diff --git a/configure.ac b/configure.ac
index 786d8dcfb9..8975fe0f26 100644
--- a/configure.ac
+++ b/configure.ac
@@ -62,27 +62,6 @@ case $host_os in
    ;;
 esac
 
-CFLAGS="$CFLAGS -W"
-
-warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wno-unused-function -Wno-long-long -Wno-overlength-strings"
-saved_CFLAGS="$CFLAGS"
-CFLAGS="$CFLAGS $warn_CFLAGS"
-AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}])
-AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
-    [ AC_MSG_RESULT([yes]) ],
-    [ AC_MSG_RESULT([no])
-      CFLAGS="$saved_CFLAGS"
-    ])
-
-saved_CFLAGS="$CFLAGS"
-CFLAGS="$CFLAGS -fvisibility=hidden"
-AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden])
-AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
-    [ AC_MSG_RESULT([yes]) ],
-    [ AC_MSG_RESULT([no])
-      CFLAGS="$saved_CFLAGS"
-    ])
-
 AC_ARG_ENABLE(benchmark,
     AS_HELP_STRING([--enable-benchmark],[compile benchmark (default is no)]),
     [use_benchmark=$enableval],
@@ -130,6 +109,42 @@ AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
 AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|no|auto]
 [Specify assembly optimizations to use. Default is auto])],[req_asm=$withval], [req_asm=auto])
 
+CFLAGS="$CFLAGS -W"
+
+dnl There are a few intentionally unused functions if you are not building with all the bells and whistles.
+warn_unused_CFLAGS="-Wno-unused-function"
+dnl if all modules are enabled and no static precomp, don't add -Wno-unused-function
+if test x"$use_ecmult_static_precomputation" = x"no"; then
+ if test x"$enable_module_ecdh" = x"yes"; then
+  if test x"$enable_module_schnorr" = x"yes"; then
+   if test x"$enable_module_recovery" = x"yes"; then
+    warn_unused_CFLAGS=""
+   fi
+  fi
+ fi
+fi
+
+dnl -Wno-overlength-strings is needed by some versions of clang due to spurious warnings on assembly code.
+warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wno-long-long -Wno-overlength-strings $warn_unused_CFLAGS"
+
+saved_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS $warn_CFLAGS"
+AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
+    [ AC_MSG_RESULT([yes]) ],
+    [ AC_MSG_RESULT([no])
+      CFLAGS="$saved_CFLAGS"
+    ])
+
+saved_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS -fvisibility=hidden"
+AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
+    [ AC_MSG_RESULT([yes]) ],
+    [ AC_MSG_RESULT([no])
+      CFLAGS="$saved_CFLAGS"
+    ])
+
 AC_CHECK_TYPES([__int128])
 
 AC_MSG_CHECKING([for __builtin_expect])
diff --git a/src/ecdsa.h b/src/ecdsa.h
index 4c0a4a89e0..54ae101b92 100644
--- a/src/ecdsa.h
+++ b/src/ecdsa.h
@@ -17,6 +17,5 @@ static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, c
 static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
 static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
 static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid);
 
 #endif
diff --git a/src/ecdsa_impl.h b/src/ecdsa_impl.h
index 4a172b3c51..07493faf74 100644
--- a/src/ecdsa_impl.h
+++ b/src/ecdsa_impl.h
@@ -187,39 +187,6 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
     return 0;
 }
 
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
-    unsigned char brx[32];
-    secp256k1_fe fx;
-    secp256k1_ge x;
-    secp256k1_gej xj;
-    secp256k1_scalar rn, u1, u2;
-    secp256k1_gej qj;
-
-    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
-        return 0;
-    }
-
-    secp256k1_scalar_get_b32(brx, sigr);
-    VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
-    if (recid & 2) {
-        if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
-            return 0;
-        }
-        secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
-    }
-    if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
-        return 0;
-    }
-    secp256k1_gej_set_ge(&xj, &x);
-    secp256k1_scalar_inverse_var(&rn, sigr);
-    secp256k1_scalar_mul(&u1, &rn, message);
-    secp256k1_scalar_negate(&u1, &u1);
-    secp256k1_scalar_mul(&u2, &rn, sigs);
-    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
-    secp256k1_ge_set_gej_var(pubkey, &qj);
-    return !secp256k1_gej_is_infinity(&qj);
-}
-
 static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
     unsigned char b[32];
     secp256k1_gej rp;
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 212cc5396a..ff18acf9fb 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -40,10 +40,6 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
     }
     VERIFY_CHECK(r == 1);
 }
-#else
-static void secp256k1_fe_verify(const secp256k1_fe *a) {
-    (void)a;
-}
 #endif
 
