Add 32 to 16 bit float conversion w.r.t rounding mode

Component: Framework

Change-Id: I9428f0dc725484b8a2f213157100326a69754cd8
(cherry picked from commit 7c0f5bea1da74f70e549e9a735c9d702c9396084)

7 files changed, 503 insertions, 7 deletions

diff --git a/framework/common/tcuApp.cpp b/framework/common/tcuApp.cpp
index 409a6774f..6227089b8 100644
--- a/framework/common/tcuApp.cpp
+++ b/framework/common/tcuApp.cpp
@@ -89,7 +89,7 @@ App::App (Platform& platform, Archive& archive, TestLog& log, const CommandLine&
 	print("dEQP Core %s (0x%08x) starting..\n", qpGetReleaseName(), qpGetReleaseId());
 	print("  target implementation = '%s'\n", qpGetTargetName());
 
-	if (!deSetRoundingMode(DE_ROUNDINGMODE_TO_NEAREST))
+	if (!deSetRoundingMode(DE_ROUNDINGMODE_TO_NEAREST_EVEN))
 		qpPrintf("WARNING: Failed to set floating-point rounding mode!\n");
 
 	try
diff --git a/framework/delibs/debase/CMakeLists.txt b/framework/delibs/debase/CMakeLists.txt
index 2f9d8d013..636d73ecf 100644
--- a/framework/delibs/debase/CMakeLists.txt
+++ b/framework/delibs/debase/CMakeLists.txt
@@ -9,6 +9,7 @@ set(DEBASE_SRCS
 	deDefs.h
 	deFloat16.c
 	deFloat16.h
+	deFloat16Test.c
 	deInt32.c
 	deInt32.h
 	deInt32Test.c
diff --git a/framework/delibs/debase/deFloat16.c b/framework/delibs/debase/deFloat16.c
index 6460f0587..e8a1057e0 100644
--- a/framework/delibs/debase/deFloat16.c
+++ b/framework/delibs/debase/deFloat16.c
@@ -99,6 +99,163 @@ deFloat16 deFloat32To16 (float val32)
 	}
 }
 
+/*--------------------------------------------------------------------*//*!
+ * \brief Round the given number `val` to nearest even by discarding
+ *        the last `numBitsToDiscard` bits.
+ * \param val value to round
+ * \param numBitsToDiscard number of (least significant) bits to discard
+ * \return The rounded value with the last `numBitsToDiscard` removed
+ *//*--------------------------------------------------------------------*/
+static deUint32 roundToNearestEven (deUint32 val, const deUint32 numBitsToDiscard)
+{
+	const deUint32	lastBits	= val & ((1 << numBitsToDiscard) - 1);
+	const deUint32	headBit		= val & (1 << (numBitsToDiscard - 1));
+
+	DE_ASSERT(numBitsToDiscard > 0 && numBitsToDiscard < 32);	/* Make sure no overflow. */
+	val >>= numBitsToDiscard;
+
+	if (headBit == 0)
+	{
+		return val;
+	}
+	else if (headBit == lastBits)
+	{
+		if ((val & 0x1) == 0x1)
+		{
+			return val + 1;
+		}
+		else
+		{
+			return val;
+		}
+	}
+	else
+	{
+		return val + 1;
+	}
+}
+
+deFloat16 deFloat32To16Round (float val32, deRoundingMode mode)
+{
+	union
+	{
+		float		f;		/* Interpret as 32-bit float */
+		deUint32	u;		/* Interpret as 32-bit unsigned integer */
+	} x;
+	deUint32	sign;		/* sign : 0000 0000 0000 0000 X000 0000 0000 0000 */
+	deUint32	exp32;		/* exp32: biased exponent for 32-bit floats */
+	int			exp16;		/* exp16: biased exponent for 16-bit floats */
+	deUint32	mantissa;
+
+	/* We only support these two rounding modes for now */
+	DE_ASSERT(mode == DE_ROUNDINGMODE_TO_ZERO || mode == DE_ROUNDINGMODE_TO_NEAREST_EVEN);
+
+	x.f			= val32;
+	sign		= (x.u >> 16u) & 0x00008000u;
+	exp32		= (x.u >> 23u) & 0x000000ffu;
+	exp16		= (int) (exp32) - 127 + 15;	/* 15/127: exponent bias for 16-bit/32-bit floats */
