diff --git a/src/typed-geometry/detail/intrinsics.hh b/src/typed-geometry/detail/intrinsics.hh
new file mode 100644
index 0000000..b722afb
--- /dev/null
+++ b/src/typed-geometry/detail/intrinsics.hh
@@ -0,0 +1,61 @@
+#pragma once
+
+#include <clean-core/macros.hh>
+
+#ifdef _MSC_VER
+#include <intrin.h>
+#elif __has_include("x86intrin.h")
+#include <x86intrin.h>
+#include <cstring>
+#endif
+
+
+namespace tg::detail
+{
+CC_FORCE_INLINE char add_with_carry(char carry, unsigned long long a, unsigned long long b, unsigned long long* out)
+{
+#if defined(__x86_64__) || defined(_M_X64)
+    return _addcarry_u64(carry, a, b, out);
+#else
+#pragma message("[typed-geometry] Using fallback for add_with_carry(...). This may be slow!")
+    unsigned long long tmp = b + carry;
+    a += tmp;
+    *out = a;
+    return (tmp < carry) + (a < tmp);
+#endif
+}
+
+CC_FORCE_INLINE unsigned long long mul128(unsigned long long a, unsigned long long b, unsigned long long* high)
+{
+#if defined(_MSC_VER)
+    return _umul128(a, b, high);
+#elif __has_include("x86intrin.h")
+    return _mulx_u64(a, b, high);
+#elif defined(__SIZEOF_INT128__)
+    __uint128_t res = __uint128_t(a) * __uint128_t(b);
+    *high = res >> 64;
+    return static_cast<unsigned long long>(res);
+#else
+#pragma message("[typed-geometry] Using fallback for mul128(...). This may be slow!")
+    using u64 = unsigned long long;
+    using u32 = unsigned int;
+    static_assert(sizeof(u64) == 8, "u64 must be exactly 64 bits");
+    static_assert(sizeof(u32) == 4, "u32 must be exactly 32 bits");
+
+    u64 a_lo = u64(u32(a));
+    u64 a_hi = a >> 32;
+    u64 b_lo = u64(u32(b));
+    u64 b_hi = b >> 32;
+
+    u64 p0 = a_lo * b_lo;
+    u64 p1 = a_lo * b_hi;
+    u64 p2 = a_hi * b_lo;
+    u64 p3 = a_hi * b_hi;
+
+    u32 cy = u32(((p0 >> 32) + u32(p1) + u32(p2)) >> 32);
+
+    *high = p3 + (p1 >> 32) + (p2 >> 32) + cy;
+    return p0 + (p1 << 32) + (p2 << 32);
+#endif
+}
+}
diff --git a/src/typed-geometry/feature/fixed_int.hh b/src/typed-geometry/feature/fixed_int.hh
index 15f8af3..ced83c4 100644
--- a/src/typed-geometry/feature/fixed_int.hh
+++ b/src/typed-geometry/feature/fixed_int.hh
@@ -2,12 +2,6 @@
 
 #include <clean-core/macros.hh>
 
-#ifdef CC_COMPILER_MSVC
-#define TG_MUL_U128 _umul128
-#else
-#define TG_MUL_U128 _mulx_u64
-#endif
-
 #include <typed-geometry/functions/fixed_int/conversions.hh>
 #include <typed-geometry/functions/fixed_int/fixed_int.hh>
 #include <typed-geometry/functions/fixed_int/fixed_int_gen.hh>
diff --git a/src/typed-geometry/functions/fixed_int/fixed_int_gen.hh b/src/typed-geometry/functions/fixed_int/fixed_int_gen.hh
index 46a529c..6ade999 100644
--- a/src/typed-geometry/functions/fixed_int/fixed_int_gen.hh
+++ b/src/typed-geometry/functions/fixed_int/fixed_int_gen.hh
@@ -2,13 +2,7 @@
 
 // This file was generated by generate_fixed_uint_multiplications.cc in TGSamples.
