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authorJoseph Myers <joseph@codesourcery.com>2016-10-17 22:48:51 +0000
committerJoseph Myers <joseph@codesourcery.com>2016-10-17 22:48:51 +0000
commit6f322a894704e7959b9cee7c2cc7ec1963a26e73 (patch)
tree817009ca0ac99f5c874ae233f8c603d0b646e849 /sysdeps/ieee754
parent8e36adc08eebb526d180b8477f1840c5bd549d83 (diff)
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Define HIGH_ORDER_BIT_IS_SET_FOR_SNAN to 0 or 1.
This patch moves the HIGH_ORDER_BIT_IS_SET_FOR_SNAN macro from being defined or undefined to the preferred convention of always being defined, to either 0 or 1, so allowing typo-proof tests with #if. The macro is moved from math_private.h to a new header nan-high-order-bit.h to make it easy for all architectures to define, either through the sysdeps/generic version of the header or through providing their own version of the header, without needing #ifndef in the generic math_private.h to give a default definition. The move also allows the macro to be used without needing math_private.h to be included; the immediate motivation of this patch is to allow tests to access this information (to know what kinds of NaNs 0 is a valid payload for) without needing to include math_private.h. Existing C level rather than preprocessor conditionals at all, but this patch does not make such a change). Tested for x86_64 and x86 (testsuite); also verified for x86_64, x86, mips64 and powerpc that installed stripped shared libraries are unchanged by the patch. * sysdeps/generic/nan-high-order-bit.h: New file. * sysdeps/hppa/nan-high-order-bit.h: Likewise. * sysdeps/mips/nan-high-order-bit.h: Likewise. * sysdeps/hppa/math_private.h: Remove file. * sysdeps/mips/math_private.h (HIGH_ORDER_BIT_IS_SET_FOR_SNAN): Do not define here. * sysdeps/ieee754/dbl-64/s_issignaling.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/dbl-64/s_totalorder.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/dbl-64/s_totalordermag.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/flt-32/s_issignalingf.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/flt-32/s_totalorderf.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/flt-32/s_totalordermagf.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-128/s_issignalingl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-128/s_totalorderl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-128/s_totalordermagl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-96/s_issignalingl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-96/s_totalorderl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef. * sysdeps/ieee754/ldbl-96/s_totalordermagl.c: Include <nan-high-order-bit.h>. [HIGH_ORDER_BIT_IS_SET_FOR_SNAN]: Test with #if not #ifdef.
Diffstat (limited to 'sysdeps/ieee754')
-rw-r--r--sysdeps/ieee754/dbl-64/s_issignaling.c3
-rw-r--r--sysdeps/ieee754/dbl-64/s_totalorder.c3
-rw-r--r--sysdeps/ieee754/dbl-64/s_totalordermag.c3
-rw-r--r--sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c3
-rw-r--r--sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c3
-rw-r--r--sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c3
-rw-r--r--sysdeps/ieee754/flt-32/s_issignalingf.c3
-rw-r--r--sysdeps/ieee754/flt-32/s_totalorderf.c3
-rw-r--r--sysdeps/ieee754/flt-32/s_totalordermagf.c3
-rw-r--r--sysdeps/ieee754/ldbl-128/s_issignalingl.c3
-rw-r--r--sysdeps/ieee754/ldbl-128/s_totalorderl.c3
-rw-r--r--sysdeps/ieee754/ldbl-128/s_totalordermagl.c3
-rw-r--r--sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c3
-rw-r--r--sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c3
-rw-r--r--sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c3
-rw-r--r--sysdeps/ieee754/ldbl-96/s_issignalingl.c3
-rw-r--r--sysdeps/ieee754/ldbl-96/s_totalorderl.c3
-rw-r--r--sysdeps/ieee754/ldbl-96/s_totalordermagl.c3
18 files changed, 36 insertions, 18 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_issignaling.c b/sysdeps/ieee754/dbl-64/s_issignaling.c
index 4b93d6a..0b845e2 100644
--- a/sysdeps/ieee754/dbl-64/s_issignaling.c
+++ b/sysdeps/ieee754/dbl-64/s_issignaling.c
@@ -18,11 +18,12 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
int
__issignaling (double x)
{
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
u_int32_t hxi;
GET_HIGH_WORD (hxi, x);
/* We only have to care about the high-order bit of x's significand, because
