diff --git a/compiler/rustc_ast/src/ast.rs b/compiler/rustc_ast/src/ast.rs
index 18888dd2be5a2..13b1a589d9ba9 100644
--- a/compiler/rustc_ast/src/ast.rs
+++ b/compiler/rustc_ast/src/ast.rs
@@ -1920,22 +1920,28 @@ pub struct FnSig {
 #[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
 #[derive(Encodable, Decodable, HashStable_Generic)]
 pub enum FloatTy {
+    F16,
     F32,
     F64,
+    F128,
 }
 
 impl FloatTy {
     pub fn name_str(self) -> &'static str {
         match self {
+            FloatTy::F16 => "f16",
             FloatTy::F32 => "f32",
             FloatTy::F64 => "f64",
+            FloatTy::F128 => "f128",
         }
     }
 
     pub fn name(self) -> Symbol {
         match self {
+            FloatTy::F16 => sym::f16,
             FloatTy::F32 => sym::f32,
             FloatTy::F64 => sym::f64,
+            FloatTy::F128 => sym::f128,
         }
     }
 }
diff --git a/compiler/rustc_codegen_llvm/src/context.rs b/compiler/rustc_codegen_llvm/src/context.rs
index 7dfcf1ab50e41..16122e5557e9c 100644
--- a/compiler/rustc_codegen_llvm/src/context.rs
+++ b/compiler/rustc_codegen_llvm/src/context.rs
@@ -685,8 +685,10 @@ impl<'ll> CodegenCx<'ll, '_> {
         let t_i64 = self.type_i64();
         let t_i128 = self.type_i128();
         let t_isize = self.type_isize();
+        let t_f16 = self.type_f16();
         let t_f32 = self.type_f32();
         let t_f64 = self.type_f64();
+        let t_f128 = self.type_f128();
         let t_metadata = self.type_metadata();
         let t_token = self.type_token();
 
@@ -728,69 +730,115 @@ impl<'ll> CodegenCx<'ll, '_> {
         ifn!("llvm.debugtrap", fn() -> void);
         ifn!("llvm.frameaddress", fn(t_i32) -> ptr);
 
+        ifn!("llvm.powi.f16", fn(t_f16, t_i32) -> t_f16);
         ifn!("llvm.powi.f32", fn(t_f32, t_i32) -> t_f32);
         ifn!("llvm.powi.f64", fn(t_f64, t_i32) -> t_f64);
+        ifn!("llvm.powi.f128", fn(t_f128, t_i32) -> t_f128);
 
+        ifn!("llvm.pow.f16", fn(t_f16, t_f16) -> t_f16);
         ifn!("llvm.pow.f32", fn(t_f32, t_f32) -> t_f32);
         ifn!("llvm.pow.f64", fn(t_f64, t_f64) -> t_f64);
+        ifn!("llvm.pow.f128", fn(t_f128, t_f128) -> t_f128);
 
+        ifn!("llvm.sqrt.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.sqrt.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.sqrt.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.sqrt.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.sin.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.sin.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.sin.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.sin.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.cos.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.cos.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.cos.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.cos.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.exp.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.exp.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.exp.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.exp.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.exp2.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.exp2.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.exp2.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.exp2.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.log.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.log.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.log.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.log.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.log10.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.log10.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.log10.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.log10.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.log2.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.log2.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.log2.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.log2.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.fma.f16", fn(t_f16, t_f16, t_f16) -> t_f16);
         ifn!("llvm.fma.f32", fn(t_f32, t_f32, t_f32) -> t_f32);
         ifn!("llvm.fma.f64", fn(t_f64, t_f64, t_f64) -> t_f64);
+        ifn!("llvm.fma.f128", fn(t_f128, t_f128, t_f128) -> t_f128);
 
+        ifn!("llvm.fabs.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.fabs.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.fabs.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.fabs.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.minnum.f16", fn(t_f16, t_f16) -> t_f16);
         ifn!("llvm.minnum.f32", fn(t_f32, t_f32) -> t_f32);
         ifn!("llvm.minnum.f64", fn(t_f64, t_f64) -> t_f64);
+        ifn!("llvm.minnum.f128", fn(t_f128, t_f128) -> t_f128);
+
+        ifn!("llvm.maxnum.f16", fn(t_f16, t_f16) -> t_f16);
         ifn!("llvm.maxnum.f32", fn(t_f32, t_f32) -> t_f32);
         ifn!("llvm.maxnum.f64", fn(t_f64, t_f64) -> t_f64);
+        ifn!("llvm.maxnum.f128", fn(t_f128, t_f128) -> t_f128);
 
