diff --git a/Cargo.lock b/Cargo.lock
index 0c105eb996..e9ebe26f42 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -167,9 +167,9 @@ checksum = "fd16c4719339c4530435d38e511904438d07cce7950afa3718a84ac36c10e89e"
 
 [[package]]
 name = "chalk-derive"
-version = "0.97.0"
+version = "0.98.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "92a0aedc4ac2adc5c0b7dc9ec38c5c816284ad28da6d4ecd01873b9683f54972"
+checksum = "9426c8fd0fe61c3da880b801d3b510524df17843a8f9ec1f5b9cec24fb7412df"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -179,9 +179,9 @@ dependencies = [
 
 [[package]]
 name = "chalk-ir"
-version = "0.97.0"
+version = "0.98.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "db18493569b190f7266a04901e520fc3a5c00564475154287906f8a27302c119"
+checksum = "d5f2eb1cd6054da221bd1ac0197fb2fe5e2caf3dcb93619398fc1433f8f09093"
 dependencies = [
  "bitflags 2.5.0",
  "chalk-derive",
@@ -189,9 +189,9 @@ dependencies = [
 
 [[package]]
 name = "chalk-recursive"
-version = "0.97.0"
+version = "0.98.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ae4ba8ce5bd2e1b59f1f79495bc8704db09a8285e51cc5ddf01d9baee1bf447d"
+checksum = "129dc03458f71cfb9c3cd621c9c68166a94e87b85b16ccd29af015d7ff9a1c61"
 dependencies = [
  "chalk-derive",
  "chalk-ir",
@@ -202,9 +202,9 @@ dependencies = [
 
 [[package]]
 name = "chalk-solve"
-version = "0.97.0"
+version = "0.98.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b2ec1b3b7f7b1ec38f099ef39c2bc3ea29335be1b8316d114baff46d96d131e9"
+checksum = "d7e8a8c1e928f98cdf227b868416ef21dcd8cc3c61b347576d783713444d41c8"
 dependencies = [
  "chalk-derive",
  "chalk-ir",
@@ -546,6 +546,7 @@ dependencies = [
  "ra-ap-rustc_abi",
  "ra-ap-rustc_parse_format",
  "rustc-hash",
+ "rustc_apfloat",
  "smallvec",
  "span",
  "stdx",
@@ -613,6 +614,7 @@ dependencies = [
  "ra-ap-rustc_index",
  "ra-ap-rustc_pattern_analysis",
  "rustc-hash",
+ "rustc_apfloat",
  "scoped-tls",
  "smallvec",
  "span",
@@ -658,6 +660,7 @@ dependencies = [
  "profile",
  "pulldown-cmark",
  "pulldown-cmark-to-cmark",
+ "rustc_apfloat",
  "smallvec",
  "span",
  "stdx",
@@ -1939,6 +1942,7 @@ dependencies = [
  "rayon",
  "rowan",
  "rustc-hash",
+ "rustc_apfloat",
  "smol_str",
  "stdx",
  "test-utils",
diff --git a/Cargo.toml b/Cargo.toml
index bea77b9c85..d4c3b7a3bf 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -104,10 +104,10 @@ arrayvec = "0.7.4"
 bitflags = "2.4.1"
 cargo_metadata = "0.18.1"
 camino = "1.1.6"
-chalk-solve = { version = "0.97.0", default-features = false }
-chalk-ir = "0.97.0"
-chalk-recursive = { version = "0.97.0", default-features = false }
-chalk-derive = "0.97.0"
+chalk-solve = { version = "0.98.0", default-features = false }
+chalk-ir = "0.98.0"
+chalk-recursive = { version = "0.98.0", default-features = false }
+chalk-derive = "0.98.0"
 crossbeam-channel = "0.5.8"
 dissimilar = "1.0.7"
 dot = "0.1.4"
diff --git a/crates/hir-def/Cargo.toml b/crates/hir-def/Cargo.toml
index 660799d610..8ac2d00313 100644
--- a/crates/hir-def/Cargo.toml
+++ b/crates/hir-def/Cargo.toml
@@ -28,6 +28,7 @@ tracing.workspace = true
 smallvec.workspace = true
 hashbrown.workspace = true
 triomphe.workspace = true
+rustc_apfloat = "0.2.0"
 
 ra-ap-rustc_parse_format.workspace = true
 ra-ap-rustc_abi.workspace = true
diff --git a/crates/hir-def/src/builtin_type.rs b/crates/hir-def/src/builtin_type.rs
index 61b2481978..f9e55559da 100644
--- a/crates/hir-def/src/builtin_type.rs
+++ b/crates/hir-def/src/builtin_type.rs
@@ -30,8 +30,10 @@ pub enum BuiltinUint {
 
 #[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub enum BuiltinFloat {
+    F16,
     F32,
     F64,
+    F128,
 }
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
@@ -65,8 +67,10 @@ impl BuiltinType {
         (name![u64],   BuiltinType::Uint(BuiltinUint::U64)),
         (name![u128],  BuiltinType::Uint(BuiltinUint::U128)),
 
