diff --git a/crates/typst-macros/src/scope.rs b/crates/typst-macros/src/scope.rs
index 07a0efe05..d86c6aea9 100644
--- a/crates/typst-macros/src/scope.rs
+++ b/crates/typst-macros/src/scope.rs
@@ -13,11 +13,26 @@ pub fn scope(_: TokenStream, item: syn::Item) -> Result<TokenStream> {
 
     let self_ty = &item.self_ty;
 
+    let mut primitive_ident_ext = None;
+    if let syn::Type::Path(syn::TypePath { path, .. }) = self_ty.as_ref() {
+        if let Some(ident) = path.get_ident() {
+            if is_primitive(ident) {
+                let ident_ext = quote::format_ident!("{ident}Ext");
+                primitive_ident_ext = Some(ident_ext);
+            }
+        }
+    }
+
+    let self_ty_expr = match &primitive_ident_ext {
+        None => quote! { #self_ty },
+        Some(ident_ext) => quote! { <#self_ty as #ident_ext> },
+    };
+
     let mut definitions = vec![];
     let mut constructor = quote! { None };
     for child in &mut item.items {
         let def = match child {
-            syn::ImplItem::Const(item) => handle_const(self_ty, item)?,
+            syn::ImplItem::Const(item) => handle_const(&self_ty_expr, item)?,
             syn::ImplItem::Fn(item) => match handle_fn(self_ty, item)? {
                 FnKind::Member(tokens) => tokens,
                 FnKind::Constructor(tokens) => {
@@ -33,14 +48,10 @@ pub fn scope(_: TokenStream, item: syn::Item) -> Result<TokenStream> {
 
     item.items.retain(|item| !matches!(item, syn::ImplItem::Verbatim(_)));
 
-    let mut base = quote! { #item };
-    if let syn::Type::Path(syn::TypePath { path, .. }) = self_ty.as_ref() {
-        if let Some(ident) = path.get_ident() {
-            if is_primitive(ident) {
-                base = rewrite_primitive_base(&item, ident);
-            }
-        }
-    }
+    let base = match &primitive_ident_ext {
+        None => quote! { #item },
+        Some(ident_ext) => rewrite_primitive_base(&item, ident_ext),
+    };
 
     Ok(quote! {
         #base
@@ -60,7 +71,7 @@ pub fn scope(_: TokenStream, item: syn::Item) -> Result<TokenStream> {
 }
 
 /// Process a const item and returns its definition.
-fn handle_const(self_ty: &syn::Type, item: &syn::ImplItemConst) -> Result<TokenStream> {
+fn handle_const(self_ty: &TokenStream, item: &syn::ImplItemConst) -> Result<TokenStream> {
     let ident = &item.ident;
     let name = ident.to_string().to_kebab_case();
     Ok(quote! { scope.define(#name, #self_ty::#ident) })
@@ -117,31 +128,39 @@ fn is_primitive(ident: &syn::Ident) -> bool {
 }
 
 /// Rewrite an impl block for a primitive into a trait + trait impl.
-fn rewrite_primitive_base(item: &syn::ItemImpl, ident: &syn::Ident) -> TokenStream {
+fn rewrite_primitive_base(item: &syn::ItemImpl, ident_ext: &syn::Ident) -> TokenStream {
     let mut sigs = vec![];
     let mut items = vec![];
     for sub in &item.items {
-        let syn::ImplItem::Fn(mut func) = sub.clone() else { continue };
-        func.vis = syn::Visibility::Inherited;
-        items.push(func.clone());
+        match sub.clone() {
+            syn::ImplItem::Fn(mut func) => {
+                func.vis = syn::Visibility::Inherited;
+                items.push(func.clone());
 
-        let mut sig = func.sig;
-        let inputs = sig.inputs.iter().cloned().map(|mut input| {
-            if let syn::FnArg::Typed(typed) = &mut input {
-                typed.attrs.clear();
+                let mut sig = func.sig;
+                let inputs = sig.inputs.iter().cloned().map(|mut input| {
+                    if let syn::FnArg::Typed(typed) = &mut input {
+                        typed.attrs.clear();
+                    }
+                    input
+                });
+                sig.inputs = parse_quote! { #(#inputs),* };
+
+                let ident_data = quote::format_ident!("{}_data", sig.ident);
+                sigs.push(quote! { #sig; });
+                sigs.push(quote! {
+                    fn #ident_data() -> &'static #foundations::NativeFuncData;
+                });
             }
-            input
-        });
-        sig.inputs = parse_quote! { #(#inputs),* };
 