+	mantissa	= x.u & 0x007fffffu;
+
+	/* Case: zero and denormalized floats */
+	if (exp32 == 0)
+	{
+		/* Denormalized floats are < 2^(1-127), not representable in 16-bit floats, rounding to zero. */
+		return (deFloat16) sign;
+	}
+	/* Case: Inf and NaN */
+	else if (exp32 == 0x000000ffu)
+	{
+		if (mantissa == 0u)
+		{
+			/* Inf */
+			return (deFloat16) (sign | 0x7c00u);
+		}
+		else
+		{
+			/* NaN */
+			mantissa >>= 13u;	/* 16-bit floats has 10-bit for mantissa, 13-bit less than 32-bit floats. */
+			/* Make sure we don't turn NaN into zero by | (mantissa == 0). */
+			return (deFloat16) (sign | 0x7c00u | mantissa | (mantissa == 0u));
+		}
+	}
+	/* The following are cases for normalized floats.
+	 *
+	 * * If exp16 is less than 0, we are experiencing underflow for the exponent. To encode this underflowed exponent,
+	 *   we can only shift the mantissa further right.
+	 *   The real exponent is exp16 - 15. A denormalized 16-bit float can represent -14 via its exponent.
+	 *   Note that the most significant bit in the mantissa of a denormalized float is already -1 as for exponent.
+	 *   So, we just need to right shift the mantissa -exp16 bits.
+	 * * If exp16 is 0, mantissa shifting requirement is similar to the above.
+	 * * If exp16 is greater than 30 (0b11110), we are experiencing overflow for the exponent of 16-bit normalized floats.
+	 */
+	/* Case: normalized floats -> zero */
+	else if (exp16 < -10)
+	{
+		/* 16-bit floats have only 10 bits for mantissa. Minimal 16-bit denormalized float is (2^-10) * (2^-14). */
+		/* Expecting a number < (2^-10) * (2^-14) here, not representable, round to zero. */
+		return (deFloat16) sign;
+	}
+	/* Case: normalized floats -> zero and denormalized halfs */
+	else if (exp16 <= 0)
+	{
+		/* Add the implicit leading 1 in mormalized float to mantissa. */
+		mantissa |= 0x00800000u;
+		/* We have a (23 + 1)-bit mantissa, but 16-bit floats only expect 10-bit mantissa.
+		 * Need to discard the last 14-bits considering rounding mode.
+		 * We also need to shift right -exp16 bits to encode the underflowed exponent.
+		 */
+		if (mode == DE_ROUNDINGMODE_TO_ZERO)
+		{
+			mantissa >>= (14 - exp16);
+		}
+		else
+		{
+			/* mantissa in the above may exceed 10-bits, in which case overflow happens.
+			 * The overflowed bit is automatically carried to exponent then.
+			 */
+			mantissa = roundToNearestEven(mantissa, 14 - exp16);
+		}
+		return (deFloat16) (sign | mantissa);
+	}
+	/* Case: normalized floats -> normalized floats */
+	else if (exp16 <= 30)
+	{
+		if (mode == DE_ROUNDINGMODE_TO_ZERO)
+		{
+			return (deFloat16) (sign | ((deUint32)exp16 << 10u) | (mantissa >> 13u));
+		}
+		else
+		{
+			mantissa	= roundToNearestEven(mantissa, 13);
+			/* Handle overflow. exp16 may overflow (and become Inf) itself, but that's correct. */
+			exp16		= (exp16 << 10u) + (mantissa & (1 << 10));
+			mantissa	&= (1u << 10) - 1;
+			return (deFloat16) (sign | ((deUint32) exp16) | mantissa);
+		}
+	}
+	/* Case: normalized floats (too large to be representable as 16-bit floats) */
+	else
+	{
+		/* According to IEEE Std 754-2008 Section 7.4,
+		 * * roundTiesToEven and roundTiesToAway carry all overflows to Inf with the sign
+		 *   of the intermediate  result.
