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diff --git a/include/CL/cl_half.h b/include/CL/cl_half.h
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+/*******************************************************************************
+ * Copyright (c) 2019-2020 The Khronos Group Inc.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ ******************************************************************************/
+
+/**
+ * This is a header-only utility library that provides OpenCL host code with
+ * routines for converting to/from cl_half values.
+ *
+ * Example usage:
+ *
+ *    #include <CL/cl_half.h>
+ *    ...
+ *    cl_half h = cl_half_from_float(0.5f, CL_HALF_RTE);
+ *    cl_float f = cl_half_to_float(h);
+ */
+
+#ifndef OPENCL_CL_HALF_H
+#define OPENCL_CL_HALF_H
+
+#include <CL/cl_platform.h>
+
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+/**
+ * Rounding mode used when converting to cl_half.
+ */
+typedef enum
+{
+  CL_HALF_RTE, // round to nearest even
+  CL_HALF_RTZ, // round towards zero
+  CL_HALF_RTP, // round towards positive infinity
+  CL_HALF_RTN, // round towards negative infinity
+} cl_half_rounding_mode;
+
+
+/* Private utility macros. */
+#define CL_HALF_EXP_MASK 0x7C00
+#define CL_HALF_MAX_FINITE_MAG 0x7BFF
+
+
+/*
+ * Utility to deal with values that overflow when converting to half precision.
+ */
+static inline cl_half cl_half_handle_overflow(cl_half_rounding_mode rounding_mode,
+                                              uint16_t sign)
+{
+  if (rounding_mode == CL_HALF_RTZ)
+  {
+    // Round overflow towards zero -> largest finite number (preserving sign)
+    return (sign << 15) | CL_HALF_MAX_FINITE_MAG;
+  }
+  else if (rounding_mode == CL_HALF_RTP && sign)
+  {
+    // Round negative overflow towards positive infinity -> most negative finite number
+    return (1 << 15) | CL_HALF_MAX_FINITE_MAG;
+  }
+  else if (rounding_mode == CL_HALF_RTN && !sign)
+  {
+    // Round positive overflow towards negative infinity -> largest finite number
+    return CL_HALF_MAX_FINITE_MAG;
+  }
+
+  // Overflow to infinity
+  return (sign << 15) | CL_HALF_EXP_MASK;
+}
+
+/*
+ * Utility to deal with values that underflow when converting to half precision.
+ */
+static inline cl_half cl_half_handle_underflow(cl_half_rounding_mode rounding_mode,
+                                               uint16_t sign)
+{
+  if (rounding_mode == CL_HALF_RTP && !sign)
+  {
+    // Round underflow towards positive infinity -> smallest positive value
+    return (sign << 15) | 1;
+  }
+  else if (rounding_mode == CL_HALF_RTN && sign)
+  {
+    // Round underflow towards negative infinity -> largest negative value
+    return (sign << 15) | 1;
+  }
+
+  // Flush to zero
+  return (sign << 15);
+}
+
+
+/**
+ * Convert a cl_float to a cl_half.
+ */
+static inline cl_half cl_half_from_float(cl_float f, cl_half_rounding_mode rounding_mode)
+{
+  // Type-punning to get direct access to underlying bits
+  union
+  {
+    cl_float f;
+    uint32_t i;
+  } f32;
+  f32.f = f;
+
+  // Extract sign bit
+  uint16_t sign = f32.i >> 31;
+
+  // Extract FP32 exponent and mantissa
+  uint32_t f_exp = (f32.i >> (CL_FLT_MANT_DIG - 1)) & 0xFF;
+  uint32_t f_mant = f32.i & ((1 << (CL_FLT_MANT_DIG - 1)) - 1);
+
+  // Remove FP32 exponent bias
+  int32_t exp = f_exp - CL_FLT_MAX_EXP + 1;
+
+  // Add FP16 exponent bias
+  uint16_t h_exp = (uint16_t)(exp + CL_HALF_MAX_EXP - 1);
+
+  // Position of the bit that will become the FP16 mantissa LSB
