diff --git a/Makefile.am b/Makefile.am
index a30a84cd59..1c19e14deb 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -34,6 +34,7 @@ noinst_HEADERS += src/field_5x52.h
 noinst_HEADERS += src/field_5x52_impl.h
 noinst_HEADERS += src/field_5x52_int128_impl.h
 noinst_HEADERS += src/field_5x52_asm_impl.h
+noinst_HEADERS += src/assumptions.h
 noinst_HEADERS += src/util.h
 noinst_HEADERS += src/scratch.h
 noinst_HEADERS += src/scratch_impl.h
diff --git a/src/assumptions.h b/src/assumptions.h
new file mode 100644
index 0000000000..f9d4e8e793
--- /dev/null
+++ b/src/assumptions.h
@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2020 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ASSUMPTIONS_H
+#define SECP256K1_ASSUMPTIONS_H
+
+#include "util.h"
+
+/* This library, like most software, relies on a number of compiler implementation defined (but not undefined)
+   behaviours. Although the behaviours we require are essentially universal we test them specifically here to
+   reduce the odds of experiencing an unwelcome surprise.
+*/
+
+struct secp256k1_assumption_checker {
+    /* This uses a trick to implement a static assertion in C89: a type with an array of negative size is not
+       allowed. */
+    int dummy_array[(
+        /* Bytes are 8 bits. */
+        CHAR_BIT == 8 &&
+
+        /* Conversions from unsigned to signed outside of the bounds of the signed type are
+           implementation-defined. Verify that they function as reinterpreting the lower
+           bits of the input in two's complement notation. Do this for conversions:
+           - from uint(N)_t to int(N)_t with negative result
+           - from uint(2N)_t to int(N)_t with negative result
+           - from int(2N)_t to int(N)_t with negative result
+           - from int(2N)_t to int(N)_t with positive result */
+
+        /* To int8_t. */
+        ((int8_t)(uint8_t)0xAB == (int8_t)-(int8_t)0x55) &&
+        ((int8_t)(uint16_t)0xABCD == (int8_t)-(int8_t)0x33) &&
+        ((int8_t)(int16_t)(uint16_t)0xCDEF == (int8_t)(uint8_t)0xEF) &&
+        ((int8_t)(int16_t)(uint16_t)0x9234 == (int8_t)(uint8_t)0x34) &&
+
+        /* To int16_t. */
+        ((int16_t)(uint16_t)0xBCDE == (int16_t)-(int16_t)0x4322) &&
+        ((int16_t)(uint32_t)0xA1B2C3D4 == (int16_t)-(int16_t)0x3C2C) &&
+        ((int16_t)(int32_t)(uint32_t)0xC1D2E3F4 == (int16_t)(uint16_t)0xE3F4) &&
+        ((int16_t)(int32_t)(uint32_t)0x92345678 == (int16_t)(uint16_t)0x5678) &&
+
+        /* To int32_t. */
+        ((int32_t)(uint32_t)0xB2C3D4E5 == (int32_t)-(int32_t)0x4D3C2B1B) &&
+        ((int32_t)(uint64_t)0xA123B456C789D012ULL == (int32_t)-(int32_t)0x38762FEE) &&
+        ((int32_t)(int64_t)(uint64_t)0xC1D2E3F4A5B6C7D8ULL == (int32_t)(uint32_t)0xA5B6C7D8) &&
+        ((int32_t)(int64_t)(uint64_t)0xABCDEF0123456789ULL == (int32_t)(uint32_t)0x23456789) &&
+
+        /* To int64_t. */
+        ((int64_t)(uint64_t)0xB123C456D789E012ULL == (int64_t)-(int64_t)0x4EDC3BA928761FEEULL) &&
+#if defined(SECP256K1_WIDEMUL_INT128)
+        ((int64_t)(((uint128_t)0xA1234567B8901234ULL << 64) + 0xC5678901D2345678ULL) == (int64_t)-(int64_t)0x3A9876FE2DCBA988ULL) &&
+        (((int64_t)(int128_t)(((uint128_t)0xB1C2D3E4F5A6B7C8ULL << 64) + 0xD9E0F1A2B3C4D5E6ULL)) == (int64_t)(uint64_t)0xD9E0F1A2B3C4D5E6ULL) &&
+        (((int64_t)(int128_t)(((uint128_t)0xABCDEF0123456789ULL << 64) + 0x0123456789ABCDEFULL)) == (int64_t)(uint64_t)0x0123456789ABCDEFULL) &&
+
+        /* To int128_t. */
+        ((int128_t)(((uint128_t)0xB1234567C8901234ULL << 64) + 0xD5678901E2345678ULL) == (int128_t)(-(int128_t)0x8E1648B3F50E80DCULL * 0x8E1648B3F50E80DDULL + 0x5EA688D5482F9464ULL)) &&
+#endif
+
+        /* Right shift on negative signed values is implementation defined. Verify that it
+           acts as a right shift in two's complement with sign extension (i.e duplicating
+           the top bit into newly added bits). */
+        ((((int8_t)0xE8) >> 2) == (int8_t)(uint8_t)0xFA) &&
+        ((((int16_t)0xE9AC) >> 4) == (int16_t)(uint16_t)0xFE9A) &&
+        ((((int32_t)0x937C918A) >> 9) == (int32_t)(uint32_t)0xFFC9BE48) &&
+        ((((int64_t)0xA8B72231DF9CF4B9ULL) >> 19) == (int64_t)(uint64_t)0xFFFFF516E4463BF3ULL) &&
+#if defined(SECP256K1_WIDEMUL_INT128)
+        ((((int128_t)(((uint128_t)0xCD833A65684A0DBCULL << 64) + 0xB349312F71EA7637ULL)) >> 39) == (int128_t)(((uint128_t)0xFFFFFFFFFF9B0674ULL << 64) + 0xCAD0941B79669262ULL)) &&
+#endif
+    1) * 2 - 1];
+};
+
+#endif /* SECP256K1_ASSUMPTIONS_H */
diff --git a/src/bench_internal.c b/src/bench_internal.c
index 20759127d3..cb8368ddff 100644
--- a/src/bench_internal.c
+++ b/src/bench_internal.c
@@ -7,6 +7,7 @@
 
