diff --git a/lib/Translation/ForthToMLIR/ForthToMLIR.cpp b/lib/Translation/ForthToMLIR/ForthToMLIR.cpp
index aa3b4cb..bea61c8 100644
--- a/lib/Translation/ForthToMLIR/ForthToMLIR.cpp
+++ b/lib/Translation/ForthToMLIR/ForthToMLIR.cpp
@@ -133,12 +133,39 @@ bool ForthLexer::isNumber(const std::string &str) const {
   return true;
 }
 
+/// Float grammar: [+-]? (D+ '.' D* | '.' D+ | D+) ([eE] [+-]? D+)?, where a
+/// bare D+ needs the exponent. Spelled out rather than using strtod, which
+/// also accepts hex, nan and inf.
 bool ForthLexer::isFloat(const std::string &str) const {
-  if (str.empty())
+  size_t i = 0;
+  size_t n = str.size();
+  auto skipDigits = [&]() {
+    size_t start = i;
+    while (i < n && std::isdigit(static_cast<unsigned char>(str[i])))
+      ++i;
+    return i - start;
+  };
+
+  if (i < n && (str[i] == '+' || str[i] == '-'))
+    ++i;
+  size_t mantissaDigits = skipDigits();
+  bool hasDot = i < n && str[i] == '.';
+  if (hasDot) {
+    ++i;
+    mantissaDigits += skipDigits();
+  }
+  if (mantissaDigits == 0)
     return false;
 
-  double value;
-  return llvm::to_float(str, value);
+  bool hasExponent = i < n && (str[i] == 'e' || str[i] == 'E');
+  if (hasExponent) {
+    ++i;
+    if (i < n && (str[i] == '+' || str[i] == '-'))
+      ++i;
+    if (skipDigits() == 0)
+      return false;
+  }
+  return i == n && (hasDot || hasExponent);
 }
 
 Token ForthLexer::nextToken() {
diff --git a/test/Translation/Forth/float-literal-strtod-spellings.forth b/test/Translation/Forth/float-literal-strtod-spellings.forth
new file mode 100644
index 0000000..9b7e4be
--- /dev/null
+++ b/test/Translation/Forth/float-literal-strtod-spellings.forth
@@ -0,0 +1,19 @@
+\ RUN: %warpforth-translate --forth-to-mlir %s | %FileCheck %s
+
+\ Hex, nan and inf spellings are ordinary words, not float literals.
+\ CHECK-NOT: f64
+\ CHECK: func.func private @NAN(
+\ CHECK: func.func private @INF(
+\ CHECK: func.func private @INFINITY(
+\ CHECK: func.func private @_0X1P3(
+\ CHECK: func.func @main()
+\ CHECK: call @NAN(
+\ CHECK: call @INF(
+\ CHECK: call @INFINITY(
+\ CHECK: call @_0X1P3(
+\! kernel main
+: nan 7 ;
+: inf 8 ;
+: infinity 9 ;
+: 0x1p3 10 ;
+nan inf infinity 0x1p3
diff --git a/test/Translation/Forth/float-literals.forth b/test/Translation/Forth/float-literals.forth
index 31d8f16..26b4c8b 100644
--- a/test/Translation/Forth/float-literals.forth
+++ b/test/Translation/Forth/float-literals.forth
@@ -5,5 +5,11 @@
 \ CHECK-NEXT: forth.constant %{{.*}}(-2.000000e+00 : f64)
 \ CHECK-NEXT: forth.constant %{{.*}}(1.000000e-05 : f64)
 \ CHECK-NEXT: forth.constant %{{.*}}(1.000000e+03 : f64)
+\ CHECK-NEXT: forth.constant %{{.*}}(1.000000e+03 : f64)
+\ CHECK-NEXT: forth.constant %{{.*}}(5.000000e-01 : f64)
+\ CHECK-NEXT: forth.constant %{{.*}}(-5.000000e-01 : f64)
+\ CHECK-NEXT: forth.constant %{{.*}}(5.000000e+00 : f64)
+\ CHECK-NEXT: forth.constant %{{.*}}(1.500000e+00 : f64)
+\ CHECK-NEXT: forth.constant %{{.*}}(2.500000e+02 : f64)
 \! kernel main
-3.14 -2.0 1.0e-5 1e3
+3.14 -2.0 1.0e-5 1e3 1E3 .5 -.5 5. +1.5 2.5e+2
diff --git a/test/Translation/Forth/hex-literal-error.forth b/test/Translation/Forth/hex-literal-error.forth
new file mode 100644
index 0000000..94ffbc2
--- /dev/null
+++ b/test/Translation/Forth/hex-literal-error.forth
@@ -0,0 +1,5 @@
+\ RUN: %not %warpforth-translate --forth-to-mlir %s 2>&1 | %FileCheck %s
+\ CHECK: {{.*}}hex-literal-error.forth:5:1: error: unknown word: 0X10
+\! kernel k
+\! param a i64[1]
+0x10 a !