+        (name![f16], BuiltinType::Float(BuiltinFloat::F16)),
         (name![f32], BuiltinType::Float(BuiltinFloat::F32)),
         (name![f64], BuiltinType::Float(BuiltinFloat::F64)),
+        (name![f128], BuiltinType::Float(BuiltinFloat::F128)),
     ];
 
     pub fn by_name(name: &Name) -> Option<Self> {
@@ -97,8 +101,10 @@ impl AsName for BuiltinType {
                 BuiltinUint::U128 => name![u128],
             },
             BuiltinType::Float(it) => match it {
+                BuiltinFloat::F16 => name![f16],
                 BuiltinFloat::F32 => name![f32],
                 BuiltinFloat::F64 => name![f64],
+                BuiltinFloat::F128 => name![f128],
             },
         }
     }
@@ -155,8 +161,10 @@ impl BuiltinUint {
 impl BuiltinFloat {
     pub fn from_suffix(suffix: &str) -> Option<BuiltinFloat> {
         let res = match suffix {
+            "f16" => BuiltinFloat::F16,
             "f32" => BuiltinFloat::F32,
             "f64" => BuiltinFloat::F64,
+            "f128" => BuiltinFloat::F128,
             _ => return None,
         };
         Some(res)
@@ -192,8 +200,10 @@ impl fmt::Display for BuiltinUint {
 impl fmt::Display for BuiltinFloat {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         f.write_str(match self {
+            BuiltinFloat::F16 => "f16",
             BuiltinFloat::F32 => "f32",
             BuiltinFloat::F64 => "f64",
+            BuiltinFloat::F128 => "f128",
         })
     }
 }
diff --git a/crates/hir-def/src/hir.rs b/crates/hir-def/src/hir.rs
index 378ce1df67..d306f9be65 100644
--- a/crates/hir-def/src/hir.rs
+++ b/crates/hir-def/src/hir.rs
@@ -20,6 +20,7 @@ use std::fmt;
 use hir_expand::name::Name;
 use intern::Interned;
 use la_arena::{Idx, RawIdx};
+use rustc_apfloat::ieee::{Half as f16, Quad as f128};
 use smallvec::SmallVec;
 use syntax::ast;
 
@@ -62,11 +63,16 @@ pub type LabelId = Idx<Label>;
 #[derive(Default, Debug, Clone, Eq, PartialEq)]
 pub struct FloatTypeWrapper(Box<str>);
 
+// FIXME(#17451): Use builtin types once stabilised.
 impl FloatTypeWrapper {
     pub fn new(value: String) -> Self {
         Self(value.into())
     }
 
+    pub fn to_f128(&self) -> f128 {
+        self.0.parse().unwrap_or_default()
+    }
+
     pub fn to_f64(&self) -> f64 {
         self.0.parse().unwrap_or_default()
     }
@@ -74,6 +80,10 @@ impl FloatTypeWrapper {
     pub fn to_f32(&self) -> f32 {
         self.0.parse().unwrap_or_default()
     }
+
+    pub fn to_f16(&self) -> f16 {
+        self.0.parse().unwrap_or_default()
+    }
 }
 
 impl fmt::Display for FloatTypeWrapper {
@@ -91,7 +101,7 @@ pub enum Literal {
     Bool(bool),
     Int(i128, Option<BuiltinInt>),
     Uint(u128, Option<BuiltinUint>),
-    // Here we are using a wrapper around float because f32 and f64 do not implement Eq, so they
+    // Here we are using a wrapper around float because float primitives do not implement Eq, so they
     // could not be used directly here, to understand how the wrapper works go to definition of
     // FloatTypeWrapper
     Float(FloatTypeWrapper, Option<BuiltinFloat>),
diff --git a/crates/hir-def/src/macro_expansion_tests/mbe/tt_conversion.rs b/crates/hir-def/src/macro_expansion_tests/mbe/tt_conversion.rs
index fb5797d6e5..c365a603d2 100644
--- a/crates/hir-def/src/macro_expansion_tests/mbe/tt_conversion.rs
+++ b/crates/hir-def/src/macro_expansion_tests/mbe/tt_conversion.rs
@@ -36,6 +36,7 @@ macro_rules! m {
         let _ = 'c';
         let _ = 1000;
         let _ = 12E+99_f64;
+        let _ = 45E+1234_f128;
         let _ = "rust1";
         let _ = -92;
     }
@@ -50,6 +51,7 @@ macro_rules! m {
         let _ = 'c';
         let _ = 1000;
         let _ = 12E+99_f64;
+        let _ = 45E+1234_f128;
         let _ = "rust1";
         let _ = -92;
     }
@@ -58,6 +60,7 @@ fn f() {
     let _ = 'c';
     let _ = 1000;
     let _ = 12E+99_f64;
+    let _ = 45E+1234_f128;
     let _ = "rust1";
     let _ = -92;
 }
diff --git a/crates/hir-expand/src/name.rs b/crates/hir-expand/src/name.rs
index 8f74bffc2b..fe754bc824 100644
--- a/crates/hir-expand/src/name.rs
+++ b/crates/hir-expand/src/name.rs
@@ -275,8 +275,10 @@ pub mod known {
         u32,
         u64,
         u128,
+        f16,
         f32,
         f64,
+        f128,
         bool,
         char,
         str,
diff --git a/crates/hir-ty/Cargo.toml b/crates/hir-ty/Cargo.toml
index a83ee9824e..b6c33683ff 100644
--- a/crates/hir-ty/Cargo.toml
+++ b/crates/hir-ty/Cargo.toml
@@ -33,6 +33,7 @@ triomphe.workspace = true
 nohash-hasher.workspace = true
 typed-arena = "2.0.1"
 indexmap.workspace = true
+rustc_apfloat = "0.2.0"
 
