diff --git a/src/lib/math/bigint/big_ops2.cpp b/src/lib/math/bigint/big_ops2.cpp
index 9441a533126..e3da4c5d3b1 100644
--- a/src/lib/math/bigint/big_ops2.cpp
+++ b/src/lib/math/bigint/big_ops2.cpp
@@ -258,17 +258,12 @@ word BigInt::operator%=(word mod) {
 * Left Shift Operator
 */
 BigInt& BigInt::operator<<=(size_t shift) {
-   const size_t shift_words = shift / BOTAN_MP_WORD_BITS;
-   const size_t shift_bits = shift % BOTAN_MP_WORD_BITS;
-   const size_t size = sig_words();
-
-   const size_t bits_free = top_bits_free();
-
-   const size_t new_size = size + shift_words + (bits_free < shift_bits);
+   const size_t sw = sig_words();
+   const size_t new_size = sw + (shift + BOTAN_MP_WORD_BITS - 1) / BOTAN_MP_WORD_BITS;
 
    m_data.grow_to(new_size);
 
-   bigint_shl1(m_data.mutable_data(), new_size, size, shift_words, shift_bits);
+   bigint_shl1(m_data.mutable_data(), new_size, sw, shift);
 
    return (*this);
 }
@@ -277,10 +272,7 @@ BigInt& BigInt::operator<<=(size_t shift) {
 * Right Shift Operator
 */
 BigInt& BigInt::operator>>=(size_t shift) {
-   const size_t shift_words = shift / BOTAN_MP_WORD_BITS;
-   const size_t shift_bits = shift % BOTAN_MP_WORD_BITS;
-
-   bigint_shr1(m_data.mutable_data(), m_data.size(), shift_words, shift_bits);
+   bigint_shr1(m_data.mutable_data(), m_data.size(), shift);
 
    if(is_negative() && is_zero()) {
       set_sign(Positive);
diff --git a/src/lib/math/bigint/big_ops3.cpp b/src/lib/math/bigint/big_ops3.cpp
index 1fd5dcbae1a..d36192a46da 100644
--- a/src/lib/math/bigint/big_ops3.cpp
+++ b/src/lib/math/bigint/big_ops3.cpp
@@ -172,12 +172,11 @@ word operator%(const BigInt& n, word mod) {
 * Left Shift Operator
 */
 BigInt operator<<(const BigInt& x, size_t shift) {
-   const size_t shift_words = shift / BOTAN_MP_WORD_BITS, shift_bits = shift % BOTAN_MP_WORD_BITS;
-
    const size_t x_sw = x.sig_words();
 
-   BigInt y = BigInt::with_capacity(x_sw + shift_words + (shift_bits ? 1 : 0));
-   bigint_shl2(y.mutable_data(), x.data(), x_sw, shift_words, shift_bits);
+   const size_t new_size = x_sw + (shift + BOTAN_MP_WORD_BITS - 1) / BOTAN_MP_WORD_BITS;
+   BigInt y = BigInt::with_capacity(new_size);
+   bigint_shl2(y.mutable_data(), x.data(), x_sw, shift);
    y.set_sign(x.sign());
    return y;
 }
@@ -187,7 +186,6 @@ BigInt operator<<(const BigInt& x, size_t shift) {
 */
 BigInt operator>>(const BigInt& x, size_t shift) {
    const size_t shift_words = shift / BOTAN_MP_WORD_BITS;
-   const size_t shift_bits = shift % BOTAN_MP_WORD_BITS;
    const size_t x_sw = x.sig_words();
 
    if(shift_words >= x_sw) {
@@ -195,7 +193,7 @@ BigInt operator>>(const BigInt& x, size_t shift) {
    }
 
