diff --git a/crates/rustc_codegen_spirv/src/abi.rs b/crates/rustc_codegen_spirv/src/abi.rs
index 04d1bf9860..622ec88915 100644
--- a/crates/rustc_codegen_spirv/src/abi.rs
+++ b/crates/rustc_codegen_spirv/src/abi.rs
@@ -3,7 +3,7 @@
 
 use crate::attr::{AggregatedSpirvAttributes, IntrinsicType};
 use crate::codegen_cx::CodegenCx;
-use crate::spirv_type::SpirvType;
+use crate::spirv_type::{SpirvType, StorageClassKind};
 use itertools::Itertools;
 use rspirv::spirv::{Dim, ImageFormat, StorageClass, Word};
 use rustc_data_structures::fx::FxHashMap;
@@ -339,6 +339,7 @@ impl<'tcx> RecursivePointeeCache<'tcx> {
                 PointeeDefState::Defining => {
                     let id = SpirvType::Pointer {
                         pointee: pointee_spv,
+                        storage_class: StorageClassKind::Inferred, // TODO(jwollen): Do we need to cache by storage class?
                     }
                     .def(span, cx);
                     entry.insert(PointeeDefState::Defined(id));
@@ -350,6 +351,7 @@ impl<'tcx> RecursivePointeeCache<'tcx> {
                     entry.insert(PointeeDefState::Defined(id));
                     SpirvType::Pointer {
                         pointee: pointee_spv,
+                        storage_class: StorageClassKind::Inferred, // TODO(jwollen): Do we need to cache by storage class?
                     }
                     .def_with_id(cx, span, id)
                 }
diff --git a/crates/rustc_codegen_spirv/src/builder/builder_methods.rs b/crates/rustc_codegen_spirv/src/builder/builder_methods.rs
index 7e61c1b989..6b9e956d6f 100644
--- a/crates/rustc_codegen_spirv/src/builder/builder_methods.rs
+++ b/crates/rustc_codegen_spirv/src/builder/builder_methods.rs
@@ -407,14 +407,15 @@ impl<'a, 'tcx> Builder<'a, 'tcx> {
         size: Size,
     ) -> Option<(SpirvValue, <Self as BackendTypes>::Type)> {
         let ptr = ptr.strip_ptrcasts();
-        let mut leaf_ty = match self.lookup_type(ptr.ty) {
-            SpirvType::Pointer { pointee } => pointee,
+        let pointee_ty = match self.lookup_type(ptr.ty) {
+            SpirvType::Pointer { pointee, .. } => pointee,
             other => self.fatal(format!("non-pointer type: {other:?}")),
         };
 
         // FIXME(eddyb) this isn't efficient, `recover_access_chain_from_offset`
         // could instead be doing all the extra digging itself.
         let mut indices = SmallVec::<[_; 8]>::new();
+        let mut leaf_ty = pointee_ty;
         while let Some((inner_indices, inner_ty)) = self.recover_access_chain_from_offset(
             leaf_ty,
             Size::ZERO,
@@ -429,7 +430,8 @@ impl<'a, 'tcx> Builder<'a, 'tcx> {
             .then(|| self.type_ptr_to(leaf_ty))?;
 
         let leaf_ptr = if indices.is_empty() {
-            assert_ty_eq!(self, ptr.ty, leaf_ptr_ty);
+            // Compare pointee types instead of pointer  types as storage class might be different.
+            assert_ty_eq!(self, pointee_ty, leaf_ty);
             ptr
         } else {
             let indices = indices
@@ -586,7 +588,7 @@ impl<'a, 'tcx> Builder<'a, 'tcx> {
         let ptr = ptr.strip_ptrcasts();
         let ptr_id = ptr.def(self);
         let original_pointee_ty = match self.lookup_type(ptr.ty) {
-            SpirvType::Pointer { pointee } => pointee,
+            SpirvType::Pointer { pointee, .. } => pointee,
             other => self.fatal(format!("gep called on non-pointer type: {other:?}")),
         };
 
@@ -1926,6 +1928,25 @@ impl<'a, 'tcx> BuilderMethods<'a, 'tcx> for Builder<'a, 'tcx> {
             return ptr;
         }
 