+        ifn!("llvm.floor.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.floor.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.floor.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.floor.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.ceil.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.ceil.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.ceil.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.ceil.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.trunc.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.trunc.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.trunc.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.trunc.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.copysign.f16", fn(t_f16, t_f16) -> t_f16);
         ifn!("llvm.copysign.f32", fn(t_f32, t_f32) -> t_f32);
         ifn!("llvm.copysign.f64", fn(t_f64, t_f64) -> t_f64);
+        ifn!("llvm.copysign.f128", fn(t_f128, t_f128) -> t_f128);
 
+        ifn!("llvm.round.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.round.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.round.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.round.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.roundeven.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.roundeven.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.roundeven.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.roundeven.f128", fn(t_f128) -> t_f128);
 
+        ifn!("llvm.rint.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.rint.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.rint.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.rint.f128", fn(t_f128) -> t_f128);
+
+        ifn!("llvm.nearbyint.f16", fn(t_f16) -> t_f16);
         ifn!("llvm.nearbyint.f32", fn(t_f32) -> t_f32);
         ifn!("llvm.nearbyint.f64", fn(t_f64) -> t_f64);
+        ifn!("llvm.nearbyint.f128", fn(t_f128) -> t_f128);
 
         ifn!("llvm.ctpop.i8", fn(t_i8) -> t_i8);
         ifn!("llvm.ctpop.i16", fn(t_i16) -> t_i16);
diff --git a/compiler/rustc_codegen_llvm/src/debuginfo/metadata.rs b/compiler/rustc_codegen_llvm/src/debuginfo/metadata.rs
index 045b6d2b651c7..1a5f9b4294754 100644
--- a/compiler/rustc_codegen_llvm/src/debuginfo/metadata.rs
+++ b/compiler/rustc_codegen_llvm/src/debuginfo/metadata.rs
@@ -695,7 +695,7 @@ impl MsvcBasicName for ty::UintTy {
 
