diff --git a/cranelift/docs/langref.rst b/cranelift/docs/langref.rst
index 3ef460de06..8acb5e793a 100644
--- a/cranelift/docs/langref.rst
+++ b/cranelift/docs/langref.rst
@@ -212,6 +212,9 @@ indicate the different kinds of immediate operands on an instruction.
     signed two's complement integer. Instruction encodings may limit the valid
     range.
 
+    In the textual format, :type:`imm64` immediates appear as decimal or
+    hexadecimal literals using the same syntax as C.
+
 .. type:: ieee32
 
     A 32-bit immediate floating point number in the IEEE 754-2008 binary32
@@ -229,6 +232,38 @@ indicate the different kinds of immediate operands on an instruction.
     bits of the operand are interpreted as if the SIMD vector was loaded from
     memory containing the immediate.
 
+The two IEEE floating point immediate types :type:`ieee32` and :type:`ieee64`
+are displayed as hexadecimal floating point literals in the textual IL format.
+Decimal floating point literals are not allowed because some computer systems
+can round differently when converting to binary. The hexadecimal floating point
+format is mostly the same as the one used by C99, but extended to represent all
+NaN bit patterns:
+
+Normal numbers
+    Compatible with C99: ``-0x1.Tpe`` where ``T`` are the trailing
+    significand bits encoded as hexadecimal, and ``e`` is the unbiased exponent
+    as a decimal number. :type:`ieee32` has 23 trailing significand bits. They
+    are padded with an extra LSB to produce 6 hexadecimal digits. This is not
+    necessary for :type:`ieee64` which has 52 trailing significand bits
+    forming 13 hexadecimal digits with no padding.
+
+Subnormal numbers
+    Compatible with C99: ``-0x0.Tpemin`` where ``T`` are the trailing
+    significand bits encoded as hexadecimal, and ``emin`` is the minimum exponent
+    as a decimal number.
+
+Infinities
+    Either ``-Inf`` or ``Inf``.
+
+Quiet NaNs
+    Quiet NaNs have the MSB of the trailing significand set. If the remaining
+    bits of the trailing significand are all zero, the value is displayed as
+    ``-qNaN`` or ``qNaN``. Otherwise, ``-qNaN:0xT`` where ``T`` are the
+    trailing significand bits encoded as hexadecimal.
+
+Signaling NaNs
+    Displayed as ``-sNaN:0xT``.
+
 Control flow
 ============
 
diff --git a/cranelift/src/libcretonne/immediates.rs b/cranelift/src/libcretonne/immediates.rs
index a60291b164..0e1e94ba07 100644
--- a/cranelift/src/libcretonne/immediates.rs
+++ b/cranelift/src/libcretonne/immediates.rs
@@ -6,6 +6,7 @@
 //! module in the meta language.
 
 use std::fmt::{self, Display, Formatter};
+use std::mem;
 
 /// 64-bit immediate integer operand.
 ///
@@ -36,9 +37,123 @@ impl Display for Imm64 {
     }
 }
 
