From 7cb029ee6ec74801aebe41af62d20a44775d0697 Mon Sep 17 00:00:00 2001 From: Joseph Myers Date: Tue, 1 May 2012 15:37:43 +0000 Subject: [PATCH] Fix nexttoward bugs (bugs 2550, 2570). --- ChangeLog | 21 +++++++++ NEWS | 29 ++++++------ math/libm-test.inc | 69 ++++++++++++++++++++++++++++- math/s_nexttowardf.c | 8 +--- sysdeps/i386/fpu/s_nexttoward.c | 12 +---- sysdeps/i386/fpu/s_nexttowardf.c | 8 +--- sysdeps/ieee754/ldbl-128/s_nexttoward.c | 12 +---- sysdeps/ieee754/ldbl-128/s_nexttowardf.c | 8 +--- sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c | 8 +--- sysdeps/ieee754/ldbl-96/s_nexttoward.c | 12 +---- sysdeps/ieee754/ldbl-96/s_nexttowardf.c | 8 +--- sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c | 8 +--- 12 files changed, 121 insertions(+), 82 deletions(-) diff --git a/ChangeLog b/ChangeLog index 55e17eb..74b4c0b 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,24 @@ +2012-05-01 Joseph Myers + + [BZ #2550] + [BZ #2570] + * math/s_nexttowardf.c (__nexttowardf): Use floating-point + comparisons to determine direction to adjust input. + * sysdeps/i386/fpu/s_nexttoward.c (__nexttoward): Likewise. + * sysdeps/i386/fpu/s_nexttowardf.c(__nexttowardf): Likewise. + * sysdeps/ieee754/ldbl-128/s_nexttoward.c (__nexttoward): + Likewise. + * sysdeps/ieee754/ldbl-128/s_nexttowardf.c (__nexttowardf): + Likewise. + * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c (__nexttowardf): + Likewise. + * sysdeps/ieee754/ldbl-96/s_nexttoward.c (__nexttoward): Likewise. + * sysdeps/ieee754/ldbl-96/s_nexttowardf.c (__nexttowardf): + Likewise. + * sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c (__nldbl_nexttowardf): + Likewise. + * math/libm-test.inc (nexttoward_test): Add more tests. + 2012-05-01 Andreas Schwab [BZ #14040] diff --git a/NEWS b/NEWS index fdf3621..e429cef 100644 --- a/NEWS +++ b/NEWS @@ -9,20 +9,21 @@ Version 2.16 * The following bugs are resolved with this release: - 174, 350, 369, 411, 706, 887, 2074, 2541, 2547, 2548, 2551, 2552, 2553, - 2554, 2562, 2563, 2565, 2566, 2576, 2636, 2678, 3335, 3768, 3866, 3868, - 3976, 3992, 4026, 4108, 4596, 4822, 5077, 5461, 5805, 5993, 6471, 6486, - 6578, 6649, 6730, 6770, 6794, 6884, 6890, 6894, 6895, 6907, 6911, 7064, - 9739, 9902, 10110, 10135, 10140, 10153, 10210, 10254, 10346, 10545, 10716, - 11174, 11322, 11365, 11451, 11494, 11521, 11959, 12047, 12340, 13058, - 13525, 13526, 13527, 13528, 13529, 13530, 13531, 13532, 13533, 13547, - 13551, 13552, 13553, 13555, 13559, 13566, 13583, 13592, 13618, 13637, - 13656, 13658, 13673, 13691, 13695, 13704, 13705, 13706, 13726, 13738, - 13739, 13758, 13760, 13761, 13786, 13792, 13806, 13824, 13840, 13841, - 13844, 13846, 13851, 13852, 13854, 13871, 13872, 13873, 13879, 13883, - 13886, 13892, 13895, 13908, 13910, 13911, 13912, 13913, 13915, 13916, - 13917, 13918, 13919, 13920, 13921, 13924, 13926, 13927, 13928, 13938, - 13941, 13942, 13963, 13967, 13970, 13973, 14027, 14033, 14034, 14040 + 174, 350, 369, 411, 706, 887, 2074, 2541, 2547, 2548, 2550, 2551, 2552, + 2553, 2554, 2562, 2563, 2565, 2566, 2570, 2576, 2636, 2678, 3335, 3768, + 3866, 3868, 3976, 3992, 4026, 4108, 4596, 4822, 5077, 5461, 5805, 5993, + 6471, 6486, 6578, 6649, 6730, 6770, 6794, 6884, 6890, 6894, 6895, 6907, + 