diff --git a/.cirrus.yml b/.cirrus.yml
index 48c9be8c..7e8ac280 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -231,17 +231,64 @@ task:
   << : *CAT_LOGS
 
 task:
-  name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)"
   << : *LINUX_CONTAINER
   env:
-    WRAPPER_CMD: wine64-stable
-    SECP256K1_TEST_ITERS: 16
-    HOST: x86_64-w64-mingw32
+    WRAPPER_CMD: wine
     WITH_VALGRIND: no
     ECDH: yes
     RECOVERY: yes
     SCHNORRSIG: yes
     CTIMETEST: no
+  matrix:
+    - name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)"
+      env:
+        HOST: x86_64-w64-mingw32
+    - name: "i686 (mingw32-w64): Windows (Debian stable, Wine)"
+      env:
+        HOST: i686-w64-mingw32
+  << : *MERGE_BASE
+  test_script:
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  << : *LINUX_CONTAINER
+  env:
+    WRAPPER_CMD: wine
+    WERROR_CFLAGS: -WX
+    WITH_VALGRIND: no
+    ECDH: yes
+    RECOVERY: yes
+    EXPERIMENTAL: yes
+    SCHNORRSIG: yes
+    ECDSA_S2C: yes
+    GENERATOR: yes
+    RANGEPROOF: yes
+    WHITELIST: yes
+    MUSIG: yes
+    ECDSAADAPTOR: yes
+    BPPP: yes
+    CTIMETEST: no
+    # Set non-essential options that affect the CLI messages here.
+    # (They depend on the user's taste, so we don't want to set them automatically in configure.ac.)
+    CFLAGS: -nologo -diagnostics:caret
+    LDFLAGS: -XCClinker -nologo -XCClinker -diagnostics:caret
+  # Use a MinGW-w64 host to tell ./configure we're building for Windows.
+  # This will detect some MinGW-w64 tools but then make will need only
+  # the MSVC tools CC, AR and NM as specified below.
+  matrix:
+    - name: "x86_64 (MSVC): Windows (Debian stable, Wine)"
+      env:
+        HOST: x86_64-w64-mingw32
+        CC: /opt/msvc/bin/x64/cl
+        AR: /opt/msvc/bin/x64/lib
+        NM: /opt/msvc/bin/x64/dumpbin -symbols -headers
+    - name: "i686 (MSVC): Windows (Debian stable, Wine)"
+      env:
+        HOST: i686-w64-mingw32
+        CC: /opt/msvc/bin/x86/cl
+        AR: /opt/msvc/bin/x86/lib
+        NM: /opt/msvc/bin/x86/dumpbin -symbols -headers
   << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
@@ -301,13 +348,12 @@ task:
   << : *CAT_LOGS
 
 task:
-  name: "C++ -fpermissive"
+  name: "C++ -fpermissive (entire project)"
   << : *LINUX_CONTAINER
   env:
-    # ./configure correctly errors out when given CC=g++.
-    # We hack around this by passing CC=g++ only to make.
-    CC: gcc
-    MAKEFLAGS: -j4 CC=g++ CFLAGS=-fpermissive\ -g
+    CC: g++
+    CFLAGS: -fpermissive -g
+    CPPFLAGS: -DSECP256K1_CPLUSPLUS_TEST_OVERRIDE
     WERROR_CFLAGS:
     ECDH: yes
     RECOVERY: yes
@@ -317,6 +363,14 @@ task:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
 
+task:
+  name: "C++ (public headers)"
+  << : *LINUX_CONTAINER
+  test_script:
+    - g++ -Werror include/*.h
+    - clang -Werror -x c++-header include/*.h
+    - /opt/msvc/bin/x64/cl.exe -c -WX -TP include/*.h
+
 task:
   name: "sage prover"
   << : *LINUX_CONTAINER
diff --git a/build-aux/m4/bitcoin_secp.m4 b/build-aux/m4/bitcoin_secp.m4
index dda770e0..98be915b 100644
--- a/build-aux/m4/bitcoin_secp.m4
+++ b/build-aux/m4/bitcoin_secp.m4
@@ -1,7 +1,7 @@
 dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell.
 AC_DEFUN([SECP_64BIT_ASM_CHECK],[
 AC_MSG_CHECKING(for x86_64 assembly availability)
-AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+AC_LINK_IFELSE([AC_LANG_PROGRAM([[
   #include <stdint.h>]],[[
   uint64_t a = 11, tmp;
   __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
@@ -10,6 +10,7 @@ AC_MSG_RESULT([$has_64bit_asm])
 ])
 
