diff --git a/src/gallium/auxiliary/util/u_half.h b/src/gallium/auxiliary/util/u_half.h
index a107dcb74b1..bbcc843c310 100644
--- a/src/gallium/auxiliary/util/u_half.h
+++ b/src/gallium/auxiliary/util/u_half.h
@@ -50,6 +50,63 @@ util_float_to_half(float f)
    return _mesa_float_to_half(f);
 }
 
+static inline uint16_t
+util_float_to_half_rtz(float f)
+{
+   uint32_t sign_mask  = 0x80000000;
+   uint32_t round_mask = ~0xfff;
+   uint32_t f32inf = 0xff << 23;
+   uint32_t f16inf = 0x1f << 23;
+   uint32_t sign;
+   union fi magic;
+   union fi f32;
+   uint16_t f16;
+
+   magic.ui = 0xf << 23;
+
+   f32.f = f;
+
+   /* Sign */
+   sign = f32.ui & sign_mask;
+   f32.ui ^= sign;
+
+   if (f32.ui == f32inf) {
+      /* Inf */
+      f16 = 0x7c00;
+   } else if (f32.ui > f32inf) {
+      /* NaN */
+      f16 = 0x7e00;
+   } else {
+      /* Number */
+      f32.ui &= round_mask;
+      f32.f  *= magic.f;
+      f32.ui -= round_mask;
+      /*
+       * XXX: The magic mul relies on denorms being available, otherwise
+       * all f16 denorms get flushed to zero - hence when this is used
+       * for tgsi_exec in softpipe we won't get f16 denorms.
+       */
+      /*
+       * Clamp to max finite value if overflowed.
+       * OpenGL has completely undefined rounding behavior for float to
+       * half-float conversions, and this matches what is mandated for float
+       * to fp11/fp10, which recommend round-to-nearest-finite too.
+       * (d3d10 is deeply unhappy about flushing such values to infinity, and
+       * while it also mandates round-to-zero it doesn't care nearly as much
+       * about that.)
+       */
+      if (f32.ui > f16inf)
+         f32.ui = f16inf - 1;
+
+      f16 = f32.ui >> 13;
+   }
+
+   /* Sign */
+   f16 |= sign >> 16;
+
+   return f16;
+}
+
 static inline float
 util_half_to_float(uint16_t f16)
 {
diff --git a/src/util/format/u_format_pack.py b/src/util/format/u_format_pack.py
index 5a1763d1e6f..c8749a2c047 100644
--- a/src/util/format/u_format_pack.py
+++ b/src/util/format/u_format_pack.py
@@ -437,7 +437,7 @@ def conversion_expr(src_channel,
             src_size = 32
 
         if dst_channel.size == 16:
-            value = 'util_float_to_half(%s)' % value
+            value = 'util_float_to_half_rtz(%s)' % value
         elif dst_channel.size == 64 and src_size < 64:
             value = '(double)%s' % value