 
-#ifdef _MSC_VER
-#include <intrin.h>
-#else
-#include <x86intrin.h>
-#include <cstring>
-#endif
-
+#include <typed-geometry/detail/intrinsics.hh>
 #include <typed-geometry/feature/fixed_int.hh>
 
 namespace tg::detail
@@ -22,7 +16,6 @@ using intrinsic_i128 = __int128;
 #endif
 
 using u64_word = fixed_int<1>::word_t;
-
 template <>
 inline i128 imul(i128 lhs, i128 rhs)
 {
@@ -31,11 +24,11 @@ inline i128 imul(i128 lhs, i128 rhs)
     u64_word l01 = 0;
     u64_word l10 = 0;
     u64_word h00 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
     l01 = u64_word(lhs.d[0]) * u64_word(rhs.d[1]);
     l10 = u64_word(lhs.d[1]) * u64_word(rhs.d[0]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
     res.d[1] = c + h00 + l01 + l10;
     return res;
 }
@@ -106,14 +99,14 @@ inline i192 imul(i128 lhs, i64 rhs)
     u64_word l10 = 0;
     u64_word h00 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h10;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -147,15 +140,15 @@ inline i192 imul(i192 lhs, i64 rhs)
     u64_word l20 = 0;
     u64_word h00 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
     l20 = u64_word(lhs.d[2]) * u64_word(rhs);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h10 + l20;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -186,14 +179,14 @@ inline i192 imul(i64 lhs, i128 rhs)
     u64_word l01 = 0;
     u64_word h00 = 0;
     u64_word h01 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
+    l00 = detail::mul128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
     res.d[2] = c + h01;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -229,17 +222,17 @@ inline i192 imul(i128 lhs, i128 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
     l11 = u64_word(lhs.d[1]) * u64_word(rhs.d[1]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + h10 + l11;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -278,18 +271,18 @@ inline i192 imul(i192 lhs, i128 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
     l11 = u64_word(lhs.d[1]) * u64_word(rhs.d[1]);
     l20 = u64_word(lhs.d[2]) * u64_word(rhs.d[0]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + h10 + l11 + l20;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -323,15 +316,15 @@ inline i192 imul(i64 lhs, i192 rhs)
     u64_word l02 = 0;
     u64_word h00 = 0;
     u64_word h01 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
+    l00 = detail::mul128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
     l02 = u64_word(lhs) * u64_word(rhs.d[2]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
     res.d[2] = c + h01 + l02;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -370,18 +363,18 @@ inline i192 imul(i128 lhs, i192 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
     l02 = u64_word(lhs.d[0]) * u64_word(rhs.d[2]);
     l11 = u64_word(lhs.d[1]) * u64_word(rhs.d[1]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + l02 + h10 + l11;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -406,19 +399,19 @@ inline i192 imul(i192 lhs, i192 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
     l02 = u64_word(lhs.d[0]) * u64_word(rhs.d[2]);
     l11 = u64_word(lhs.d[1]) * u64_word(rhs.d[1]);
     l20 = u64_word(lhs.d[2]) * u64_word(rhs.d[0]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + l02 + h10 + l11 + l20;
     return res;
 }
@@ -446,19 +439,19 @@ inline i256 imul(i192 lhs, i64 rhs)
     u64_word h00 = 0;
     u64_word h10 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs), &h20);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h20;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -498,20 +491,20 @@ inline i256 imul(i256 lhs, i64 rhs)
     u64_word h00 = 0;
     u64_word h10 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs), &h00);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs), &h10);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs), &h20);
     l30 = u64_word(lhs.d[3]) * u64_word(rhs);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h20 + l30;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -550,22 +543,22 @@ inline i256 imul(i128 lhs, i128 rhs)
     u64_word h01 = 0;
     u64_word h10 = 0;
     u64_word h11 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
     res.d[3] = c + h11;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -609,25 +602,25 @@ inline i256 imul(i192 lhs, i128 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
     l21 = u64_word(lhs.d[2]) * u64_word(rhs.d[1]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h11 + h20 + l21;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -674,26 +667,26 @@ inline i256 imul(i256 lhs, i128 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