 #include "include/secp256k1.h"
 
+#include "assumptions.h"
 #include "util.h"
 #include "hash_impl.h"
 #include "num_impl.h"
diff --git a/src/gen_context.c b/src/gen_context.c
index 539f574bfd..8b7729aee4 100644
--- a/src/gen_context.c
+++ b/src/gen_context.c
@@ -13,6 +13,7 @@
 #include "basic-config.h"
 
 #include "include/secp256k1.h"
+#include "assumptions.h"
 #include "util.h"
 #include "field_impl.h"
 #include "scalar_impl.h"
diff --git a/src/secp256k1.c b/src/secp256k1.c
index 3e79265038..b43a9592eb 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -7,6 +7,7 @@
 #include "include/secp256k1.h"
 #include "include/secp256k1_preallocated.h"
 
+#include "assumptions.h"
 #include "util.h"
 #include "num_impl.h"
 #include "field_impl.h"
diff --git a/src/tests_exhaustive.c b/src/tests_exhaustive.c
index 8f346701aa..681ed80bd0 100644
--- a/src/tests_exhaustive.c
+++ b/src/tests_exhaustive.c
@@ -22,6 +22,7 @@
 #endif
 
 #include "include/secp256k1.h"
+#include "assumptions.h"
 #include "group.h"
 #include "secp256k1.c"
 #include "testrand_impl.h"
diff --git a/src/util.h b/src/util.h
index eb4db4faf5..1070e0aca2 100644
--- a/src/util.h
+++ b/src/util.h
@@ -238,6 +238,7 @@ static SECP256K1_INLINE void secp256k1_int_cmov(int *r, const int *a, int flag)
 #endif
 #if defined(SECP256K1_WIDEMUL_INT128)
 SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
+SECP256K1_GNUC_EXT typedef __int128 int128_t;
 #endif
 
 #endif /* SECP256K1_UTIL_H */
diff --git a/src/valgrind_ctime_test.c b/src/valgrind_ctime_test.c
index 60a82d599e..090fde2b6e 100644
--- a/src/valgrind_ctime_test.c
+++ b/src/valgrind_ctime_test.c
@@ -6,6 +6,7 @@
 
 #include <valgrind/memcheck.h>
 #include "include/secp256k1.h"
+#include "assumptions.h"
 #include "util.h"
 
 #if ENABLE_MODULE_ECDH