 impl MsvcBasicName for ty::FloatTy {
     fn msvc_basic_name(self) -> &'static str {
-        // FIXME: f16 and f128 have no MSVE representation. We could improve the debuginfo.
+        // FIXME: f16 and f128 have no MSVC representation. We could improve the debuginfo.
         // See: <https://github.com/rust-lang/rust/pull/114607/files#r1454683264>
         match self {
             ty::FloatTy::F16 => "half",
diff --git a/compiler/rustc_codegen_llvm/src/intrinsic.rs b/compiler/rustc_codegen_llvm/src/intrinsic.rs
index 1d4ab866cb3fe..f33a672aff0d7 100644
--- a/compiler/rustc_codegen_llvm/src/intrinsic.rs
+++ b/compiler/rustc_codegen_llvm/src/intrinsic.rs
@@ -28,51 +28,118 @@ fn get_simple_intrinsic<'ll>(
     name: Symbol,
 ) -> Option<(&'ll Type, &'ll Value)> {
     let llvm_name = match name {
+        sym::sqrtf16 => "llvm.sqrt.f16",
         sym::sqrtf32 => "llvm.sqrt.f32",
         sym::sqrtf64 => "llvm.sqrt.f64",
+        sym::sqrtf128 => "llvm.sqrt.f128",
+
+        sym::powif16 => "llvm.powi.f16",
         sym::powif32 => "llvm.powi.f32",
         sym::powif64 => "llvm.powi.f64",
+        sym::powif128 => "llvm.powi.f128",
+
+        sym::sinf16 => "llvm.sin.f16",
         sym::sinf32 => "llvm.sin.f32",
         sym::sinf64 => "llvm.sin.f64",
+        sym::sinf128 => "llvm.sin.f128",
+
+        sym::cosf16 => "llvm.cos.f16",
         sym::cosf32 => "llvm.cos.f32",
         sym::cosf64 => "llvm.cos.f64",
+        sym::cosf128 => "llvm.cos.f128",
+
+        sym::powf16 => "llvm.pow.f16",
         sym::powf32 => "llvm.pow.f32",
         sym::powf64 => "llvm.pow.f64",
+        sym::powf128 => "llvm.pow.f128",
+
+        sym::expf16 => "llvm.exp.f16",
         sym::expf32 => "llvm.exp.f32",
         sym::expf64 => "llvm.exp.f64",
+        sym::expf128 => "llvm.exp.f128",
+
+        sym::exp2f16 => "llvm.exp2.f16",
         sym::exp2f32 => "llvm.exp2.f32",
         sym::exp2f64 => "llvm.exp2.f64",
+        sym::exp2f128 => "llvm.exp2.f128",
+
+        sym::logf16 => "llvm.log.f16",
         sym::logf32 => "llvm.log.f32",
         sym::logf64 => "llvm.log.f64",
+        sym::logf128 => "llvm.log.f128",
+
+        sym::log10f16 => "llvm.log10.f16",
         sym::log10f32 => "llvm.log10.f32",
         sym::log10f64 => "llvm.log10.f64",
+        sym::log10f128 => "llvm.log10.f128",
+
+        sym::log2f16 => "llvm.log2.f16",
         sym::log2f32 => "llvm.log2.f32",
         sym::log2f64 => "llvm.log2.f64",
+        sym::log2f128 => "llvm.log2.f128",
+
+        sym::fmaf16 => "llvm.fma.f16",
         sym::fmaf32 => "llvm.fma.f32",
         sym::fmaf64 => "llvm.fma.f64",
+        sym::fmaf128 => "llvm.fma.f128",
+
+        sym::fabsf16 => "llvm.fabs.f16",
         sym::fabsf32 => "llvm.fabs.f32",
         sym::fabsf64 => "llvm.fabs.f64",
+        sym::fabsf128 => "llvm.fabs.f128",
+
+        sym::minnumf16 => "llvm.minnum.f16",
         sym::minnumf32 => "llvm.minnum.f32",
         sym::minnumf64 => "llvm.minnum.f64",
+        sym::minnumf128 => "llvm.minnum.f128",
+
+        sym::maxnumf16 => "llvm.maxnum.f16",
         sym::maxnumf32 => "llvm.maxnum.f32",
         sym::maxnumf64 => "llvm.maxnum.f64",
+        sym::maxnumf128 => "llvm.maxnum.f128",
+
+        sym::copysignf16 => "llvm.copysign.f16",
         sym::copysignf32 => "llvm.copysign.f32",
         sym::copysignf64 => "llvm.copysign.f64",
+        sym::copysignf128 => "llvm.copysign.f128",
+
+        sym::floorf16 => "llvm.floor.f16",
         sym::floorf32 => "llvm.floor.f32",
         sym::floorf64 => "llvm.floor.f64",
+        sym::floorf128 => "llvm.floor.f128",
+
+        sym::ceilf16 => "llvm.ceil.f16",
         sym::ceilf32 => "llvm.ceil.f32",
         sym::ceilf64 => "llvm.ceil.f64",
+        sym::ceilf128 => "llvm.ceil.f128",
+
+        sym::truncf16 => "llvm.trunc.f16",
         sym::truncf32 => "llvm.trunc.f32",
         sym::truncf64 => "llvm.trunc.f64",
+        sym::truncf128 => "llvm.trunc.f128",
+
+        sym::rintf16 => "llvm.rint.f16",
         sym::rintf32 => "llvm.rint.f32",
         sym::rintf64 => "llvm.rint.f64",
+        sym::rintf128 => "llvm.rint.f128",
+
+        sym::nearbyintf16 => "llvm.nearbyint.f16",
         sym::nearbyintf32 => "llvm.nearbyint.f32",
         sym::nearbyintf64 => "llvm.nearbyint.f64",
+        sym::nearbyintf128 => "llvm.nearbyint.f128",
+