     l21 = u64_word(lhs.d[2]) * u64_word(rhs.d[1]);
     l30 = u64_word(lhs.d[3]) * u64_word(rhs.d[0]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h11 + h20 + l21 + l30;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -730,19 +723,19 @@ inline i256 imul(i64 lhs, i192 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h02 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[2]), &h02);
+    l00 = detail::mul128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs), u64_word(rhs.d[2]), &h02);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
     res.d[3] = c + h02;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -786,25 +779,25 @@ inline i256 imul(i128 lhs, i192 rhs)
     u64_word h02 = 0;
     u64_word h10 = 0;
     u64_word h11 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
     l12 = u64_word(lhs.d[1]) * u64_word(rhs.d[2]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
     res.d[3] = c + h02 + h11 + l12;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -853,28 +846,28 @@ inline i256 imul(i192 lhs, i192 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
     l12 = u64_word(lhs.d[1]) * u64_word(rhs.d[2]);
     l21 = u64_word(lhs.d[2]) * u64_word(rhs.d[1]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + h11 + l12 + h20 + l21;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -926,29 +919,29 @@ inline i256 imul(i256 lhs, i192 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
     l12 = u64_word(lhs.d[1]) * u64_word(rhs.d[2]);
     l21 = u64_word(lhs.d[2]) * u64_word(rhs.d[1]);
     l30 = u64_word(lhs.d[3]) * u64_word(rhs.d[0]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + h11 + l12 + h20 + l21 + l30;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -988,20 +981,20 @@ inline i256 imul(i64 lhs, i256 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h02 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs), u64_word(rhs.d[2]), &h02);
+    l00 = detail::mul128(u64_word(lhs), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs), u64_word(rhs.d[2]), &h02);
     l03 = u64_word(lhs) * u64_word(rhs.d[3]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
     res.d[3] = c + h02 + l03;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -1048,26 +1041,26 @@ inline i256 imul(i128 lhs, i256 rhs)
     u64_word h02 = 0;
     u64_word h10 = 0;
     u64_word h11 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
     l03 = u64_word(lhs.d[0]) * u64_word(rhs.d[3]);
     l12 = u64_word(lhs.d[1]) * u64_word(rhs.d[2]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
     res.d[3] = c + h02 + l03 + h11 + l12;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -1119,29 +1112,29 @@ inline i256 imul(i192 lhs, i256 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
     l03 = u64_word(lhs.d[0]) * u64_word(rhs.d[3]);
     l12 = u64_word(lhs.d[1]) * u64_word(rhs.d[2]);
     l21 = u64_word(lhs.d[2]) * u64_word(rhs.d[1]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + l03 + h11 + l12 + h20 + l21;
     { // conditional inversion
         res.d[0] = ((u64_word(res.d[0]) ^ s_res) - s_res);
@@ -1175,30 +1168,30 @@ inline i256 imul(i256 lhs, i256 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
-    l01 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
-    l02 = TG_MUL_U128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
-    l10 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
-    l11 = TG_MUL_U128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
-    l20 = TG_MUL_U128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
+    l00 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[0]), &h00);
+    l01 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[1]), &h01);
+    l02 = detail::mul128(u64_word(lhs.d[0]), u64_word(rhs.d[2]), &h02);
+    l10 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[0]), &h10);
+    l11 = detail::mul128(u64_word(lhs.d[1]), u64_word(rhs.d[1]), &h11);
+    l20 = detail::mul128(u64_word(lhs.d[2]), u64_word(rhs.d[0]), &h20);
     l03 = u64_word(lhs.d[0]) * u64_word(rhs.d[3]);
     l12 = u64_word(lhs.d[1]) * u64_word(rhs.d[2]);
     l21 = u64_word(lhs.d[2]) * u64_word(rhs.d[1]);
     l30 = u64_word(lhs.d[3]) * u64_word(rhs.d[0]);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + l03 + h11 + l12 + h20 + l21 + l30;
     return res;
 }
diff --git a/src/typed-geometry/functions/fixed_int/fixed_uint_gen.hh b/src/typed-geometry/functions/fixed_int/fixed_uint_gen.hh
index fad16c9..786f44c 100644
--- a/src/typed-geometry/functions/fixed_int/fixed_uint_gen.hh
+++ b/src/typed-geometry/functions/fixed_int/fixed_uint_gen.hh
@@ -2,27 +2,21 @@
 
 // This file was generated by generate_fixed_uint_multiplications.cc in TGSamples.