+		 * * roundTowardZero carries all overflows to the format’s largest finite number
+		 *   with the sign of the intermediate result.
+		 */
+		if (mode == DE_ROUNDINGMODE_TO_ZERO)
+		{
+			return (deFloat16) (sign | 0x7bffu); /* 111 1011 1111 1111 */
+		}
+		else
+		{
+			return (deFloat16) (sign | (0x1f << 10));
+		}
+	}
+
+	/* Make compiler happy */
+	return (deFloat16) 0;
+}
+
 float deFloat16To32 (deFloat16 val16)
 {
 	deUint32 sign;
diff --git a/framework/delibs/debase/deFloat16.h b/framework/delibs/debase/deFloat16.h
index d2d71dc29..ab81199e4 100644
--- a/framework/delibs/debase/deFloat16.h
+++ b/framework/delibs/debase/deFloat16.h
@@ -24,6 +24,7 @@
  *//*--------------------------------------------------------------------*/
 
 #include "deDefs.h"
+#include "deMath.h"
 
 DE_BEGIN_EXTERN_C
 
@@ -38,7 +39,9 @@ typedef		deFloat16			DEfloat16;
  * \param val32	Input value.
  * \return Converted 16-bit floating-point value.
  *//*--------------------------------------------------------------------*/
-deFloat16	deFloat32To16		(float val32);
+deFloat16	deFloat32To16				(float val32);
+deFloat16	deFloat32To16Round			(float val32, deRoundingMode mode);
+void		deFloat16_selfTest			(void);
 
 /*--------------------------------------------------------------------*//*!
  * \brief Convert 16-bit floating point number to 32 bit.
diff --git a/framework/delibs/debase/deFloat16Test.c b/framework/delibs/debase/deFloat16Test.c
new file mode 100644
index 000000000..ea5d21707
--- /dev/null
+++ b/framework/delibs/debase/deFloat16Test.c
@@ -0,0 +1,335 @@
+/*-------------------------------------------------------------------------
+ * drawElements Base Portability Library
+ * -------------------------------------
+ *
+ * Copyright 2017 Google 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.
+ *
+ *//*!
+ * \file
+ * \brief Testing of deFloat16 functions.
+ *//*--------------------------------------------------------------------*/
+
+#include "deFloat16.h"
+#include "deRandom.h"
+
+DE_BEGIN_EXTERN_C
+
+static float getFloat32 (deUint32 sign, deUint32 biased_exponent, deUint32 mantissa)
+{
+	union
+	{
+		float		f;
+		deUint32	u;
+	} x;
+
+	x.u = (sign << 31) | (biased_exponent << 23) | mantissa;
+
+	return x.f;
+}
+
+static deFloat16 getFloat16 (deUint16 sign, deUint16 biased_exponent, deUint16 mantissa)
+{
+	return (deFloat16) ((sign << 15) | (biased_exponent << 10) | mantissa);
+}
+
+
+static deFloat16 deFloat32To16RTZ (float val32)
+{
+	return deFloat32To16Round(val32, DE_ROUNDINGMODE_TO_ZERO);
+}
+
+static deFloat16 deFloat32To16RTE (float val32)
+{
+	return deFloat32To16Round(val32, DE_ROUNDINGMODE_TO_NEAREST_EVEN);
+}
+
+void deFloat16_selfTest (void)
+{
+	/* 16-bit: 1	5 (0x00--0x1f)	10 (0x000--0x3ff)
+	 * 32-bit: 1	8 (0x00--0xff)	23 (0x000000--0x7fffff)
+	 */
+	deRandom	rnd;
+	int			idx;
+
+	deRandom_init(&rnd, 0xdeadbeefu-1);
+
+	/* --- For rounding mode RTZ --- */
+
+	/* Zero */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0, 0)) == getFloat16(0, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0, 0)) == getFloat16(1, 0, 0));
+
+	/* Inf */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0)) == getFloat16(0, 0x1f, 0));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0)) == getFloat16(1, 0x1f, 0));
+
+	/* SNaN */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 1)) == getFloat16(0, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 1)) == getFloat16(1, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x3fffff)) == getFloat16(0, 0x1f, 0x1ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x3fffff)) == getFloat16(1, 0x1f, 0x1ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x0003ff)) == getFloat16(0, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x0003ff)) == getFloat16(1, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x123456)) == getFloat16(0, 0x1f, 0x123456 >> 13));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x123456)) == getFloat16(1, 0x1f, 0x123456 >> 13));