+  uint32_t lsb_pos = CL_FLT_MANT_DIG - CL_HALF_MANT_DIG;
+
+  // Check for NaN / infinity
+  if (f_exp == 0xFF)
+  {
+    if (f_mant)
+    {
+      // NaN -> propagate mantissa and silence it
+      uint16_t h_mant = (uint16_t)(f_mant >> lsb_pos);
+      h_mant |= 0x200;
+      return (sign << 15) | CL_HALF_EXP_MASK | h_mant;
+    }
+    else
+    {
+      // Infinity -> zero mantissa
+      return (sign << 15) | CL_HALF_EXP_MASK;
+    }
+  }
+
+  // Check for zero
+  if (!f_exp && !f_mant)
+  {
+    return (sign << 15);
+  }
+
+  // Check for overflow
+  if (exp >= CL_HALF_MAX_EXP)
+  {
+    return cl_half_handle_overflow(rounding_mode, sign);
+  }
+
+  // Check for underflow
+  if (exp < (CL_HALF_MIN_EXP - CL_HALF_MANT_DIG - 1))
+  {
+    return cl_half_handle_underflow(rounding_mode, sign);
+  }
+
+  // Check for value that will become denormal
+  if (exp < -14)
+  {
+    // Denormal -> include the implicit 1 from the FP32 mantissa
+    h_exp = 0;
+    f_mant |= 1 << (CL_FLT_MANT_DIG - 1);
+
+    // Mantissa shift amount depends on exponent
+    lsb_pos = -exp + (CL_FLT_MANT_DIG - 25);
+  }
+
+  // Generate FP16 mantissa by shifting FP32 mantissa
+  uint16_t h_mant = (uint16_t)(f_mant >> lsb_pos);
+
+  // Check whether we need to round
+  uint32_t halfway = 1 << (lsb_pos - 1);
+  uint32_t mask = (halfway << 1) - 1;
+  switch (rounding_mode)
+  {
+    case CL_HALF_RTE:
+      if ((f_mant & mask) > halfway)
+      {
+        // More than halfway -> round up
+        h_mant += 1;
+      }
+      else if ((f_mant & mask) == halfway)
+      {
+        // Exactly halfway -> round to nearest even
+        if (h_mant & 0x1)
+          h_mant += 1;
+      }
+      break;
+    case CL_HALF_RTZ:
+      // Mantissa has already been truncated -> do nothing
+      break;
+    case CL_HALF_RTP:
+      if ((f_mant & mask) && !sign)
+      {
+        // Round positive numbers up
+        h_mant += 1;
+      }
+      break;
+    case CL_HALF_RTN:
+      if ((f_mant & mask) && sign)
+      {
+        // Round negative numbers down
+        h_mant += 1;
+      }
+      break;
+  }
+
+  // Check for mantissa overflow
+  if (h_mant & 0x400)
+  {
+    h_exp += 1;
+    h_mant = 0;
+  }
+
+  return (sign << 15) | (h_exp << 10) | h_mant;
+}
+
+
+/**
+ * Convert a cl_double to a cl_half.
+ */
+static inline cl_half cl_half_from_double(cl_double d, cl_half_rounding_mode rounding_mode)
+{
+  // Type-punning to get direct access to underlying bits
+  union
+  {
+    cl_double d;
+    uint64_t i;
+  } f64;
+  f64.d = d;
+
+  // Extract sign bit
+  uint16_t sign = f64.i >> 63;
+
+  // Extract FP64 exponent and mantissa
+  uint64_t d_exp = (f64.i >> (CL_DBL_MANT_DIG - 1)) & 0x7FF;
+  uint64_t d_mant = f64.i & (((uint64_t)1 << (CL_DBL_MANT_DIG - 1)) - 1);
+
+  // Remove FP64 exponent bias
+  int64_t exp = d_exp - CL_DBL_MAX_EXP + 1;
+
+  // Add FP16 exponent bias
+  uint16_t h_exp = (uint16_t)(exp + CL_HALF_MAX_EXP - 1);
+
+  // Position of the bit that will become the FP16 mantissa LSB
+  uint32_t lsb_pos = CL_DBL_MANT_DIG - CL_HALF_MANT_DIG;
+
+  // Check for NaN / infinity
+  if (d_exp == 0x7FF)
+  {
+    if (d_mant)
+    {
+      // NaN -> propagate mantissa and silence it
+      uint16_t h_mant = (uint16_t)(d_mant >> lsb_pos);
+      h_mant |= 0x200;
+      return (sign << 15) | CL_HALF_EXP_MASK | h_mant;
+    }
+    else
+    {
+      // Infinity -> zero mantissa
+      return (sign << 15) | CL_HALF_EXP_MASK;
+    }
+  }
+
+  // Check for zero
