extern "C" {
#endif
-extern const uint32_t util_half_to_float_mantissa_table[2048];
-extern const uint32_t util_half_to_float_exponent_table[64];
-extern const uint32_t util_half_to_float_offset_table[64];
-extern const uint16_t util_float_to_half_base_table[512];
-extern const uint8_t util_float_to_half_shift_table[512];
-
/*
- * Note that if the half float is a signaling NaN, the x87 FPU will turn
- * it into a quiet NaN immediately upon loading into a float.
- *
- * Additionally, denormals may be flushed to zero.
+ * References for float <-> half conversions
*
- * To avoid this, use the floatui functions instead of the float ones
- * when just doing conversion rather than computation on the resulting
- * floats.
+ * http://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/
+ * https://gist.github.com/2156668
+ * https://gist.github.com/2144712
*/
-static INLINE uint32_t
-util_half_to_floatui(uint16_t h)
+static INLINE uint16_t
+util_float_to_half(float f)
{
- unsigned exp = h >> 10;
- return util_half_to_float_mantissa_table[util_half_to_float_offset_table[exp] + (h & 0x3ff)] + util_half_to_float_exponent_table[exp];
+ 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;
+
+ /* Clamp to infinity if overflowed */
+ if (f32.ui > f16inf)
+ f32.ui = f16inf;
+
+ f16 = f32.ui >> 13;
+ }
+
+ /* Sign */
+ f16 |= sign >> 16;
+
+ return f16;
}
static INLINE float
-util_half_to_float(uint16_t h)
+util_half_to_float(uint16_t f16)
{
- union fi r;
- r.ui = util_half_to_floatui(h);
- return r.f;
-}
+ union fi infnan;
+ union fi magic;
+ union fi f32;
-static INLINE uint16_t
-util_floatui_to_half(uint32_t v)
-{
- unsigned signexp = v >> 23;
- return util_float_to_half_base_table[signexp] + ((v & 0x007fffff) >> util_float_to_half_shift_table[signexp]);
-}
+ infnan.ui = 0x8f << 23;
+ infnan.f = 65536.0f;
+ magic.ui = 0xef << 23;
-static INLINE uint16_t
-util_float_to_half(float f)
-{
- union fi i;
- i.f = f;
- return util_floatui_to_half(i.ui);
+ /* Exponent / Mantissa */
+ f32.ui = (f16 & 0x7fff) << 13;
+
+ /* Adjust */
+ f32.f *= magic.f;
+
+ /* Inf / NaN */
+ if (f32.f >= infnan.f)
+ f32.ui |= 0xff << 23;
+
+ /* Sign */
+ f32.ui |= (f16 & 0x8000) << 16;
+
+ return f32.f;
}
#ifdef __cplusplus
+++ /dev/null
-# Copyright 2010 Luca Barbieri
-#
-# Permission is hereby granted, free of charge, to any person obtaining
-# a copy of this software and associated documentation files (the
-# "Software"), to deal in the Software without restriction, including
-# without limitation the rights to use, copy, modify, merge, publish,
-# distribute, sublicense, and/or sell copies of the Software, and to
-# permit persons to whom the Software is furnished to do so, subject to
-# the following conditions:
-#
-# The above copyright notice and this permission notice (including the
-# next paragraph) shall be included in all copies or substantial
-# portions of the Software.
-#
-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
-# IN NO EVENT SHALL THE COPYRIGHT OWNER(S) AND/OR ITS SUPPLIERS BE
-# LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
-# OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
-# WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
-#
-# *************************************************************************
-
-# The code is a reimplementation of the algorithm in
-# www.fox-toolkit.org/ftp/fasthalffloatconversion.pdf
-# "Fast Half Float Conversions" by Jeroen van der Zijp, Nov 2008
-#
-# The table contents have been slightly changed so that the exponent
-# bias is now in the exponent table instead of the mantissa table (mostly
-# for cosmetic reasons, and because it theoretically allows a variant
-# that flushes denormal to zero but uses a mantissa table with 24-bit
-# entries).
-#
-# The tables are also constructed slightly differently.
-#
-
-# Note that using a 64K * 4 table is a terrible idea since it will not fit
-# in the L1 cache and will massively pollute the L2 cache as well
-#
-# These should instead fit in the L1 cache.
-#
-# TODO: we could use a denormal bias table instead of the mantissa/offset
-# tables: this would reduce the L1 cache usage from 8704 to 2304 bytes
-# but would involve more computation
-#
-# Note however that if denormals are never encountered, the L1 cache usage
-# is only about 4608 bytes anyway.
-
-table_index = None
-table_length = None
-
-def begin(t, n, l):
- global table_length
- global table_index
- table_index = 0
- table_length = l
- print
- print "const " + t + " " + n + "[" + str(l) + "] = {"
-
-def value(v):
- global table_index
- table_index += 1
- print "\t" + hex(v) + ","
-
-def end():
- global table_length
- global table_index
- print "};"
- assert table_index == table_length
-
-print "/* This file is autogenerated by u_half.py. Do not edit directly. */"
-print "#include \"util/u_half.h\""
-
-begin("uint32_t", "util_half_to_float_mantissa_table", 2048)
-# zero
-value(0)
-
-# denormals
-for i in xrange(1, 1024):
- m = i << 13
- e = 0
-
- # normalize number
- while (m & 0x00800000) == 0:
- e -= 0x00800000
- m <<= 1
-
- m &= ~0x00800000
- e += 0x38800000
- value(m | e)
-
-# normals
-for i in xrange(1024, 2048):
- value((i - 1024) << 13)
-end()
-
-begin("uint32_t", "util_half_to_float_exponent_table", 64)
-# positive zero or denormals
-value(0)
-
-# positive numbers
-for i in xrange(1, 31):
- value(0x38000000 + (i << 23))
-
-# positive infinity/NaN
-value(0x7f800000)
-
-# negative zero or denormals
-value(0x80000000)
-
-# negative numbers
-for i in range(33, 63):
- value(0xb8000000 + ((i - 32) << 23))
-
-# negative infinity/NaN
-value(0xff800000)
-end()
-
-begin("uint32_t", "util_half_to_float_offset_table", 64)
-# positive zero or denormals
-value(0)
-
-# positive normals
-for i in range(1, 32):
- value(1024)
-
-# negative zero or denormals
-value(0)
-
-# negative normals
-for i in xrange(33, 64):
- value(1024)
-end()
-
-begin("uint16_t", "util_float_to_half_base_table", 512)
-for sign in (0, 0x8000):
- # very small numbers mapping to zero
- for i in xrange(-127, -24):
- value(sign | 0)
-
- # small numbers mapping to denormals
- for i in xrange(-24, -14):
- value(sign | (0x400 >> (-14 -i)))
-
- # normal numbers
- for i in xrange(-14, 16):
- value(sign | ((i + 15) << 10))
-
- # large numbers mapping to infinity
- for i in xrange(16, 128):
- value(sign | 0x7c00)
-
- # infinity and NaNs
- value(sign | 0x7c00)
-end()
-
-begin("uint8_t", "util_float_to_half_shift_table", 512)
-for sign in (0, 0x8000):
- # very small numbers mapping to zero
- for i in xrange(-127, -24):
- value(24)
-
- # small numbers mapping to denormals
- for i in xrange(-24, -14):
- value(-1 - i)
-
- # normal numbers
- for i in xrange(-14, 16):
- value(13)
-
- # large numbers mapping to infinity
- for i in xrange(16, 128):
- value(24)
-
- # infinity and NaNs
- value(13)
-end()
-
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