+
+	/* QNaN */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x400000)) == getFloat16(0, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x400000)) == getFloat16(1, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x7fffff)) == getFloat16(0, 0x1f, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x7fffff)) == getFloat16(1, 0x1f, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x4003ff)) == getFloat16(0, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x4003ff)) == getFloat16(1, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0xff, 0x723456)) == getFloat16(0, 0x1f, 0x723456 >> 13));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0xff, 0x723456)) == getFloat16(1, 0x1f, 0x723456 >> 13));
+
+	/* Denormalized */
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		mantissa	&= 0x7fffffu;		/* Take the last 23 bits */
+		mantissa	|= (mantissa == 0);	/* Make sure it is not zero */
+
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 0, mantissa)) == getFloat16(0, 0, 0));
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 0, mantissa)) == getFloat16(1, 0, 0));
+	}
+
+	/* Normalized -> zero */
+	/* Absolute value: minimal 32-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 1, 0)) == getFloat16(0, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 1, 0)) == getFloat16(1, 0, 0));
+	/* Absolute value: 2^-24 - e, extremely near minimal 16-bit denormalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 25, 0x7fffff)) == getFloat16(0, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 25, 0x7fffff)) == getFloat16(1, 0, 0));
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	exponent	= deRandom_getUint32(&rnd);
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		exponent	= exponent % (127 - 25) + 1;	/* Make sure >= 1, <= 127 - 25 */
+		mantissa	&= 0x7fffffu;					/* Take the last 23 bits */
+
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, exponent, mantissa)) == getFloat16(0, 0, 0));
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, exponent, mantissa)) == getFloat16(1, 0, 0));
+	}
+
+	/* Normalized -> denormalized */
+	/* Absolute value: 2^-24, minimal 16-bit denormalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 24, 0)) == getFloat16(0, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 24, 0)) == getFloat16(1, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 24, 1)) == getFloat16(0, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 24, 1)) == getFloat16(1, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 20, 0x123456)) == getFloat16(0, 0, 0x12));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 20, 0x123456)) == getFloat16(1, 0, 0x12));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 18, 0x654321)) == getFloat16(0, 0, 0x72));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 18, 0x654321)) == getFloat16(1, 0, 0x72));
+	/* Absolute value: 2^-14 - 2^-24 = (2 - 2^-9) * 2^-15, maximal 16-bit denormalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 15, 0x7fc000)) == getFloat16(0, 0, 0x3ff));	/* 0x7fc000: 0111 1111 1100 0000 0000 0000 */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 15, 0x7fc000)) == getFloat16(1, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 15, 0x7fc000 - 1)) == getFloat16(0, 0, 0x3fe));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 15, 0x7fc000 - 1)) == getFloat16(1, 0, 0x3fe));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 15, 0x7fc000 + 1)) == getFloat16(0, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 15, 0x7fc000 + 1)) == getFloat16(1, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 15, 0x7fffff)) == getFloat16(0, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 15, 0x7fffff)) == getFloat16(1, 0, 0x3ff));
