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authormarha <marha@users.sourceforge.net>2012-07-02 08:51:35 +0200
committermarha <marha@users.sourceforge.net>2012-07-02 08:51:35 +0200
commitfcc2cc7dabb46c39a76351fc12da4e9ad9d1d817 (patch)
treebcc60a76e7cc205710b91c67ff700c26886ea3e8 /mesalib/src/gallium/auxiliary
parent393178cdbca247c6ad077f7dab9a97d6817c625c (diff)
parentfdef5bff99e6079f64bc6b91c91b42195c85adeb (diff)
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Merge remote-tracking branch 'origin/released'
Conflicts: pixman/pixman/pixman-sse2.c
Diffstat (limited to 'mesalib/src/gallium/auxiliary')
-rw-r--r--mesalib/src/gallium/auxiliary/Android.mk3
-rw-r--r--mesalib/src/gallium/auxiliary/Makefile2
-rw-r--r--mesalib/src/gallium/auxiliary/Makefile.sources3
-rw-r--r--mesalib/src/gallium/auxiliary/SConscript7
-rw-r--r--mesalib/src/gallium/auxiliary/util/.gitignore1
-rw-r--r--mesalib/src/gallium/auxiliary/util/u_format.c32
-rw-r--r--mesalib/src/gallium/auxiliary/util/u_format.h7
-rw-r--r--mesalib/src/gallium/auxiliary/util/u_format_tests.c40
-rw-r--r--mesalib/src/gallium/auxiliary/util/u_half.h101
-rw-r--r--mesalib/src/gallium/auxiliary/util/u_half.py179
-rw-r--r--mesalib/src/gallium/auxiliary/util/u_math.h104
11 files changed, 249 insertions, 230 deletions
diff --git a/mesalib/src/gallium/auxiliary/Android.mk b/mesalib/src/gallium/auxiliary/Android.mk
index 0c37dd31a..11fc2256a 100644
--- a/mesalib/src/gallium/auxiliary/Android.mk
+++ b/mesalib/src/gallium/auxiliary/Android.mk
@@ -44,8 +44,7 @@ $(LOCAL_GENERATED_SOURCES): PRIVATE_CUSTOM_TOOL = $(PRIVATE_PYTHON) $^ > $@
$(intermediates)/indices/u_indices_gen.c \
$(intermediates)/indices/u_unfilled_gen.c \
-$(intermediates)/util/u_format_srgb.c \
-$(intermediates)/util/u_half.c: $(intermediates)/%.c: $(LOCAL_PATH)/%.py
+$(intermediates)/util/u_format_srgb.c: $(intermediates)/%.c: $(LOCAL_PATH)/%.py
$(transform-generated-source)
$(intermediates)/util/u_format_table.c: $(intermediates)/%.c: $(LOCAL_PATH)/%.py $(LOCAL_PATH)/util/u_format.csv
diff --git a/mesalib/src/gallium/auxiliary/Makefile b/mesalib/src/gallium/auxiliary/Makefile
index a70ae7384..3ba3f9c40 100644
--- a/mesalib/src/gallium/auxiliary/Makefile
+++ b/mesalib/src/gallium/auxiliary/Makefile
@@ -39,6 +39,4 @@ util/u_format_srgb.c: util/u_format_srgb.py
util/u_format_table.c: util/u_format_table.py util/u_format_pack.py util/u_format_parse.py util/u_format.csv
$(PYTHON2) util/u_format_table.py util/u_format.csv > $@
-util/u_half.c: util/u_half.py
- $(PYTHON2) util/u_half.py > $@
# DO NOT DELETE
diff --git a/mesalib/src/gallium/auxiliary/Makefile.sources b/mesalib/src/gallium/auxiliary/Makefile.sources
index 277428b38..28a176d68 100644
--- a/mesalib/src/gallium/auxiliary/Makefile.sources
+++ b/mesalib/src/gallium/auxiliary/Makefile.sources
@@ -155,8 +155,7 @@ GENERATED_SOURCES := \
indices/u_indices_gen.c \
indices/u_unfilled_gen.c \
util/u_format_srgb.c \
- util/u_format_table.c \
- util/u_half.c
+ util/u_format_table.c
GALLIVM_SOURCES := \
gallivm/lp_bld_arit.c \
diff --git a/mesalib/src/gallium/auxiliary/SConscript b/mesalib/src/gallium/auxiliary/SConscript
index 07c420e13..bfd5ec34c 100644
--- a/mesalib/src/gallium/auxiliary/SConscript