6911, 7064, 9739, 9902, 10110, 10135, 10140, 10153, 10210, 10254, 10346, + 10545, 10716, 11174, 11322, 11365, 11451, 11494, 11521, 11959, 12047, + 12340, 13058, 13525, 13526, 13527, 13528, 13529, 13530, 13531, 13532, + 13533, 13547, 13551, 13552, 13553, 13555, 13559, 13566, 13583, 13592, + 13618, 13637, 13656, 13658, 13673, 13691, 13695, 13704, 13705, 13706, + 13726, 13738, 13739, 13758, 13760, 13761, 13786, 13792, 13806, 13824, + 13840, 13841, 13844, 13846, 13851, 13852, 13854, 13871, 13872, 13873, + 13879, 13883, 13886, 13892, 13895, 13908, 13910, 13911, 13912, 13913, + 13915, 13916, 13917, 13918, 13919, 13920, 13921, 13924, 13926, 13927, + 13928, 13938, 13941, 13942, 13963, 13967, 13970, 13973, 14027, 14033, + 14034, 14040 * ISO C11 support: diff --git a/math/libm-test.inc b/math/libm-test.inc index d643bad..0875e2c 100644 --- a/math/libm-test.inc +++ b/math/libm-test.inc @@ -5743,8 +5743,73 @@ nexttoward_test (void) TEST_ff_f (nexttoward, 1.1L, nan_value, nan_value); TEST_ff_f (nexttoward, nan_value, nan_value, nan_value); - /* XXX We need the hexadecimal FP number representation here for further - tests. */ +#ifdef TEST_FLOAT + TEST_ff_f (nexttoward, 1.0, 1.1L, 0x1.000002p0); + TEST_ff_f (nexttoward, 1.0, LDBL_MAX, 0x1.000002p0); + TEST_ff_f (nexttoward, 1.0, 0x1.0000000000001p0, 0x1.000002p0); + TEST_ff_f (nexttoward, 1.0, 0.9L, 0x0.ffffffp0); + TEST_ff_f (nexttoward, 1.0, -LDBL_MAX, 0x0.ffffffp0); + TEST_ff_f (nexttoward, 1.0, 0x0.fffffffffffff8p0, 0x0.ffffffp0); + TEST_ff_f (nexttoward, -1.0, -1.1L, -0x1.000002p0); + TEST_ff_f (nexttoward, -1.0, -LDBL_MAX, -0x1.000002p0); + TEST_ff_f (nexttoward, -1.0, -0x1.0000000000001p0, -0x1.000002p0); + TEST_ff_f (nexttoward, -1.0, -0.9L, -0x0.ffffffp0); + TEST_ff_f (nexttoward, -1.0, LDBL_MAX, -0x0.ffffffp0); + TEST_ff_f (nexttoward, -1.0, -0x0.fffffffffffff8p0, -0x0.ffffffp0); + TEST_ff_f (nexttoward, -0x1.3p-145, -0xap-148L, -0x1.4p-145); +# if LDBL_MANT_DIG >= 64 + TEST_ff_f (nexttoward, 1.0, 0x1.000000000000002p0L, 0x1.000002p0); + TEST_ff_f (nexttoward, 1.0, 0x0.ffffffffffffffffp0L, 0x0.ffffffp0); + TEST_ff_f (nexttoward, -1.0, -0x1.000000000000002p0L, -0x1.000002p0); + TEST_ff_f (nexttoward, -1.0, -0x0.ffffffffffffffffp0L, -0x0.ffffffp0); +# endif +# if LDBL_MANT_DIG >= 106 + TEST_ff_f (nexttoward, 1.0, 0x1.000000000000000000000000008p0L, 0x1.000002p0); + TEST_ff_f (nexttoward, 1.0, 0x0.ffffffffffffffffffffffffffcp0L, 0x0.ffffffp0); + TEST_ff_f (nexttoward, -1.0, -0x1.000000000000000000000000008p0L, -0x1.000002p0); + TEST_ff_f (nexttoward, -1.0, -0x0.ffffffffffffffffffffffffffcp0L, -0x0.ffffffp0); +# endif +# if LDBL_MANT_DIG >= 113 + TEST_ff_f (nexttoward, 1.0, 0x1.0000000000000000000000000001p0L, 0x1.000002p0); + TEST_ff_f (nexttoward, 1.0, 0x0.ffffffffffffffffffffffffffff8p0L, 0x0.ffffffp0); + TEST_ff_f (nexttoward, -1.0, -0x1.0000000000000000000000000001p0L, -0x1.000002p0); + TEST_ff_f (nexttoward, -1.0, -0x0.ffffffffffffffffffffffffffff8p0L, -0x0.ffffffp0); +# endif +#endif +#ifdef TEST_DOUBLE + TEST_ff_f (nexttoward, 1.0, 1.1L, 0x1.0000000000001p0); + TEST_ff_f (nexttoward, 1.0, LDBL_MAX, 0x1.0000000000001p0); + TEST_ff_f (nexttoward, 1.0, 0x1.0000000000001p0, 0x1.0000000000001p0); + TEST_ff_f (nexttoward, 1.0, 0.9L, 