    BigInt y = BigInt::with_capacity(x_sw - shift_words);
-   bigint_shr2(y.mutable_data(), x.data(), x_sw, shift_words, shift_bits);
+   bigint_shr2(y.mutable_data(), x.data(), x_sw, shift);
 
    if(x.is_negative() && y.is_zero()) {
       y.set_sign(BigInt::Positive);
diff --git a/src/lib/math/bigint/bigint.cpp b/src/lib/math/bigint/bigint.cpp
index 41f0817344c..a6e59b275ad 100644
--- a/src/lib/math/bigint/bigint.cpp
+++ b/src/lib/math/bigint/bigint.cpp
@@ -433,14 +433,14 @@ void BigInt::ct_cond_add(bool predicate, const BigInt& value) {
 void BigInt::ct_shift_left(size_t shift) {
    auto shl_bit = [](const BigInt& a, BigInt& result) {
       BOTAN_DEBUG_ASSERT(a.size() + 1 == result.size());
-      bigint_shl2(result.mutable_data(), a.data(), a.size(), 0, 1);
+      bigint_shl2(result.mutable_data(), a.data(), a.size(), 1);
       // shl2 may have shifted a bit into the next word, which must be dropped
       clear_mem(result.mutable_data() + result.size() - 1, 1);
    };
 
    auto shl_word = [](const BigInt& a, BigInt& result) {
       // the most significant word is not copied, aka. shifted out
-      bigint_shl2(result.mutable_data(), a.data(), a.size() - 1 /* ignore msw */, 1, 0);
+      bigint_shl2(result.mutable_data(), a.data(), a.size() - 1 /* ignore msw */, BOTAN_MP_WORD_BITS);
       // we left-shifted by a full word, the least significant word must be zero'ed
       clear_mem(result.mutable_data(), 1);
    };
diff --git a/src/lib/math/bigint/divide.cpp b/src/lib/math/bigint/divide.cpp
index 341ebd8f0b9..5d91510473b 100644
--- a/src/lib/math/bigint/divide.cpp
+++ b/src/lib/math/bigint/divide.cpp
@@ -202,7 +202,7 @@ void vartime_divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt&
 
       word qjt = bigint_divop_vartime(x_j0, x_j1, y_t0);
 
-      qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(MP_WORD_MAX, qjt);
+      qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(WordInfo<word>::max, qjt);
 
       // Per HAC 14.23, this operation is required at most twice
       qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);
diff --git a/src/lib/math/mp/mp_asmi.h b/src/lib/math/mp/mp_asmi.h
index 307645c40f8..2c0245c4a70 100644
--- a/src/lib/math/mp/mp_asmi.h
+++ b/src/lib/math/mp/mp_asmi.h
@@ -34,24 +34,30 @@ template <typename T>
 concept WordType = (std::same_as<T, uint32_t> || std::same_as<T, uint64_t>);
 
 template <WordType W>
-struct DwordType {};
+struct WordInfo {};
 
 template <>
-struct DwordType<uint32_t> {
+struct WordInfo<uint32_t> {
    public:
-      typedef uint64_t type;
-      static const bool is_native = true;
+      static const constexpr size_t bits = 32;
+      static const constexpr uint32_t max = 0xFFFFFFFF;
+
+      typedef uint64_t dword;
+      static const constexpr bool dword_is_native = true;
 };
 
 template <>
-struct DwordType<uint64_t> {
+struct WordInfo<uint64_t> {
    public:
+      static const constexpr size_t bits = 64;
+      static const constexpr uint64_t max = 0xFFFFFFFFFFFFFFFF;
+
 #if defined(BOTAN_TARGET_HAS_NATIVE_UINT128)
-      typedef uint128_t type;
-      static const bool is_native = true;
+      typedef uint128_t dword;
+      static const constexpr bool dword_is_native = true;
 #else
-      typedef donna128 type;
-      static const bool is_native = false;
+      typedef donna128 dword;
+      static const constexpr bool dword_is_native = false;
 #endif
 };
 
@@ -90,7 +96,7 @@ inline constexpr auto word_madd2(W a, W b, W* c) -> W {
    }
 #endif
 
-   typedef typename DwordType<W>::type dword;
+   typedef typename WordInfo<W>::dword dword;
    const dword s = dword(a) * b + *c;
    *c = static_cast<W>(s >> (sizeof(W) * 8));
    return static_cast<W>(s);
@@ -139,7 +145,7 @@ inline constexpr auto word_madd3(W a, W b, W c, W* d) -> W {
    }
 #endif
 