 
-#ifdef _MSC_VER
-#include <intrin.h>
-#else
-#include <x86intrin.h>
-#endif
-
+#include <typed-geometry/detail/intrinsics.hh>
 #include <typed-geometry/feature/fixed_int.hh>
 
 namespace tg::detail
 {
 using u64_word = fixed_uint<1>::word_t;
-
 template <>
 inline u128 mul(u64 lhs, u64 rhs)
 {
     u128 res;
     u64_word l00 = 0;
     u64_word h00 = 0;
-    l00 = TG_MUL_U128(lhs, rhs, &h00);
+    l00 = detail::mul128(lhs, rhs, &h00);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
     res.d[1] = c + h00;
     return res;
 }
@@ -34,10 +28,10 @@ inline u128 mul(u128 lhs, u64 rhs)
     u64_word l00 = 0;
     u64_word l10 = 0;
     u64_word h00 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs, &h00);
+    l00 = detail::mul128(lhs.d[0], rhs, &h00);
     l10 = lhs.d[1] * rhs;
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
     res.d[1] = c + h00 + l10;
     return res;
 }
@@ -49,10 +43,10 @@ inline u128 mul(u64 lhs, u128 rhs)
     u64_word l00 = 0;
     u64_word l01 = 0;
     u64_word h00 = 0;
-    l00 = TG_MUL_U128(lhs, rhs.d[0], &h00);
+    l00 = detail::mul128(lhs, rhs.d[0], &h00);
     l01 = lhs * rhs.d[1];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
     res.d[1] = c + h00 + l01;
     return res;
 }
@@ -65,11 +59,11 @@ inline u128 mul(u128 lhs, u128 rhs)
     u64_word l01 = 0;
     u64_word l10 = 0;
     u64_word h00 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
     l01 = lhs.d[0] * rhs.d[1];
     l10 = lhs.d[1] * rhs.d[0];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
     res.d[1] = c + h00 + l01 + l10;
     return res;
 }
@@ -82,14 +76,14 @@ inline u192 mul(u128 lhs, u64 rhs)
     u64_word l10 = 0;
     u64_word h00 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs, &h00);
-    l10 = TG_MUL_U128(lhs.d[1], rhs, &h10);
+    l00 = detail::mul128(lhs.d[0], rhs, &h00);
+    l10 = detail::mul128(lhs.d[1], rhs, &h10);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h10;
     return res;
 }
@@ -103,15 +97,15 @@ inline u192 mul(u192 lhs, u64 rhs)
     u64_word l20 = 0;
     u64_word h00 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs, &h00);
-    l10 = TG_MUL_U128(lhs.d[1], rhs, &h10);
+    l00 = detail::mul128(lhs.d[0], rhs, &h00);
+    l10 = detail::mul128(lhs.d[1], rhs, &h10);
     l20 = lhs.d[2] * rhs;
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h10 + l20;
     return res;
 }
@@ -124,14 +118,14 @@ inline u192 mul(u64 lhs, u128 rhs)
     u64_word l01 = 0;
     u64_word h00 = 0;
     u64_word h01 = 0;
-    l00 = TG_MUL_U128(lhs, rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs, rhs.d[1], &h01);
+    l00 = detail::mul128(lhs, rhs.d[0], &h00);
+    l01 = detail::mul128(lhs, rhs.d[1], &h01);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
     res.d[2] = c + h01;
     return res;
 }
@@ -147,17 +141,17 @@ inline u192 mul(u128 lhs, u128 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
     l11 = lhs.d[1] * rhs.d[1];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + h10 + l11;
     return res;
 }
@@ -174,18 +168,18 @@ inline u192 mul(u192 lhs, u128 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
     l11 = lhs.d[1] * rhs.d[1];
     l20 = lhs.d[2] * rhs.d[0];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + h10 + l11 + l20;
     return res;
 }
@@ -199,15 +193,15 @@ inline u192 mul(u64 lhs, u192 rhs)
     u64_word l02 = 0;
     u64_word h00 = 0;
     u64_word h01 = 0;
-    l00 = TG_MUL_U128(lhs, rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs, rhs.d[1], &h01);
+    l00 = detail::mul128(lhs, rhs.d[0], &h00);
+    l01 = detail::mul128(lhs, rhs.d[1], &h01);
     l02 = lhs * rhs.d[2];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
     res.d[2] = c + h01 + l02;
     return res;
 }
@@ -224,18 +218,18 @@ inline u192 mul(u128 lhs, u192 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
     l02 = lhs.d[0] * rhs.d[2];
     l11 = lhs.d[1] * rhs.d[1];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + l02 + h10 + l11;
     return res;
 }
@@ -253,19 +247,19 @@ inline u192 mul(u192 lhs, u192 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h10 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
     l02 = lhs.d[0] * rhs.d[2];
     l11 = lhs.d[1] * rhs.d[1];