+
+	/* Normalized -> normalized */
+	/* Absolute value: 2^-14, minimal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 - 14, 0)) == getFloat16(0, 1, 0));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 - 14, 0)) == getFloat16(1, 1, 0));
+	/* Absolute value: 65504 - 2^-23, extremely near maximal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 + 15, (0x3ff << 13) - 1)) == getFloat16(0, 0x1e, 0x3fe));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 + 15, (0x3ff << 13) - 1)) == getFloat16(1, 0x1e, 0x3fe));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 + 15, (0x3ff << 13) - 0x456)) == getFloat16(0, 0x1e, 0x3fe));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 + 15, (0x3ff << 13) - 0x456)) == getFloat16(1, 0x1e, 0x3fe));
+	/* Absolute value: 65504, maximal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 + 15, 0x3ff << 13)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 + 15, 0x3ff << 13)) == getFloat16(1, 0x1e, 0x3ff));
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	exponent	= deRandom_getUint32(&rnd);
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		exponent	= exponent % ((127 + 14) - (127 -14) + 1) + (127 - 14);	/* Make sure >= 127 - 14, <= 127 + 14 */
+		mantissa	&= 0x7fffffu;											/* Take the last 23 bits */
+
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, exponent, mantissa)) == getFloat16(0, (deUint16) (exponent + 15 - 127), (deUint16) (mantissa >> 13)));
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, exponent, mantissa)) == getFloat16(1, (deUint16) (exponent + 15 - 127), (deUint16) (mantissa >> 13)));
+	}
+
+	/* Normalized -> minimal/maximal normalized */
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 + 15, (0x3ff << 13) + 1)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 + 15, (0x3ff << 13) + 1)) == getFloat16(1, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, 127 + 15, (0x3ff << 13) + 0x123)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, 127 + 15, (0x3ff << 13) + 0x123)) == getFloat16(1, 0x1e, 0x3ff));
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	exponent	= deRandom_getUint32(&rnd);
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		exponent	= exponent % (0xfe - (127 + 16) + 1) + (127 + 16);	/* Make sure >= 127 + 16, <= 0xfe */
+		mantissa	&= 0x7fffffu;										/* Take the last 23 bits */
+
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(0, exponent, mantissa)) == getFloat16(0, 0x1e, 0x3ff));
+		DE_TEST_ASSERT(deFloat32To16RTZ(getFloat32(1, exponent, mantissa)) == getFloat16(1, 0x1e, 0x3ff));
+	}
+
+	/* --- For rounding mode RTE --- */
+
+	/* Zero */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0, 0)) == getFloat16(0, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0, 0)) == getFloat16(1, 0, 0));
+
+	/* Inf */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0)) == getFloat16(0, 0x1f, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0)) == getFloat16(1, 0x1f, 0));
+
+	/* SNaN */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 1)) == getFloat16(0, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 1)) == getFloat16(1, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x3fffff)) == getFloat16(0, 0x1f, 0x1ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x3fffff)) == getFloat16(1, 0x1f, 0x1ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x0003ff)) == getFloat16(0, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x0003ff)) == getFloat16(1, 0x1f, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x123456)) == getFloat16(0, 0x1f, 0x123456 >> 13));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x123456)) == getFloat16(1, 0x1f, 0x123456 >> 13));