 AC_DEFUN([SECP_VALGRIND_CHECK],[
+AC_MSG_CHECKING([for valgrind support])
 if test x"$has_valgrind" != x"yes"; then
   CPPFLAGS_TEMP="$CPPFLAGS"
   CPPFLAGS="$VALGRIND_CPPFLAGS $CPPFLAGS"
@@ -21,6 +22,7 @@ if test x"$has_valgrind" != x"yes"; then
     #endif
   ]])], [has_valgrind=yes; AC_DEFINE(HAVE_VALGRIND,1,[Define this symbol if valgrind is installed, and it supports the host platform])])
 fi
+AC_MSG_RESULT($has_valgrind)
 ])
 
 dnl SECP_TRY_APPEND_CFLAGS(flags, VAR)
diff --git a/ci/cirrus.sh b/ci/cirrus.sh
index 14c8dbe9..5f80964e 100755
--- a/ci/cirrus.sh
+++ b/ci/cirrus.sh
@@ -5,10 +5,20 @@ set -x
 
 export LC_ALL=C
 
+# Start persistent wineserver if necessary.
+# This speeds up jobs with many invocations of wine (e.g., ./configure with MSVC) tremendously.
+case "$WRAPPER_CMD" in
+    *wine*)
+        # This is apparently only reliable when we run a dummy command such as "hh.exe" afterwards.
+        wineserver -p && wine hh.exe
+        ;;
+esac
+
 env >> test_env.log
 
 $CC -v || true
 valgrind --version || true
+$WRAPPER_CMD --version || true
 
 ./autogen.sh
 
@@ -71,6 +81,9 @@ then
     make precomp
 fi
 
+# Shutdown wineserver again
+wineserver -k || true
+
 # Check that no repo files have been modified by the build.
 # (This fails for example if the precomp files need to be updated in the repo.)
 git diff --exit-code
diff --git a/ci/linux-debian.Dockerfile b/ci/linux-debian.Dockerfile
index 5cccbb55..a83a4e36 100644
--- a/ci/linux-debian.Dockerfile
+++ b/ci/linux-debian.Dockerfile
@@ -1,15 +1,14 @@
 FROM debian:stable
 
-RUN dpkg --add-architecture i386
-RUN dpkg --add-architecture s390x
-RUN dpkg --add-architecture armhf
-RUN dpkg --add-architecture arm64
-RUN dpkg --add-architecture ppc64el
-RUN apt-get update
+RUN dpkg --add-architecture i386 && \
+    dpkg --add-architecture s390x && \
+    dpkg --add-architecture armhf && \
+    dpkg --add-architecture arm64 && \
+    dpkg --add-architecture ppc64el
 
 # dkpg-dev: to make pkg-config work in cross-builds
 # llvm: for llvm-symbolizer, which is used by clang's UBSan for symbolized stack traces
-RUN apt-get install --no-install-recommends --no-upgrade -y \
+RUN apt-get update && apt-get install --no-install-recommends -y \
         git ca-certificates \
         make automake libtool pkg-config dpkg-dev valgrind qemu-user \
         gcc clang llvm libc6-dbg \
@@ -19,8 +18,20 @@ RUN apt-get install --no-install-recommends --no-upgrade -y \
         gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \
         gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \
         gcc-powerpc64le-linux-gnu libc6-dev-ppc64el-cross libc6-dbg:ppc64el \
-        wine gcc-mingw-w64-x86-64 \
+        gcc-mingw-w64-x86-64-win32 wine64 wine \
+        gcc-mingw-w64-i686-win32 wine32 \
         sagemath
 
