util: Add functions to convert float to/from bfloat16

Reviewed-by: Rohan Garg <rohan.garg@intel.com>
Reviewed-by: Ian Romanick <ian.d.romanick@intel.com>
Reviewed-by: Georg Lehmann <dadschoorse@gmail.com>
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/34105>

src/util/bfloat.h

@@ -0,0 +1,69 @@
+/*
+ * Copyright © 2025 Intel Corporation
+ * SPDX-License-Identifier: MIT
+ */
+
+#pragma once
+
+#include <assert.h>
+#include <math.h>
+#include <stdint.h>
+#include "u_math.h"
+
+/* When converting a Float NaN value to BFloat16 it is possible that the
+ * significand bits that make the value a NaN will be rounded/truncated off
+ * so ensure at least one significand bit is set.
+ */
+static inline uint16_t
+_mesa_float_nan_to_bfloat_bits(union fi x)
+{
+   assert(isnan(x.f));
+   return x.ui >> 16 | 1 << 6;
+}
+
+/* Round-towards-zero. */
+static inline uint16_t
+_mesa_float_to_bfloat16_bits_rtz(float f)
+{
+   union fi x;
+   x.f = f;
+
+   if (isnan(f))
+      _mesa_float_nan_to_bfloat_bits(x);
+
+   return x.ui >> 16;
+}
+
+/* Round-to-nearest-even. */
+static inline uint16_t
+_mesa_float_to_bfloat16_bits_rte(float f)
+{
+   union fi x;
+   x.f = f;
+
+   if (isnan(f))
+      _mesa_float_nan_to_bfloat_bits(x);
+
+   /* Use the tail part that is discarded to decide rounding,
+    * break the tie with the nearest even.
+    *
+    * Overflow of the significand value will turn to zero and
+    * increment the exponent.  If exponent reaches 0xff, the
+    * value will correctly end up as +/- Inf.
+    */
+   uint32_t result = x.ui >> 16;
+   const uint32_t tail = x.ui & 0xffff;
+   if (tail > 0x8000 || (tail == 0x8000 && (result & 1) == 1))
+      result++;
+
+   return result;
+}
+
+static inline float
+_mesa_bfloat16_bits_to_float(uint16_t bf)
+{
+   union fi x;
+   x.ui = bf << 16;
+
+   return x.f;
+}