 static void secp256k1_fe_normalize(secp256k1_fe *r) {
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index b31e24ab81..b9399f4a1f 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -50,10 +50,6 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
     }
     VERIFY_CHECK(r == 1);
 }
-#else
-static void secp256k1_fe_verify(const secp256k1_fe *a) {
-    (void)a;
-}
 #endif
 
 static void secp256k1_fe_normalize(secp256k1_fe *r) {
diff --git a/src/group.h b/src/group.h
index 3310af9a71..04cf2bbf93 100644
--- a/src/group.h
+++ b/src/group.h
@@ -58,6 +58,9 @@ static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
 /** Set a group element equal to another which is given in jacobian coordinates */
 static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
 
+/** Set a group element equal to another which is given in jacobian coordinates */
+static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a);
+
 /** Set a batch of group elements equal to the inputs given in jacobian coordinates */
 static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb);
 
diff --git a/src/group_impl.h b/src/group_impl.h
index bb999df3e6..aed24d24da 100644
--- a/src/group_impl.h
+++ b/src/group_impl.h
@@ -211,26 +211,6 @@ static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
     return a->infinity;
 }
 
-static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
-    secp256k1_fe y2, x3, z2, z6;
-    if (a->infinity) {
-        return 0;
-    }
-    /** y^2 = x^3 + 7
-     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
-     *  Y^2 / Z^6 = X^3 / Z^6 + 7
-     *  Y^2 = X^3 + 7*Z^6
-     */
-    secp256k1_fe_sqr(&y2, &a->y);
-    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
-    secp256k1_fe_sqr(&z2, &a->z);
-    secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
-    secp256k1_fe_mul_int(&z6, 7);
-    secp256k1_fe_add(&x3, &z6);
-    secp256k1_fe_normalize_weak(&x3);
-    return secp256k1_fe_equal_var(&y2, &x3);
-}
-
 static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
     secp256k1_fe y2, x3, c;
     if (a->infinity) {
diff --git a/src/modules/recovery/main_impl.h b/src/modules/recovery/main_impl.h
index 75b6958940..143993e99c 100644
--- a/src/modules/recovery/main_impl.h
+++ b/src/modules/recovery/main_impl.h
@@ -130,6 +130,39 @@ int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecd
     return ret;
 }
 
+static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
+    unsigned char brx[32];
+    secp256k1_fe fx;
+    secp256k1_ge x;
+    secp256k1_gej xj;
+    secp256k1_scalar rn, u1, u2;
+    secp256k1_gej qj;
+
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+
+    secp256k1_scalar_get_b32(brx, sigr);
+    VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
+    if (recid & 2) {
+        if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+            return 0;
+        }
+        secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
+    }
+    if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&xj, &x);
+    secp256k1_scalar_inverse_var(&rn, sigr);
+    secp256k1_scalar_mul(&u1, &rn, message);
+    secp256k1_scalar_negate(&u1, &u1);
+    secp256k1_scalar_mul(&u2, &rn, sigs);
+    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
+    secp256k1_ge_set_gej_var(pubkey, &qj);
+    return !secp256k1_gej_is_infinity(&qj);
+}
+
 int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32) {
     secp256k1_ge q;
     secp256k1_scalar r, s;
diff --git a/src/num.h b/src/num.h
index ebfa71eb44..0739fdd83a 100644
--- a/src/num.h
+++ b/src/num.h
@@ -19,8 +19,6 @@
 #error "Please select num implementation"
 #endif
 
-/** Copy a number. */
-static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a);
 
 /** Convert a number's absolute value to a binary big-endian string.
  *  There must be enough place. */
@@ -32,37 +30,6 @@ static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsi
 /** Compute a modular inverse. The input must be less than the modulus. */
 static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
 