+
+/// An IEEE binary32 immediate floating point value.
+///
+/// All bit patterns are allowed.
+pub struct Ieee32(f32);
+
+/// An IEEE binary64 immediate floating point value.
+///
+/// All bit patterns are allowed.
+pub struct Ieee64(f64);
+
+// Format a floating point number in a way that is reasonably human-readable, and that can be
+// converted back to binary without any rounding issues. The hexadecimal formatting of normal and
+// subnormal numbers is compatible with C99 and the printf "%a" format specifier. The NaN and Inf
+// formats are not supported by C99.
+//
+// The encoding parameters are:
+//
+// w - exponent field width in bits
+// t - trailing significand field width in bits
+//
+fn format_float(bits: u64, w: u8, t: u8, f: &mut Formatter) -> fmt::Result {
+    assert!(w > 0 && w <= 16, "Invalid exponent range");
+    assert!(1 + w + t <= 64, "Too large IEEE format for u64");
+
+    let max_e_bits = (1u64 << w) - 1;
+    let t_bits = bits & ((1u64 << t) - 1); // Trailing significand.
+    let e_bits = (bits >> t) & max_e_bits; // Biased exponent.
+    let sign_bit = (bits >> w + t) & 1;
+
+    let bias: i32 = (1 << (w - 1)) - 1;
+    let e = e_bits as i32 - bias; // Unbiased exponent.
+    let emin = 1 - bias; // Minimum exponent.
+
+    // How many hexadecimal digits are needed for the trailing significand?
+    let digits = (t + 3) / 4;
+    // Trailing significand left-aligned in `digits` hexadecimal digits.
+    let left_t_bits = t_bits << (4 * digits - t);
+
+    // All formats share the leading sign.
+    if sign_bit != 0 {
+        try!(write!(f, "-"));
+    }
+
+    if e_bits == 0 {
+        if t_bits == 0 {
+            // Zero.
+            write!(f, "0.0")
+        } else {
+            // Subnormal.
+            write!(f, "0x0.{0:01$x}p{2}", left_t_bits, digits as usize, emin)
+        }
+    } else if e_bits == max_e_bits {
+        if t_bits == 0 {
+            // Infinity.
+            write!(f, "Inf")
+        } else {
+            // NaN.
+            let payload = t_bits & ((1 << (t - 1)) - 1);
+            if t_bits & (1 << (t - 1)) != 0 {
+                // Quiet NaN.
+                if payload != 0 {
+                    write!(f, "qNaN:0x{:x}", payload)
+                } else {
+                    write!(f, "qNaN")
+                }
+            } else {
+                // Signaling NaN.
+                write!(f, "sNaN:0x{:x}", payload)
+            }
+        }
+    } else {
+        // Normal number.
+        write!(f, "0x1.{0:01$x}p{2}", left_t_bits, digits as usize, e)
+    }
+}
+
+impl Ieee32 {
+    pub fn new(x: f32) -> Ieee32 {
+        Ieee32(x)
+    }
+
+    /// Construct Ieee32 immediate from raw bits.
+    pub fn new_from_bits(x: u32) -> Ieee32 {
+        Ieee32(unsafe { mem::transmute(x) })
+    }
+}
+
+impl Display for Ieee32 {
+    fn fmt(&self, f: &mut Formatter) -> fmt::Result {
+        let bits: u32 = unsafe { mem::transmute(self.0) };
+        format_float(bits as u64, 8, 23, f)
+    }
+}
+
+impl Ieee64 {
+    pub fn new(x: f64) -> Ieee64 {
+        Ieee64(x)
+    }
+
+    /// Construct Ieee64 immediate from raw bits.
+    pub fn new_from_bits(x: u64) -> Ieee64 {
+        Ieee64(unsafe { mem::transmute(x) })
+    }
+}
+
+impl Display for Ieee64 {
+    fn fmt(&self, f: &mut Formatter) -> fmt::Result {
+        let bits: u64 = unsafe { mem::transmute(self.0) };
+        format_float(bits, 11, 52, f)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
+    use std::{f32, f64};
 