-   typedef typename DwordType<W>::type dword;
+   typedef typename WordInfo<W>::dword dword;
    const dword s = dword(a) * b + c + *d;
    *d = static_cast<W>(s >> (sizeof(W) * 8));
    return static_cast<W>(s);
diff --git a/src/lib/math/mp/mp_core.h b/src/lib/math/mp/mp_core.h
index 79044b9f15e..4ecd319e190 100644
--- a/src/lib/math/mp/mp_core.h
+++ b/src/lib/math/mp/mp_core.h
@@ -19,8 +19,6 @@
 
 namespace Botan {
 
-const word MP_WORD_MAX = ~static_cast<word>(0);
-
 /*
 * If cond == 0, does nothing.
 * If cond > 0, swaps x[0:size] with y[0:size]
@@ -396,12 +394,15 @@ inline constexpr auto bigint_sub_abs(W z[], const W x[], const W y[], size_t N,
 * Shift Operations
 */
 template <WordType W>
-inline constexpr void bigint_shl1(W x[], size_t x_size, size_t x_words, size_t word_shift, size_t bit_shift) {
+inline constexpr void bigint_shl1(W x[], size_t x_size, size_t x_words, size_t shift) {
+   const size_t word_shift = shift / WordInfo<W>::bits;
+   const size_t bit_shift = shift % WordInfo<W>::bits;
+
    copy_mem(x + word_shift, x, x_words);
    clear_mem(x, word_shift);
 
    const auto carry_mask = CT::Mask<W>::expand(bit_shift);
-   const W carry_shift = carry_mask.if_set_return(sizeof(W) * 8 - bit_shift);
+   const W carry_shift = carry_mask.if_set_return(WordInfo<W>::bits - bit_shift);
 
    W carry = 0;
    for(size_t i = word_shift; i != x_size; ++i) {
@@ -412,7 +413,10 @@ inline constexpr void bigint_shl1(W x[], size_t x_size, size_t x_words, size_t w
 }
 
 template <WordType W>
-inline constexpr void bigint_shr1(W x[], size_t x_size, size_t word_shift, size_t bit_shift) {
+inline constexpr void bigint_shr1(W x[], size_t x_size, size_t shift) {
+   const size_t word_shift = shift / WordInfo<W>::bits;
+   const size_t bit_shift = shift % WordInfo<W>::bits;
+
    const size_t top = x_size >= word_shift ? (x_size - word_shift) : 0;
 
    if(top > 0) {
@@ -421,7 +425,7 @@ inline constexpr void bigint_shr1(W x[], size_t x_size, size_t word_shift, size_
    clear_mem(x + top, std::min(word_shift, x_size));
 
    const auto carry_mask = CT::Mask<W>::expand(bit_shift);
-   const W carry_shift = carry_mask.if_set_return(sizeof(W) * 8 - bit_shift);
+   const W carry_shift = carry_mask.if_set_return(WordInfo<W>::bits - bit_shift);
 
    W carry = 0;
 
@@ -433,11 +437,14 @@ inline constexpr void bigint_shr1(W x[], size_t x_size, size_t word_shift, size_
 }
 
 template <WordType W>
-inline constexpr void bigint_shl2(W y[], const W x[], size_t x_size, size_t word_shift, size_t bit_shift) {
+inline constexpr void bigint_shl2(W y[], const W x[], size_t x_size, size_t shift) {
+   const size_t word_shift = shift / WordInfo<W>::bits;
+   const size_t bit_shift = shift % WordInfo<W>::bits;
+
    copy_mem(y + word_shift, x, x_size);
 
    const auto carry_mask = CT::Mask<W>::expand(bit_shift);
-   const W carry_shift = carry_mask.if_set_return(sizeof(W) * 8 - bit_shift);
+   const W carry_shift = carry_mask.if_set_return(WordInfo<W>::bits - bit_shift);
 
