diff --git a/include/xsimd/arch/common/xsimd_common_arithmetic.hpp b/include/xsimd/arch/common/xsimd_common_arithmetic.hpp
index c160670d4..457c78286 100644
--- a/include/xsimd/arch/common/xsimd_common_arithmetic.hpp
+++ b/include/xsimd/arch/common/xsimd_common_arithmetic.hpp
@@ -16,6 +16,7 @@
 #include <limits>
 #include <type_traits>
 
+#include "../xsimd_common_fwd.hpp"
 #include "./xsimd_common_details.hpp"
 
 namespace xsimd
@@ -26,7 +27,7 @@ namespace xsimd
 
         using namespace types;
 
-        // bitwise_lshift
+        // bitwise_lshift multiple (dynamic)
         template <class A, class T, class /*=typename std::enable_if<std::is_integral<T>::value>::type*/>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, batch<T, A> const& other, requires_arch<common>) noexcept
         {
@@ -34,6 +35,15 @@ namespace xsimd
                                  { return x << y; },
                                  self, other);
         }
+
+        // bitwise_lshift multiple (constant)
+        template <class A, class T, T... Vals, detail::enable_integral_t<T>>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& lhs, batch_constant<T, A, Vals...> const& rhs, requires_arch<common> req) noexcept
+        {
+            return bitwise_lshift(lhs, rhs.as_batch(), req);
+        }
+
+        // bitwise_lshift single (constant)
         template <size_t shift, class A, class T, class /*=typename std::enable_if<std::is_integral<T>::value>::type*/>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, requires_arch<common>) noexcept
         {
diff --git a/include/xsimd/arch/utils/shifts.hpp b/include/xsimd/arch/utils/shifts.hpp
new file mode 100644
index 000000000..8ddb5edb8
--- /dev/null
+++ b/include/xsimd/arch/utils/shifts.hpp
@@ -0,0 +1,63 @@
+/***************************************************************************
+ * Copyright (c) Johan Mabille, Sylvain Corlay, Wolf Vollprecht and         *
+ * Martin Renou                                                             *
+ * Copyright (c) QuantStack                                                 *
+ * Copyright (c) Serge Guelton                                              *
+ * Copyright (c) Marco Barbone                                              *
+ *                                                                          *
+ * Distributed under the terms of the BSD 3-Clause License.                 *
+ *                                                                          *
+ * The full license is in the file LICENSE, distributed with this software. *
+ ****************************************************************************/
+
+#ifndef XSIMD_UTILS_SHIFTS_HPP
+#define XSIMD_UTILS_SHIFTS_HPP
+
+#include "xsimd/config/xsimd_inline.hpp"
+#include "xsimd/types/xsimd_batch.hpp"
+
+namespace xsimd
+{
+    namespace kernel
+    {
+        namespace utils
+        {
+            template <typename I, I offset, I length, I... Vs>
+            struct select_stride
+            {
+                static constexpr I values_array[] = { Vs... };
+
+                template <typename K>
+                static constexpr K get(K i, K)
+                {
+                    return static_cast<K>(values_array[length * i + offset]);
+                }
+            };
+
+            template <class T, class T2, class A, class R, T... Vs>
+            XSIMD_INLINE batch<T, A> bitwise_lshift_as_twice_larger(
+                batch<T, A> const& self, batch_constant<T, A, Vs...>, R req) noexcept
+            {
+                static_assert(sizeof(T2) == 2 * sizeof(T), "One size must be twice the other");
+
+                const auto self2 = bitwise_cast<T2>(self);
+
+                // Lower byte: shift as twice the size and mask bits flowing to higher byte.
+                constexpr auto shifts_lo = make_batch_constant<T2, select_stride<T, 0, 2, Vs...>, A>();
+                const auto shifted_lo = bitwise_lshift<A>(self2, shifts_lo, req);
+                const batch<T2, A> mask_lo { T2 { 0x00FF } };
+                const auto masked_lo = bitwise_and<A>(shifted_lo, mask_lo, req);
+
+                // Higher byte: mask bits that would flow from lower byte and shift as twice the size.
+                constexpr auto shifts_hi = make_batch_constant<T2, select_stride<T, 1, 2, Vs...>, A>();
+                const batch<T2, A> mask_hi { T2 { 0xFF00 } };
+                const auto masked_hi = bitwise_and<A>(self2, mask_hi, req);
+                const auto shifted_hi = bitwise_lshift<A>(masked_hi, shifts_hi, req);
+
+                return bitwise_cast<T>(bitwise_or(masked_lo, shifted_hi, req));
+            }
+        }
+    }
+}
+
+#endif
diff --git a/include/xsimd/arch/xsimd_avx.hpp b/include/xsimd/arch/xsimd_avx.hpp
index f8545d11c..c5504ef32 100644
--- a/include/xsimd/arch/xsimd_avx.hpp
+++ b/include/xsimd/arch/xsimd_avx.hpp
@@ -249,7 +249,7 @@ namespace xsimd
                                       self, other);
         }
 