+        sym::roundf16 => "llvm.round.f16",
         sym::roundf32 => "llvm.round.f32",
         sym::roundf64 => "llvm.round.f64",
+        sym::roundf128 => "llvm.round.f128",
+
         sym::ptr_mask => "llvm.ptrmask",
+
+        sym::roundevenf16 => "llvm.roundeven.f16",
         sym::roundevenf32 => "llvm.roundeven.f32",
         sym::roundevenf64 => "llvm.roundeven.f64",
+        sym::roundevenf128 => "llvm.roundeven.f128",
+
         _ => return None,
     };
     Some(cx.get_intrinsic(llvm_name))
diff --git a/compiler/rustc_hir/src/hir.rs b/compiler/rustc_hir/src/hir.rs
index 78e7c636a3e74..3dac6880f17e1 100644
--- a/compiler/rustc_hir/src/hir.rs
+++ b/compiler/rustc_hir/src/hir.rs
@@ -2460,6 +2460,7 @@ impl PrimTy {
         Self::Uint(UintTy::Usize),
         Self::Float(FloatTy::F32),
         Self::Float(FloatTy::F64),
+        // FIXME(f16_f128): add these when enabled below
         Self::Bool,
         Self::Char,
         Self::Str,
@@ -2509,6 +2510,10 @@ impl PrimTy {
             sym::usize => Self::Uint(UintTy::Usize),
             sym::f32 => Self::Float(FloatTy::F32),
             sym::f64 => Self::Float(FloatTy::F64),
+            // FIXME(f16_f128): enabling these will open the gates of f16 and f128 being
+            // understood by rustc.
+            // sym::f16 => Self::Float(FloatTy::F16),
+            // sym::f128 => Self::Float(FloatTy::F128),
             sym::bool => Self::Bool,
             sym::char => Self::Char,
             sym::str => Self::Str,
diff --git a/compiler/rustc_hir_analysis/src/check/intrinsic.rs b/compiler/rustc_hir_analysis/src/check/intrinsic.rs
index 6e9b4236e2088..9d8eb6ad60b31 100644
--- a/compiler/rustc_hir_analysis/src/check/intrinsic.rs
+++ b/compiler/rustc_hir_analysis/src/check/intrinsic.rs
@@ -112,11 +112,15 @@ pub fn intrinsic_operation_unsafety(tcx: TyCtxt<'_>, intrinsic_id: LocalDefId) -
         | sym::likely
         | sym::unlikely
         | sym::ptr_guaranteed_cmp
+        | sym::minnumf16
         | sym::minnumf32
         | sym::minnumf64
+        | sym::minnumf128
+        | sym::maxnumf16
         | sym::maxnumf32
-        | sym::rustc_peek
         | sym::maxnumf64
+        | sym::maxnumf128
+        | sym::rustc_peek
         | sym::type_name
         | sym::forget
         | sym::black_box
@@ -302,50 +306,118 @@ pub fn check_intrinsic_type(
                 ],
                 Ty::new_unit(tcx),
             ),
+
+            sym::sqrtf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::sqrtf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::sqrtf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::sqrtf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::powif16 => (0, 0, vec![tcx.types.f16, tcx.types.i32], tcx.types.f16),
             sym::powif32 => (0, 0, vec![tcx.types.f32, tcx.types.i32], tcx.types.f32),
             sym::powif64 => (0, 0, vec![tcx.types.f64, tcx.types.i32], tcx.types.f64),
+            sym::powif128 => (0, 0, vec![tcx.types.f128, tcx.types.i32], tcx.types.f128),
+
+            sym::sinf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::sinf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::sinf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::sinf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::cosf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::cosf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::cosf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::cosf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::powf16 => (0, 0, vec![tcx.types.f16, tcx.types.f16], tcx.types.f16),
             sym::powf32 => (0, 0, vec![tcx.types.f32, tcx.types.f32], tcx.types.f32),
             sym::powf64 => (0, 0, vec![tcx.types.f64, tcx.types.f64], tcx.types.f64),
+            sym::powf128 => (0, 0, vec![tcx.types.f128, tcx.types.f128], tcx.types.f128),
+