 ra-ap-rustc_abi.workspace = true
 ra-ap-rustc_index.workspace = true
diff --git a/crates/hir-ty/src/chalk_ext.rs b/crates/hir-ty/src/chalk_ext.rs
index d0d217d270..5765262b08 100644
--- a/crates/hir-ty/src/chalk_ext.rs
+++ b/crates/hir-ty/src/chalk_ext.rs
@@ -119,8 +119,10 @@ impl TyExt for Ty {
             TyKind::Scalar(Scalar::Bool) => Some(BuiltinType::Bool),
             TyKind::Scalar(Scalar::Char) => Some(BuiltinType::Char),
             TyKind::Scalar(Scalar::Float(fty)) => Some(BuiltinType::Float(match fty {
+                FloatTy::F128 => BuiltinFloat::F128,
                 FloatTy::F64 => BuiltinFloat::F64,
                 FloatTy::F32 => BuiltinFloat::F32,
+                FloatTy::F16 => BuiltinFloat::F16,
             })),
             TyKind::Scalar(Scalar::Int(ity)) => Some(BuiltinType::Int(match ity {
                 IntTy::Isize => BuiltinInt::Isize,
diff --git a/crates/hir-ty/src/consteval/tests.rs b/crates/hir-ty/src/consteval/tests.rs
index 1b4584a18d..095f2eb6c9 100644
--- a/crates/hir-ty/src/consteval/tests.rs
+++ b/crates/hir-ty/src/consteval/tests.rs
@@ -1,6 +1,10 @@
 use base_db::FileId;
 use chalk_ir::Substitution;
 use hir_def::db::DefDatabase;
+use rustc_apfloat::{
+    ieee::{Half as f16, Quad as f128},
+    Float,
+};
 use test_fixture::WithFixture;
 use test_utils::skip_slow_tests;
 
@@ -140,6 +144,14 @@ fn bit_op() {
 
 #[test]
 fn floating_point() {
+    check_number(
+        r#"const GOAL: f128 = 2.0 + 3.0 * 5.5 - 8.;"#,
+        "10.5".parse::<f128>().unwrap().to_bits() as i128,
+    );
+    check_number(
+        r#"const GOAL: f128 = -90.0 + 36.0;"#,
+        "-54.0".parse::<f128>().unwrap().to_bits() as i128,
+    );
     check_number(
         r#"const GOAL: f64 = 2.0 + 3.0 * 5.5 - 8.;"#,
         i128::from_le_bytes(pad16(&f64::to_le_bytes(10.5), true)),
@@ -152,6 +164,20 @@ fn floating_point() {
         r#"const GOAL: f32 = -90.0 + 36.0;"#,
         i128::from_le_bytes(pad16(&f32::to_le_bytes(-54.0), true)),
     );
+    check_number(
+        r#"const GOAL: f16 = 2.0 + 3.0 * 5.5 - 8.;"#,
+        i128::from_le_bytes(pad16(
+            &u16::try_from("10.5".parse::<f16>().unwrap().to_bits()).unwrap().to_le_bytes(),
+            true,
+        )),
+    );
+    check_number(
+        r#"const GOAL: f16 = -90.0 + 36.0;"#,
+        i128::from_le_bytes(pad16(
+            &u16::try_from("-54.0".parse::<f16>().unwrap().to_bits()).unwrap().to_le_bytes(),
+            true,
+        )),
+    );
 }
 
 #[test]
diff --git a/crates/hir-ty/src/consteval/tests/intrinsics.rs b/crates/hir-ty/src/consteval/tests/intrinsics.rs
index 543328a57e..5972b80d16 100644
--- a/crates/hir-ty/src/consteval/tests/intrinsics.rs
+++ b/crates/hir-ty/src/consteval/tests/intrinsics.rs
@@ -411,6 +411,7 @@ fn likely() {
 
 #[test]
 fn floating_point() {
+    // FIXME(#17451): Add `f16` and `f128` tests once intrinsics are added.
     check_number(
         r#"
         extern "rust-intrinsic" {
diff --git a/crates/hir-ty/src/display.rs b/crates/hir-ty/src/display.rs
index 75508707e9..a9a5d829f5 100644
--- a/crates/hir-ty/src/display.rs
+++ b/crates/hir-ty/src/display.rs
@@ -28,6 +28,10 @@ use hir_expand::name::Name;
 use intern::{Internable, Interned};
 use itertools::Itertools;
 use la_arena::ArenaMap;
+use rustc_apfloat::{
+    ieee::{Half as f16, Quad as f128},
+    Float,
+};
 use smallvec::SmallVec;
 use stdx::{never, IsNoneOr};
 use triomphe::Arc;
@@ -545,6 +549,17 @@ fn render_const_scalar(
                 write!(f, "{it}")
             }
             Scalar::Float(fl) => match fl {
+                chalk_ir::FloatTy::F16 => {
+                    // FIXME(#17451): Replace with builtins once they are stabilised.
+                    let it = f16::from_bits(u16::from_le_bytes(b.try_into().unwrap()).into());
+                    let s = it.to_string();
+                    if s.strip_prefix('-').unwrap_or(&s).chars().all(|c| c.is_ascii_digit()) {
+                        // Match Rust debug formatting
+                        write!(f, "{s}.0")
+                    } else {
+                        write!(f, "{s}")
+                    }
+                }
                 chalk_ir::FloatTy::F32 => {
                     let it = f32::from_le_bytes(b.try_into().unwrap());
                     write!(f, "{it:?}")
@@ -553,6 +568,17 @@ fn render_const_scalar(
                     let it = f64::from_le_bytes(b.try_into().unwrap());
                     write!(f, "{it:?}")
                 }
+                chalk_ir::FloatTy::F128 => {
+                    // FIXME(#17451): Replace with builtins once they are stabilised.
+                    let it = f128::from_bits(u128::from_le_bytes(b.try_into().unwrap()));
+                    let s = it.to_string();
+                    if s.strip_prefix('-').unwrap_or(&s).chars().all(|c| c.is_ascii_digit()) {
+                        // Match Rust debug formatting
+                        write!(f, "{s}.0")
+                    } else {
+                        write!(f, "{s}")
+                    }
+                }
             },
         },
         TyKind::Ref(_, _, t) => match t.kind(Interner) {
diff --git a/crates/hir-ty/src/layout.rs b/crates/hir-ty/src/layout.rs
index d9fd029d37..034b9c773c 100644
--- a/crates/hir-ty/src/layout.rs
+++ b/crates/hir-ty/src/layout.rs
@@ -265,8 +265,10 @@ pub fn layout_of_ty_query(
             chalk_ir::Scalar::Float(f) => scalar(
                 dl,
                 Primitive::Float(match f {
+                    FloatTy::F16 => Float::F16,
                     FloatTy::F32 => Float::F32,
                     FloatTy::F64 => Float::F64,
+                    FloatTy::F128 => Float::F128,
                 }),
             ),
         },
diff --git a/crates/hir-ty/src/layout/tests.rs b/crates/hir-ty/src/layout/tests.rs
index 392bda51b5..35ea13eb11 100644
--- a/crates/hir-ty/src/layout/tests.rs
+++ b/crates/hir-ty/src/layout/tests.rs
@@ -426,6 +426,7 @@ fn enums() {
 