-/** Compare the absolute value of two numbers. */
-static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
-
-/** Test whether two number are equal (including sign). */
-static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b);
-
-/** Add two (signed) numbers. */
-static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
-
-/** Subtract two (signed) numbers. */
-static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
-
-/** Multiply two (signed) numbers. */
-static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
-
-/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
-    even if r was negative. */
-static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m);
-
-/** Right-shift the passed number by bits bits. */
-static void secp256k1_num_shift(secp256k1_num *r, int bits);
-
-/** Check whether a number is zero. */
-static int secp256k1_num_is_zero(const secp256k1_num *a);
-
-/** Check whether a number is strictly negative. */
-static int secp256k1_num_is_neg(const secp256k1_num *a);
-
-/** Change a number's sign. */
-static void secp256k1_num_negate(secp256k1_num *r);
-
 #endif
 
 #endif
diff --git a/src/num_gmp_impl.h b/src/num_gmp_impl.h
index f43e7a56cc..b677447675 100644
--- a/src/num_gmp_impl.h
+++ b/src/num_gmp_impl.h
@@ -22,10 +22,6 @@ static void secp256k1_num_sanity(const secp256k1_num *a) {
 #define secp256k1_num_sanity(a) do { } while(0)
 #endif
 
-static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
-    *r = *a;
-}
-
 static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) {
     unsigned char tmp[65];
     int len = 0;
@@ -59,44 +55,6 @@ static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsi
     }
 }
 
-static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
-    mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
-    r->limbs = a->limbs;
-    if (c != 0) {
-        VERIFY_CHECK(r->limbs < 2*NUM_LIMBS);
-        r->data[r->limbs++] = c;
-    }
-}
-
-static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
-    mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
-    VERIFY_CHECK(c == 0);
-    r->limbs = a->limbs;
-    while (r->limbs > 1 && r->data[r->limbs-1]==0) {
-        r->limbs--;
-    }
-}
-
-static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
-    secp256k1_num_sanity(r);
-    secp256k1_num_sanity(m);
-
-    if (r->limbs >= m->limbs) {
-        mp_limb_t t[2*NUM_LIMBS];
-        mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
-        memset(t, 0, sizeof(t));
-        r->limbs = m->limbs;
-        while (r->limbs > 1 && r->data[r->limbs-1]==0) {
-            r->limbs--;
-        }
-    }
-
-    if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
-        secp256k1_num_sub_abs(r, m, r);
-        r->neg = 0;
-    }
-}
-
 static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) {
     int i;
     mp_limb_t g[NUM_LIMBS+1];
@@ -142,119 +100,4 @@ static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a,
     memset(v, 0, sizeof(v));
 }
 