     #[test]
     fn format_imm64() {
@@ -50,4 +165,73 @@ mod tests {
         assert_eq!(format!("{}", Imm64(0xffff)), "0xffff");
         assert_eq!(format!("{}", Imm64(0x10000)), "0x0001_0000");
     }
+
+    #[test]
+    fn format_ieee32() {
+        assert_eq!(format!("{}", Ieee32::new(0.0)), "0.0");
+        assert_eq!(format!("{}", Ieee32::new(-0.0)), "-0.0");
+        assert_eq!(format!("{}", Ieee32::new(1.0)), "0x1.000000p0");
+        assert_eq!(format!("{}", Ieee32::new(1.5)), "0x1.800000p0");
+        assert_eq!(format!("{}", Ieee32::new(0.5)), "0x1.000000p-1");
+        assert_eq!(format!("{}", Ieee32::new(f32::EPSILON)), "0x1.000000p-23");
+        assert_eq!(format!("{}", Ieee32::new(f32::MIN)), "-0x1.fffffep127");
+        assert_eq!(format!("{}", Ieee32::new(f32::MAX)), "0x1.fffffep127");
+        // Smallest positive normal number.
+        assert_eq!(format!("{}", Ieee32::new(f32::MIN_POSITIVE)),
+                   "0x1.000000p-126");
+        // Subnormals.
+        assert_eq!(format!("{}", Ieee32::new(f32::MIN_POSITIVE / 2.0)),
+                   "0x0.800000p-126");
+        assert_eq!(format!("{}", Ieee32::new(f32::MIN_POSITIVE * f32::EPSILON)),
+                   "0x0.000002p-126");
+        assert_eq!(format!("{}", Ieee32::new(f32::INFINITY)), "Inf");
+        assert_eq!(format!("{}", Ieee32::new(f32::NEG_INFINITY)), "-Inf");
+        assert_eq!(format!("{}", Ieee32::new(f32::NAN)), "qNaN");
+        assert_eq!(format!("{}", Ieee32::new(-f32::NAN)), "-qNaN");
+        // Construct some qNaNs with payloads.
+        assert_eq!(format!("{}", Ieee32::new_from_bits(0x7fc00001)), "qNaN:0x1");
+        assert_eq!(format!("{}", Ieee32::new_from_bits(0x7ff00001)),
+                   "qNaN:0x300001");
+        // Signaling NaNs.
+        assert_eq!(format!("{}", Ieee32::new_from_bits(0x7f800001)), "sNaN:0x1");
+        assert_eq!(format!("{}", Ieee32::new_from_bits(0x7fa00001)),
+                   "sNaN:0x200001");
+    }
+
+    #[test]
+    fn format_ieee64() {
+        assert_eq!(format!("{}", Ieee64::new(0.0)), "0.0");
+        assert_eq!(format!("{}", Ieee64::new(-0.0)), "-0.0");
+        assert_eq!(format!("{}", Ieee64::new(1.0)), "0x1.0000000000000p0");
+        assert_eq!(format!("{}", Ieee64::new(1.5)), "0x1.8000000000000p0");
+        assert_eq!(format!("{}", Ieee64::new(0.5)), "0x1.0000000000000p-1");
+        assert_eq!(format!("{}", Ieee64::new(f64::EPSILON)),
+                   "0x1.0000000000000p-52");
+        assert_eq!(format!("{}", Ieee64::new(f64::MIN)),
+                   "-0x1.fffffffffffffp1023");
+        assert_eq!(format!("{}", Ieee64::new(f64::MAX)),
+                   "0x1.fffffffffffffp1023");
+        // Smallest positive normal number.
+        assert_eq!(format!("{}", Ieee64::new(f64::MIN_POSITIVE)),
+                   "0x1.0000000000000p-1022");
+        // Subnormals.
+        assert_eq!(format!("{}", Ieee64::new(f64::MIN_POSITIVE / 2.0)),
+                   "0x0.8000000000000p-1022");
+        assert_eq!(format!("{}", Ieee64::new(f64::MIN_POSITIVE * f64::EPSILON)),
+                   "0x0.0000000000001p-1022");
+        assert_eq!(format!("{}", Ieee64::new(f64::INFINITY)), "Inf");
+        assert_eq!(format!("{}", Ieee64::new(f64::NEG_INFINITY)), "-Inf");
+        assert_eq!(format!("{}", Ieee64::new(f64::NAN)), "qNaN");
+        assert_eq!(format!("{}", Ieee64::new(-f64::NAN)), "-qNaN");
+        // Construct some qNaNs with payloads.
+        assert_eq!(format!("{}", Ieee64::new_from_bits(0x7ff8000000000001)),
+                   "qNaN:0x1");
+        assert_eq!(format!("{}", Ieee64::new_from_bits(0x7ffc000000000001)),
+                   "qNaN:0x4000000000001");
+        // Signaling NaNs.
+        assert_eq!(format!("{}", Ieee64::new_from_bits(0x7ff0000000000001)),
+                   "sNaN:0x1");
+        assert_eq!(format!("{}", Ieee64::new_from_bits(0x7ff4000000000001)),
+                   "sNaN:0x4000000000001");
+    }
 }