0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, 1.0, -LDBL_MAX, 0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, 1.0, 0x0.fffffffffffff8p0, 0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, -1.1L, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, -1.0, -LDBL_MAX, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, -1.0, -0x1.0000000000001p0, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, -1.0, -0.9L, -0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, LDBL_MAX, -0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, -0x0.fffffffffffff8p0, -0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, -0x8.00346dc5d6388p-3L, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, 0x1p-1074, 0x1p-1073L, 0x1p-1073); +# if LDBL_MANT_DIG >= 64 + TEST_ff_f (nexttoward, 1.0, 0x1.000000000000002p0L, 0x1.0000000000001p0); + TEST_ff_f (nexttoward, 1.0, 0x0.ffffffffffffffffp0L, 0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, -0x1.000000000000002p0L, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, -1.0, -0x0.ffffffffffffffffp0L, -0x0.fffffffffffff8p0); +# endif +# if LDBL_MANT_DIG >= 106 + TEST_ff_f (nexttoward, 1.0, 0x1.000000000000000000000000008p0L, 0x1.0000000000001p0); + TEST_ff_f (nexttoward, 1.0, 0x0.ffffffffffffffffffffffffffcp0L, 0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, -0x1.000000000000000000000000008p0L, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, -1.0, -0x0.ffffffffffffffffffffffffffcp0L, -0x0.fffffffffffff8p0); +# endif +# if LDBL_MANT_DIG >= 113 + TEST_ff_f (nexttoward, 1.0, 0x1.0000000000000000000000000001p0L, 0x1.0000000000001p0); + TEST_ff_f (nexttoward, 1.0, 0x0.ffffffffffffffffffffffffffff8p0L, 0x0.fffffffffffff8p0); + TEST_ff_f (nexttoward, -1.0, -0x1.0000000000000000000000000001p0L, -0x1.0000000000001p0); + TEST_ff_f (nexttoward, -1.0, -0x0.ffffffffffffffffffffffffffff8p0L, -0x0.fffffffffffff8p0); +# endif +#endif END (nexttoward); } diff --git a/math/s_nexttowardf.c b/math/s_nexttowardf.c index fb008d5..e8c4dd1 100644 --- a/math/s_nexttowardf.c +++ b/math/s_nexttowardf.c @@ -47,16 +47,12 @@ float __nexttowardf(float x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if(hy<0||(ix>>23)>(iy>>20)-0x380 - || ((ix>>23)==(iy>>20)-0x380 - && (ix&0x7fffff)>(((hy<<3)|(ly>>29))&0x7fffff))) /* x > y, x -= ulp */ + if(x > y) /* x -= ulp */ hx -= 1; else /* x < y, x += ulp */ hx += 1; } else { /* x < 0 */ - if(hy>=0||(ix>>23)>(iy>>20)-0x380 - || ((ix>>23)==(iy>>20)-0x380 - && (ix&0x7fffff)>(((hy<<3)|(ly>>29))&0x7fffff))) /* x < y, x -= ulp */ + if(x < y) /* x -= ulp */ hx -= 1; else /* x > y, x += ulp */ hx += 1; diff --git a/sysdeps/i386/fpu/s_nexttoward.c b/sysdeps/i386/fpu/s_nexttoward.c index e5f0164..74147c4 100644 --- a/sysdeps/i386/fpu/s_nexttoward.c +++ b/sysdeps/i386/fpu/s_nexttoward.c @@ -55,11 +55,7 @@ double __nexttoward(double x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if (esy>=0x8000||((ix>>20)&0x7ff)>iy-0x3c00 - || (((ix>>20)&0x7ff)==iy-0x3c00 - && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) - || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) - && (lx<<11)>ly)))) { /* x > y, x -= ulp */ + if (x > y) { /* x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x < y, x += ulp */ @@ -67,11 +63,7 @@ double __nexttoward(double x, long double y) if(lx==0) hx += 1; } } else { /* x < 0 */ - if (esy<0x8000||((ix>>20)&0x7ff)>iy-0x3c00 - || (((ix>>20)&0x7ff)==iy-0x3c00 - && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) - || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) - && (lx<<11)>ly)))) {/* x < y, x -= ulp */ + if (x < y) { /* x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x > y, x += ulp */ diff --git a/sysdeps/i386/fpu/s_nexttowardf.c b/sysdeps/i386/fpu/s_nexttowardf.c index 89e8771..49651be 100644 --- a/sysdeps/i386/fpu/s_nexttowardf.c +++ b/sysdeps/i386/fpu/s_nexttowardf.c @@ -47,17 +47,13 @@ float __nexttowardf(float x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if(esy>=0x8000||((ix>>23)&0xff)>iy-0x3f80 - || (((ix>>23)&0xff)==iy-0x3f80 - && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x > y, x -= ulp */ + if(x > y) { /* x -= ulp */ hx -= 1; } else { /* x < y, x += ulp */ hx += 1; } } else { /* x < 0 */ - if(esy<0x8000||((ix>>23)&0xff)>iy-0x3f80 - || (((ix>>23)&0xff)==iy-0x3f80 - && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x < y, x -= ulp */ + if(x < y) { /* x -= ulp */ hx -= 1; } else { /* x > y, x += ulp */ hx += 1; diff --git a/sysdeps/ieee754/ldbl-128/s_nexttoward.c b/sysdeps/ieee754/ldbl-128/s_nexttoward.c index 87a9a6c..1ea0b64 100644 --- a/sysdeps/ieee754/ldbl-128/s_nexttoward.c +++ b/sysdeps/ieee754/ldbl-128/s_nexttoward.c @@ -55,11 +55,7 @@ double __nexttoward(double x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if (hy<0||(ix>>20)>(iy>>48)-0x3c00 - || ((ix>>20)==(iy>>48)-0x3c00 - && (((((int64_t)hx)<<28)|(lx>>4))>(hy&0x0000ffffffffffffLL) - || (((((int64_t)hx)<<28)|(lx>>4))==(hy&0x0000ffffffffffffLL) - && (lx&0xf)>(ly>>60))))) { /* x > y, x -= ulp */ + if (x > y) { /* x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x < y, x += ulp */ @@ -67,11 +63,7 @@ double __nexttoward(double x, long double y) if(lx==0) hx += 1; } } else { /* x < 0 */ - if (hy>=0||(ix>>20)>(iy>>48)-0x3c00 - || ((ix>>20)==(iy>>48)-0x3c00 - && (((((int64_t)hx)<<28)|(lx>>4))>(hy&0x0000ffffffffffffLL) - || (((((int64_t)hx)<<28)|(lx>>4))==(hy&0x0000ffffffffffffLL) - && (lx&0xf)>(ly>>60))))) { /* x < y, x -= ulp */ + if (x < y) { /* x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x > y, x += ulp */ diff --git a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c index 371fa80..02a1407 100644 --- a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c +++ b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c @@ -46,17 +46,13 @@ float __nexttowardf(float x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if(hy<0||(ix>>23)>(iy>>48)-0x3f80 - || ((ix>>23)==(iy>>48)-0x3f80 - && (ix&0x7fffff)>((hy>>25)&0x7fffff))) {/* x > y, x -= ulp */ + if(x > y) { /* x -= ulp */ hx -= 1; } else { /* x < y, x += ulp */ hx += 1; } } else { /* x < 0 */ - if(hy>=0||(ix>>23)>(iy>>48)-0x3f80 - || ((ix>>23)==(iy>>48)-0x3f80 - && (ix&0x7fffff)>((hy>>25)&0x7fffff))) {/* x < y, x -= ulp */ + if(x < y) { /* x < y, x -= ulp */ hx -= 1; } else { /* x > y, x += ulp */ hx += 1; diff --git a/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c b/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c index a674583..b387a91 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c @@ -49,17 +49,13 @@ float __nexttowardf(float x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if(hy<0||(ix>>23)>(iy>>52)-0x380 - || ((ix>>23)==(iy>>52)-0x380 - && (ix&0x7fffff)>((hy>>29)&0x7fffff))) {/* x > y, x -= ulp */ + if(x > y) { /* x -= ulp */ hx -= 1; } else { /* x < y, x += ulp */ hx += 1; } } else { /* x < 0 */ - if(hy>=0||(ix>>23)>(iy>>52)-0x380 - || ((ix>>23)==(iy>>52)-0x380 - && (ix&0x7fffff)>((hy>>29)&0x7fffff))) {/* x < y, x -= ulp */ + if(x < y) { /* x -= ulp */ hx -= 1; } else { /* x > y, x += ulp */ hx += 1; diff --git a/sysdeps/ieee754/ldbl-96/s_nexttoward.c b/sysdeps/ieee754/ldbl-96/s_nexttoward.c index 9b93eca..f7a8b21 100644 --- a/sysdeps/ieee754/ldbl-96/s_nexttoward.c +++ b/sysdeps/ieee754/ldbl-96/s_nexttoward.c @@ -52,11 +52,7 @@ double __nexttoward(double x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if (esy>=0x8000||((ix>>20)&0x7ff)>iy-0x3c00 - || (((ix>>20)&0x7ff)==iy-0x3c00 - && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) - || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) - && (lx<<11)>ly)))) { /* x > y, x -= ulp */ + if (x > y) { /* x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x < y, x += ulp */ @@ -64,11 +60,7 @@ double __nexttoward(double x, long double y) if(lx==0) hx += 1; } } else { /* x < 0 */ - if (esy<0x8000||((ix>>20)&0x7ff)>iy-0x3c00 - || (((ix>>20)&0x7ff)==iy-0x3c00 - && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) - || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) - && (lx<<11)>ly)))) {/* x < y, x -= ulp */ + if (x < y) { /* x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x > y, x += ulp */ diff --git a/sysdeps/ieee754/ldbl-96/s_nexttowardf.c b/sysdeps/ieee754/ldbl-96/s_nexttowardf.c index aeb92b6..a96f9da 100644 --- a/sysdeps/ieee754/ldbl-96/s_nexttowardf.c +++ b/sysdeps/ieee754/ldbl-96/s_nexttowardf.c @@ -44,17 +44,13 @@ float __nexttowardf(float x, long double y) return x; } if(hx>=0) { /* x > 0 */ - if(esy>=0x8000||((ix>>23)&0xff)>iy-0x3f80 - || (((ix>>23)&0xff)==iy-0x3f80 - && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x > y, x -= ulp */ + if(x > y) { /* x -= ulp */ hx -= 1; } else { /* x < y, x += ulp */ hx += 1; } } else { /* x < 0 */ - if(esy<0x8000||((ix>>23)&0xff)>iy-0x3f80 - || (((ix>>23)&0xff)==iy-0x3f80 - && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x < y, x -= ulp */ + if(x < y) { /* x -= ulp */ hx -= 1; } else { /* x > y, x += ulp */ hx += 1; diff --git a/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c b/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c index 68027f2..7eca121 100644 --- a/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c +++ b/sysdeps/ieee754/ldbl-opt/s_nexttowardfd.c @@ -50,16 +50,12 @@ float __nldbl_nexttowardf(float x, double y) return x; } if(hx>=0) { /* x > 0 */ - if(hy<0||(ix>>23)>(iy>>20)-0x380 - || ((ix>>23)==(iy>>20)-0x380 - && (ix&0x7fffff)>(((hy<<3)|(ly>>29))&0x7fffff))) /* x > y, x -= ulp */ + if(x > y) /* x -= ulp */ hx -= 1; else /* x < y, x += ulp */ hx += 1; } else { /* x < 0 */ - if(hy>=0||(ix>>23)>(iy>>20)-0x380 - || ((ix>>23)==(iy>>20)-0x380 - && (ix&0x7fffff)>(((hy<<3)|(ly>>29))&0x7fffff))) /* x < y, x -= ulp */ + if(x < y) /* x -= ulp */ hx -= 1; else /* x > y, x += ulp */ hx += 1; -- 2.7.4