-        let ident_data = quote::format_ident!("{}_data", sig.ident);
-        sigs.push(quote! { #sig; });
-        sigs.push(quote! {
-            fn #ident_data() -> &'static #foundations::NativeFuncData;
-        });
+            syn::ImplItem::Const(cons) => {
+                sigs.push(quote! { #cons });
+            }
+
+            _ => {}
+        }
     }
 
-    let ident_ext = quote::format_ident!("{ident}Ext");
     let self_ty = &item.self_ty;
     quote! {
         trait #ident_ext {
diff --git a/crates/typst/src/foundations/calc.rs b/crates/typst/src/foundations/calc.rs
index d07b23c5a..287bc828a 100644
--- a/crates/typst/src/foundations/calc.rs
+++ b/crates/typst/src/foundations/calc.rs
@@ -50,7 +50,6 @@ pub fn module() -> Module {
     scope.define_func::<rem_euclid>();
     scope.define_func::<quo>();
     scope.define("inf", f64::INFINITY);
-    scope.define("nan", f64::NAN);
     scope.define("pi", std::f64::consts::PI);
     scope.define("tau", std::f64::consts::TAU);
     scope.define("e", std::f64::consts::E);
diff --git a/crates/typst/src/foundations/float.rs b/crates/typst/src/foundations/float.rs
index d346c3296..fd094950b 100644
--- a/crates/typst/src/foundations/float.rs
+++ b/crates/typst/src/foundations/float.rs
@@ -13,6 +13,9 @@ use crate::layout::Ratio;
 ///
 /// You can convert a value to a float with this type's constructor.
 ///
+/// NaN and positive infinity are available as `{float.nan}` and `{float.inf}`
+/// respectively.
+///
 /// # Example
 /// ```example
 /// #3.14 \
@@ -24,6 +27,13 @@ type f64;
 
 #[scope]
 impl f64 {
+    /// Positive infinity.
+    const INF: f64 = f64::INFINITY;
+
+    /// A NaN value, as defined by the
+    /// [IEEE 754 standard](https://en.wikipedia.org/wiki/IEEE_754).
+    const NAN: f64 = f64::NAN;
+
     /// Converts a value to a float.
     ///
     /// - Booleans are converted to `0.0` or `1.0`.
@@ -58,7 +68,7 @@ impl f64 {
     /// ```example
     /// #float.is-nan(0) \
     /// #float.is-nan(1) \
-    /// #float.is-nan(calc.nan)
+    /// #float.is-nan(float.nan)
     /// ```
     #[func]
     pub fn is_nan(self) -> bool {
@@ -73,7 +83,7 @@ impl f64 {
     /// ```example
     /// #float.is-infinite(0) \
     /// #float.is-infinite(1) \
-    /// #float.is-infinite(calc.inf)
+    /// #float.is-infinite(float.inf)
     /// ```
     #[func]
     pub fn is_infinite(self) -> bool {
@@ -84,13 +94,13 @@ impl f64 {
     ///
     /// - If the number is positive (including `{+0.0}`), returns `{1.0}`.
     /// - If the number is negative (including `{-0.0}`), returns `{-1.0}`.
-    /// - If the number is `{calc.nan}`, returns `{calc.nan}`.
+    /// - If the number is `{float.nan}`, returns `{float.nan}`.
     ///
     /// ```example
     /// #(5.0).signum() \
     /// #(-5.0).signum() \
     /// #(0.0).signum() \
-    /// #calc.nan.signum()
+    /// #float.nan.signum()
     /// ```
     #[func]
     pub fn signum(self) -> f64 {
diff --git a/crates/typst/src/foundations/repr.rs b/crates/typst/src/foundations/repr.rs
index 68c94c56d..9c098bd19 100644
--- a/crates/typst/src/foundations/repr.rs
+++ b/crates/typst/src/foundations/repr.rs
@@ -76,7 +76,7 @@ pub fn format_int_with_base(mut n: i64, base: i64) -> EcoString {
 /// unit, all with a single allocation.
 ///
 /// The returned string is always valid Typst code. As such, it might not be a
-/// float literal. For example, it may return `"calc.inf"`.
+/// float literal. For example, it may return `"float.inf"`.
 pub fn format_float(
     mut value: f64,
     precision: Option<u8>,
@@ -91,10 +91,10 @@ pub fn format_float(
     // when necessary.
     let unit_multiplication = if unit.is_empty() { "" } else { " * 1" };
     if value.is_nan() {
-        eco_format!("calc.nan{unit_multiplication}{unit}")
+        eco_format!("float.nan{unit_multiplication}{unit}")
     } else if value.is_infinite() {
         let sign = if value < 0.0 { "-" } else { "" };
-        eco_format!("{sign}calc.inf{unit_multiplication}{unit}")
+        eco_format!("{sign}float.inf{unit_multiplication}{unit}")
     } else if force_separator {
         eco_format!("{value:?}{unit}")
     } else {
diff --git a/tests/ref/float-repr.png b/tests/ref/float-repr.png
index 7b49e9d15..e73ee3280 100644
Binary files a/tests/ref/float-repr.png and b/tests/ref/float-repr.png differ
diff --git a/tests/ref/grid-rowspan-split-15.png b/tests/ref/grid-rowspan-split-15.png
index bbefe0da0..bd435f3c0 100644
Binary files a/tests/ref/grid-rowspan-split-15.png and b/tests/ref/grid-rowspan-split-15.png differ
diff --git a/tests/ref/ops-multiply-inf-with-length.png b/tests/ref/ops-multiply-inf-with-length.png
index 0662d568b..b7c458a15 100644
Binary files a/tests/ref/ops-multiply-inf-with-length.png and b/tests/ref/ops-multiply-inf-with-length.png differ
diff --git a/tests/suite/foundations/float.typ b/tests/suite/foundations/float.typ
index 206013acd..01769260e 100644
--- a/tests/suite/foundations/float.typ
+++ b/tests/suite/foundations/float.typ
@@ -18,7 +18,7 @@
 