 #[test]
 fn primitives() {
+    // FIXME(#17451): Add `f16` and `f128` once they are stabilised.
     size_and_align! {
         struct Goal(i32, i128, isize, usize, f32, f64, bool, char);
     }
diff --git a/crates/hir-ty/src/method_resolution.rs b/crates/hir-ty/src/method_resolution.rs
index ac11da789a..fad74c2448 100644
--- a/crates/hir-ty/src/method_resolution.rs
+++ b/crates/hir-ty/src/method_resolution.rs
@@ -127,9 +127,11 @@ pub(crate) const ALL_INT_FPS: [TyFingerprint; 12] = [
     TyFingerprint::Scalar(Scalar::Uint(UintTy::Usize)),
 ];
 
-pub(crate) const ALL_FLOAT_FPS: [TyFingerprint; 2] = [
+pub(crate) const ALL_FLOAT_FPS: [TyFingerprint; 4] = [
+    TyFingerprint::Scalar(Scalar::Float(FloatTy::F16)),
     TyFingerprint::Scalar(Scalar::Float(FloatTy::F32)),
     TyFingerprint::Scalar(Scalar::Float(FloatTy::F64)),
+    TyFingerprint::Scalar(Scalar::Float(FloatTy::F128)),
 ];
 
 type TraitFpMap = FxHashMap<TraitId, FxHashMap<Option<TyFingerprint>, Box<[ImplId]>>>;
diff --git a/crates/hir-ty/src/mir/eval.rs b/crates/hir-ty/src/mir/eval.rs
index 4ee96a66a3..2d9c221b73 100644
--- a/crates/hir-ty/src/mir/eval.rs
+++ b/crates/hir-ty/src/mir/eval.rs
@@ -18,6 +18,10 @@ use hir_expand::{mod_path::ModPath, HirFileIdExt, InFile};
 use intern::Interned;
 use la_arena::ArenaMap;
 use rustc_abi::TargetDataLayout;
+use rustc_apfloat::{
+    ieee::{Half as f16, Quad as f128},
+    Float,
+};
 use rustc_hash::{FxHashMap, FxHashSet};
 use stdx::never;
 use syntax::{SyntaxNodePtr, TextRange};
@@ -55,6 +59,13 @@ macro_rules! from_bytes {
             Err(_) => return Err(MirEvalError::InternalError(stringify!(mismatched size in constructing $ty).into())),
         }))
     };
+    ($apfloat:tt, $bits:tt, $value:expr) => {
+        // FIXME(#17451): Switch to builtin `f16` and `f128` once they are stable.
+        $apfloat::from_bits($bits::from_le_bytes(match ($value).try_into() {
+            Ok(it) => it,
+            Err(_) => return Err(MirEvalError::InternalError(stringify!(mismatched size in constructing $apfloat).into())),
+        }).into())
+    };
 }
 