+++ b/mesalib/src/gallium/auxiliary/SConscript
@@ -35,13 +35,6 @@ env.CodeGenerate(
command = python_cmd + ' $SCRIPT $SOURCE > $TARGET'
)
-env.CodeGenerate(
- target = 'util/u_half.c',
- script = 'util/u_half.py',
- source = [],
- command = python_cmd + ' $SCRIPT > $TARGET'
-)
-
env.Depends('util/u_format_table.c', [
'#src/gallium/auxiliary/util/u_format_parse.py',
'util/u_format_pack.py',
diff --git a/mesalib/src/gallium/auxiliary/util/.gitignore b/mesalib/src/gallium/auxiliary/util/.gitignore
index 5dd0408ef..da74de623 100644
--- a/mesalib/src/gallium/auxiliary/util/.gitignore
+++ b/mesalib/src/gallium/auxiliary/util/.gitignore
@@ -1,3 +1,2 @@
u_format_srgb.c
u_format_table.c
-u_half.c
diff --git a/mesalib/src/gallium/auxiliary/util/u_format.c b/mesalib/src/gallium/auxiliary/util/u_format.c
index cfc4a17a0..6f4529835 100644
--- a/mesalib/src/gallium/auxiliary/util/u_format.c
+++ b/mesalib/src/gallium/auxiliary/util/u_format.c
@@ -159,6 +159,38 @@ util_format_is_pure_uint(enum pipe_format format)
}
boolean
+util_format_is_array(const struct util_format_description *desc)
+{
+ unsigned chan;
+
+ if (desc->layout != UTIL_FORMAT_LAYOUT_PLAIN ||
+ desc->colorspace != UTIL_FORMAT_COLORSPACE_RGB ||
+ desc->block.width != 1 ||
+ desc->block.height != 1) {
+ return FALSE;
+ }
+
+ for (chan = 0; chan < desc->nr_channels; ++chan) {
+ if (desc->swizzle[chan] != chan)
+ return FALSE;
+
+ if (desc->channel[chan].type != desc->channel[0].type)
+ return FALSE;
+
+ if (desc->channel[chan].normalized != desc->channel[0].normalized)
+ return FALSE;
+
+ if (desc->channel[chan].pure_integer != desc->channel[0].pure_integer)
+ return FALSE;
+
+ if (desc->channel[chan].size != desc->channel[0].size)
+ return FALSE;
+ }
+
+ return TRUE;
+}
+
+boolean
util_format_is_luminance_alpha(enum pipe_format format)
{
const struct util_format_description *desc =
diff --git a/mesalib/src/gallium/auxiliary/util/u_format.h b/mesalib/src/gallium/auxiliary/util/u_format.h
index 1718fb5e2..e35e164b4 100644
--- a/mesalib/src/gallium/auxiliary/util/u_format.h
+++ b/mesalib/src/gallium/auxiliary/util/u_format.h
@@ -591,6 +591,13 @@ boolean
util_format_is_pure_uint(enum pipe_format format);
/**
+ * Whether the format is a simple array format where all channels
+ * are of the same type and can be loaded from memory as a vector
+ */
+boolean
+util_format_is_array(const struct util_format_description *desc);
+
+/**
* Check if the src format can be blitted to the destination format with
* a simple memcpy. For example, blitting from RGBA to RGBx is OK, but not
* the reverse.
diff --git a/mesalib/src/gallium/auxiliary/util/u_format_tests.c b/mesalib/src/gallium/auxiliary/util/u_format_tests.c
index fc29d8d48..457fda6c8 100644
--- a/mesalib/src/gallium/auxiliary/util/u_format_tests.c
+++ b/mesalib/src/gallium/auxiliary/util/u_format_tests.c
@@ -26,6 +26,9 @@
**************************************************************************/
+#include <float.h>
+
+#include "pipe/p_config.h"
#include "u_memory.h"
#include "u_format_tests.h"
@@ -63,6 +66,9 @@
{{ 0, 0, 0, 0}, { 0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}
+#define NAN (0.0 / 0.0)
+#define INF (1.0 / 0.0)
+
/**
* Test cases.