diff --git a/sysdeps/ieee754/dbl-64/s_totalorder.c b/sysdeps/ieee754/dbl-64/s_totalorder.c
index 73ac32f..c4ec917 100644
--- a/sysdeps/ieee754/dbl-64/s_totalorder.c
+++ b/sysdeps/ieee754/dbl-64/s_totalorder.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -27,7 +28,7 @@ totalorder (double x, double y)
uint32_t lx, ly;
EXTRACT_WORDS (hx, lx, x);
EXTRACT_WORDS (hy, ly, y);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
uint32_t uhx = hx & 0x7fffffff, uhy = hy & 0x7fffffff;
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the arguments interpreted as
diff --git a/sysdeps/ieee754/dbl-64/s_totalordermag.c b/sysdeps/ieee754/dbl-64/s_totalordermag.c
index e41dade..3850c33 100644
--- a/sysdeps/ieee754/dbl-64/s_totalordermag.c
+++ b/sysdeps/ieee754/dbl-64/s_totalordermag.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -29,7 +30,7 @@ totalordermag (double x, double y)
EXTRACT_WORDS (hy, ly, y);
hx &= 0x7fffffff;
hy &= 0x7fffffff;
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the absolute values of the
arguments. If both arguments are NaNs, invert the
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c b/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c
index c22e608..18d1acd 100644
--- a/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c
+++ b/sysdeps/ieee754/dbl-64/wordsize-64/s_issignaling.c
@@ -18,13 +18,14 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
int
__issignaling (double x)
{
u_int64_t xi;
EXTRACT_WORDS64 (xi, x);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
used to designate infinity. */
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c b/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c
index 02cd799..dd5587b 100644
--- a/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c
+++ b/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -26,7 +27,7 @@ totalorder (double x, double y)
int64_t ix, iy;
EXTRACT_WORDS64 (ix, x);
EXTRACT_WORDS64 (iy, y);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the arguments interpreted as
sign-magnitude integers. If both arguments are NaNs, invert the
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c b/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c
index 38f2e1b..999a919 100644
--- a/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c
+++ b/sysdeps/ieee754/dbl-64/wordsize-64/s_totalordermag.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -28,7 +29,7 @@ totalordermag (double x, double y)
EXTRACT_WORDS64 (iy, y);
ix &= 0x7fffffffffffffffULL;
iy &= 0x7fffffffffffffffULL;
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the absolute values of the
arguments. If both arguments are NaNs, invert the
diff --git a/sysdeps/ieee754/flt-32/s_issignalingf.c b/sysdeps/ieee754/flt-32/s_issignalingf.c
index 2409ff4..965ba92 100644
--- a/sysdeps/ieee754/flt-32/s_issignalingf.c
+++ b/sysdeps/ieee754/flt-32/s_issignalingf.c
@@ -18,13 +18,14 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
int
__issignalingf (float x)
{
u_int32_t xi;
GET_FLOAT_WORD (xi, x);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
used to designate infinity. */
diff --git a/sysdeps/ieee754/flt-32/s_totalorderf.c b/sysdeps/ieee754/flt-32/s_totalorderf.c
index 1ed30d8..243387b 100644
--- a/sysdeps/ieee754/flt-32/s_totalorderf.c
+++ b/sysdeps/ieee754/flt-32/s_totalorderf.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -26,7 +27,7 @@ totalorderf (float x, float y)
int32_t ix, iy;
GET_FLOAT_WORD (ix, x);
GET_FLOAT_WORD (iy, y);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the arguments interpreted as
sign-magnitude integers. If both arguments are NaNs, invert the
diff --git a/sysdeps/ieee754/flt-32/s_totalordermagf.c b/sysdeps/ieee754/flt-32/s_totalordermagf.c
index 7c01edc..be78eae 100644
--- a/sysdeps/ieee754/flt-32/s_totalordermagf.c
+++ b/sysdeps/ieee754/flt-32/s_totalordermagf.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -28,7 +29,7 @@ totalordermagf (float x, float y)
GET_FLOAT_WORD (iy, y);
ix &= 0x7fffffff;
iy &= 0x7fffffff;
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the absolute values of the
arguments. If both arguments are NaNs, invert the
diff --git a/sysdeps/ieee754/ldbl-128/s_issignalingl.c b/sysdeps/ieee754/ldbl-128/s_issignalingl.c
index 6af1db4..cb0f2a5 100644
--- a/sysdeps/ieee754/ldbl-128/s_issignalingl.c
+++ b/sysdeps/ieee754/ldbl-128/s_issignalingl.c
@@ -18,13 +18,14 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
int
__issignalingl (_Float128 x)
{