+        // No cast is needed if only the storage class mismatches.
+        let ptr_pointee = match self.lookup_type(ptr.ty) {
+            SpirvType::Pointer { pointee, .. } => pointee,
+            other => self.fatal(format!(
+                "pointercast called on non-pointer source type: {other:?}"
+            )),
+        };
+        let dest_pointee = match self.lookup_type(dest_ty) {
+            SpirvType::Pointer { pointee, .. } => pointee,
+            other => self.fatal(format!(
+                "pointercast called on non-pointer dest type: {other:?}"
+            )),
+        };
+
+        // FIXME(jwollen) Do we need to choose `dest_ty` if it has a fixed storage class and `ptr` has none?
+        if ptr_pointee == dest_pointee {
+            return ptr;
+        }
+
         // Strip a previous `pointercast`, to reveal the original pointer type.
         let ptr = ptr.strip_ptrcasts();
 
@@ -1934,17 +1955,16 @@ impl<'a, 'tcx> BuilderMethods<'a, 'tcx> for Builder<'a, 'tcx> {
         }
 
         let ptr_pointee = match self.lookup_type(ptr.ty) {
-            SpirvType::Pointer { pointee } => pointee,
+            SpirvType::Pointer { pointee, .. } => pointee,
             other => self.fatal(format!(
                 "pointercast called on non-pointer source type: {other:?}"
             )),
         };
-        let dest_pointee = match self.lookup_type(dest_ty) {
-            SpirvType::Pointer { pointee } => pointee,
-            other => self.fatal(format!(
-                "pointercast called on non-pointer dest type: {other:?}"
-            )),
-        };
+
+        if ptr_pointee == dest_pointee {
+            return ptr;
+        }
+
         let dest_pointee_size = self.lookup_type(dest_pointee).sizeof(self);
 
         if let Some((indices, _)) = self.recover_access_chain_from_offset(
@@ -2324,7 +2344,7 @@ impl<'a, 'tcx> BuilderMethods<'a, 'tcx> for Builder<'a, 'tcx> {
             .and_then(|size| Some(Size::from_bytes(u64::try_from(size).ok()?)));
 
         let elem_ty = match self.lookup_type(ptr.ty) {
-            SpirvType::Pointer { pointee } => pointee,
+            SpirvType::Pointer { pointee, .. } => pointee,
             _ => self.fatal(format!(
                 "memset called on non-pointer type: {}",
                 self.debug_type(ptr.ty)
@@ -2696,7 +2716,7 @@ impl<'a, 'tcx> BuilderMethods<'a, 'tcx> for Builder<'a, 'tcx> {
                 (callee.def(self), return_type, arguments)
             }
 
-            SpirvType::Pointer { pointee } => match self.lookup_type(pointee) {
+            SpirvType::Pointer { pointee, .. } => match self.lookup_type(pointee) {
                 SpirvType::Function {
                     return_type,
                     arguments,
diff --git a/crates/rustc_codegen_spirv/src/builder/mod.rs b/crates/rustc_codegen_spirv/src/builder/mod.rs
index 972432267e..041d948008 100644
--- a/crates/rustc_codegen_spirv/src/builder/mod.rs
+++ b/crates/rustc_codegen_spirv/src/builder/mod.rs
@@ -15,8 +15,8 @@ use crate::maybe_pqp_cg_ssa as rustc_codegen_ssa;
 use crate::abi::ConvSpirvType;
 use crate::builder_spirv::{BuilderCursor, SpirvValue, SpirvValueExt};
 use crate::codegen_cx::CodegenCx;
-use crate::spirv_type::SpirvType;
-use rspirv::spirv::Word;
+use crate::spirv_type::{SpirvType, StorageClassKind};
+use rspirv::spirv::{StorageClass, Word};
 use rustc_codegen_ssa::mir::operand::{OperandRef, OperandValue};
 use rustc_codegen_ssa::mir::place::PlaceRef;
 use rustc_codegen_ssa::traits::{
@@ -104,7 +104,23 @@ impl<'a, 'tcx> Builder<'a, 'tcx> {
 