*
@@ -876,7 +882,39 @@ util_format_test_cases[] =
* Half float formats
*/
- {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x0000), UNPACKED_1x1( 0.0, 0.0, 0.0, 1.0)},
+ /* Minimum positive normal */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x0400), UNPACKED_1x1( 6.10352E-5, 0.0, 0.0, 1.0)},
+
+ /* Max denormal */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x03FF), UNPACKED_1x1( 6.09756E-5, 0.0, 0.0, 1.0)},
+
+ /* Minimum positive denormal */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x0001), UNPACKED_1x1( 5.96046E-8, 0.0, 0.0, 1.0)},
+
+ /* Min representable value */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0xfbff), UNPACKED_1x1( -65504.0, 0.0, 0.0, 1.0)},
+
+ /* Max representable value */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x7bff), UNPACKED_1x1( 65504.0, 0.0, 0.0, 1.0)},
+
+#if !defined(PIPE_CC_MSVC)
+
+ /* NaNs */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x7c01), UNPACKED_1x1( NAN, 0.0, 0.0, 1.0)},
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0xfc01), UNPACKED_1x1( -NAN, 0.0, 0.0, 1.0)},
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x7fff), UNPACKED_1x1( NAN, 0.0, 0.0, 1.0)},
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0xffff), UNPACKED_1x1( -NAN, 0.0, 0.0, 1.0)},
+
+ /* Inf */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x7c00), UNPACKED_1x1( INF, 0.0, 0.0, 1.0)},
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0xfc00), UNPACKED_1x1( -INF, 0.0, 0.0, 1.0)},
+
+#endif
+
+ /* Zero, ignore sign */
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0x7fff), PACKED_1x16(0x8000), UNPACKED_1x1( -0.0, 0.0, 0.0, 1.0)},
+ {PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0x7fff), PACKED_1x16(0x0000), UNPACKED_1x1( 0.0, 0.0, 0.0, 1.0)},
+
{PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0x3c00), UNPACKED_1x1( 1.0, 0.0, 0.0, 1.0)},
{PIPE_FORMAT_R16_FLOAT, PACKED_1x16(0xffff), PACKED_1x16(0xbc00), UNPACKED_1x1( -1.0, 0.0, 0.0, 1.0)},
diff --git a/mesalib/src/gallium/auxiliary/util/u_half.h b/mesalib/src/gallium/auxiliary/util/u_half.h
index ad030e90c..f7009f548 100644
--- a/mesalib/src/gallium/auxiliary/util/u_half.h
+++ b/mesalib/src/gallium/auxiliary/util/u_half.h
@@ -35,51 +35,84 @@
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
diff --git a/mesalib/src/gallium/auxiliary/util/u_half.py b/mesalib/src/gallium/auxiliary/util/u_half.py
deleted file mode 100644
index 915cf3b92..000000000
--- a/mesalib/src/gallium/auxiliary/util/u_half.py
+++ /dev/null
@@ -1,179 +0,0 @@
-# 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()
-
diff --git a/mesalib/src/gallium/auxiliary/util/u_math.h b/mesalib/src/gallium/auxiliary/util/u_math.h
index f6196665f..724b136b5 100644
--- a/mesalib/src/gallium/auxiliary/util/u_math.h
+++ b/mesalib/src/gallium/auxiliary/util/u_math.h
@@ -183,6 +183,13 @@ union fi {
};
+union di {
+ double d;
+ int64_t i;
+ uint64_t ui;
+};
+
+
/**
* Fast version of 2^x
* Identity: exp2(a + b) = exp2(a) * exp2(b)
@@ -325,14 +332,107 @@ util_is_approx(float a, float b, float tol)
/**
- * Test if x is NaN or +/- infinity.
+ * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
+ * util_is_X_nan = test if x is NaN
+ * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
+ *
+ * NaN can be checked with x != x, however this fails with the fast math flag
+ **/
+
+
+/**
+ * Single-float
*/
static INLINE boolean
util_is_inf_or_nan(float x)
{
union fi tmp;
tmp.f = x;
- return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
+ return (tmp.ui & 0x7f800000) == 0x7f800000;
+}
+
+
+static INLINE boolean
+util_is_nan(float x)
+{
+ union fi tmp;
+ tmp.f = x;
+ return (tmp.ui & 0x7fffffff) > 0x7f800000;
+}
+
+
+static INLINE int
+util_inf_sign(float x)
+{
+ union fi tmp;
+ tmp.f = x;
+ if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
+ return 0;
+ }
+
+ return (x < 0) ? -1 : 1;
+}
+
+
+/**
+ * Double-float
+ */
+static INLINE boolean
+util_is_double_inf_or_nan(double x)
+{
+ union di tmp;
+ tmp.d = x;
+ return (tmp.ui & 0x7ff0000000000000) == 0x7ff0000000000000;
+}
+
+
+static INLINE boolean
+util_is_double_nan(double x)
+{
+ union di tmp;
+ tmp.d = x;
+ return (tmp.ui & 0x7fffffffffffffff) > 0x7ff0000000000000;
+}
+
+
+static INLINE int
+util_double_inf_sign(double x)
+{
+ union di tmp;
+ tmp.d = x;
+ if ((tmp.ui & 0x7fffffffffffffff) != 0x7ff0000000000000) {
+ return 0;
+ }
+
+ return (x < 0) ? -1 : 1;
+}
+
+
+/**
+ * Half-float
+ */
+static INLINE boolean
+util_is_half_inf_or_nan(int16_t x)
+{
+ return (x & 0x7c00) == 0x7c00;
+}
+
+
+static INLINE boolean
+util_is_half_nan(int16_t x)
+{
+ return (x & 0x7fff) > 0x7c00;
+}
+
+
+static INLINE int
+util_half_inf_sign(int16_t x)
+{
+ if ((x & 0x7fff) != 0x7c00) {
+ return 0;
+ }
+
+ return (x < 0) ? -1 : 1;
}