     l20 = lhs.d[2] * rhs.d[0];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
     res.d[2] = c + h01 + l02 + h10 + l11 + l20;
     return res;
 }
@@ -280,19 +274,19 @@ inline u256 mul(u192 lhs, u64 rhs)
     u64_word h00 = 0;
     u64_word h10 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs, &h00);
-    l10 = TG_MUL_U128(lhs.d[1], rhs, &h10);
-    l20 = TG_MUL_U128(lhs.d[2], rhs, &h20);
+    l00 = detail::mul128(lhs.d[0], rhs, &h00);
+    l10 = detail::mul128(lhs.d[1], rhs, &h10);
+    l20 = detail::mul128(lhs.d[2], rhs, &h20);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h20;
     return res;
 }
@@ -308,20 +302,20 @@ inline u256 mul(u256 lhs, u64 rhs)
     u64_word h00 = 0;
     u64_word h10 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs, &h00);
-    l10 = TG_MUL_U128(lhs.d[1], rhs, &h10);
-    l20 = TG_MUL_U128(lhs.d[2], rhs, &h20);
+    l00 = detail::mul128(lhs.d[0], rhs, &h00);
+    l10 = detail::mul128(lhs.d[1], rhs, &h10);
+    l20 = detail::mul128(lhs.d[2], rhs, &h20);
     l30 = lhs.d[3] * rhs;
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h20 + l30;
     return res;
 }
@@ -338,22 +332,22 @@ inline u256 mul(u128 lhs, u128 rhs)
     u64_word h01 = 0;
     u64_word h10 = 0;
     u64_word h11 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
     res.d[3] = c + h11;
     return res;
 }
@@ -373,25 +367,25 @@ inline u256 mul(u192 lhs, u128 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
-    l20 = TG_MUL_U128(lhs.d[2], rhs.d[0], &h20);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
+    l20 = detail::mul128(lhs.d[2], rhs.d[0], &h20);
     l21 = lhs.d[2] * rhs.d[1];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h11 + h20 + l21;
     return res;
 }
@@ -412,26 +406,26 @@ inline u256 mul(u256 lhs, u128 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
-    l20 = TG_MUL_U128(lhs.d[2], rhs.d[0], &h20);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
+    l20 = detail::mul128(lhs.d[2], rhs.d[0], &h20);
     l21 = lhs.d[2] * rhs.d[1];
     l30 = lhs.d[3] * rhs.d[0];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h11 + h20 + l21 + l30;
     return res;
 }
@@ -446,19 +440,19 @@ inline u256 mul(u64 lhs, u192 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h02 = 0;
-    l00 = TG_MUL_U128(lhs, rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs, rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs, rhs.d[2], &h02);
+    l00 = detail::mul128(lhs, rhs.d[0], &h00);
+    l01 = detail::mul128(lhs, rhs.d[1], &h01);
+    l02 = detail::mul128(lhs, rhs.d[2], &h02);
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
     res.d[3] = c + h02;
     return res;
 }
@@ -478,25 +472,25 @@ inline u256 mul(u128 lhs, u192 rhs)
     u64_word h02 = 0;
     u64_word h10 = 0;
     u64_word h11 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs.d[0], rhs.d[2], &h02);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l02 = detail::mul128(lhs.d[0], rhs.d[2], &h02);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
     l12 = lhs.d[1] * rhs.d[2];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
     res.d[3] = c + h02 + h11 + l12;
     return res;
 }
@@ -519,28 +513,28 @@ inline u256 mul(u192 lhs, u192 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs.d[0], rhs.d[2], &h02);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
-    l20 = TG_MUL_U128(lhs.d[2], rhs.d[0], &h20);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l02 = detail::mul128(lhs.d[0], rhs.d[2], &h02);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
+    l20 = detail::mul128(lhs.d[2], rhs.d[0], &h20);
     l12 = lhs.d[1] * rhs.d[2];
     l21 = lhs.d[2] * rhs.d[1];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + h11 + l12 + h20 + l21;
     return res;
 }
@@ -564,29 +558,29 @@ inline u256 mul(u256 lhs, u192 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs.d[0], rhs.d[2], &h02);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
-    l20 = TG_MUL_U128(lhs.d[2], rhs.d[0], &h20);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l02 = detail::mul128(lhs.d[0], rhs.d[2], &h02);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
+    l20 = detail::mul128(lhs.d[2], rhs.d[0], &h20);
     l12 = lhs.d[1] * rhs.d[2];
     l21 = lhs.d[2] * rhs.d[1];