     // HACK(eddyb) like the `CodegenCx` method but with `self.span()` awareness.
     pub fn type_ptr_to(&self, ty: Word) -> Word {
-        SpirvType::Pointer { pointee: ty }.def(self.span(), self)
+        SpirvType::Pointer {
+            pointee: ty,
+            storage_class: StorageClassKind::Inferred,
+        }
+        .def(self.span(), self)
+    }
+
+    pub fn type_ptr_with_storage_class_to(
+        &self,
+        ty: Word,
+        storage_class: StorageClassKind,
+    ) -> Word {
+        SpirvType::Pointer {
+            pointee: ty,
+            storage_class,
+        }
+        .def(self.span(), self)
     }
 
     // TODO: Definitely add tests to make sure this impl is right.
diff --git a/crates/rustc_codegen_spirv/src/builder/spirv_asm.rs b/crates/rustc_codegen_spirv/src/builder/spirv_asm.rs
index 91da22473d..b50e139f56 100644
--- a/crates/rustc_codegen_spirv/src/builder/spirv_asm.rs
+++ b/crates/rustc_codegen_spirv/src/builder/spirv_asm.rs
@@ -4,7 +4,7 @@ use crate::maybe_pqp_cg_ssa as rustc_codegen_ssa;
 use super::Builder;
 use crate::builder_spirv::{BuilderCursor, SpirvValue};
 use crate::codegen_cx::CodegenCx;
-use crate::spirv_type::SpirvType;
+use crate::spirv_type::{SpirvType, StorageClassKind};
 use rspirv::dr;
 use rspirv::grammar::{LogicalOperand, OperandKind, OperandQuantifier, reflect};
 use rspirv::spirv::{
@@ -307,19 +307,14 @@ impl<'cx, 'tcx> Builder<'cx, 'tcx> {
             }
             .def(self.span(), self),
             Op::TypePointer => {
-                let storage_class = inst.operands[0].unwrap_storage_class();
-                if storage_class != StorageClass::Generic {
-                    self.struct_err("TypePointer in asm! requires `Generic` storage class")
-                        .with_note(format!(
-                            "`{storage_class:?}` storage class was specified"
-                        ))
-                        .with_help(format!(
-                            "the storage class will be inferred automatically (e.g. to `{storage_class:?}`)"
-                        ))
-                        .emit();
-                }
+                // The storage class can be specified explicitly or inferred later by using StorageClass::Generic.
+                let storage_class = match inst.operands[0].unwrap_storage_class() {
+                    StorageClass::Generic => StorageClassKind::Inferred,
+                    storage_class => StorageClassKind::Explicit(storage_class),
+                };
                 SpirvType::Pointer {
                     pointee: inst.operands[1].unwrap_id_ref(),
+                    storage_class,
                 }
                 .def(self.span(), self)
             }
@@ -678,6 +673,7 @@ impl<'cx, 'tcx> Builder<'cx, 'tcx> {
 
                 TyPat::Pointer(_, pat) => SpirvType::Pointer {
                     pointee: subst_ty_pat(cx, pat, ty_vars, leftover_operands)?,
+                    storage_class: StorageClassKind::Inferred,
                 }
                 .def(DUMMY_SP, cx),
 