+
+	/* QNaN */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x400000)) == getFloat16(0, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x400000)) == getFloat16(1, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x7fffff)) == getFloat16(0, 0x1f, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x7fffff)) == getFloat16(1, 0x1f, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x4003ff)) == getFloat16(0, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x4003ff)) == getFloat16(1, 0x1f, 0x200));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0xff, 0x723456)) == getFloat16(0, 0x1f, 0x723456 >> 13));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0xff, 0x723456)) == getFloat16(1, 0x1f, 0x723456 >> 13));
+
+	/* Denormalized */
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		mantissa	&= 0x7fffffu;		/* Take the last 23 bits */
+		mantissa	|= (mantissa == 0);	/* Make sure it is not zero */
+
+		DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 0, mantissa)) == getFloat16(0, 0, 0));
+		DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 0, mantissa)) == getFloat16(1, 0, 0));
+	}
+
+	/* Normalized -> zero and denormalized */
+	/* Absolute value: minimal 32-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 1, 0)) == getFloat16(0, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 1, 0)) == getFloat16(1, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 42, 0x7abcde)) == getFloat16(0, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 42, 0x7abcde)) == getFloat16(1, 0, 0));
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	exponent	= deRandom_getUint32(&rnd);
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		exponent	= exponent % (127 - 26) + 1;	/* Make sure >= 1, <= 127 - 26 */
+		mantissa	&= 0x7fffffu;					/* Take the last 23 bits */
+
+		DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, exponent, mantissa)) == getFloat16(0, 0, 0));
+		DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, exponent, mantissa)) == getFloat16(1, 0, 0));
+	}
+	/* Absolute value: 2^-25, minimal 16-bit denormalized: 2^-24 */
+	/* The following six cases need to right shift mantissa (with leading 1) 10 bits  --------------------> to here */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 25, 0)) == getFloat16(0, 0, 0));	/* XX XXXX XXXX 1 000 0000 0000 0000 0000 0000 */
+	/*													Take the first 10 bits with RTE ------ 00 0000 0000 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 25, 0)) == getFloat16(1, 0, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 25, 1)) == getFloat16(0, 0, 1));	/* XX XXXX XXXX 1 000 0000 0000 0000 0000 0001 */
+	/*													Take the first 10 bits with RTE ------ 00 0000 0001 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 25, 1)) == getFloat16(1, 0, 1));
+	/* Absolute value: 2^-24 - e, extremely near minimal 16-bit denormalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 25, 0x7fffff)) == getFloat16(0, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 25, 0x7fffff)) == getFloat16(1, 0, 1));
+	/* Absolute value: 2^-24, minimal 16-bit denormalized */
+	/* The following (127 - 24) cases need to right shift mantissa (with leading 1) 9 bits  -----------------> to here */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 24, 0)) == getFloat16(0, 0, 1));		/* X XXXX XXXX 1 000 0000 0000 0000 0000 0000 */
+	/*													Take the first 10 bits with RTE ---------- 0 0000 0000 1 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 24, 0)) == getFloat16(1, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 24, 1)) == getFloat16(0, 0, 1));		/* X XXXX XXXX 1 000 0000 0000 0000 0000 0001 */