 macro_rules! not_supported {
@@ -1110,6 +1121,10 @@ impl Evaluator<'_> {
                 }
                 if let TyKind::Scalar(chalk_ir::Scalar::Float(f)) = ty.kind(Interner) {
                     match f {
+                        chalk_ir::FloatTy::F16 => {
+                            let c = -from_bytes!(f16, u16, c);
+                            Owned(u16::try_from(c.to_bits()).unwrap().to_le_bytes().into())
+                        }
                         chalk_ir::FloatTy::F32 => {
                             let c = -from_bytes!(f32, c);
                             Owned(c.to_le_bytes().into())
@@ -1118,6 +1133,10 @@ impl Evaluator<'_> {
                             let c = -from_bytes!(f64, c);
                             Owned(c.to_le_bytes().into())
                         }
+                        chalk_ir::FloatTy::F128 => {
+                            let c = -from_bytes!(f128, u128, c);
+                            Owned(c.to_bits().to_le_bytes().into())
+                        }
                     }
                 } else {
                     let mut c = c.to_vec();
@@ -1169,6 +1188,39 @@ impl Evaluator<'_> {
                 }
                 if let TyKind::Scalar(chalk_ir::Scalar::Float(f)) = ty.kind(Interner) {
                     match f {
+                        chalk_ir::FloatTy::F16 => {
+                            let l = from_bytes!(f16, u16, lc);
+                            let r = from_bytes!(f16, u16, rc);
+                            match op {
+                                BinOp::Ge
+                                | BinOp::Gt
+                                | BinOp::Le
+                                | BinOp::Lt
+                                | BinOp::Eq
+                                | BinOp::Ne => {
+                                    let r = op.run_compare(l, r) as u8;
+                                    Owned(vec![r])
+                                }
+                                BinOp::Add | BinOp::Sub | BinOp::Mul | BinOp::Div => {
+                                    let r = match op {
+                                        BinOp::Add => l + r,
+                                        BinOp::Sub => l - r,
+                                        BinOp::Mul => l * r,
+                                        BinOp::Div => l / r,
+                                        _ => unreachable!(),
+                                    };
+                                    Owned(
+                                        u16::try_from(r.value.to_bits())
+                                            .unwrap()
+                                            .to_le_bytes()
+                                            .into(),
+                                    )
+                                }
+                                it => not_supported!(
+                                    "invalid binop {it:?} on floating point operators"
+                                ),
+                            }
+                        }
                         chalk_ir::FloatTy::F32 => {
                             let l = from_bytes!(f32, lc);
                             let r = from_bytes!(f32, rc);
@@ -1225,6 +1277,34 @@ impl Evaluator<'_> {
                                 ),
                             }
                         }
+                        chalk_ir::FloatTy::F128 => {
+                            let l = from_bytes!(f128, u128, lc);
+                            let r = from_bytes!(f128, u128, rc);
+                            match op {
+                                BinOp::Ge
+                                | BinOp::Gt
+                                | BinOp::Le
+                                | BinOp::Lt
+                                | BinOp::Eq
+                                | BinOp::Ne => {
+                                    let r = op.run_compare(l, r) as u8;
+                                    Owned(vec![r])
+                                }
+                                BinOp::Add | BinOp::Sub | BinOp::Mul | BinOp::Div => {
+                                    let r = match op {
+                                        BinOp::Add => l + r,
+                                        BinOp::Sub => l - r,
+                                        BinOp::Mul => l * r,
+                                        BinOp::Div => l / r,
+                                        _ => unreachable!(),
+                                    };
+                                    Owned(r.value.to_bits().to_le_bytes().into())
+                                }
+                                it => not_supported!(
+                                    "invalid binop {it:?} on floating point operators"
+                                ),
+                            }
+                        }
                     }
                 } else {
                     let is_signed = matches!(ty.as_builtin(), Some(BuiltinType::Int(_)));
diff --git a/crates/hir-ty/src/mir/eval/shim.rs b/crates/hir-ty/src/mir/eval/shim.rs
index 3438712049..ce22e9d2c2 100644
--- a/crates/hir-ty/src/mir/eval/shim.rs
+++ b/crates/hir-ty/src/mir/eval/shim.rs
@@ -627,6 +627,7 @@ impl Evaluator<'_> {
         if let Some(name) = name.strip_prefix("atomic_") {
             return self.exec_atomic_intrinsic(name, args, generic_args, destination, locals, span);
         }
+        // FIXME(#17451): Add `f16` and `f128` intrinsics.
         if let Some(name) = name.strip_suffix("f64") {
             let result = match name {
                 "sqrt" | "sin" | "cos" | "exp" | "exp2" | "log" | "log10" | "log2" | "fabs"
diff --git a/crates/hir-ty/src/mir/lower.rs b/crates/hir-ty/src/mir/lower.rs
index 3ceb94ad7a..1a0a1b780a 100644
--- a/crates/hir-ty/src/mir/lower.rs
+++ b/crates/hir-ty/src/mir/lower.rs
@@ -19,6 +19,7 @@ use hir_def::{
 };
 use hir_expand::name::Name;
 use la_arena::ArenaMap;
+use rustc_apfloat::Float;
 use rustc_hash::FxHashMap;
 use syntax::TextRange;
 use triomphe::Arc;
@@ -1432,10 +1433,14 @@ impl<'ctx> MirLowerCtx<'ctx> {
             hir_def::hir::Literal::Int(it, _) => Box::from(&it.to_le_bytes()[0..size()?]),
             hir_def::hir::Literal::Uint(it, _) => Box::from(&it.to_le_bytes()[0..size()?]),
             hir_def::hir::Literal::Float(f, _) => match size()? {
+                16 => Box::new(f.to_f128().to_bits().to_le_bytes()),
                 8 => Box::new(f.to_f64().to_le_bytes()),
                 4 => Box::new(f.to_f32().to_le_bytes()),
+                2 => Box::new(u16::try_from(f.to_f16().to_bits()).unwrap().to_le_bytes()),
                 _ => {
-                    return Err(MirLowerError::TypeError("float with size other than 4 or 8 bytes"))
+                    return Err(MirLowerError::TypeError(
+                        "float with size other than 2, 4, 8 or 16 bytes",
+                    ))
                 }
             },
         };
diff --git a/crates/hir-ty/src/primitive.rs b/crates/hir-ty/src/primitive.rs
index d7f48c69a5..a4e077ba63 100644
--- a/crates/hir-ty/src/primitive.rs
+++ b/crates/hir-ty/src/primitive.rs
@@ -27,8 +27,10 @@ pub fn uint_ty_to_string(ty: UintTy) -> &'static str {
 
 pub fn float_ty_to_string(ty: FloatTy) -> &'static str {
     match ty {
+        FloatTy::F16 => "f16",
         FloatTy::F32 => "f32",
         FloatTy::F64 => "f64",
+        FloatTy::F128 => "f128",
     }
 }
 