-        // bitwise_lshift
+        // bitwise_lshift single
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, int32_t other, requires_arch<avx>) noexcept
         {
@@ -258,6 +258,13 @@ namespace xsimd
                                       self, other);
         }
 
+        // bitwise_lshift multiple
+        template <class A, class T, T... Vals, detail::enable_integral_t<T> = 0>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& lhs, batch_constant<T, A, Vals...> const& rhs, requires_arch<avx> req) noexcept
+        {
+            return bitwise_lshift(lhs, rhs.as_batch(), req);
+        }
+
         // bitwise_not
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_not(batch<T, A> const& self, requires_arch<avx>) noexcept
diff --git a/include/xsimd/arch/xsimd_avx2.hpp b/include/xsimd/arch/xsimd_avx2.hpp
index 2c44df461..3b5d5c81c 100644
--- a/include/xsimd/arch/xsimd_avx2.hpp
+++ b/include/xsimd/arch/xsimd_avx2.hpp
@@ -13,11 +13,11 @@
 #define XSIMD_AVX2_HPP
 
 #include <complex>
+#include <limits>
 #include <type_traits>
 
 #include "../types/xsimd_avx2_register.hpp"
-
-#include <limits>
+#include "./utils/shifts.hpp"
 
 namespace xsimd
 {
@@ -152,7 +152,19 @@ namespace xsimd
             return _mm256_xor_si256(self, _mm256_set1_epi32(-1));
         }
 
-        // bitwise_lshift
+        // bitwise_or
+        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
+        XSIMD_INLINE batch<T, A> bitwise_or(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx2>) noexcept
+        {
+            return _mm256_or_si256(self, other);
+        }
+        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
+        XSIMD_INLINE batch_bool<T, A> bitwise_or(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx2>) noexcept
+        {
+            return _mm256_or_si256(self, other);
+        }
+
+        // bitwise_lshift single (dynamic)
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, int32_t other, requires_arch<avx2>) noexcept
         {
@@ -174,6 +186,7 @@ namespace xsimd
             }
         }
 
+        // bitwise_lshift single (constant)
         template <size_t shift, class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, requires_arch<avx2>) noexcept
         {
@@ -197,6 +210,7 @@ namespace xsimd
             }
         }
 
+        // bitwise_lshift multiple (dynamic)
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx2>) noexcept
         {
@@ -214,16 +228,20 @@ namespace xsimd
             }
         }
 
-        // bitwise_or
-        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
-        XSIMD_INLINE batch<T, A> bitwise_or(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx2>) noexcept
+        // bitwise_lshift multiple (constant)
+        template <class A, uint16_t... Vs>
+        XSIMD_INLINE batch<uint16_t, A> bitwise_lshift(
+            batch<uint16_t, A> const& self, batch_constant<uint16_t, A, Vs...> shifts, requires_arch<avx2>) noexcept
         {
-            return _mm256_or_si256(self, other);
+            constexpr auto mults = batch_constant<uint16_t, A, static_cast<uint16_t>(1u << Vs)...>();
+            return _mm256_mullo_epi16(self, mults.as_batch());
         }
-        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
-        XSIMD_INLINE batch_bool<T, A> bitwise_or(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx2>) noexcept
+
+        template <class A, uint8_t... Vs>
+        XSIMD_INLINE batch<uint8_t, A> bitwise_lshift(
+            batch<uint8_t, A> const& self, batch_constant<uint8_t, A, Vs...> shifts, requires_arch<avx2> req) noexcept
         {
-            return _mm256_or_si256(self, other);
+            return utils::bitwise_lshift_as_twice_larger<uint8_t, uint16_t>(self, shifts, req);
         }
 
         // bitwise_rshift
diff --git a/include/xsimd/arch/xsimd_common_fwd.hpp b/include/xsimd/arch/xsimd_common_fwd.hpp
index 2b401155b..8cc73da46 100644
--- a/include/xsimd/arch/xsimd_common_fwd.hpp
+++ b/include/xsimd/arch/xsimd_common_fwd.hpp
@@ -26,6 +26,8 @@ namespace xsimd
         XSIMD_INLINE batch<T, A> abs(batch<T, A> const& self, requires_arch<common>) noexcept;
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, batch<T, A> const& other, requires_arch<common>) noexcept;
+        template <class A, class T, T... Vals, detail::enable_integral_t<T> = 0>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& lhs, batch_constant<T, A, Vals...> const& rhs, requires_arch<common> req) noexcept;
         template <size_t shift, class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
         XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, requires_arch<common>) noexcept;
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
diff --git a/include/xsimd/arch/xsimd_sse2.hpp b/include/xsimd/arch/xsimd_sse2.hpp
index deb1af542..c7b21c745 100644
--- a/include/xsimd/arch/xsimd_sse2.hpp
+++ b/include/xsimd/arch/xsimd_sse2.hpp
@@ -17,6 +17,7 @@
 #include <type_traits>
 