-static int secp256k1_num_is_zero(const secp256k1_num *a) {
-    return (a->limbs == 1 && a->data[0] == 0);
-}
-
-static int secp256k1_num_is_neg(const secp256k1_num *a) {
-    return (a->limbs > 1 || a->data[0] != 0) && a->neg;
-}
-
-static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
-    if (a->limbs > b->limbs) {
-        return 1;
-    }
-    if (a->limbs < b->limbs) {
-        return -1;
-    }
-    return mpn_cmp(a->data, b->data, a->limbs);
-}
-
-static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
-    if (a->limbs > b->limbs) {
-        return 0;
-    }
-    if (a->limbs < b->limbs) {
-        return 0;
-    }
-    if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) {
-        return 0;
-    }
-    return mpn_cmp(a->data, b->data, a->limbs) == 0;
-}
-
-static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
-    if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
-        r->neg = a->neg;
-        if (a->limbs >= b->limbs) {
-            secp256k1_num_add_abs(r, a, b);
-        } else {
-            secp256k1_num_add_abs(r, b, a);
-        }
-    } else {
-        if (secp256k1_num_cmp(a, b) > 0) {
-            r->neg = a->neg;
-            secp256k1_num_sub_abs(r, a, b);
-        } else {
-            r->neg = b->neg ^ bneg;
-            secp256k1_num_sub_abs(r, b, a);
-        }
-    }
-}
-
-static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
-    secp256k1_num_sanity(a);
-    secp256k1_num_sanity(b);
-    secp256k1_num_subadd(r, a, b, 0);
-}
-
-static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
-    secp256k1_num_sanity(a);
-    secp256k1_num_sanity(b);
-    secp256k1_num_subadd(r, a, b, 1);
-}
-
-static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
-    mp_limb_t tmp[2*NUM_LIMBS+1];
-    secp256k1_num_sanity(a);
-    secp256k1_num_sanity(b);
-
-    VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
-    if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
-        r->limbs = 1;
-        r->neg = 0;
-        r->data[0] = 0;
-        return;
-    }
-    if (a->limbs >= b->limbs) {
-        mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
-    } else {
-        mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
-    }
-    r->limbs = a->limbs + b->limbs;
-    if (r->limbs > 1 && tmp[r->limbs - 1]==0) {
-        r->limbs--;
-    }
-    VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS);
-    mpn_copyi(r->data, tmp, r->limbs);
-    r->neg = a->neg ^ b->neg;
-    memset(tmp, 0, sizeof(tmp));
-}
-
-static void secp256k1_num_shift(secp256k1_num *r, int bits) {
-    if (bits % GMP_NUMB_BITS) {
-        /* Shift within limbs. */
-        mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
-    }
-    if (bits >= GMP_NUMB_BITS) {
-        int i;
-        /* Shift full limbs. */
-        for (i = 0; i < r->limbs; i++) {
-            int index = i + (bits / GMP_NUMB_BITS);
-            if (index < r->limbs && index < 2*NUM_LIMBS) {
-                r->data[i] = r->data[index];
-            } else {
-                r->data[i] = 0;
-            }
-        }
-    }
-    while (r->limbs>1 && r->data[r->limbs-1]==0) {
-        r->limbs--;
-    }
-}
-
-static void secp256k1_num_negate(secp256k1_num *r) {
-    r->neg ^= 1;
-}
-
 #endif
diff --git a/src/scalar.h b/src/scalar.h
index b590ccd6dd..5e52fb24bc 100644
--- a/src/scalar.h
+++ b/src/scalar.h
@@ -81,9 +81,6 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
 static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
 
 #ifndef USE_NUM_NONE
-/** Convert a scalar to a number. */
-static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
-
 /** Get the order of the group as a number. */
 static void secp256k1_scalar_order_get_num(secp256k1_num *r);
 #endif
diff --git a/src/scalar_impl.h b/src/scalar_impl.h
index 88ea97de86..ac5fab28d4 100644
--- a/src/scalar_impl.h
+++ b/src/scalar_impl.h
@@ -25,12 +25,6 @@
 #endif
 
 #ifndef USE_NUM_NONE
-static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
-    unsigned char c[32];
-    secp256k1_scalar_get_b32(c, a);
-    secp256k1_num_set_bin(r, c, 32);
-}
-
 /** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
 static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
     static const unsigned char order[32] = {
diff --git a/src/tests.c b/src/tests.c
index 3366d90fca..ea8def2be3 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -276,6 +276,182 @@ void run_rfc6979_hmac_sha256_tests(void) {
 /***** NUM TESTS *****/
 