    W carry = 0;
    for(size_t i = word_shift; i != x_size + word_shift + 1; ++i) {
@@ -448,7 +455,9 @@ inline constexpr void bigint_shl2(W y[], const W x[], size_t x_size, size_t word
 }
 
 template <WordType W>
-inline constexpr void bigint_shr2(W y[], const W x[], size_t x_size, size_t word_shift, size_t bit_shift) {
+inline constexpr void bigint_shr2(W y[], const W x[], size_t x_size, size_t shift) {
+   const size_t word_shift = shift / WordInfo<W>::bits;
+   const size_t bit_shift = shift % WordInfo<W>::bits;
    const size_t new_size = x_size < word_shift ? 0 : (x_size - word_shift);
 
    if(new_size > 0) {
@@ -456,7 +465,7 @@ inline constexpr void bigint_shr2(W y[], const W x[], size_t x_size, size_t word
    }
 
    const auto carry_mask = CT::Mask<W>::expand(bit_shift);
-   const W carry_shift = carry_mask.if_set_return(sizeof(W) * 8 - bit_shift);
+   const W carry_shift = carry_mask.if_set_return(WordInfo<W>::bits - bit_shift);
 
    W carry = 0;
    for(size_t i = new_size; i > 0; --i) {
@@ -701,22 +710,20 @@ inline constexpr auto bigint_divop_vartime(W n1, W n0, W d) -> W {
       throw Invalid_Argument("bigint_divop_vartime divide by zero");
    }
 
-   constexpr const size_t W_bits = sizeof(W) * 8;
-
-   if constexpr(DwordType<W>::is_native) {
-      typename DwordType<W>::type n = n1;
-      n <<= W_bits;
+   if constexpr(WordInfo<W>::dword_is_native) {
+      typename WordInfo<W>::dword n = n1;
+      n <<= WordInfo<W>::bits;
       n |= n0;
       return static_cast<W>(n / d);
    } else {
       W high = n1 % d;
       W quotient = 0;
 
-      for(size_t i = 0; i != W_bits; ++i) {
-         const W high_top_bit = high >> (W_bits - 1);
+      for(size_t i = 0; i != WordInfo<W>::bits; ++i) {
+         const W high_top_bit = high >> (WordInfo<W>::bits - 1);
 
          high <<= 1;
-         high |= (n0 >> (W_bits - 1 - i)) & 1;
+         high |= (n0 >> (WordInfo<W>::bits - 1 - i)) & 1;
          quotient <<= 1;
 
          if(high_top_bit || high >= d) {
diff --git a/src/lib/math/numbertheory/mod_inv.cpp b/src/lib/math/numbertheory/mod_inv.cpp
index 29d7f169a76..97e8bbd02d1 100644
--- a/src/lib/math/numbertheory/mod_inv.cpp
+++ b/src/lib/math/numbertheory/mod_inv.cpp
@@ -62,7 +62,7 @@ BigInt inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) {
    // compute (mod + 1) / 2 which [because mod is odd] is equal to
    // (mod / 2) + 1
    copy_mem(mp1o2, mod.data(), std::min(mod.size(), mod_words));
-   bigint_shr1(mp1o2, mod_words, 0, 1);
+   bigint_shr1(mp1o2, mod_words, 1);
    word carry = bigint_add2_nc(mp1o2, mod_words, u_w, 1);
    BOTAN_ASSERT_NOMSG(carry == 0);
 
@@ -81,7 +81,7 @@ BigInt inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) {
       bigint_cnd_swap(underflow, u_w, v_w, mod_words);
 
       // a >>= 1
-      bigint_shr1(a_w, mod_words, 0, 1);
+      bigint_shr1(a_w, mod_words, 1);
 
       //if(odd_a) u -= v;
       word borrow = bigint_cnd_sub(odd_a, u_w, v_w, mod_words);
@@ -92,7 +92,7 @@ BigInt inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) {
       const word odd_u = u_w[0] & 1;
 
       // u >>= 1
-      bigint_shr1(u_w, mod_words, 0, 1);
+      bigint_shr1(u_w, mod_words, 1);
 