+            sym::expf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::expf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::expf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::expf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::exp2f16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::exp2f32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::exp2f64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::exp2f128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::logf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::logf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::logf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::logf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::log10f16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::log10f32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::log10f64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::log10f128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::log2f16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::log2f32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::log2f64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::log2f128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::fmaf16 => (0, 0, vec![tcx.types.f16, tcx.types.f16, tcx.types.f16], tcx.types.f16),
             sym::fmaf32 => (0, 0, vec![tcx.types.f32, tcx.types.f32, tcx.types.f32], tcx.types.f32),
             sym::fmaf64 => (0, 0, vec![tcx.types.f64, tcx.types.f64, tcx.types.f64], tcx.types.f64),
+            sym::fmaf128 => {
+                (0, 0, vec![tcx.types.f128, tcx.types.f128, tcx.types.f128], tcx.types.f128)
+            }
+
+            sym::fabsf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::fabsf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::fabsf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::fabsf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::minnumf16 => (0, 0, vec![tcx.types.f16, tcx.types.f16], tcx.types.f16),
             sym::minnumf32 => (0, 0, vec![tcx.types.f32, tcx.types.f32], tcx.types.f32),
             sym::minnumf64 => (0, 0, vec![tcx.types.f64, tcx.types.f64], tcx.types.f64),
+            sym::minnumf128 => (0, 0, vec![tcx.types.f128, tcx.types.f128], tcx.types.f128),
+
+            sym::maxnumf16 => (0, 0, vec![tcx.types.f16, tcx.types.f16], tcx.types.f16),
             sym::maxnumf32 => (0, 0, vec![tcx.types.f32, tcx.types.f32], tcx.types.f32),
             sym::maxnumf64 => (0, 0, vec![tcx.types.f64, tcx.types.f64], tcx.types.f64),
+            sym::maxnumf128 => (0, 0, vec![tcx.types.f128, tcx.types.f128], tcx.types.f128),
+
+            sym::copysignf16 => (0, 0, vec![tcx.types.f16, tcx.types.f16], tcx.types.f16),
             sym::copysignf32 => (0, 0, vec![tcx.types.f32, tcx.types.f32], tcx.types.f32),
             sym::copysignf64 => (0, 0, vec![tcx.types.f64, tcx.types.f64], tcx.types.f64),
+            sym::copysignf128 => (0, 0, vec![tcx.types.f128, tcx.types.f128], tcx.types.f128),
+
+            sym::floorf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::floorf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::floorf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::floorf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::ceilf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::ceilf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::ceilf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::ceilf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::truncf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::truncf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::truncf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::truncf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::rintf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::rintf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::rintf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::rintf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::nearbyintf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::nearbyintf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::nearbyintf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::nearbyintf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::roundf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::roundf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::roundf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::roundf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
+
+            sym::roundevenf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
             sym::roundevenf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
             sym::roundevenf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+            sym::roundevenf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
 