@@ -931,7 +927,7 @@ impl<'cx, 'tcx> Builder<'cx, 'tcx> {
                     Some(match kind {
                         TypeofKind::Plain => ty,
                         TypeofKind::Dereference => match self.lookup_type(ty) {
-                            SpirvType::Pointer { pointee } => pointee,
+                            SpirvType::Pointer { pointee, .. } => pointee,
                             other => {
                                 self.tcx.dcx().span_err(
                                     span,
@@ -953,7 +949,7 @@ impl<'cx, 'tcx> Builder<'cx, 'tcx> {
                     self.check_reg(span, reg);
                     if let Some(place) = place {
                         match self.lookup_type(place.val.llval.ty) {
-                            SpirvType::Pointer { pointee } => Some(pointee),
+                            SpirvType::Pointer { pointee, .. } => Some(pointee),
                             other => {
                                 self.tcx.dcx().span_err(
                                     span,
diff --git a/crates/rustc_codegen_spirv/src/builder_spirv.rs b/crates/rustc_codegen_spirv/src/builder_spirv.rs
index 3c91b48872..ca89379969 100644
--- a/crates/rustc_codegen_spirv/src/builder_spirv.rs
+++ b/crates/rustc_codegen_spirv/src/builder_spirv.rs
@@ -101,7 +101,7 @@ impl SpirvValue {
                 match entry.val {
                     SpirvConst::PtrTo { pointee } => {
                         let ty = match cx.lookup_type(self.ty) {
-                            SpirvType::Pointer { pointee } => pointee,
+                            SpirvType::Pointer { pointee, .. } => pointee,
                             ty => bug!("load called on value that wasn't a pointer: {:?}", ty),
                         };
                         // FIXME(eddyb) deduplicate this `if`-`else` and its other copies.
diff --git a/crates/rustc_codegen_spirv/src/codegen_cx/constant.rs b/crates/rustc_codegen_spirv/src/codegen_cx/constant.rs
index 162eb9dc8c..e32bfad3b5 100644
--- a/crates/rustc_codegen_spirv/src/codegen_cx/constant.rs
+++ b/crates/rustc_codegen_spirv/src/codegen_cx/constant.rs
@@ -239,7 +239,7 @@ impl<'tcx> ConstCodegenMethods<'tcx> for CodegenCx<'tcx> {
                 let (base_addr, _base_addr_space) = match self.tcx.global_alloc(alloc_id) {
                     GlobalAlloc::Memory(alloc) => {
                         let pointee = match self.lookup_type(ty) {
-                            SpirvType::Pointer { pointee } => pointee,
+                            SpirvType::Pointer { pointee, .. } => pointee,
                             other => self.tcx.dcx().fatal(format!(
                                 "GlobalAlloc::Memory type not implemented: {}",
                                 other.debug(ty, self)
@@ -259,7 +259,7 @@ impl<'tcx> ConstCodegenMethods<'tcx> for CodegenCx<'tcx> {
                             .global_alloc(self.tcx.vtable_allocation((vty, dyn_ty.principal())))
                             .unwrap_memory();
                         let pointee = match self.lookup_type(ty) {
-                            SpirvType::Pointer { pointee } => pointee,
+                            SpirvType::Pointer { pointee, .. } => pointee,
                             other => self.tcx.dcx().fatal(format!(
                                 "GlobalAlloc::VTable type not implemented: {}",
                                 other.debug(ty, self)
@@ -328,7 +328,7 @@ impl<'tcx> CodegenCx<'tcx> {
                 if let Some(SpirvConst::ConstDataFromAlloc(alloc)) =
                     self.builder.lookup_const_by_id(pointee)
                 {
-                    if let SpirvType::Pointer { pointee } = self.lookup_type(ty) {
+                    if let SpirvType::Pointer { pointee, .. } = self.lookup_type(ty) {
                         let mut offset = Size::ZERO;
                         let init = self.read_from_const_alloc(alloc, &mut offset, pointee);
                         return self.static_addr_of(init, alloc.inner().align, None);
diff --git a/crates/rustc_codegen_spirv/src/codegen_cx/declare.rs b/crates/rustc_codegen_spirv/src/codegen_cx/declare.rs
index eae83d8e93..592cdaa434 100644
--- a/crates/rustc_codegen_spirv/src/codegen_cx/declare.rs
+++ b/crates/rustc_codegen_spirv/src/codegen_cx/declare.rs
@@ -6,7 +6,7 @@ use crate::abi::ConvSpirvType;
 use crate::attr::AggregatedSpirvAttributes;
 use crate::builder_spirv::{SpirvConst, SpirvValue, SpirvValueExt};
 use crate::custom_decorations::{CustomDecoration, SrcLocDecoration};
-use crate::spirv_type::SpirvType;
+use crate::spirv_type::{SpirvType, StorageClassKind};
 use itertools::Itertools;
 use rspirv::spirv::{FunctionControl, LinkageType, StorageClass, Word};
 use rustc_attr::InlineAttr;
@@ -267,7 +267,12 @@ impl<'tcx> CodegenCx<'tcx> {
     }
 