       //if(odd_u) u += mp1o2;
       bigint_cnd_add(odd_u, u_w, mp1o2, mod_words);
diff --git a/src/lib/math/numbertheory/monty.cpp b/src/lib/math/numbertheory/monty.cpp
index 0c9809b9de7..ceec2090f1f 100644
--- a/src/lib/math/numbertheory/monty.cpp
+++ b/src/lib/math/numbertheory/monty.cpp
@@ -26,17 +26,17 @@ word monty_inverse(word a) {
    word b = 1;
    word r = 0;
 
-   for(size_t i = 0; i != BOTAN_MP_WORD_BITS; ++i) {
+   for(size_t i = 0; i != WordInfo<word>::bits; ++i) {
       const word bi = b % 2;
       r >>= 1;
-      r += bi << (BOTAN_MP_WORD_BITS - 1);
+      r += bi << (WordInfo<word>::bits - 1);
 
       b -= a * bi;
       b >>= 1;
    }
 
    // Now invert in addition space
-   r = (MP_WORD_MAX - r) + 1;
+   r = (WordInfo<word>::max - r) + 1;
 
    return r;
 }
diff --git a/src/lib/math/numbertheory/nistp_redc.cpp b/src/lib/math/numbertheory/nistp_redc.cpp
index 923507cd34c..03ed2742b6f 100644
--- a/src/lib/math/numbertheory/nistp_redc.cpp
+++ b/src/lib/math/numbertheory/nistp_redc.cpp
@@ -62,7 +62,7 @@ void redc_p521(BigInt& x, secure_vector<word>& ws) {
    }
 
    clear_mem(ws.data(), ws.size());
-   bigint_shr2(ws.data(), x.data(), std::min(x.size(), 2 * p_words), p_full_words, p_top_bits);
+   bigint_shr2(ws.data(), x.data(), std::min(x.size(), 2 * p_words), 521);
 
    x.mask_bits(521);
    x.grow_to(p_words);
@@ -81,11 +81,12 @@ void redc_p521(BigInt& x, secure_vector<word>& ws) {
    */
    const auto bit_522_set = CT::Mask<word>::expand(top_word >> p_top_bits);
 
-   word and_512 = MP_WORD_MAX;
+   const word max = WordInfo<word>::max;
+   word and_512 = max;
    for(size_t i = 0; i != p_full_words; ++i) {
       and_512 &= x.word_at(i);
    }
-   const auto all_512_low_bits_set = CT::Mask<word>::is_equal(and_512, MP_WORD_MAX);
+   const auto all_512_low_bits_set = CT::Mask<word>::is_equal(and_512, max);
    const auto has_p521_top_word = CT::Mask<word>::is_equal(top_word, 0x1FF);
    const auto is_p521 = all_512_low_bits_set & has_p521_top_word;
 
diff --git a/src/lib/math/numbertheory/numthry.cpp b/src/lib/math/numbertheory/numthry.cpp
index c1b592c7b23..7ab4e52cc04 100644
--- a/src/lib/math/numbertheory/numthry.cpp
+++ b/src/lib/math/numbertheory/numthry.cpp
@@ -240,11 +240,11 @@ BigInt gcd(const BigInt& a, const BigInt& b) {
       factors_of_two += (u_is_even & v_is_even).if_set_return(1);
 
       // remove one factor of 2, if u is even
-      bigint_shr2(tmp.mutable_data(), u.data(), sz, 0, 1);
+      bigint_shr2(tmp.mutable_data(), u.data(), sz, 1);
       u.ct_cond_assign(u_is_even.as_bool(), tmp);
 
       // remove one factor of 2, if v is even
-      bigint_shr2(tmp.mutable_data(), v.data(), sz, 0, 1);
+      bigint_shr2(tmp.mutable_data(), v.data(), sz, 1);
       v.ct_cond_assign(v_is_even.as_bool(), tmp);
    }
 
diff --git a/src/lib/pubkey/curve448/curve448_scalar.cpp b/src/lib/pubkey/curve448/curve448_scalar.cpp
index f2357a05e91..a45b748ed90 100644
--- a/src/lib/pubkey/curve448/curve448_scalar.cpp
+++ b/src/lib/pubkey/curve448/curve448_scalar.cpp
@@ -28,11 +28,8 @@ auto div_mod_2_446(std::span<const word, S> x) {
       // Clear the two most significant bits
       r[Scalar448::WORDS - 1] &= ~(word(0b11) << (sizeof(word) * 8 - 2));
 