-# Run a dummy command in wine to make it set up configuration
-RUN wine64-stable xcopy || true
+WORKDIR /root
+# The "wine" package provides a convience wrapper that we need
+RUN apt-get update && apt-get install --no-install-recommends -y \
+        git ca-certificates wine64 wine python3-simplejson python3-six msitools winbind procps && \
+    git clone https://github.com/mstorsjo/msvc-wine && \
+    mkdir /opt/msvc && \
+    python3 msvc-wine/vsdownload.py --accept-license --dest /opt/msvc Microsoft.VisualStudio.Workload.VCTools && \
+    msvc-wine/install.sh /opt/msvc
+
+# Initialize the wine environment. Wait until the wineserver process has
+# exited before closing the session, to avoid corrupting the wine prefix.
+RUN wine64 wineboot --init && \
+    while (ps -A | grep wineserver) > /dev/null; do sleep 1; done
diff --git a/configure.ac b/configure.ac
index c168694c..e2407db9 100644
--- a/configure.ac
+++ b/configure.ac
@@ -33,14 +33,18 @@ AM_INIT_AUTOMAKE([1.11.2 foreign subdir-objects])
 m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])])
 
 AC_PROG_CC
-if test x"$ac_cv_prog_cc_c89" = x"no"; then
-  AC_MSG_ERROR([c89 compiler support required])
-fi
 AM_PROG_AS
 AM_PROG_AR
 
+# Clear some cache variables as a workaround for a bug that appears due to a bad
+# interaction between AM_PROG_AR and LT_INIT when combining MSVC's archiver lib.exe.
+# https://debbugs.gnu.org/cgi/bugreport.cgi?bug=54421
+AS_UNSET(ac_cv_prog_AR)
+AS_UNSET(ac_cv_prog_ac_ct_AR)
 LT_INIT([win32-dll])
 
+PKG_PROG_PKG_CONFIG
+
 build_windows=no
 
 case $host_os in
@@ -87,23 +91,35 @@ esac
 #
 # TODO We should analogously not touch CPPFLAGS and LDFLAGS but currently there are no issues.
 AC_DEFUN([SECP_TRY_APPEND_DEFAULT_CFLAGS], [
-    # Try to append -Werror=unknown-warning-option to CFLAGS temporarily. Otherwise clang will
-    # not error out if it gets unknown warning flags and the checks here will always succeed
-    # no matter if clang knows the flag or not.
-    SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS="$CFLAGS"
-    SECP_TRY_APPEND_CFLAGS([-Werror=unknown-warning-option], CFLAGS)
+    # GCC and compatible (incl. clang)
+    if test "x$GCC" = "xyes"; then
+      # Try to append -Werror=unknown-warning-option to CFLAGS temporarily. Otherwise clang will
+      # not error out if it gets unknown warning flags and the checks here will always succeed
+      # no matter if clang knows the flag or not.
+      SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS="$CFLAGS"
+      SECP_TRY_APPEND_CFLAGS([-Werror=unknown-warning-option], CFLAGS)
 
-    SECP_TRY_APPEND_CFLAGS([-std=c89 -pedantic -Wno-long-long -Wnested-externs -Wshadow -Wstrict-prototypes -Wundef], $1) # GCC >= 3.0, -Wlong-long is implied by -pedantic.
-    SECP_TRY_APPEND_CFLAGS([-Wno-overlength-strings], $1) # GCC >= 4.2, -Woverlength-strings is implied by -pedantic.
-    SECP_TRY_APPEND_CFLAGS([-Wall], $1) # GCC >= 2.95 and probably many other compilers
-    SECP_TRY_APPEND_CFLAGS([-Wno-unused-function], $1) # GCC >= 3.0, -Wunused-function is implied by -Wall.
-    SECP_TRY_APPEND_CFLAGS([-Wextra], $1) # GCC >= 3.4, this is the newer name of -W, which we don't use because older GCCs will warn about unused functions.
-    SECP_TRY_APPEND_CFLAGS([-Wcast-align], $1) # GCC >= 2.95
-    SECP_TRY_APPEND_CFLAGS([-Wcast-align=strict], $1) # GCC >= 8.0
-    SECP_TRY_APPEND_CFLAGS([-Wconditional-uninitialized], $1) # Clang >= 3.0 only
-    SECP_TRY_APPEND_CFLAGS([-fvisibility=hidden], $1) # GCC >= 4.0
+      SECP_TRY_APPEND_CFLAGS([-std=c89 -pedantic -Wno-long-long -Wnested-externs -Wshadow -Wstrict-prototypes -Wundef], $1) # GCC >= 3.0, -Wlong-long is implied by -pedantic.
+      SECP_TRY_APPEND_CFLAGS([-Wno-overlength-strings], $1) # GCC >= 4.2, -Woverlength-strings is implied by -pedantic.
+      SECP_TRY_APPEND_CFLAGS([-Wall], $1) # GCC >= 2.95 and probably many other compilers
+      SECP_TRY_APPEND_CFLAGS([-Wno-unused-function], $1) # GCC >= 3.0, -Wunused-function is implied by -Wall.
+      SECP_TRY_APPEND_CFLAGS([-Wextra], $1) # GCC >= 3.4, this is the newer name of -W, which we don't use because older GCCs will warn about unused functions.
+      SECP_TRY_APPEND_CFLAGS([-Wcast-align], $1) # GCC >= 2.95
+      SECP_TRY_APPEND_CFLAGS([-Wcast-align=strict], $1) # GCC >= 8.0
+      SECP_TRY_APPEND_CFLAGS([-Wconditional-uninitialized], $1) # Clang >= 3.0 only
+      SECP_TRY_APPEND_CFLAGS([-fvisibility=hidden], $1) # GCC >= 4.0
 