     fn declare_global(&self, span: Span, ty: Word) -> SpirvValue {
-        let ptr_ty = SpirvType::Pointer { pointee: ty }.def(span, self);
+        // Could be explicitly StorageClass::Private but is inferred anyway.
+        let ptr_ty = SpirvType::Pointer {
+            pointee: ty,
+            storage_class: StorageClassKind::Inferred,
+        }
+        .def(span, self);
         // FIXME(eddyb) figure out what the correct storage class is.
         let result = self
             .emit_global()
@@ -353,7 +358,7 @@ impl<'tcx> StaticCodegenMethods for CodegenCx<'tcx> {
             Err(_) => return,
         };
         let value_ty = match self.lookup_type(g.ty) {
-            SpirvType::Pointer { pointee } => pointee,
+            SpirvType::Pointer { pointee, .. } => pointee,
             other => self.tcx.dcx().fatal(format!(
                 "global had non-pointer type {}",
                 other.debug(g.ty, self)
diff --git a/crates/rustc_codegen_spirv/src/codegen_cx/entry.rs b/crates/rustc_codegen_spirv/src/codegen_cx/entry.rs
index a2ad70a010..297c91be30 100644
--- a/crates/rustc_codegen_spirv/src/codegen_cx/entry.rs
+++ b/crates/rustc_codegen_spirv/src/codegen_cx/entry.rs
@@ -967,7 +967,7 @@ impl<'tcx> CodegenCx<'tcx> {
                 | SpirvType::Matrix { element, .. }
                 | SpirvType::Array { element, .. }
                 | SpirvType::RuntimeArray { element }
-                | SpirvType::Pointer { pointee: element }
+                | SpirvType::Pointer { pointee: element, .. }
                 | SpirvType::InterfaceBlock {
                     inner_type: element,
                 } => recurse(cx, element, has_bool, must_be_flat),
diff --git a/crates/rustc_codegen_spirv/src/codegen_cx/mod.rs b/crates/rustc_codegen_spirv/src/codegen_cx/mod.rs
index f3a3828018..6435a43e86 100644
--- a/crates/rustc_codegen_spirv/src/codegen_cx/mod.rs
+++ b/crates/rustc_codegen_spirv/src/codegen_cx/mod.rs
@@ -6,7 +6,7 @@ mod type_;
 use crate::builder::{ExtInst, InstructionTable};
 use crate::builder_spirv::{BuilderCursor, BuilderSpirv, SpirvConst, SpirvValue, SpirvValueKind};
 use crate::custom_decorations::{CustomDecoration, SrcLocDecoration, ZombieDecoration};
-use crate::spirv_type::{SpirvType, SpirvTypePrinter, TypeCache};
+use crate::spirv_type::{SpirvType, SpirvTypePrinter, StorageClassKind, TypeCache};
 use crate::symbols::Symbols;
 use crate::target::SpirvTarget;
 
@@ -234,11 +234,19 @@ impl<'tcx> CodegenCx<'tcx> {
     }
 
     pub fn type_ptr_to(&self, ty: Word) -> Word {
-        SpirvType::Pointer { pointee: ty }.def(DUMMY_SP, self)
+        SpirvType::Pointer {
+            pointee: ty,
+            storage_class: StorageClassKind::Inferred,
+        }
+        .def(DUMMY_SP, self)
     }
 
     pub fn type_ptr_to_ext(&self, ty: Word, _address_space: AddressSpace) -> Word {
-        SpirvType::Pointer { pointee: ty }.def(DUMMY_SP, self)
+        SpirvType::Pointer {
+            pointee: ty,
+            storage_class: StorageClassKind::Inferred,
+        }
+        .def(DUMMY_SP, self)
     }
 
     /// Zombie system:
@@ -866,6 +874,7 @@ impl<'tcx> MiscCodegenMethods<'tcx> for CodegenCx<'tcx> {
 
         let ty = SpirvType::Pointer {
             pointee: function.ty,
+            storage_class: StorageClassKind::Inferred,
         }
         .def(span, self);
 