     l30 = lhs.d[3] * rhs.d[0];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + h11 + l12 + h20 + l21 + l30;
     return res;
 }
@@ -602,20 +596,20 @@ inline u256 mul(u64 lhs, u256 rhs)
     u64_word h00 = 0;
     u64_word h01 = 0;
     u64_word h02 = 0;
-    l00 = TG_MUL_U128(lhs, rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs, rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs, rhs.d[2], &h02);
+    l00 = detail::mul128(lhs, rhs.d[0], &h00);
+    l01 = detail::mul128(lhs, rhs.d[1], &h01);
+    l02 = detail::mul128(lhs, rhs.d[2], &h02);
     l03 = lhs * rhs.d[3];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
     c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
     c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
     res.d[3] = c + h02 + l03;
     return res;
 }
@@ -636,26 +630,26 @@ inline u256 mul(u128 lhs, u256 rhs)
     u64_word h02 = 0;
     u64_word h10 = 0;
     u64_word h11 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs.d[0], rhs.d[2], &h02);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l02 = detail::mul128(lhs.d[0], rhs.d[2], &h02);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
     l03 = lhs.d[0] * rhs.d[3];
     l12 = lhs.d[1] * rhs.d[2];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
     res.d[3] = c + h02 + l03 + h11 + l12;
     return res;
 }
@@ -679,29 +673,29 @@ inline u256 mul(u192 lhs, u256 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs.d[0], rhs.d[2], &h02);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
-    l20 = TG_MUL_U128(lhs.d[2], rhs.d[0], &h20);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l02 = detail::mul128(lhs.d[0], rhs.d[2], &h02);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
+    l20 = detail::mul128(lhs.d[2], rhs.d[0], &h20);
     l03 = lhs.d[0] * rhs.d[3];
     l12 = lhs.d[1] * rhs.d[2];
     l21 = lhs.d[2] * rhs.d[1];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + l03 + h11 + l12 + h20 + l21;
     return res;
 }
@@ -726,30 +720,30 @@ inline u256 mul(u256 lhs, u256 rhs)
     u64_word h10 = 0;
     u64_word h11 = 0;
     u64_word h20 = 0;
-    l00 = TG_MUL_U128(lhs.d[0], rhs.d[0], &h00);
-    l01 = TG_MUL_U128(lhs.d[0], rhs.d[1], &h01);
-    l02 = TG_MUL_U128(lhs.d[0], rhs.d[2], &h02);
-    l10 = TG_MUL_U128(lhs.d[1], rhs.d[0], &h10);
-    l11 = TG_MUL_U128(lhs.d[1], rhs.d[1], &h11);
-    l20 = TG_MUL_U128(lhs.d[2], rhs.d[0], &h20);
+    l00 = detail::mul128(lhs.d[0], rhs.d[0], &h00);
+    l01 = detail::mul128(lhs.d[0], rhs.d[1], &h01);
+    l02 = detail::mul128(lhs.d[0], rhs.d[2], &h02);
+    l10 = detail::mul128(lhs.d[1], rhs.d[0], &h10);
+    l11 = detail::mul128(lhs.d[1], rhs.d[1], &h11);
+    l20 = detail::mul128(lhs.d[2], rhs.d[0], &h20);
     l03 = lhs.d[0] * rhs.d[3];
     l12 = lhs.d[1] * rhs.d[2];
     l21 = lhs.d[2] * rhs.d[1];
     l30 = lhs.d[3] * rhs.d[0];
     unsigned char c = 0;
-    c += _addcarry_u64(0, res.d[0], l00, &res.d[0]);
-    c += _addcarry_u64(0, res.d[1], c, &res.d[1]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[1], h00, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l01, &res.d[1]);
-    c += _addcarry_u64(0, res.d[1], l10, &res.d[1]);
-    c += _addcarry_u64(0, res.d[2], c, &res.d[2]);
-    c = 0;
-    c += _addcarry_u64(0, res.d[2], h01, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l02, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], h10, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l11, &res.d[2]);
-    c += _addcarry_u64(0, res.d[2], l20, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[0], l00, &res.d[0]);
+    c += detail::add_with_carry(0, res.d[1], c, &res.d[1]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[1], h00, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l01, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[1], l10, &res.d[1]);
+    c += detail::add_with_carry(0, res.d[2], c, &res.d[2]);
+    c = 0;
+    c += detail::add_with_carry(0, res.d[2], h01, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l02, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], h10, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l11, &res.d[2]);
+    c += detail::add_with_carry(0, res.d[2], l20, &res.d[2]);
     res.d[3] = c + h02 + l03 + h11 + l12 + h20 + l21 + l30;
     return res;
 }