-    CFLAGS="$SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS"
+      CFLAGS="$SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS"
+    fi
+
+    # MSVC
+    # Assume MSVC if we're building for Windows but not with GCC or compatible;
+    # libtool makes the same assumption internally.
+    # Note that "/opt" and "-opt" are equivalent for MSVC; we use "-opt" because "/opt" looks like a path.
+    if test x"$GCC" != x"yes" && test x"$build_windows" = x"yes"; then
+      SECP_TRY_APPEND_CFLAGS([-W2 -wd4146], $1) # Moderate warning level, disable warning C4146 "unary minus operator applied to unsigned type, result still unsigned"
+      SECP_TRY_APPEND_CFLAGS([-external:anglebrackets -external:W0], $1) # Suppress warnings from #include <...> files
+    fi
 ])
 SECP_TRY_APPEND_DEFAULT_CFLAGS(SECP_CFLAGS)
 
@@ -383,7 +399,9 @@ if test x"$enable_valgrind" = x"yes"; then
   SECP_INCLUDES="$SECP_INCLUDES $VALGRIND_CPPFLAGS"
 fi
 
-# Add -Werror and similar flags passed from the outside (for testing, e.g., in CI)
+# Add -Werror and similar flags passed from the outside (for testing, e.g., in CI).
+# We don't want to set the user variable CFLAGS in CI because this would disable
+# autoconf's logic for setting default CFLAGS, which we would like to test in CI.
 SECP_CFLAGS="$SECP_CFLAGS $WERROR_CFLAGS"
 
 ###
diff --git a/include/secp256k1.h b/include/secp256k1.h
index 86ab7e55..dddab346 100644
--- a/include/secp256k1.h
+++ b/include/secp256k1.h
@@ -141,9 +141,13 @@ typedef int (*secp256k1_nonce_function)(
 # define SECP256K1_NO_BUILD
 #endif
 
+/** At secp256k1 build-time DLL_EXPORT is defined when building objects destined
+ *  for a shared library, but not for those intended for static libraries.
+ */
+
 #ifndef SECP256K1_API
 # if defined(_WIN32)
-#  ifdef SECP256K1_BUILD
+#  if defined(SECP256K1_BUILD) && defined(DLL_EXPORT)
 #   define SECP256K1_API __declspec(dllexport)
 #  else
 #   define SECP256K1_API
diff --git a/sage/prove_group_implementations.sage b/sage/prove_group_implementations.sage
index 96ce3350..652bd87f 100644
--- a/sage/prove_group_implementations.sage
+++ b/sage/prove_group_implementations.sage
@@ -40,29 +40,26 @@ def formula_secp256k1_gej_add_var(branch, a, b):
   s2 = s2 * a.Z
   h = -u1
   h = h + u2
-  i = -s1
-  i = i + s2
+  i = -s2
+  i = i + s1
   if branch == 2:
     r = formula_secp256k1_gej_double_var(a)
     return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r)
   if branch == 3:
     return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity())
-  i2 = i^2
+  t = h * b.Z
+  rz = a.Z * t
   h2 = h^2
+  h2 = -h2
   h3 = h2 * h
-  h = h * b.Z
-  rz = a.Z * h
   t = u1 * h2
-  rx = t
-  rx = rx * 2
+  rx = i^2
   rx = rx + h3
-  rx = -rx
-  rx = rx + i2
-  ry = -rx
-  ry = ry + t
-  ry = ry * i
+  rx = rx + t
+  rx = rx + t
+  t = t + rx
+  ry = t * i
   h3 = h3 * s1
-  h3 = -h3
   ry = ry + h3
   return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
 