diff --git a/crates/rustc_codegen_spirv/src/codegen_cx/type_.rs b/crates/rustc_codegen_spirv/src/codegen_cx/type_.rs
index f0005a9e42..256f43b8af 100644
--- a/crates/rustc_codegen_spirv/src/codegen_cx/type_.rs
+++ b/crates/rustc_codegen_spirv/src/codegen_cx/type_.rs
@@ -219,7 +219,7 @@ impl<'tcx> BaseTypeCodegenMethods<'tcx> for CodegenCx<'tcx> {
     }
     fn element_type(&self, ty: Self::Type) -> Self::Type {
         match self.lookup_type(ty) {
-            SpirvType::Pointer { pointee } => pointee,
+            SpirvType::Pointer { pointee, .. } => pointee,
             SpirvType::Vector { element, .. } => element,
             spirv_type => self.tcx.dcx().fatal(format!(
                 "element_type called on invalid type: {spirv_type:?}"
diff --git a/crates/rustc_codegen_spirv/src/linker/specializer.rs b/crates/rustc_codegen_spirv/src/linker/specializer.rs
index 01c4c9f9b1..893102c048 100644
--- a/crates/rustc_codegen_spirv/src/linker/specializer.rs
+++ b/crates/rustc_codegen_spirv/src/linker/specializer.rs
@@ -1615,6 +1615,14 @@ impl<'a, S: Specialization> InferCx<'a, S> {
 
         #[allow(clippy::match_same_arms)]
         Ok(match (a.clone(), b.clone()) {
+            // Concrete result types explicitly created inside functions
+            // can be assigned to instances.
+            // FIXME(jwollen) do we need to infere instance generics?
+            (InferOperand::Instance(_), InferOperand::Concrete(new))
+            | (InferOperand::Concrete(new), InferOperand::Instance(_)) => {
+                InferOperand::Concrete(new)
+            }
+
             // Instances of "generic" globals/functions must be of the same ID,
             // and their `generic_args` inference variables must be unified.
             (
@@ -1999,13 +2007,13 @@ impl<'a, S: Specialization> InferCx<'a, S> {
 
         if let Some(type_of_result) = type_of_result {
             // Keep the (instantiated) *Result Type*, for future instructions to use
-            // (but only if it has any `InferVar`s at all).
+            // if it has any `InferVar`s at all or if it was a concrete type.
             match type_of_result {
-                InferOperand::Var(_) | InferOperand::Instance(_) => {
+                InferOperand::Var(_) | InferOperand::Instance(_) | InferOperand::Concrete(_) => {
                     self.type_of_result
                         .insert(inst.result_id.unwrap(), type_of_result);
                 }
-                InferOperand::Unknown | InferOperand::Concrete(_) => {}
+                InferOperand::Unknown => {}
             }
         }
     }
diff --git a/crates/rustc_codegen_spirv/src/spirv_type.rs b/crates/rustc_codegen_spirv/src/spirv_type.rs
index 0c8ce42ba0..dc584484ec 100644
--- a/crates/rustc_codegen_spirv/src/spirv_type.rs
+++ b/crates/rustc_codegen_spirv/src/spirv_type.rs
@@ -61,6 +61,7 @@ pub enum SpirvType<'tcx> {
     },
     Pointer {
         pointee: Word,
+        storage_class: StorageClassKind,
     },
     Function {
         return_type: Word,
@@ -90,6 +91,17 @@ pub enum SpirvType<'tcx> {
     RayQueryKhr,
 }
 