+	/*													Take the first 10 bits with RTE ---------- 0 0000 0000 1 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 24, 1)) == getFloat16(1, 0, 1));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 24, 0x400000)) == getFloat16(0, 0, 2));	/* X XXXX XXXX 1 100 0000 0000 0000 0000 0000 */
+	/*													Take the first 10 bits with RTE ---------- 0 0000 0000 2 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 24, 0x400000)) == getFloat16(1, 0, 2));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 24, 0x400001)) == getFloat16(0, 0, 2));	/* X XXXX XXXX 1 100 0000 0000 0000 0000 0001 */
+	/*													Take the first 10 bits with RTE ---------- 0 0000 0000 2 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 24, 0x400001)) == getFloat16(1, 0, 2));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 24, 0x4fffff)) == getFloat16(0, 0, 2));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 24, 0x4fffff)) == getFloat16(1, 0, 2));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 20, 0x123456)) == getFloat16(0, 0, 0x12));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 20, 0x123456)) == getFloat16(1, 0, 0x12));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 18, 0x654321)) == getFloat16(0, 0, 0x73));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 18, 0x654321)) == getFloat16(1, 0, 0x73));
+	/* Absolute value: 2^-14 - 2^-24 = (2 - 2^-9) * 2^-15, maximal 16-bit denormalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 15, 0x7fc000)) == getFloat16(0, 0, 0x3ff));	/* 0x7fc000: 0111 1111 1100 0000 0000 0000 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 15, 0x7fc000)) == getFloat16(1, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 15, 0x7fc000 - 1)) == getFloat16(0, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 15, 0x7fc000 - 1)) == getFloat16(1, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 15, 0x7fc000 + 1)) == getFloat16(0, 0, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 15, 0x7fc000 + 1)) == getFloat16(1, 0, 0x3ff));
+
+	/* Normalized -> normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 15, 0x7fe000)) == getFloat16(0, 1, 0));	/* 0x7fe000: 0111 1111 1110 0000 0000 0000 */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 15, 0x7fe000)) == getFloat16(1, 1, 0));
+	/* Absolute value: (2 - 2^-23) * 2^-15, extremely near 2^-14, minimal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 15, 0x7fffff)) == getFloat16(0, 1, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 15, 0x7fffff)) == getFloat16(1, 1, 0));
+	/* Absolute value: 2^-14, minimal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 - 14, 0)) == getFloat16(0, 1, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 - 14, 0)) == getFloat16(1, 1, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3fe << 13) + (1 << 12))) == getFloat16(0, 0x1e, 0x3fe));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3fe << 13) + (1 << 12))) == getFloat16(1, 0x1e, 0x3fe));
+
+	/* Normalized -> minimal/maximal normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3fe << 13) + (1 << 12) + 1)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3fe << 13) + (1 << 12) + 1)) == getFloat16(1, 0x1e, 0x3ff));
+	/* Absolute value: 65504 - 2^-23, extremely near maximal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3ff << 13) - 1)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3ff << 13) - 1)) == getFloat16(1, 0x1e, 0x3ff));