@@ -80,28 +77,25 @@ def formula_secp256k1_gej_add_ge_var(branch, a, b):
   s2 = s2 * a.Z
   h = -u1
   h = h + u2
-  i = -s1
-  i = i + s2
+  i = -s2
+  i = i + s1
   if (branch == 2):
     r = formula_secp256k1_gej_double_var(a)
     return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
   if (branch == 3):
     return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
-  i2 = i^2
-  h2 = h^2
-  h3 = h * h2
   rz = a.Z * h
+  h2 = h^2
+  h2 = -h2
+  h3 = h2 * h
   t = u1 * h2
-  rx = t
-  rx = rx * 2
+  rx = i^2
   rx = rx + h3
-  rx = -rx
-  rx = rx + i2
-  ry = -rx
-  ry = ry + t
-  ry = ry * i
+  rx = rx + t
+  rx = rx + t
+  t = t + rx
+  ry = t * i
   h3 = h3 * s1
-  h3 = -h3
   ry = ry + h3
   return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
 
@@ -109,14 +103,15 @@ def formula_secp256k1_gej_add_zinv_var(branch, a, b):
   """libsecp256k1's secp256k1_gej_add_zinv_var"""
   bzinv = b.Z^(-1)
   if branch == 0:
-    return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a)
-  if branch == 1:
+    rinf = b.Infinity
     bzinv2 = bzinv^2
     bzinv3 = bzinv2 * bzinv
     rx = b.X * bzinv2
     ry = b.Y * bzinv3
     rz = 1
-    return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz))
+    return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz, rinf))
+  if branch == 1:
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
   azz = a.Z * bzinv
   z12 = azz^2
   u1 = a.X
@@ -126,29 +121,25 @@ def formula_secp256k1_gej_add_zinv_var(branch, a, b):
   s2 = s2 * azz
   h = -u1
   h = h + u2
-  i = -s1
-  i = i + s2
+  i = -s2
+  i = i + s1
   if branch == 2:
     r = formula_secp256k1_gej_double_var(a)
     return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
   if branch == 3:
     return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
-  i2 = i^2
+  rz = a.Z * h
   h2 = h^2
-  h3 = h * h2
-  rz = a.Z
-  rz = rz * h
+  h2 = -h2
+  h3 = h2 * h
   t = u1 * h2
-  rx = t
-  rx = rx * 2
+  rx = i^2
   rx = rx + h3
-  rx = -rx
-  rx = rx + i2
-  ry = -rx
-  ry = ry + t
-  ry = ry * i
+  rx = rx + t
+  rx = rx + t
+  t = t + rx
+  ry = t * i
   h3 = h3 * s1
-  h3 = -h3
   ry = ry + h3
   return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
 
diff --git a/src/bench.h b/src/bench.h
index aa275fe9..611ba11f 100644
--- a/src/bench.h
+++ b/src/bench.h
@@ -7,15 +7,31 @@
 #ifndef SECP256K1_BENCH_H
 #define SECP256K1_BENCH_H
 
+#include <stdlib.h>
 #include <stdint.h>
 #include <stdio.h>
 #include <string.h>
-#include "sys/time.h"
+
+#if (defined(_MSC_VER) && _MSC_VER >= 1900)
+#  include <time.h>
+#else
+#  include "sys/time.h"
+#endif
 
 static int64_t gettime_i64(void) {
+#if (defined(_MSC_VER) && _MSC_VER >= 1900)
+    /* C11 way to get wallclock time */
+    struct timespec tv;
+    if (!timespec_get(&tv, TIME_UTC)) {
+        fputs("timespec_get failed!", stderr);
+        exit(1);
+    }
+    return (int64_t)tv.tv_nsec / 1000 + (int64_t)tv.tv_sec * 1000000LL;
+#else
     struct timeval tv;
     gettimeofday(&tv, NULL);
     return (int64_t)tv.tv_usec + (int64_t)tv.tv_sec * 1000000LL;
+#endif
 }
 