 #ifndef USE_NUM_NONE
+/** Convert a scalar to a number. */
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
+    unsigned char c[32];
+    secp256k1_scalar_get_b32(c, a);
+    secp256k1_num_set_bin(r, c, 32);
+}
+
+/** Check whether a number is zero. */
+static int secp256k1_num_is_zero(const secp256k1_num *a) {
+    return (a->limbs == 1 && a->data[0] == 0);
+}
+
+/** Compare the absolute value of two numbers. */
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
+    if (a->limbs > b->limbs) {
+        return 1;
+    }
+    if (a->limbs < b->limbs) {
+        return -1;
+    }
+    return mpn_cmp(a->data, b->data, a->limbs);
+}
+
+/** Copy a number. */
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
+    *r = *a;
+}
+
+/** Test whether two number are equal (including sign). */
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
+    if (a->limbs > b->limbs) {
+        return 0;
+    }
+    if (a->limbs < b->limbs) {
+        return 0;
+    }
+    if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) {
+        return 0;
+    }
+    return mpn_cmp(a->data, b->data, a->limbs) == 0;
+}
+
+static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
+    r->limbs = a->limbs;
+    if (c != 0) {
+        VERIFY_CHECK(r->limbs < 2*NUM_LIMBS);
+        r->data[r->limbs++] = c;
+    }
+}
+
+static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
+    VERIFY_CHECK(c == 0);
+    r->limbs = a->limbs;
+    while (r->limbs > 1 && r->data[r->limbs-1]==0) {
+        r->limbs--;
+    }
+}
+
+static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
+    if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
+        r->neg = a->neg;
+        if (a->limbs >= b->limbs) {
+            secp256k1_num_add_abs(r, a, b);
+        } else {
+            secp256k1_num_add_abs(r, b, a);
+        }
+    } else {
+        if (secp256k1_num_cmp(a, b) > 0) {
+            r->neg = a->neg;
+            secp256k1_num_sub_abs(r, a, b);
+        } else {
+            r->neg = b->neg ^ bneg;
+            secp256k1_num_sub_abs(r, b, a);
+        }
+    }
+}
+
+/** Add two (signed) numbers. */
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+    secp256k1_num_subadd(r, a, b, 0);
+}
+
+/** Subtract two (signed) numbers. */
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+    secp256k1_num_subadd(r, a, b, 1);
+}
+
+/** Multiply two (signed) numbers. */
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    mp_limb_t tmp[2*NUM_LIMBS+1];
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+
+    VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
+    if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
+        r->limbs = 1;
+        r->neg = 0;
+        r->data[0] = 0;
+        return;
+    }
+    if (a->limbs >= b->limbs) {
+        mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
+    } else {
+        mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
+    }
+    r->limbs = a->limbs + b->limbs;
+    if (r->limbs > 1 && tmp[r->limbs - 1]==0) {
+        r->limbs--;
+    }
+    VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS);
+    mpn_copyi(r->data, tmp, r->limbs);
+    r->neg = a->neg ^ b->neg;
+    memset(tmp, 0, sizeof(tmp));
+}
+
+/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
+    even if r was negative. */
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
+    secp256k1_num_sanity(r);
+    secp256k1_num_sanity(m);
+
+    if (r->limbs >= m->limbs) {
+        mp_limb_t t[2*NUM_LIMBS];
+        mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
+        memset(t, 0, sizeof(t));
+        r->limbs = m->limbs;
+        while (r->limbs > 1 && r->data[r->limbs-1]==0) {
+            r->limbs--;
+        }
+    }
+
+    if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
+        secp256k1_num_sub_abs(r, m, r);
+        r->neg = 0;
+    }
+}
+
+/** Right-shift the passed number by bits bits. */
+static void secp256k1_num_shift(secp256k1_num *r, int bits) {
+    if (bits % GMP_NUMB_BITS) {
+        /* Shift within limbs. */
+        mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
+    }
+    if (bits >= GMP_NUMB_BITS) {
+        int i;
+        /* Shift full limbs. */
+        for (i = 0; i < r->limbs; i++) {
+            int index = i + (bits / GMP_NUMB_BITS);
+            if (index < r->limbs && index < 2*NUM_LIMBS) {
+                r->data[i] = r->data[index];
+            } else {
+                r->data[i] = 0;
+            }
+        }
+    }
+    while (r->limbs>1 && r->data[r->limbs-1]==0) {
+        r->limbs--;
+    }
+}
+
+/** Check whether a number is strictly negative. */
+static int secp256k1_num_is_neg(const secp256k1_num *a) {
+    return (a->limbs > 1 || a->data[0] != 0) && a->neg;
+}
+
+/** Change a number's sign. */
+static void secp256k1_num_negate(secp256k1_num *r) {
+    r->neg ^= 1;
+}
+
 void random_num_negate(secp256k1_num *num) {
     if (secp256k1_rand32() & 1) {
         secp256k1_num_negate(num);
@@ -944,6 +1120,26 @@ void run_sqrt(void) {
 
 /***** GROUP TESTS *****/
 
+static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
+    secp256k1_fe y2, x3, z2, z6;
+    if (a->infinity) {
+        return 0;
+    }
+    /** y^2 = x^3 + 7
+     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
+     *  Y^2 / Z^6 = X^3 / Z^6 + 7
+     *  Y^2 = X^3 + 7*Z^6
+     */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
+    secp256k1_fe_mul_int(&z6, 7);
+    secp256k1_fe_add(&x3, &z6);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
 void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
     CHECK(a->infinity == b->infinity);
     if (a->infinity) {