@@ -56,7 +58,9 @@ pub(super) fn uint_ty_from_builtin(t: BuiltinUint) -> UintTy {
 
 pub(super) fn float_ty_from_builtin(t: BuiltinFloat) -> FloatTy {
     match t {
+        BuiltinFloat::F16 => FloatTy::F16,
         BuiltinFloat::F32 => FloatTy::F32,
         BuiltinFloat::F64 => FloatTy::F64,
+        BuiltinFloat::F128 => FloatTy::F128,
     }
 }
diff --git a/crates/hir-ty/src/tests/patterns.rs b/crates/hir-ty/src/tests/patterns.rs
index 5e040a60e2..1c1f7055ef 100644
--- a/crates/hir-ty/src/tests/patterns.rs
+++ b/crates/hir-ty/src/tests/patterns.rs
@@ -111,8 +111,10 @@ fn infer_literal_pattern() {
             if let "foo" = any() {}
             if let 1 = any() {}
             if let 1u32 = any() {}
+            if let 1f16 = any() {}
             if let 1f32 = any() {}
             if let 1.0 = any() {}
+            if let 1f128 = any() {}
             if let true = any() {}
         }
         "#,
@@ -121,7 +123,7 @@ fn infer_literal_pattern() {
             19..26 'loop {}': !
             24..26 '{}': ()
             37..38 'x': &'? i32
-            46..208 '{     ...) {} }': ()
+            46..263 '{     ...) {} }': ()
             52..75 'if let...y() {}': ()
             55..72 'let "f... any()': bool
             59..64 '"foo"': &'static str
@@ -145,25 +147,39 @@ fn infer_literal_pattern() {
             124..126 '{}': ()
             131..153 'if let...y() {}': ()
             134..150 'let 1f... any()': bool
-            138..142 '1f32': f32
-            138..142 '1f32': f32
-            145..148 'any': fn any<f32>() -> f32
-            145..150 'any()': f32
+            138..142 '1f16': f16
+            138..142 '1f16': f16
+            145..148 'any': fn any<f16>() -> f16
+            145..150 'any()': f16
             151..153 '{}': ()
-            158..179 'if let...y() {}': ()
-            161..176 'let 1.0 = any()': bool
-            165..168 '1.0': f64
-            165..168 '1.0': f64
-            171..174 'any': fn any<f64>() -> f64
-            171..176 'any()': f64
-            177..179 '{}': ()
-            184..206 'if let...y() {}': ()
-            187..203 'let tr... any()': bool
-            191..195 'true': bool
-            191..195 'true': bool
-            198..201 'any': fn any<bool>() -> bool
-            198..203 'any()': bool
+            158..180 'if let...y() {}': ()
+            161..177 'let 1f... any()': bool
+            165..169 '1f32': f32
+            165..169 '1f32': f32
+            172..175 'any': fn any<f32>() -> f32
+            172..177 'any()': f32
+            178..180 '{}': ()
+            185..206 'if let...y() {}': ()
+            188..203 'let 1.0 = any()': bool
+            192..195 '1.0': f64
+            192..195 '1.0': f64
+            198..201 'any': fn any<f64>() -> f64
+            198..203 'any()': f64
             204..206 '{}': ()
+            211..234 'if let...y() {}': ()
+            214..231 'let 1f... any()': bool
+            218..223 '1f128': f128
+            218..223 '1f128': f128
+            226..229 'any': fn any<f128>() -> f128
+            226..231 'any()': f128
+            232..234 '{}': ()
+            239..261 'if let...y() {}': ()
+            242..258 'let tr... any()': bool
+            246..250 'true': bool
+            246..250 'true': bool
+            253..256 'any': fn any<bool>() -> bool
+            253..258 'any()': bool
+            259..261 '{}': ()
         "#]],
     );
 }
diff --git a/crates/hir-ty/src/tests/simple.rs b/crates/hir-ty/src/tests/simple.rs
index e2cd7fa26b..d83a34298e 100644
--- a/crates/hir-ty/src/tests/simple.rs
+++ b/crates/hir-ty/src/tests/simple.rs
@@ -397,8 +397,10 @@ fn infer_literals() {
         r##"
         fn test() {
             5i32;
+            5f16;
             5f32;
             5f64;
+            5f128;
             "hello";
             b"bytes";
             'c';
@@ -421,26 +423,28 @@ h";
         }
         "##,
         expect![[r##"
-            18..478 '{     ...     }': ()
+            18..515 '{     ...     }': ()
             32..36 '5i32': i32
-            50..54 '5f32': f32
-            68..72 '5f64': f64
-            86..93 '"hello"': &'static str
-            107..115 'b"bytes"': &'static [u8; 5]
-            129..132 ''c'': char
-            146..150 'b'b'': u8
-            164..168 '3.14': f64
-            182..186 '5000': i32
-            200..205 'false': bool
-            219..223 'true': bool
-            237..333 'r#"   ...    "#': &'static str
-            347..357 'br#"yolo"#': &'static [u8; 4]
-            375..376 'a': &'static [u8; 4]
-            379..403 'b"a\x2...    c"': &'static [u8; 4]
-            421..422 'b': &'static [u8; 4]
-            425..433 'br"g\ h"': &'static [u8; 4]
-            451..452 'c': &'static [u8; 6]
-            455..467 'br#"x"\"yb"#': &'static [u8; 6]
+            50..54 '5f16': f16
+            68..72 '5f32': f32
+            86..90 '5f64': f64
+            104..109 '5f128': f128
+            123..130 '"hello"': &'static str
+            144..152 'b"bytes"': &'static [u8; 5]
+            166..169 ''c'': char
+            183..187 'b'b'': u8
+            201..205 '3.14': f64
+            219..223 '5000': i32
+            237..242 'false': bool
+            256..260 'true': bool
+            274..370 'r#"   ...    "#': &'static str
+            384..394 'br#"yolo"#': &'static [u8; 4]
+            412..413 'a': &'static [u8; 4]
+            416..440 'b"a\x2...    c"': &'static [u8; 4]
+            458..459 'b': &'static [u8; 4]
+            462..470 'br"g\ h"': &'static [u8; 4]
+            488..489 'c': &'static [u8; 6]
+            492..504 'br#"x"\"yb"#': &'static [u8; 6]
         "##]],
     );
 }
diff --git a/crates/hir/src/lib.rs b/crates/hir/src/lib.rs
index 18a5325db6..016f341851 100644
--- a/crates/hir/src/lib.rs
+++ b/crates/hir/src/lib.rs
@@ -2622,6 +2622,13 @@ impl BuiltinType {
         matches!(self.inner, hir_def::builtin_type::BuiltinType::Float(_))
     }
 