 #define FP_EXP (6)
diff --git a/src/bench_internal.c b/src/bench_internal.c
index 898c7801..b415316a 100644
--- a/src/bench_internal.c
+++ b/src/bench_internal.c
@@ -283,6 +283,15 @@ void bench_group_jacobi_var(void* arg, int iters) {
     CHECK(j <= iters);
 }
 
+void bench_group_add_zinv_var(void* arg, int iters) {
+    int i;
+    bench_inv *data = (bench_inv*)arg;
+
+    for (i = 0; i < iters; i++) {
+        secp256k1_gej_add_zinv_var(&data->gej[0], &data->gej[0], &data->ge[1], &data->gej[0].y);
+    }
+}
+
 void bench_group_to_affine_var(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
@@ -405,6 +414,7 @@ int main(int argc, char **argv) {
     if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, iters*10);
     if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, iters*10);
     if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "jacobi")) run_benchmark("group_jacobi_var", bench_group_jacobi_var, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_zinv_var", bench_group_add_zinv_var, bench_setup, NULL, &data, 10, iters*10);
     if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "to_affine")) run_benchmark("group_to_affine_var", bench_group_to_affine_var, bench_setup, NULL, &data, 10, iters);
 
     if (d || have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, iters);
diff --git a/src/group.h b/src/group.h
index 8a6adfe9..633b50c3 100644
--- a/src/group.h
+++ b/src/group.h
@@ -23,7 +23,7 @@ typedef struct {
 #define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
 
 /** A group element of the secp256k1 curve, in jacobian coordinates.
- *  Note: For exhastive test mode, sepc256k1 is replaced by a small subgroup of a different curve.
+ *  Note: For exhastive test mode, secp256k1 is replaced by a small subgroup of a different curve.
  */
 typedef struct {
     secp256k1_fe x; /* actual X: x/z^2 */
diff --git a/src/group_impl.h b/src/group_impl.h
index d52bba45..541728a4 100644
--- a/src/group_impl.h
+++ b/src/group_impl.h
@@ -334,15 +334,14 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
 }
 
 static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
-    /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
-    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    /* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
+    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         *r = *b;
         return;
     }
-
     if (b->infinity) {
         if (rzr != NULL) {
             secp256k1_fe_set_int(rzr, 1);
@@ -351,7 +350,6 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
         return;
     }
 
-    r->infinity = 0;
     secp256k1_fe_sqr(&z22, &b->z);
     secp256k1_fe_sqr(&z12, &a->z);
     secp256k1_fe_mul(&u1, &a->x, &z22);
@@ -359,7 +357,7 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
     secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
     secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, rzr);
@@ -371,24 +369,33 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
         }
         return;
     }
-    secp256k1_fe_sqr(&i2, &i);
-    secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
-    secp256k1_fe_mul(&h, &h, &b->z);
+
+    r->infinity = 0;
+    secp256k1_fe_mul(&t, &h, &b->z);
     if (rzr != NULL) {
-        *rzr = h;
+        *rzr = t;
     }
-    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&r->z, &a->z, &t);
+
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_negate(&h2, &h2, 1);
+    secp256k1_fe_mul(&h3, &h2, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+
+    secp256k1_fe_sqr(&r->x, &i);
+    secp256k1_fe_add(&r->x, &h3);
+    secp256k1_fe_add(&r->x, &t);
+    secp256k1_fe_add(&r->x, &t);
+
+    secp256k1_fe_add(&t, &r->x);
+    secp256k1_fe_mul(&r->y, &t, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
 }
 
 static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
-    /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
-    secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    /* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
+    secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t;
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         secp256k1_gej_set_ge(r, b);
@@ -401,7 +408,6 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
         *r = *a;
         return;
     }
-    r->infinity = 0;
 