 #include "../types/xsimd_sse2_register.hpp"
+#include "./utils/shifts.hpp"
 
 namespace xsimd
 {
@@ -266,63 +267,6 @@ namespace xsimd
             return _mm_andnot_pd(other, self);
         }
 
-        // bitwise_lshift
-        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
-        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, int32_t other, requires_arch<sse2>) noexcept
-        {
-            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
-            {
-                return _mm_and_si128(_mm_set1_epi8(0xFF << other), _mm_slli_epi32(self, other));
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
-            {
-                return _mm_slli_epi16(self, other);
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
-            {
-                return _mm_slli_epi32(self, other);
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
-            {
-                return _mm_slli_epi64(self, other);
-            }
-            else
-            {
-                assert(false && "unsupported arch/op combination");
-                return {};
-            }
-        }
-        template <size_t shift, class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
-        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, requires_arch<sse2>) noexcept
-        {
-            constexpr auto bits = std::numeric_limits<T>::digits + std::numeric_limits<T>::is_signed;
-            static_assert(shift < bits, "Count must be less than the number of bits in T");
-            XSIMD_IF_CONSTEXPR(shift == 0)
-            {
-                return self;
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
-            {
-                // 8-bit left shift via 16-bit shift + mask
-                __m128i shifted = _mm_slli_epi16(self, static_cast<int>(shift));
-                __m128i mask = _mm_set1_epi8(static_cast<char>(0xFF << shift));
-                return _mm_and_si128(shifted, mask);
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
-            {
-                return _mm_slli_epi16(self, static_cast<int>(shift));
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
-            {
-                return _mm_slli_epi32(self, static_cast<int>(shift));
-            }
-            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
-            {
-                return _mm_slli_epi64(self, static_cast<int>(shift));
-            }
-            return bitwise_lshift<shift>(self, common {});
-        }
-
         // bitwise_not
         template <class A>
         XSIMD_INLINE batch<float, A> bitwise_not(batch<float, A> const& self, requires_arch<sse2>) noexcept
@@ -577,6 +521,81 @@ namespace xsimd
             return _mm_castpd_si128(self);
         }
 
+        // bitwise_lshift single (dynamic)
+        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, int32_t other, requires_arch<sse2>) noexcept
+        {
+            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
+            {
+                return _mm_and_si128(_mm_set1_epi8(0xFF << other), _mm_slli_epi32(self, other));
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
+            {
+                return _mm_slli_epi16(self, other);
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
+            {
+                return _mm_slli_epi32(self, other);
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
+            {
+                return _mm_slli_epi64(self, other);
+            }
+            else
+            {
+                assert(false && "unsupported arch/op combination");
+                return {};
+            }
+        }
+
+        // bitwise_lshift single (constant)
+        template <size_t shift, class A, class T, class = typename std::enable_if<std::is_integral<T>::value>::type>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& self, requires_arch<sse2>) noexcept
+        {
+            constexpr auto bits = std::numeric_limits<T>::digits + std::numeric_limits<T>::is_signed;
+            static_assert(shift < bits, "Count must be less than the number of bits in T");
+            XSIMD_IF_CONSTEXPR(shift == 0)
+            {
+                return self;
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
+            {
+                // 8-bit left shift via 16-bit shift + mask
+                __m128i shifted = _mm_slli_epi16(self, static_cast<int>(shift));
+                __m128i mask = _mm_set1_epi8(static_cast<char>(0xFF << shift));
+                return _mm_and_si128(shifted, mask);
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
+            {
+                return _mm_slli_epi16(self, static_cast<int>(shift));
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
+            {
+                return _mm_slli_epi32(self, static_cast<int>(shift));
+            }
+            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
+            {
+                return _mm_slli_epi64(self, static_cast<int>(shift));
+            }
+            return bitwise_lshift<shift>(self, common {});
+        }
+
+        // bitwise_lshift multiple (constant)
+        template <class A, uint16_t... Vs>
+        XSIMD_INLINE batch<uint16_t, A> bitwise_lshift(
+            batch<uint16_t, A> const& self, batch_constant<uint16_t, A, Vs...>, requires_arch<sse2>) noexcept
+        {
+            constexpr auto mults = batch_constant<uint16_t, A, static_cast<uint16_t>(1u << Vs)...>();
+            return _mm_mullo_epi16(self, mults.as_batch());
+        }
+
+        template <class A, uint8_t... Vs>
+        XSIMD_INLINE batch<uint8_t, A> bitwise_lshift(
+            batch<uint8_t, A> const& self, batch_constant<uint8_t, A, Vs...> shifts, requires_arch<sse2> req) noexcept
+        {
+            return utils::bitwise_lshift_as_twice_larger<uint8_t, uint16_t>(self, shifts, req);
+        }
+
         // broadcast
         template <class A>
         batch<float, A> XSIMD_INLINE broadcast(float val, requires_arch<sse2>) noexcept
diff --git a/include/xsimd/arch/xsimd_sse4_1.hpp b/include/xsimd/arch/xsimd_sse4_1.hpp
index 1a64fc878..96b9186d0 100644
--- a/include/xsimd/arch/xsimd_sse4_1.hpp
+++ b/include/xsimd/arch/xsimd_sse4_1.hpp
@@ -41,6 +41,15 @@ namespace xsimd
             return _mm_ceil_pd(self);
         }
 