+	/* Absolute value: 65504, maximal 16-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, 0x3ff << 13)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, 0x3ff << 13)) == getFloat16(1, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3ff << 13) + 1)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3ff << 13) + 1)) == getFloat16(1, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3ff << 13) + 0x456)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3ff << 13) + 0x456)) == getFloat16(1, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3ff << 13) + (1 << 12) - 1)) == getFloat16(0, 0x1e, 0x3ff));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3ff << 13) + (1 << 12) - 1)) == getFloat16(1, 0x1e, 0x3ff));
+
+	/* Normalized -> Inf */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, (0x3ff << 13) + (1 << 12))) == getFloat16(0, 0x1f, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, (0x3ff << 13) + (1 << 12))) == getFloat16(1, 0x1f, 0));
+	/* Absolute value: maximal 32-bit normalized */
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, 127 + 15, 0x7fffff)) == getFloat16(0, 0x1f, 0));
+	DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, 127 + 15, 0x7fffff)) == getFloat16(1, 0x1f, 0));
+	for (idx = 0; idx < 256; ++idx)
+	{
+		deUint32	exponent	= deRandom_getUint32(&rnd);
+		deUint32	mantissa	= deRandom_getUint32(&rnd);
+
+		exponent	= exponent % (0xfe - (127 + 16) + 1) + (127 + 16);	/* Make sure >= 127 + 16, <= 0xfe */
+		mantissa	&= 0x7fffffu;										/* Take the last 23 bits */
+
+		DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(0, exponent, mantissa)) == getFloat16(0, 0x1f, 0));
+		DE_TEST_ASSERT(deFloat32To16RTE(getFloat32(1, exponent, mantissa)) == getFloat16(1, 0x1f, 0));
+	}
+}
+
+DE_END_EXTERN_C
diff --git a/framework/delibs/debase/deMath.c b/framework/delibs/debase/deMath.c
index 26e2aef67..c76175140 100644
--- a/framework/delibs/debase/deMath.c
+++ b/framework/delibs/debase/deMath.c
@@ -46,7 +46,7 @@ deRoundingMode deGetRoundingMode (void)
 		case _RC_CHOP:	return DE_ROUNDINGMODE_TO_ZERO;
 		case _RC_UP:	return DE_ROUNDINGMODE_TO_POSITIVE_INF;
 		case _RC_DOWN:	return DE_ROUNDINGMODE_TO_NEGATIVE_INF;
-		case _RC_NEAR:	return DE_ROUNDINGMODE_TO_NEAREST;
+		case _RC_NEAR:	return DE_ROUNDINGMODE_TO_NEAREST_EVEN;
 		default:		return DE_ROUNDINGMODE_LAST;
 	}
 #elif (DE_COMPILER == DE_COMPILER_GCC) || (DE_COMPILER == DE_COMPILER_CLANG)
@@ -56,7 +56,7 @@ deRoundingMode deGetRoundingMode (void)
 		case FE_TOWARDZERO:	return DE_ROUNDINGMODE_TO_ZERO;
 		case FE_UPWARD:		return DE_ROUNDINGMODE_TO_POSITIVE_INF;
 		case FE_DOWNWARD:	return DE_ROUNDINGMODE_TO_NEGATIVE_INF;
-		case FE_TONEAREST:	return DE_ROUNDINGMODE_TO_NEAREST;
+		case FE_TONEAREST:	return DE_ROUNDINGMODE_TO_NEAREST_EVEN;
 		default:			return DE_ROUNDINGMODE_LAST;
 	}
 #else
@@ -76,7 +76,7 @@ deBool deSetRoundingMode (deRoundingMode mode)
 		case DE_ROUNDINGMODE_TO_ZERO:			flag = _RC_CHOP;	break;
 		case DE_ROUNDINGMODE_TO_POSITIVE_INF:	flag = _RC_UP;		break;
 		case DE_ROUNDINGMODE_TO_NEGATIVE_INF:	flag = _RC_DOWN;	break;
-		case DE_ROUNDINGMODE_TO_NEAREST:		flag = _RC_NEAR;	break;
+		case DE_ROUNDINGMODE_TO_NEAREST_EVEN:	flag = _RC_NEAR;	break;
 		default:
 			DE_ASSERT(DE_FALSE);
 	}
@@ -92,7 +92,7 @@ deBool deSetRoundingMode (deRoundingMode mode)
 		case DE_ROUNDINGMODE_TO_ZERO:			flag = FE_TOWARDZERO;	break;
 		case DE_ROUNDINGMODE_TO_POSITIVE_INF:	flag = FE_UPWARD;		break;
 		case DE_ROUNDINGMODE_TO_NEGATIVE_INF:	flag = FE_DOWNWARD;		break;
-		case DE_ROUNDINGMODE_TO_NEAREST:		flag = FE_TONEAREST;	break;
+		case DE_ROUNDINGMODE_TO_NEAREST_EVEN:	flag = FE_TONEAREST;	break;
 		default:
 			DE_ASSERT(DE_FALSE);
 	}
diff --git a/framework/delibs/debase/deMath.h b/framework/delibs/debase/deMath.h
index 4ab86fb87..61f2d1483 100644
--- a/framework/delibs/debase/deMath.h
+++ b/framework/delibs/debase/deMath.h
@@ -45,7 +45,7 @@ DE_BEGIN_EXTERN_C
 
 typedef enum deRoundingMode_e
 {
-	DE_ROUNDINGMODE_TO_NEAREST = 0,
+	DE_ROUNDINGMODE_TO_NEAREST_EVEN = 0,
 	DE_ROUNDINGMODE_TO_ZERO,
 	DE_ROUNDINGMODE_TO_POSITIVE_INF,
 	DE_ROUNDINGMODE_TO_NEGATIVE_INF,