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+pub enum StorageClassKind {
+    /// Inferred based on globals and other pointers with explicit storage classes.
+    /// This corresponds to `StorageClass::Generic` in inline `asm!` and intermediate SPIR-V.
+    Inferred,
+
+    /// Explicitly set by an instruction that needs to create a storage class,
+    /// regardless of inputs.
+    Explicit(StorageClass),
+}
+
 impl SpirvType<'_> {
     /// Note: `Builder::type_*` should be called *nowhere else* but here, to ensure
     /// `CodegenCx::type_defs` stays up-to-date
@@ -213,13 +225,18 @@ impl SpirvType<'_> {
                 );
                 result
             }
-            Self::Pointer { pointee } => {
+            Self::Pointer {
+                pointee,
+                storage_class,
+            } => {
                 // NOTE(eddyb) we emit `StorageClass::Generic` here, but later
                 // the linker will specialize the entire SPIR-V module to use
                 // storage classes inferred from `OpVariable`s.
-                let result = cx
-                    .emit_global()
-                    .type_pointer(id, StorageClass::Generic, pointee);
+                let storage_class = match storage_class {
+                    StorageClassKind::Inferred => StorageClass::Generic,
+                    StorageClassKind::Explicit(storage_class) => storage_class,
+                };
+                let result = cx.emit_global().type_pointer(id, storage_class, pointee);
                 // no pointers to functions
                 if let SpirvType::Function { .. } = cx.lookup_type(pointee) {
                     // FIXME(eddyb) use the `SPV_INTEL_function_pointers` extension.
@@ -286,13 +303,20 @@ impl SpirvType<'_> {
             return cached;
         }
         let result = match self {
-            Self::Pointer { pointee } => {
+            Self::Pointer {
+                pointee,
+                storage_class,
+            } => {
                 // NOTE(eddyb) we emit `StorageClass::Generic` here, but later
                 // the linker will specialize the entire SPIR-V module to use
                 // storage classes inferred from `OpVariable`s.
-                let result =
-                    cx.emit_global()
-                        .type_pointer(Some(id), StorageClass::Generic, pointee);
+                let storage_class = match storage_class {
+                    StorageClassKind::Inferred => StorageClass::Generic,
+                    StorageClassKind::Explicit(storage_class) => storage_class,
+                };
+                let result = cx
+                    .emit_global()
+                    .type_pointer(Some(id), storage_class, pointee);
                 // no pointers to functions
                 if let SpirvType::Function { .. } = cx.lookup_type(pointee) {
                     // FIXME(eddyb) use the `SPV_INTEL_function_pointers` extension.
@@ -412,7 +436,13 @@ impl SpirvType<'_> {
             SpirvType::Matrix { element, count } => SpirvType::Matrix { element, count },
             SpirvType::Array { element, count } => SpirvType::Array { element, count },
             SpirvType::RuntimeArray { element } => SpirvType::RuntimeArray { element },
-            SpirvType::Pointer { pointee } => SpirvType::Pointer { pointee },
+            SpirvType::Pointer {
+                pointee,
+                storage_class,
+            } => SpirvType::Pointer {
+                pointee,
+                storage_class,
+            },
             SpirvType::Image {
                 sampled_type,
                 dim,
@@ -557,10 +587,14 @@ impl fmt::Debug for SpirvTypePrinter<'_, '_> {
                 .field("id", &self.id)
                 .field("element", &self.cx.debug_type(element))
                 .finish(),
-            SpirvType::Pointer { pointee } => f
+            SpirvType::Pointer {
+                pointee,
+                storage_class,
+            } => f
                 .debug_struct("Pointer")
                 .field("id", &self.id)
                 .field("pointee", &self.cx.debug_type(pointee))
+                .field("storage_class", &storage_class)
                 .finish(),
             SpirvType::Function {
                 return_type,
@@ -710,8 +744,14 @@ impl SpirvTypePrinter<'_, '_> {
                 ty(self.cx, stack, f, element)?;
                 f.write_str("]")
             }
-            SpirvType::Pointer { pointee } => {
+            SpirvType::Pointer {
+                pointee,
+                storage_class,
+            } => {
                 f.write_str("*")?;
+                if let StorageClassKind::Explicit(storage_class) = storage_class {
+                    write!(f, "{:?}", storage_class)?;
+                }
                 ty(self.cx, stack, f, pointee)
             }
             SpirvType::Function {
diff --git a/crates/rustc_codegen_spirv/src/spirv_type_constraints.rs b/crates/rustc_codegen_spirv/src/spirv_type_constraints.rs
index 148b44c61f..1321722903 100644
--- a/crates/rustc_codegen_spirv/src/spirv_type_constraints.rs
+++ b/crates/rustc_codegen_spirv/src/spirv_type_constraints.rs
@@ -427,7 +427,10 @@ pub fn instruction_signatures(op: Op) -> Option<&'static [InstSig<'static>]> {
         Op::ConvertPtrToU | Op::SatConvertSToU | Op::SatConvertUToS | Op::ConvertUToPtr => {}
         Op::PtrCastToGeneric | Op::GenericCastToPtr => sig! { (Pointer(_, T)) -> Pointer(_, T) },
         Op::GenericCastToPtrExplicit => sig! { {S} (Pointer(_, T)) -> Pointer(S, T) },
-        Op::Bitcast => {}
+        Op::Bitcast => sig! {
+            (Pointer(S, _)) -> Pointer(S, _) |
+            (_) -> _
+        },
 
         // 3.37.12. Composite Instructions
         Op::VectorExtractDynamic => sig! { (Vector(T), _) -> T },