+    pub fn is_f16(&self) -> bool {
+        matches!(
+            self.inner,
+            hir_def::builtin_type::BuiltinType::Float(hir_def::builtin_type::BuiltinFloat::F16)
+        )
+    }
+
     pub fn is_f32(&self) -> bool {
         matches!(
             self.inner,
@@ -2636,6 +2643,13 @@ impl BuiltinType {
         )
     }
 
+    pub fn is_f128(&self) -> bool {
+        matches!(
+            self.inner,
+            hir_def::builtin_type::BuiltinType::Float(hir_def::builtin_type::BuiltinFloat::F128)
+        )
+    }
+
     pub fn is_char(&self) -> bool {
         matches!(self.inner, hir_def::builtin_type::BuiltinType::Char)
     }
diff --git a/crates/ide/Cargo.toml b/crates/ide/Cargo.toml
index a535015a27..9d8400ba3a 100644
--- a/crates/ide/Cargo.toml
+++ b/crates/ide/Cargo.toml
@@ -25,6 +25,7 @@ dot.workspace = true
 smallvec.workspace = true
 triomphe.workspace = true
 nohash-hasher.workspace = true
+rustc_apfloat = "0.2.0"
 
 # local deps
 cfg.workspace = true
diff --git a/crates/ide/src/hover/render.rs b/crates/ide/src/hover/render.rs
index 99568c9922..7091b15b8a 100644
--- a/crates/ide/src/hover/render.rs
+++ b/crates/ide/src/hover/render.rs
@@ -16,6 +16,10 @@ use ide_db::{
     RootDatabase,
 };
 use itertools::Itertools;
+use rustc_apfloat::{
+    ieee::{Half as f16, Quad as f128},
+    Float,
+};
 use stdx::format_to;
 use syntax::{algo, ast, match_ast, AstNode, AstToken, Direction, SyntaxToken, T};
 
@@ -540,13 +544,22 @@ pub(super) fn literal(sema: &Semantics<'_, RootDatabase>, token: SyntaxToken) ->
             ast::Char(char)         => char  .value().as_ref().map_err(|e| format!("{e:?}")).map(ToString::to_string),
             ast::Byte(byte)         => byte  .value().as_ref().map_err(|e| format!("{e:?}")).map(|it| format!("0x{it:X}")),
             ast::FloatNumber(num) => {
-                let (text, _) = num.split_into_parts();
-                let text = text.replace('_', "");
-                if ty.as_builtin().map(|it| it.is_f32()).unwrap_or(false) {
+                let text = num.value_string();
+                if ty.as_builtin().map(|it| it.is_f16()).unwrap_or(false) {
+                    match text.parse::<f16>() {
+                        Ok(num) => Ok(format!("{num} (bits: 0x{:X})", num.to_bits())),
+                        Err(e) => Err(e.0.to_owned()),
+                    }
+                } else if ty.as_builtin().map(|it| it.is_f32()).unwrap_or(false) {
                     match text.parse::<f32>() {
                         Ok(num) => Ok(format!("{num} (bits: 0x{:X})", num.to_bits())),
                         Err(e) => Err(e.to_string()),
                     }
+                } else if ty.as_builtin().map(|it| it.is_f128()).unwrap_or(false) {
+                    match text.parse::<f128>() {
+                        Ok(num) => Ok(format!("{num} (bits: 0x{:X})", num.to_bits())),
+                        Err(e) => Err(e.0.to_owned()),
+                    }
                 } else {
                     match text.parse::<f64>() {
                         Ok(num) => Ok(format!("{num} (bits: 0x{:X})", num.to_bits())),
diff --git a/crates/ide/src/hover/tests.rs b/crates/ide/src/hover/tests.rs
index 51b60df7cc..5036770fec 100644
--- a/crates/ide/src/hover/tests.rs
+++ b/crates/ide/src/hover/tests.rs
@@ -5329,6 +5329,49 @@ const FOO$0: f32 = 1.9999999403953552_f32;
 
             ---
 
+            This is a doc
+        "#]],
+    );
+    // Check `f16` and `f128`
+    check(
+        r#"
+/// This is a doc
+const FOO$0: f16 = -1.0f16;
+"#,
+        expect![[r#"
+            *FOO*
+
+            ```rust
+            test
+            ```
+
+            ```rust
+            const FOO: f16 = -1.0
+            ```
+
+            ---
+
+            This is a doc
+        "#]],
+    );
+    check(
+        r#"
+/// This is a doc
+const FOO$0: f128 = -1.0f128;
+"#,
+        expect![[r#"
+            *FOO*
+
+            ```rust
+            test
+            ```
+
+            ```rust
+            const FOO: f128 = -1.0
+            ```
+
+            ---
+
             This is a doc
         "#]],
     );
@@ -8045,6 +8088,22 @@ fn main() {
     );
     check(
         r#"
+fn main() {
+    $01.0f16;
+}
+"#,
+        expect![[r#"
+            *1.0f16*
+            ```rust
+            f16
+            ```
+            ___
+
+            value of literal: 1 (bits: 0x3C00)
+        "#]],
+    );
+    check(
+        r#"
 fn main() {
     $01.0f32;
 }
@@ -8061,6 +8120,22 @@ fn main() {
     );
     check(
         r#"
+fn main() {
+    $01.0f128;
+}
+"#,
+        expect![[r#"
+            *1.0f128*
+            ```rust
+            f128
+            ```
+            ___
+
+            value of literal: 1 (bits: 0x3FFF0000000000000000000000000000)
+        "#]],
+    );
+    check(
+        r#"
 fn main() {
     $0134e12;
 }
@@ -8390,8 +8465,8 @@ impl Iterator for S {
                                 file_id: FileId(
                                     1,
                                 ),
-                                full_range: 7791..7999,
-                                focus_range: 7856..7862,
+                                full_range: 7800..8008,
+                                focus_range: 7865..7871,
                                 name: "Future",
                                 kind: Trait,
                                 container_name: "future",
@@ -8404,8 +8479,8 @@ impl Iterator for S {
                                 file_id: FileId(
                                     1,
                                 ),
-                                full_range: 8629..9095,
-                                focus_range: 8673..8681,
+                                full_range: 8638..9104,
+                                focus_range: 8682..8690,
                                 name: "Iterator",
                                 kind: Trait,
                                 container_name: "iterator",
diff --git a/crates/syntax/Cargo.toml b/crates/syntax/Cargo.toml
index 1809ca7dea..b371ec6ebd 100644
--- a/crates/syntax/Cargo.toml
+++ b/crates/syntax/Cargo.toml
@@ -33,6 +33,7 @@ text-edit.workspace = true
 [dev-dependencies]
 rayon.workspace = true
 expect-test = "1.4.0"
+rustc_apfloat = "0.2.0"
 