             sym::volatile_load | sym::unaligned_volatile_load => {
                 (1, 0, vec![Ty::new_imm_ptr(tcx, param(0))], param(0))
diff --git a/compiler/rustc_middle/src/ty/mod.rs b/compiler/rustc_middle/src/ty/mod.rs
index 6fdb03c0babb5..f005a24050442 100644
--- a/compiler/rustc_middle/src/ty/mod.rs
+++ b/compiler/rustc_middle/src/ty/mod.rs
@@ -1991,8 +1991,10 @@ pub fn uint_ty(uty: ast::UintTy) -> UintTy {
 
 pub fn float_ty(fty: ast::FloatTy) -> FloatTy {
     match fty {
+        ast::FloatTy::F16 => FloatTy::F16,
         ast::FloatTy::F32 => FloatTy::F32,
         ast::FloatTy::F64 => FloatTy::F64,
+        ast::FloatTy::F128 => FloatTy::F128,
     }
 }
 
diff --git a/compiler/rustc_span/src/symbol.rs b/compiler/rustc_span/src/symbol.rs
index 2e86a8bd58177..ee8d9ae9c5388 100644
--- a/compiler/rustc_span/src/symbol.rs
+++ b/compiler/rustc_span/src/symbol.rs
@@ -490,6 +490,8 @@ symbols! {
         catch_unwind,
         cause,
         cdylib,
+        ceilf128,
+        ceilf16,
         ceilf32,
         ceilf64,
         cfg,
@@ -595,6 +597,8 @@ symbols! {
         copy,
         copy_closures,
         copy_nonoverlapping,
+        copysignf128,
+        copysignf16,
         copysignf32,
         copysignf64,
         core,
@@ -607,6 +611,8 @@ symbols! {
         coroutine_resume,
         coroutine_state,
         coroutines,
+        cosf128,
+        cosf16,
         cosf32,
         cosf64,
         count,
@@ -737,10 +743,14 @@ symbols! {
         exhaustive_integer_patterns,
         exhaustive_patterns,
         existential_type,
+        exp2f128,
+        exp2f16,
         exp2f32,
         exp2f64,
         expect,
         expected,
+        expf128,
+        expf16,
         expf32,
         expf64,
         explicit_generic_args_with_impl_trait,
@@ -759,7 +769,9 @@ symbols! {
         external_doc,
         f,
         f128,
+        f128_nan,
         f16,
+        f16_nan,
         f16c_target_feature,
         f32,
         f32_legacy_const_digits,
@@ -793,6 +805,8 @@ symbols! {
         f64_legacy_const_neg_infinity,
         f64_legacy_const_radix,
         f64_nan,
+        fabsf128,
+        fabsf16,
         fabsf32,
         fabsf64,
         fadd_algebraic,
@@ -813,8 +827,12 @@ symbols! {
         file,
         float,
         float_to_int_unchecked,
+        floorf128,
+        floorf16,
         floorf32,
         floorf64,
+        fmaf128,
+        fmaf16,
         fmaf32,
         fmaf64,
         fmt,
@@ -1030,11 +1048,17 @@ symbols! {
         loaded_from_disk,
         local,
         local_inner_macros,
+        log10f128,
+        log10f16,
         log10f32,
         log10f64,
+        log2f128,
+        log2f16,
         log2f32,
         log2f64,
         log_syntax,
+        logf128,
+        logf16,
         logf32,
         logf64,
         loongarch_target_feature,
@@ -1062,6 +1086,8 @@ symbols! {
         match_beginning_vert,
         match_default_bindings,
         matches_macro,
+        maxnumf128,
+        maxnumf16,
         maxnumf32,
         maxnumf64,
         may_dangle,
@@ -1093,6 +1119,8 @@ symbols! {
         min_exhaustive_patterns,
         min_specialization,
         min_type_alias_impl_trait,
+        minnumf128,
+        minnumf16,
         minnumf32,
         minnumf64,
         mips_target_feature,
@@ -1155,6 +1183,8 @@ symbols! {
         native_link_modifiers_whole_archive,
         natvis_file,
         ne,
+        nearbyintf128,
+        nearbyintf16,
         nearbyintf32,
         nearbyintf64,
         needs_allocator,
@@ -1289,8 +1319,12 @@ symbols! {
         poll_next,
         post_dash_lto: "post-lto",
         powerpc_target_feature,
+        powf128,
+        powf16,
         powf32,
         powf64,
+        powif128,
+        powif16,
         powif32,
         powif64,
         pre_dash_lto: "pre-lto",
@@ -1416,6 +1450,8 @@ symbols! {
         return_position_impl_trait_in_trait,
         return_type_notation,
         rhs,
+        rintf128,
+        rintf16,
         rintf32,
         rintf64,
         riscv_target_feature,
@@ -1424,8 +1460,12 @@ symbols! {
         ropi_rwpi: "ropi-rwpi",
         rotate_left,
         rotate_right,
+        roundevenf128,
+        roundevenf16,
         roundevenf32,
         roundevenf64,
+        roundf128,
+        roundf16,
         roundf32,
         roundf64,
         rt,
@@ -1630,6 +1670,8 @@ symbols! {
         simd_trunc,
         simd_xor,
         since,
+        sinf128,
+        sinf16,
         sinf32,
         sinf64,
         size,
@@ -1647,6 +1689,8 @@ symbols! {
         specialization,
         speed,
         spotlight,
+        sqrtf128,
+        sqrtf16,
         sqrtf32,
         sqrtf64,
         sreg,
@@ -1746,6 +1790,8 @@ symbols! {
         transparent_enums,
         transparent_unions,
         trivial_bounds,
+        truncf128,
+        truncf16,
         truncf32,
         truncf64,
         try_blocks,
diff --git a/compiler/rustc_symbol_mangling/src/typeid/typeid_itanium_cxx_abi.rs b/compiler/rustc_symbol_mangling/src/typeid/typeid_itanium_cxx_abi.rs
index 8742204218010..51e2c96120caa 100644
--- a/compiler/rustc_symbol_mangling/src/typeid/typeid_itanium_cxx_abi.rs
+++ b/compiler/rustc_symbol_mangling/src/typeid/typeid_itanium_cxx_abi.rs
@@ -464,16 +464,17 @@ fn encode_ty<'tcx>(
             typeid.push_str(&s);
         }
 
