diff --git a/CHANGELOG.md b/CHANGELOG.md
index d90b4f46..efa0aae2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -18,8 +18,9 @@ and this project does not currently adhere to a particular versioning scheme.
 
 ### Added
 
-- Add `log` and `atan2` builtin functions. ([#583][gh-583])
 - Create new type of top-level definition for writing native HVM definitions. ([#586][gh-586])
+- Add `log` and `atan2` builtin functions. ([#583][gh-583])
+- Add `to_f24`, `to_u24` and `to_i24` number casting builtin functions. ([#582][gh-582])
 
 ## [0.2.35] - 2024-06-06
 
@@ -340,6 +341,7 @@ and this project does not currently adhere to a particular versioning scheme.
 [gh-516]: https://github.com/HigherOrderCO/Bend/issues/516
 [gh-526]: https://github.com/HigherOrderCO/Bend/issues/526
 [gh-528]: https://github.com/HigherOrderCO/Bend/issues/528
+[gh-582]: https://github.com/HigherOrderCO/Bend/issues/582
 [gh-583]: https://github.com/HigherOrderCO/Bend/issues/583
 [gh-586]: https://github.com/HigherOrderCO/Bend/issues/586
 [Unreleased]: https://github.com/HigherOrderCO/Bend/compare/0.2.35...HEAD
diff --git a/docs/builtins.md b/docs/builtins.md
index 109c164d..d20dca4d 100644
--- a/docs/builtins.md
+++ b/docs/builtins.md
@@ -226,3 +226,37 @@ A Natural Number can be written with literals with a `#` before the literal numb
 
 ## IO
 IO Functions are in the **next milestone**!
+
+## Numeric operations
+
+### log
+```py
+def log(x: f24, base: f24) -> f24
+```
+Computes the logarithm of `x` with the specified `base`.
+
+### atan2
+```py
+def atan2(x: f24, y: f24) -> f24
+```
+Computes the arctangent of `y / x`.
+
+Has the same behaviour as `atan2f` in the C math lib.
+
+### to_f24
+```py
+def to_f24(x: any number) -> f24
+```
+Casts any native number to an f24.
+
+### to_u24
+```py
+def to_u24(x: any number) -> u24
+```
+Casts any native number to a u24.
+
+### to_i24
+```py
+def to_i24(x: any number) -> i24
+```
+Casts any native number to an i24.
diff --git a/src/fun/builtins.bend b/src/fun/builtins.bend
index 822eef05..fd262b3c 100644
--- a/src/fun/builtins.bend
+++ b/src/fun/builtins.bend
@@ -95,7 +95,10 @@ print text = (IO/Call IO/MAGIC "PUT_TEXT" text @x (IO/Done IO/MAGIC x))
 #read_file path = (IO/Call IO/MAGIC "GET_FILE" path @x (IO/Done IO/MAGIC x))
 #write_file path text = (IO/Call IO/MAGIC "PUT_FILE" (path, text) @x (IO/Done IO/MAGIC x))
 
+# Returns a monotonically increasing nanosecond timestamp as an u48 encoded as a pair of u24s.
 get_time = (IO/Call IO/MAGIC "GET_TIME" * @x (IO/Done IO/MAGIC x))
+
+# Sleeps for the given number of nanoseconds, given by an u48 encoded as a pair of u24s.
 sleep hi_lo = (IO/Call IO/MAGIC "PUT_TIME" hi_lo @x (IO/Done IO/MAGIC x))
 
 
@@ -110,10 +113,31 @@ defer val = @x (x val)
 defer_arg defered arg = @x (defered x arg)
 undefer defered = (defered @x x)
 
-# log :: f24 -> f24 -> f24
+
+# Native numeric operations
+
+# log(x: f24, base: f24) -> f24
 # Computes the logarithm of `x` with the specified `base`.
-log x base = (| base x)
-# atan2 :: f24 -> f24 -> f24
+hvm log:
+  (x ($([|] $(x ret)) ret))
+
+# atan2(x: f24, y: f24) -> f24
 # Has the same behaviour as `atan2f` in the C math lib.
 # Computes the arctangent of the quotient of its two arguments.
-atan2 x y = (& x y)
+hvm atan2:
+  ($([&] $(y ret)) (y ret))
+
+# to_f24(x: native number) -> f24
+# Casts any native number to an f24.
+hvm to_f24:
+  ($([f24] ret) ret)
+
+# to_u24(x: native number) -> u24
+# Casts any native number to a u24.
+hvm to_u24:
+  ($([u24] ret) ret)
+
+# to_i24(x: native number) -> i24
+# Casts any native number to an i24.
+hvm to_i24:
+  ($([i24] ret) ret)
diff --git a/src/fun/transform/definition_pruning.rs b/src/fun/transform/definition_pruning.rs
index 2270909d..9dcebc83 100644
--- a/src/fun/transform/definition_pruning.rs
+++ b/src/fun/transform/definition_pruning.rs
@@ -49,8 +49,19 @@ impl Ctx<'_> {
       }
     }
 