-      constexpr size_t word_shift = 446 / (sizeof(word) * 8);
-      constexpr size_t bit_shift = 446 % (sizeof(word) * 8);
-
       std::array<word, S - Scalar448::WORDS + 1> q;
-      bigint_shr2(q.data(), x.data(), x.size(), word_shift, bit_shift);
+      bigint_shr2(q.data(), x.data(), x.size(), 446);
 
       return std::make_pair(q, r);
    }
diff --git a/src/lib/utils/mem_pool/mem_pool.cpp b/src/lib/utils/mem_pool/mem_pool.cpp
index ebd92259fa4..93c40d6ee8d 100644
--- a/src/lib/utils/mem_pool/mem_pool.cpp
+++ b/src/lib/utils/mem_pool/mem_pool.cpp
@@ -185,14 +185,12 @@ class BitMap final {
    private:
 #if defined(BOTAN_ENABLE_DEBUG_ASSERTS)
       using bitmask_type = uint8_t;
-
-      enum { BITMASK_BITS = 8 };
 #else
       using bitmask_type = word;
-
-      enum { BITMASK_BITS = BOTAN_MP_WORD_BITS };
 #endif
 
+      static const size_t BITMASK_BITS = sizeof(bitmask_type) * 8;
+
       size_t m_len;
       bitmask_type m_main_mask;
       bitmask_type m_last_mask;
diff --git a/src/tests/test_mp.cpp b/src/tests/test_mp.cpp
index ff07e0bb763..dd976c22c54 100644
--- a/src/tests/test_mp.cpp
+++ b/src/tests/test_mp.cpp
@@ -33,7 +33,7 @@ class MP_Unit_Tests final : public Test {
       static Result test_cnd_add() {
          Result result("bigint_cnd_add");
 
-         const Botan::word max = Botan::MP_WORD_MAX;
+         const Botan::word max = ~static_cast<Botan::word>(0);
 
          Botan::word a = 2;
          Botan::word c = Botan::bigint_cnd_add<Botan::word>(0, &a, &max, 1);
@@ -63,7 +63,7 @@ class MP_Unit_Tests final : public Test {
 
          c = Botan::bigint_cnd_sub<Botan::word>(1, &a, &b, 1);
 
-         result.test_int_eq(a, Botan::MP_WORD_MAX, "Sub");
+         result.test_int_eq(a, ~static_cast<Botan::word>(0), "Sub");
          result.test_int_eq(c, 1, "Borrow");
 
          return result;
@@ -72,7 +72,9 @@ class MP_Unit_Tests final : public Test {
       static Result test_cnd_abs() {
          Result result("bigint_cnd_abs");
 
-         Botan::word x1 = Botan::MP_WORD_MAX;
+         const Botan::word max = Botan::WordInfo<Botan::word>::max;
+
+         Botan::word x1 = max;
          Botan::bigint_cnd_abs<Botan::word>(1, &x1, 1);
          result.test_int_eq(x1, 1, "Abs");
 
@@ -82,13 +84,13 @@ class MP_Unit_Tests final : public Test {
 
          x1 = 1;
          Botan::bigint_cnd_abs<Botan::word>(1, &x1, 1);
-         result.test_int_eq(x1, Botan::MP_WORD_MAX, "Abs");
+         result.test_int_eq(x1, max, "Abs");
 
          x1 = 1;
          Botan::bigint_cnd_abs<Botan::word>(0, &x1, 1);
          result.test_int_eq(x1, 1, "No change");
 
-         Botan::word x2[2] = {Botan::MP_WORD_MAX, Botan::MP_WORD_MAX};
+         Botan::word x2[2] = {max, max};
 
          Botan::bigint_cnd_abs<Botan::word>(1, x2, 2);
          result.test_int_eq(x2[0], 1, "Abs");