-        // Rust's f32 and f64 single (32-bit) and double (64-bit) precision floating-point types
-        // have IEEE-754 binary32 and binary64 floating-point layouts, respectively.
+        // Rust's f16, f32, f64, and f126 half (16-bit), single (32-bit), double (64-bit), and
+        // quad (128-bit)  precision floating-point types have IEEE-754 binary16, binary32,
+        // binary64, and binary128 floating-point layouts, respectively.
         //
         // (See https://rust-lang.github.io/unsafe-code-guidelines/layout/scalars.html#fixed-width-floating-point-types.)
         ty::Float(float_ty) => {
-            typeid.push(match float_ty {
-                FloatTy::F16 => unimplemented!("f16_f128"),
-                FloatTy::F32 => 'f',
-                FloatTy::F64 => 'd',
-                FloatTy::F128 => unimplemented!("f16_f128"),
+            typeid.push_str(match float_ty {
+                FloatTy::F16 => "Dh",
+                FloatTy::F32 => "f",
+                FloatTy::F64 => "d",
+                FloatTy::F128 => "g",
             });
         }
 
@@ -557,7 +558,7 @@ fn encode_ty<'tcx>(
                         // https://itanium-cxx-abi.github.io/cxx-abi/abi.html#mangling-compression).
                         let builtin_types = [
                             "v", "w", "b", "c", "a", "h", "s", "t", "i", "j", "l", "m", "x", "y",
-                            "n", "o", "f", "d", "e", "g", "z",
+                            "n", "o", "f", "d", "e", "g", "z", "Dh",
                         ];
                         if !builtin_types.contains(&str) {
                             compress(dict, DictKey::Ty(ty, TyQ::None), &mut s);
diff --git a/compiler/rustc_symbol_mangling/src/v0.rs b/compiler/rustc_symbol_mangling/src/v0.rs
index 747c945960af6..f1b1b4ed2bb84 100644
--- a/compiler/rustc_symbol_mangling/src/v0.rs
+++ b/compiler/rustc_symbol_mangling/src/v0.rs
@@ -320,8 +320,11 @@ impl<'tcx> Printer<'tcx> for SymbolMangler<'tcx> {
             ty::Uint(UintTy::U64) => "y",
             ty::Uint(UintTy::U128) => "o",
             ty::Uint(UintTy::Usize) => "j",
+            // FIXME(f16_f128): update these once `rustc-demangle` supports the new types
+            ty::Float(FloatTy::F16) => unimplemented!("f16_f128"),
             ty::Float(FloatTy::F32) => "f",
             ty::Float(FloatTy::F64) => "d",
+            ty::Float(FloatTy::F128) => unimplemented!("f16_f128"),
             ty::Never => "z",
 