 test-utils.workspace = true
 
diff --git a/crates/syntax/src/ast/token_ext.rs b/crates/syntax/src/ast/token_ext.rs
index f00e5c6d0e..df017ddde6 100644
--- a/crates/syntax/src/ast/token_ext.rs
+++ b/crates/syntax/src/ast/token_ext.rs
@@ -489,6 +489,8 @@ impl ast::Byte {
 
 #[cfg(test)]
 mod tests {
+    use rustc_apfloat::ieee::Quad as f128;
+
     use crate::ast::{self, make, FloatNumber, IntNumber};
 
     fn check_float_suffix<'a>(lit: &str, expected: impl Into<Option<&'a str>>) {
@@ -499,14 +501,16 @@ mod tests {
         assert_eq!(IntNumber { syntax: make::tokens::literal(lit) }.suffix(), expected.into());
     }
 
-    fn check_float_value(lit: &str, expected: impl Into<Option<f64>> + Copy) {
+    // FIXME(#17451) Use `expected: f128` once `f128` is stabilised.
+    fn check_float_value(lit: &str, expected: &str) {
+        let expected = Some(expected.parse::<f128>().unwrap());
         assert_eq!(
-            FloatNumber { syntax: make::tokens::literal(lit) }.value_string().parse::<f64>().ok(),
-            expected.into()
+            FloatNumber { syntax: make::tokens::literal(lit) }.value_string().parse::<f128>().ok(),
+            expected
         );
         assert_eq!(
-            IntNumber { syntax: make::tokens::literal(lit) }.value_string().parse::<f64>().ok(),
-            expected.into()
+            IntNumber { syntax: make::tokens::literal(lit) }.value_string().parse::<f128>().ok(),
+            expected
         );
     }
 
@@ -520,9 +524,9 @@ mod tests {
         check_float_suffix("123f32", "f32");
         check_float_suffix("123.0e", None);
         check_float_suffix("123.0e4", None);
-        check_float_suffix("123.0ef32", "f32");
+        check_float_suffix("123.0ef16", "f16");
         check_float_suffix("123.0E4f32", "f32");
-        check_float_suffix("1_2_3.0_f32", "f32");
+        check_float_suffix("1_2_3.0_f128", "f128");
     }
 
     #[test]
@@ -589,8 +593,10 @@ bcde", b"abcde",
 
     #[test]
     fn test_value_underscores() {
-        check_float_value("1.234567891011121_f64", 1.234567891011121_f64);
-        check_float_value("1__0.__0__f32", 10.0);
+        check_float_value("1.3_4665449586950493453___6_f128", "1.346654495869504934536");
+        check_float_value("1.234567891011121_f64", "1.234567891011121");
+        check_float_value("1__0.__0__f32", "10.0");
+        check_float_value("3._0_f16", "3.0");
         check_int_value("0b__1_0_", 2);
         check_int_value("1_1_1_1_1_1", 111111);
     }
diff --git a/crates/test-utils/src/minicore.rs b/crates/test-utils/src/minicore.rs
index 0257ed9ab4..d1862f7d73 100644
--- a/crates/test-utils/src/minicore.rs
+++ b/crates/test-utils/src/minicore.rs
@@ -123,7 +123,7 @@ pub mod marker {
         impl_copy! {
             usize u8 u16 u32 u64 u128
             isize i8 i16 i32 i64 i128
-            f32 f64
+            f16 f32 f64 f128
             bool char
         }
 
@@ -180,7 +180,7 @@ pub mod default {
         0; usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128
     }
     impl_default! {
-        0.0; f32 f64
+        0.0; f16 f32 f64 f128
     }
     // endregion:builtin_impls
 }
@@ -276,7 +276,7 @@ pub mod clone {
     impl_clone! {
         usize u8 u16 u32 u64 u128
         isize i8 i16 i32 i64 i128
-        f32 f64
+        f16 f32 f64 f128
         bool char
     }
 
@@ -796,7 +796,7 @@ pub mod ops {
         )*)
     }
 
-    add_impl! { usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f32 f64 }
+    add_impl! { usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 f16 f32 f64 f128 }
     // endregion:builtin_impls
     // endregion:add
 
@@ -1043,7 +1043,7 @@ pub mod fmt {
     impl_debug! {
         usize u8 u16 u32 u64 u128
         isize i8 i16 i32 i64 i128
-        f32 f64
+        f16 f32 f64 f128
         bool char
     }