32 @@ case $set_scalar in
   ;;
 esac
 
+#set ecmult window size
+if test x"$req_ecmult_window" = x"auto"; then
+    if test x"$use_endomorphism" = x"yes"; then
+        set_ecmult_window=16
+    else
+        set_ecmult_window=15
+    fi
+else
+  set_ecmult_window=$req_ecmult_window
+fi
+
+error_window_size=['window size for ecmult precomputation not an integer in range [3..24] or "auto"']
+case $set_ecmult_window in
+''|*[[!0-9]]*)
+  # no valid integer
+  AC_MSG_ERROR($error_window_size)
+  ;;
+*)
+  if test "$set_ecmult_window" -lt 3 -o "$set_ecmult_window" -gt 24 ; then
+    # not in range
+    AC_MSG_ERROR($error_window_size)
+  fi
+  AC_DEFINE_UNQUOTED(ECMULT_WINDOW_SIZE, $set_ecmult_window, [Set window size for ecmult precomputation])
+  ;;
+esac
+
 if test x"$use_tests" = x"yes"; then
   SECP_OPENSSL_CHECK
   if test x"$has_openssl_ec" = x"yes"; then
@@ -623,6 +659,7 @@ echo "  asm                     = $set_asm"
 echo "  bignum                  = $set_bignum"
 echo "  field                   = $set_field"
 echo "  scalar                  = $set_scalar"
+echo "  ecmult window size      = $set_ecmult_window"
 echo
 echo "  CC                      = $CC"
 echo "  CFLAGS                  = $CFLAGS"

src/ecmult_impl.h

@@ -31,16 +31,27 @@
 #  endif
 #else
 /* optimal for 128-bit and 256-bit exponents. */
-#define WINDOW_A 5
-/** larger numbers may result in slightly better performance, at the cost of
-    exponentially larger precomputed tables. */
-#ifdef USE_ENDOMORPHISM
-/** Two tables for window size 15: 1.375 MiB. */
-#define WINDOW_G 15
-#else
-/** One table for window size 16: 1.375 MiB. */
-#define WINDOW_G 16
+#  define WINDOW_A 5
+/** Larger values for ECMULT_WINDOW_SIZE result in possibly better
+ * performance at the cost of an exponentially larger precomputed
+ * table. The exact table size is
+ *     (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage)  bytes,
+ * where sizeof(secp256k1_ge_storage) is typically 64 bytes but can
+ * be larger due to platform-specific padding and alignment.
+ */
+#  ifdef USE_ENDOMORPHISM
+#    define WINDOW_G ((ECMULT_WINDOW_SIZE)-1)
+#  else
+#    define WINDOW_G (ECMULT_WINDOW_SIZE)
+#  endif
 #endif
+
+/* Noone will ever need more than a window size of 24.
+ * (The code probably works with window sizes up to 33 but
+ * it is not tested for it. For WINDOW_G >= 34, the
+ * expansion of ECMULT_TABLE_SIZE(WINDOW_G) will overflow. */
+#if ECMULT_WINDOW_SIZE < 3 || ECMULT_WINDOW_SIZE > 24
+#  error Set ECMULT_WINDOW_SIZE to an integer in range [3..24].
 #endif
 
 #ifdef USE_ENDOMORPHISM