 --- float-is-nan ---
 // Test float `is-nan()`.
-#test(float(calc.nan).is-nan(), true)
+#test(float(float.nan).is-nan(), true)
 #test(float(10).is-nan(), false)
 #test(float(calc.inf).is-nan(), false)
 #test(float(-calc.inf).is-nan(), false)
@@ -29,7 +29,7 @@
 #test(float(-calc.inf).is-infinite(), true)
 #test(float(10).is-infinite(), false)
 #test(float(-10).is-infinite(), false)
-#test(float(calc.nan).is-infinite(), false)
+#test(float(float.nan).is-infinite(), false)
 
 --- float-signum ---
 // Test float `signum()`
@@ -40,7 +40,7 @@
 #test(float(-10.0).signum(), -1.0)
 #test(float(calc.inf).signum(), 1.0)
 #test(float(-calc.inf).signum(), -1.0)
-#test(float(calc.nan).signum().is-nan(), true)
+#test(float(float.nan).signum().is-nan(), true)
 
 --- float-repr ---
 // Test the `repr` function with floats.
@@ -55,9 +55,9 @@
 #repr(-0987654321.0) \
 #repr(-3.14) \
 #repr(4.0 - 8.0) \
-#repr(calc.inf) \
-#repr(-calc.inf) \
-#repr(calc.nan)
+#repr(float.inf) \
+#repr(-float.inf) \
+#repr(float.nan)
 
 --- float-display ---
 // Test floats.
@@ -72,6 +72,6 @@
 #(-0987654321.0) \
 #(-3.14) \
 #(4.0 - 8.0) \
-#calc.inf \
-#(-calc.inf) \
-#calc.nan
+#float.inf \
+#(-float.inf) \
+#float.nan
diff --git a/tests/suite/scripting/ops.typ b/tests/suite/scripting/ops.typ
index 0df4b82da..1c9572173 100644
--- a/tests/suite/scripting/ops.typ
+++ b/tests/suite/scripting/ops.typ
@@ -335,7 +335,7 @@
 #(1em <= 10pt)
 
 --- ops-compare-normal-float-with-nan ---
-// Error: 3-22 cannot compare 2.2 with calc.nan
+// Error: 3-22 cannot compare 2.2 with float.nan
 #(2.2 <= float("nan"))
 
 --- ops-compare-int-and-str ---
@@ -343,7 +343,7 @@
 #((0, 1, 3) > (0, 1, "a"))
 
 --- ops-compare-array-nested-failure ---
-// Error: 3-42 cannot compare 3.5 with calc.nan
+// Error: 3-42 cannot compare 3.5 with float.nan
 #((0, "a", 3.5) <= (0, "a", float("nan")))
 
 --- ops-divide-by-zero-float ---