             // Placeholders (should be demangled as `_`).
diff --git a/src/librustdoc/clean/types.rs b/src/librustdoc/clean/types.rs
index 1707b514ef862..c35baeb4cf587 100644
--- a/src/librustdoc/clean/types.rs
+++ b/src/librustdoc/clean/types.rs
@@ -1777,8 +1777,10 @@ impl PrimitiveType {
             hir::PrimTy::Uint(UintTy::U32) => PrimitiveType::U32,
             hir::PrimTy::Uint(UintTy::U64) => PrimitiveType::U64,
             hir::PrimTy::Uint(UintTy::U128) => PrimitiveType::U128,
+            hir::PrimTy::Float(FloatTy::F16) => PrimitiveType::F16,
             hir::PrimTy::Float(FloatTy::F32) => PrimitiveType::F32,
             hir::PrimTy::Float(FloatTy::F64) => PrimitiveType::F64,
+            hir::PrimTy::Float(FloatTy::F128) => PrimitiveType::F128,
             hir::PrimTy::Str => PrimitiveType::Str,
             hir::PrimTy::Bool => PrimitiveType::Bool,
             hir::PrimTy::Char => PrimitiveType::Char,
@@ -1977,8 +1979,10 @@ impl From<ast::UintTy> for PrimitiveType {
 impl From<ast::FloatTy> for PrimitiveType {
     fn from(float_ty: ast::FloatTy) -> PrimitiveType {
         match float_ty {
+            ast::FloatTy::F16 => PrimitiveType::F16,
             ast::FloatTy::F32 => PrimitiveType::F32,
             ast::FloatTy::F64 => PrimitiveType::F64,
+            ast::FloatTy::F128 => PrimitiveType::F128,
         }
     }
 }
diff --git a/src/tools/clippy/clippy_lints/src/approx_const.rs b/src/tools/clippy/clippy_lints/src/approx_const.rs
index 409ae0c85acfc..25606f4253e4a 100644
--- a/src/tools/clippy/clippy_lints/src/approx_const.rs
+++ b/src/tools/clippy/clippy_lints/src/approx_const.rs
@@ -75,9 +75,12 @@ impl ApproxConstant {
     fn check_lit(&self, cx: &LateContext<'_>, lit: &LitKind, e: &Expr<'_>) {
         match *lit {
             LitKind::Float(s, LitFloatType::Suffixed(fty)) => match fty {
+                FloatTy::F16 => self.check_known_consts(cx, e, s, "f16"),
                 FloatTy::F32 => self.check_known_consts(cx, e, s, "f32"),
                 FloatTy::F64 => self.check_known_consts(cx, e, s, "f64"),
+                FloatTy::F128 => self.check_known_consts(cx, e, s, "f128"),
             },
+            // FIXME(f16_f128): add `f16` and `f128` when these types become stable.
             LitKind::Float(s, LitFloatType::Unsuffixed) => self.check_known_consts(cx, e, s, "f{32, 64}"),
             _ => (),
         }
diff --git a/src/tools/clippy/clippy_lints/src/float_literal.rs b/src/tools/clippy/clippy_lints/src/float_literal.rs
index cffca952e47a1..07fbb1cb5c9f8 100644
--- a/src/tools/clippy/clippy_lints/src/float_literal.rs
+++ b/src/tools/clippy/clippy_lints/src/float_literal.rs
@@ -76,8 +76,10 @@ impl<'tcx> LateLintPass<'tcx> for FloatLiteral {
             let digits = count_digits(sym_str);
             let max = max_digits(fty);
             let type_suffix = match lit_float_ty {
+                LitFloatType::Suffixed(ast::FloatTy::F16) => Some("f16"),
                 LitFloatType::Suffixed(ast::FloatTy::F32) => Some("f32"),
                 LitFloatType::Suffixed(ast::FloatTy::F64) => Some("f64"),
+                LitFloatType::Suffixed(ast::FloatTy::F128) => Some("f128"),
                 LitFloatType::Unsuffixed => None,
             };
             let (is_whole, is_inf, mut float_str) = match fty {
diff --git a/src/tools/clippy/clippy_utils/src/consts.rs b/src/tools/clippy/clippy_utils/src/consts.rs
index 1f2b2d54efd60..07ed4fbbf8e9e 100644
--- a/src/tools/clippy/clippy_utils/src/consts.rs
+++ b/src/tools/clippy/clippy_utils/src/consts.rs
@@ -277,12 +277,16 @@ pub fn lit_to_mir_constant<'tcx>(lit: &LitKind, ty: Option<Ty<'tcx>>) -> Constan
         LitKind::Char(c) => Constant::Char(c),
         LitKind::Int(n, _) => Constant::Int(n.get()),
         LitKind::Float(ref is, LitFloatType::Suffixed(fty)) => match fty {
+            ast::FloatTy::F16 => unimplemented!("f16_f128"),
             ast::FloatTy::F32 => Constant::F32(is.as_str().parse().unwrap()),
             ast::FloatTy::F64 => Constant::F64(is.as_str().parse().unwrap()),
+            ast::FloatTy::F128 => unimplemented!("f16_f128"),
         },
         LitKind::Float(ref is, LitFloatType::Unsuffixed) => match ty.expect("type of float is known").kind() {
+            ty::Float(FloatTy::F16) => unimplemented!("f16_f128"),
             ty::Float(FloatTy::F32) => Constant::F32(is.as_str().parse().unwrap()),
             ty::Float(FloatTy::F64) => Constant::F64(is.as_str().parse().unwrap()),
+            ty::Float(FloatTy::F128) => unimplemented!("f16_f128"),
             _ => bug!(),
         },
         LitKind::Bool(b) => Constant::Bool(b),