+        // bitwise_lshift multiple (constant)
+        template <class A, uint32_t... Vs>
+        XSIMD_INLINE batch<uint32_t, A> bitwise_lshift(
+            batch<uint32_t, A> const& self, batch_constant<uint32_t, A, Vs...> shifts, requires_arch<sse4_1>) noexcept
+        {
+            constexpr auto mults = batch_constant<uint32_t, A, static_cast<uint32_t>(1u << Vs)...>();
+            return _mm_mullo_epi32(self, mults.as_batch());
+        }
+
         // fast_cast
         namespace detail
         {
diff --git a/include/xsimd/types/xsimd_api.hpp b/include/xsimd/types/xsimd_api.hpp
index 12bd9d95e..03a5e36a2 100644
--- a/include/xsimd/types/xsimd_api.hpp
+++ b/include/xsimd/types/xsimd_api.hpp
@@ -379,6 +379,12 @@ namespace xsimd
         detail::static_check_supported_config<T, A>();
         return kernel::bitwise_lshift<shift, A>(x, A {});
     }
+    template <class T, class A, class Vt, Vt... Values>
+    XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& x, batch_constant<Vt, A, Values...> shift) noexcept
+    {
+        detail::static_check_supported_config<T, A>();
+        return kernel::bitwise_lshift<A>(x, shift, A {});
+    }
 
     /**
      * @ingroup batch_bitwise
diff --git a/test/test_xsimd_api.cpp b/test/test_xsimd_api.cpp
index a61c0e6ad..96c6e87bf 100644
--- a/test/test_xsimd_api.cpp
+++ b/test/test_xsimd_api.cpp
@@ -351,7 +351,15 @@ struct xsimd_api_integral_types_functions
 {
     using value_type = typename scalar_type<T>::type;
 
-    void test_bitwise_lshift()
+    struct arrange
+    {
+        static constexpr value_type get(size_t index, size_t /*size*/)
+        {
+            return static_cast<value_type>(index);
+        }
+    };
+
+    void test_bitwise_lshift_single()
     {
         constexpr int shift = 3;
         value_type val0(12);
@@ -364,6 +372,25 @@ struct xsimd_api_integral_types_functions
         CHECK_EQ(extract(cr), r);
     }
 
+    void test_bitwise_lshift_multiple()
+    {
+        constexpr auto Max = static_cast<value_type>(std::numeric_limits<value_type>::digits);
+        constexpr auto max_batch = xsimd::make_batch_constant<value_type, Max>();
+        constexpr auto shifts = xsimd::make_batch_constant<value_type, arrange>() % max_batch;
+
+        auto shifted = xsimd::bitwise_lshift(T(1), shifts.as_batch());
+        for (std::size_t i = 0; i < shifts.size; ++i)
+        {
+            CHECK_EQ(shifted.get(i), 1 << shifts.get(i));
+        }
+
+        auto shifted_cst = xsimd::bitwise_lshift(T(1), shifts);
+        for (std::size_t i = 0; i < shifts.size; ++i)
+        {
+            CHECK_EQ(shifted_cst.get(i), 1 << shifts.get(i));
+        }
+    }
+
     void test_bitwise_rshift()
     {
         constexpr int shift = 3;
@@ -426,9 +453,17 @@ TEST_CASE_TEMPLATE("[xsimd api | integral types functions]", B, INTEGRAL_TYPES)
 {
     xsimd_api_integral_types_functions<B> Test;
 
-    SUBCASE("bitwise_lshift")
+    SUBCASE("test_bitwise_lshift_single")
     {
-        Test.test_bitwise_lshift();
+        Test.test_bitwise_lshift_single();
+    }
+
+    SUBCASE("bitwise_lshift_multiple")
+    {
+        XSIMD_IF_CONSTEXPR(xsimd::is_batch<B>::value)
+        {
+            Test.test_bitwise_lshift_multiple();
+        }
     }
 
     SUBCASE("bitwise_rshift")