u_int64_t hxi, lxi __attribute__ ((unused));
GET_LDOUBLE_WORDS64 (hxi, lxi, x);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
used to designate infinity. */
diff --git a/sysdeps/ieee754/ldbl-128/s_totalorderl.c b/sysdeps/ieee754/ldbl-128/s_totalorderl.c
index dc76ccf..32ede1f 100644
--- a/sysdeps/ieee754/ldbl-128/s_totalorderl.c
+++ b/sysdeps/ieee754/ldbl-128/s_totalorderl.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -27,7 +28,7 @@ totalorderl (_Float128 x, _Float128 y)
uint64_t lx, ly;
GET_LDOUBLE_WORDS64 (hx, lx, x);
GET_LDOUBLE_WORDS64 (hy, ly, y);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
uint64_t uhx = hx & 0x7fffffffffffffffULL;
uint64_t uhy = hy & 0x7fffffffffffffffULL;
/* For the preferred quiet NaN convention, this operation is a
diff --git a/sysdeps/ieee754/ldbl-128/s_totalordermagl.c b/sysdeps/ieee754/ldbl-128/s_totalordermagl.c
index bcfeecd..5446809 100644
--- a/sysdeps/ieee754/ldbl-128/s_totalordermagl.c
+++ b/sysdeps/ieee754/ldbl-128/s_totalordermagl.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -29,7 +30,7 @@ totalordermagl (_Float128 x, _Float128 y)
GET_LDOUBLE_WORDS64 (hy, ly, y);
hx &= 0x7fffffffffffffffULL;
hy &= 0x7fffffffffffffffULL;
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the absolute values of the
arguments. If both arguments are NaNs, invert the
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c b/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c
index 0915139..94cfffcd 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
int
__issignalingl (long double x)
@@ -29,7 +30,7 @@ __issignalingl (long double x)
xhi = ldbl_high (x);
EXTRACT_WORDS64 (xi, xhi);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error untested
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c b/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c
index 1535b2f..ff55779 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -30,7 +31,7 @@ totalorderl (long double x, long double y)
EXTRACT_WORDS64 (hx, xhi);
ldbl_unpack (y, &yhi, &ylo);
EXTRACT_WORDS64 (hy, yhi);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error not implemented
#endif
uint64_t hx_sign = hx >> 63;
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c b/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c
index 509a23a..739e231 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c
@@ -18,6 +18,7 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -30,7 +31,7 @@ totalordermagl (long double x, long double y)
EXTRACT_WORDS64 (hx, xhi);
ldbl_unpack (y, &yhi, &ylo);
EXTRACT_WORDS64 (hy, yhi);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error not implemented
#endif
uint64_t x_sign = hx & 0x8000000000000000ULL;
diff --git a/sysdeps/ieee754/ldbl-96/s_issignalingl.c b/sysdeps/ieee754/ldbl-96/s_issignalingl.c
index 73646ca..364e5db 100644
--- a/sysdeps/ieee754/ldbl-96/s_issignalingl.c
+++ b/sysdeps/ieee754/ldbl-96/s_issignalingl.c
@@ -18,13 +18,14 @@
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
int
__issignalingl (long double x)
{
u_int32_t exi, hxi, lxi;
GET_LDOUBLE_WORDS (exi, hxi, lxi, x);
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error not implemented
#else
/* To keep the following comparison simple, toggle the quiet/signaling bit,
diff --git a/sysdeps/ieee754/ldbl-96/s_totalorderl.c b/sysdeps/ieee754/ldbl-96/s_totalorderl.c
index 4f14baf..ddc28b8 100644
--- a/sysdeps/ieee754/ldbl-96/s_totalorderl.c
+++ b/sysdeps/ieee754/ldbl-96/s_totalorderl.c
@@ -19,6 +19,7 @@
#include <float.h>
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -41,7 +42,7 @@ totalorderl (long double x, long double y)
if ((expy & 0x7fff) == 0x7fff)
hy |= 0x80000000;
}
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error not implemented
#endif
uint32_t x_sign = expx >> 15;
diff --git a/sysdeps/ieee754/ldbl-96/s_totalordermagl.c b/sysdeps/ieee754/ldbl-96/s_totalordermagl.c
index 0167f0f..4ca28e7 100644
--- a/sysdeps/ieee754/ldbl-96/s_totalordermagl.c
+++ b/sysdeps/ieee754/ldbl-96/s_totalordermagl.c
@@ -19,6 +19,7 @@
#include <float.h>
#include <math.h>
#include <math_private.h>
+#include <nan-high-order-bit.h>
#include <stdint.h>
int
@@ -43,7 +44,7 @@ totalordermagl (long double x, long double y)
if (expy == 0x7fff)
hy |= 0x80000000;
}
-#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error not implemented
#endif
return expx < expy || (expx == expy && (hx < hy || (hx == hy && lx <= ly)));