+  if (!d_exp && !d_mant)
+  {
+    return (sign << 15);
+  }
+
+  // Check for overflow
+  if (exp >= CL_HALF_MAX_EXP)
+  {
+    return cl_half_handle_overflow(rounding_mode, sign);
+  }
+
+  // Check for underflow
+  if (exp < (CL_HALF_MIN_EXP - CL_HALF_MANT_DIG - 1))
+  {
+    return cl_half_handle_underflow(rounding_mode, sign);
+  }
+
+  // Check for value that will become denormal
+  if (exp < -14)
+  {
+    // Include the implicit 1 from the FP64 mantissa
+    h_exp = 0;
+    d_mant |= (uint64_t)1 << (CL_DBL_MANT_DIG - 1);
+
+    // Mantissa shift amount depends on exponent
+    lsb_pos = (uint32_t)(-exp + (CL_DBL_MANT_DIG - 25));
+  }
+
+  // Generate FP16 mantissa by shifting FP64 mantissa
+  uint16_t h_mant = (uint16_t)(d_mant >> lsb_pos);
+
+  // Check whether we need to round
+  uint64_t halfway = (uint64_t)1 << (lsb_pos - 1);
+  uint64_t mask = (halfway << 1) - 1;
+  switch (rounding_mode)
+  {
+    case CL_HALF_RTE:
+      if ((d_mant & mask) > halfway)
+      {
+        // More than halfway -> round up
+        h_mant += 1;
+      }
+      else if ((d_mant & mask) == halfway)
+      {
+        // Exactly halfway -> round to nearest even
+        if (h_mant & 0x1)
+          h_mant += 1;
+      }
+      break;
+    case CL_HALF_RTZ:
+      // Mantissa has already been truncated -> do nothing
+      break;
+    case CL_HALF_RTP:
+      if ((d_mant & mask) && !sign)
+      {
+        // Round positive numbers up
+        h_mant += 1;
+      }
+      break;
+    case CL_HALF_RTN:
+      if ((d_mant & mask) && sign)
+      {
+        // Round negative numbers down
+        h_mant += 1;
+      }
+      break;
+  }
+
+  // Check for mantissa overflow
+  if (h_mant & 0x400)
+  {
+    h_exp += 1;
+    h_mant = 0;
+  }
+
+  return (sign << 15) | (h_exp << 10) | h_mant;
+}
+
+
+/**
+ * Convert a cl_half to a cl_float.
+ */
+static inline cl_float cl_half_to_float(cl_half h)
+{
+  // Type-punning to get direct access to underlying bits
+  union
+  {
+    cl_float f;
+    uint32_t i;
+  } f32;
+
+  // Extract sign bit
+  uint16_t sign = h >> 15;
+
+  // Extract FP16 exponent and mantissa
+  uint16_t h_exp = (h >> (CL_HALF_MANT_DIG - 1)) & 0x1F;
+  uint16_t h_mant = h & 0x3FF;
+
+  // Remove FP16 exponent bias
+  int32_t exp = h_exp - CL_HALF_MAX_EXP + 1;
+
+  // Add FP32 exponent bias
+  uint32_t f_exp = exp + CL_FLT_MAX_EXP - 1;
+
+  // Check for NaN / infinity
+  if (h_exp == 0x1F)
+  {
+    if (h_mant)
+    {
+      // NaN -> propagate mantissa and silence it
+      uint32_t f_mant = h_mant << (CL_FLT_MANT_DIG - CL_HALF_MANT_DIG);
+      f_mant |= 0x400000;
+      f32.i = (sign << 31) | 0x7F800000 | f_mant;
+      return f32.f;
+    }
+    else
+    {
+      // Infinity -> zero mantissa
+      f32.i = (sign << 31) | 0x7F800000;
+      return f32.f;
+    }
+  }
+
+  // Check for zero / denormal
+  if (h_exp == 0)
+  {
+    if (h_mant == 0)
+    {
+      // Zero -> zero exponent
+      f_exp = 0;
+    }
+    else
+    {
+      // Denormal -> normalize it
+      // - Shift mantissa to make most-significant 1 implicit
+      // - Adjust exponent accordingly
+      uint32_t shift = 0;
+      while ((h_mant & 0x400) == 0)
+      {
+        h_mant <<= 1;
+        shift++;
+      }
+      h_mant &= 0x3FF;
+      f_exp -= shift - 1;
+    }
+  }
+
+  f32.i = (sign << 31) | (f_exp << 23) | (h_mant << 13);
+  return f32.f;
+}
+
+
+#undef CL_HALF_EXP_MASK
+#undef CL_HALF_MAX_FINITE_MAG
+
+
+#ifdef __cplusplus
+}
+#endif
+
+
+#endif  /* OPENCL_CL_HALF_H */