+    fn rm_def(book: &mut Book, def_name: &Name) {
+      if book.defs.contains_key(def_name) {
+        book.defs.shift_remove(def_name);
+      } else if book.hvm_defs.contains_key(def_name) {
+        book.hvm_defs.shift_remove(def_name);
+      } else {
+        unreachable!()
+      }
+    }
+
     // Remove unused definitions.
-    for def in self.book.defs.keys().cloned().collect::<Vec<_>>() {
+    let names = self.book.defs.keys().cloned().chain(self.book.hvm_defs.keys().cloned()).collect::<Vec<_>>();
+    for def in names {
       if let Some(use_) = used.get(&def) {
         match use_ {
           Used::Main => {
@@ -60,7 +71,7 @@ impl Ctx<'_> {
             // Used by a non-builtin definition.
             // Prune if `prune_all`, otherwise show a warning.
             if prune_all {
-              self.book.defs.shift_remove(&def);
+              rm_def(self.book, &def);
             } else {
               self.info.add_rule_warning("Definition is unused.", WarningType::UnusedDefinition, def);
             }
@@ -69,7 +80,7 @@ impl Ctx<'_> {
             // Unused, but a user-defined constructor.
             // Prune if `prune_all`, otherwise nothing.
             if prune_all {
-              self.book.defs.shift_remove(&def);
+              rm_def(self.book, &def);
             } else {
               // Don't show warning if it's a user-defined constructor.
             }
@@ -77,7 +88,7 @@ impl Ctx<'_> {
         }
       } else {
         // Unused builtin, can always be pruned.
-        self.book.defs.shift_remove(&def);
+        rm_def(self.book, &def);
       }
     }
   }
diff --git a/src/lib.rs b/src/lib.rs
index aedaab42..8f361629 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -129,21 +129,21 @@ pub fn desugar_book(
 
   ctx.book.make_var_names_unique();
   ctx.book.desugar_use();
+
   ctx.book.make_var_names_unique();
   ctx.book.linearize_vars();
 
   // sanity check
   ctx.check_unbound_vars()?;
 
-  // Optimizing passes
   if opts.float_combinators {
     ctx.book.float_combinators(MAX_NET_SIZE);
   }
-
+  // sanity check
   ctx.check_unbound_refs()?;
 
+  // Optimizing passes
   ctx.prune(opts.prune);
-
   if opts.merge {
     ctx.book.merge_definitions();
   }
diff --git a/tests/golden_tests/run_file/hvm_def_cast.bend b/tests/golden_tests/run_file/hvm_def_cast.bend
index 0fb66229..eff6aba1 100644
--- a/tests/golden_tests/run_file/hvm_def_cast.bend
+++ b/tests/golden_tests/run_file/hvm_def_cast.bend
@@ -1,5 +1,5 @@
 # Expected +42.0
-hvm to_f24:
+hvm to_f24_:
   ($([f24] a) a)
 
-main = (to_f24 42)
\ No newline at end of file
+main = (to_f24_ 42)
\ No newline at end of file
diff --git a/tests/golden_tests/run_file/num_cast.bend b/tests/golden_tests/run_file/num_cast.bend
new file mode 100644
index 00000000..cd93d43d
--- /dev/null
+++ b/tests/golden_tests/run_file/num_cast.bend
@@ -0,0 +1,48 @@
+main = 
+use inf = (** 9.0 (** 9.0 9.0))
+(
+  (to_u24 0),
+  (to_u24 1),
+  (to_u24 123456),
+  (to_u24 -1),
+  (to_u24 +1),
+  (to_u24 +0),
+  (to_u24 +400),
+  (to_u24 1.0),
+  (to_u24 1.5),
+  (to_u24 -3.0),
+  (to_u24 -3.5),
+  (to_u24 inf), # inf
+  (to_u24 (* -1.0 inf)), # -inf
+  (to_u24 (/ inf inf)), # nan (inf/inf)
+  99999,
+  (to_i24 0),
+  (to_i24 1),
+  (to_i24 123456),
+  (to_i24 -1),
+  (to_i24 +1),
+  (to_i24 +0),
+  (to_i24 +400),
+  (to_i24 1.0),
+  (to_i24 1.5),
+  (to_i24 -3.0),
+  (to_i24 -3.5),
+  (to_i24 inf), # inf
+  (to_i24 (* -1.0 inf)), # -inf
+  (to_i24 (/ inf inf)), # nan (inf/inf)
+  99999,
+  (to_f24 0),
+  (to_f24 1),
+  (to_f24 123456),
+  (to_f24 -1),
+  (to_f24 +1),
+  (to_f24 +0),
+  (to_f24 +400),
+  (to_f24 1.0),
+  (to_f24 1.5),
+  (to_f24 -3.0),
+  (to_f24 -3.5),
+  (to_f24 inf), # inf
+  (to_f24 (* -1.0 inf)), # -inf
+  (to_f24 (/ inf inf)) # nan (inf/inf)
+)
\ No newline at end of file
diff --git a/tests/snapshots/run_file__num_cast.bend.snap b/tests/snapshots/run_file__num_cast.bend.snap
new file mode 100644
index 00000000..320e6cb2
--- /dev/null
+++ b/tests/snapshots/run_file__num_cast.bend.snap
@@ -0,0 +1,9 @@
+---
+source: tests/golden_tests.rs
+input_file: tests/golden_tests/run_file/num_cast.bend
+---
+NumScott:
+(0, (1, (123456, (16777215, (1, (0, (400, (1, (1, (0, (0, (16777215, (0, (0, (99999, (+0, (+1, (+123456, (-1, (+1, (+0, (+400, (+1, (+1, (-3, (-3, (+8388607, (-8388608, (+0, (99999, (0.000, (1.000, (123456.000, (-1.000, (1.000, (0.000, (400.000, (1.000, (1.500, (-3.000, (-3.500, (inf, (-inf, NaN)))))))))))))))))))))))))))))))))))))))))))
+
+Scott:
+(0, (1, (123456, (16777215, (1, (0, (400, (1, (1, (0, (0, (16777215, (0, (0, (99999, (+0, (+1, (+123456, (-1, (+1, (+0, (+400, (+1, (+1, (-3, (-3, (+8388607, (-8388608, (+0, (99999, (0.000, (1.000, (123456.000, (-1.000, (1.000, (0.000, (400.000, (1.000, (1.500, (-3.000, (-3.500, (inf, (-inf, NaN)))))))))))))))))))))))))))))))))))))))))))