     secp256k1_fe_sqr(&z12, &a->z);
     u1 = a->x; secp256k1_fe_normalize_weak(&u1);
@@ -409,7 +415,7 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
     s1 = a->y; secp256k1_fe_normalize_weak(&s1);
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
     secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, rzr);
@@ -421,28 +427,33 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
         }
         return;
     }
-    secp256k1_fe_sqr(&i2, &i);
-    secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
+
+    r->infinity = 0;
     if (rzr != NULL) {
         *rzr = h;
     }
     secp256k1_fe_mul(&r->z, &a->z, &h);
+
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_negate(&h2, &h2, 1);
+    secp256k1_fe_mul(&h3, &h2, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+
+    secp256k1_fe_sqr(&r->x, &i);
+    secp256k1_fe_add(&r->x, &h3);
+    secp256k1_fe_add(&r->x, &t);
+    secp256k1_fe_add(&r->x, &t);
+
+    secp256k1_fe_add(&t, &r->x);
+    secp256k1_fe_mul(&r->y, &t, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
 }
 
 static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
-    /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
-    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    /* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
+    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
-    if (b->infinity) {
-        *r = *a;
-        return;
-    }
     if (a->infinity) {
         secp256k1_fe bzinv2, bzinv3;
         r->infinity = b->infinity;
@@ -453,7 +464,10 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
         secp256k1_fe_set_int(&r->z, 1);
         return;
     }
-    r->infinity = 0;
+    if (b->infinity) {
+        *r = *a;
+        return;
+    }
 
     /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
      *  secp256k1's isomorphism we can multiply the Z coordinates on both sides
@@ -471,7 +485,7 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
     s1 = a->y; secp256k1_fe_normalize_weak(&s1);
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
     secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, NULL);
@@ -480,14 +494,23 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
         }
         return;
     }
-    secp256k1_fe_sqr(&i2, &i);
+
+    r->infinity = 0;
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+
     secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
-    r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
+    secp256k1_fe_negate(&h2, &h2, 1);
+    secp256k1_fe_mul(&h3, &h2, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+
+    secp256k1_fe_sqr(&r->x, &i);
+    secp256k1_fe_add(&r->x, &h3);
+    secp256k1_fe_add(&r->x, &t);
+    secp256k1_fe_add(&r->x, &t);
+
+    secp256k1_fe_add(&t, &r->x);
+    secp256k1_fe_mul(&r->y, &t, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
 }
 
diff --git a/src/modules/schnorrsig/bench_impl.h b/src/modules/schnorrsig/bench_impl.h
index 41f393c8..84a17274 100644
--- a/src/modules/schnorrsig/bench_impl.h
+++ b/src/modules/schnorrsig/bench_impl.h
@@ -91,10 +91,12 @@ void run_schnorrsig_bench(int iters, int argc, char** argv) {
         free((void *)data.msgs[i]);
         free((void *)data.sigs[i]);
     }
-    free(data.keypairs);
-    free(data.pk);
-    free(data.msgs);
-    free(data.sigs);
+
+    /* Casting to (void *) avoids a stupid warning in MSVC. */
+    free((void *)data.keypairs);
+    free((void *)data.pk);
+    free((void *)data.msgs);
+    free((void *)data.sigs);
 
     secp256k1_context_destroy(data.ctx);
 }
diff --git a/src/scratch_impl.h b/src/scratch_impl.h
index 688e18eb..f71a20b9 100644
--- a/src/scratch_impl.h
+++ b/src/scratch_impl.h
@@ -25,11 +25,11 @@ static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* err
 
 static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch) {
     if (scratch != NULL) {
-        VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */
         if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
             secp256k1_callback_call(error_callback, "invalid scratch space");
             return;
         }
+        VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */
         memset(scratch->magic, 0, sizeof(scratch->magic));
         free(scratch);
     }
diff --git a/src/secp256k1.c b/src/secp256k1.c
index bc07b290..bbe9567b 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -4,6 +4,17 @@
  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  ***********************************************************************/
 
+/* This is a C project. It should not be compiled with a C++ compiler,
+ * and we error out if we detect one.
+ *
+ * We still want to be able to test the project with a C++ compiler
+ * because it is still good to know if this will lead to real trouble, so
+ * there is a possibility to override the check. But be warned that
+ * compiling with a C++ compiler is not supported. */
+#if defined(__cplusplus) && !defined(SECP256K1_CPLUSPLUS_TEST_OVERRIDE)
+#error Trying to compile a C project with a C++ compiler.
+#endif
+
 #define SECP256K1_BUILD
 
 #include "../include/secp256k1.h"