Fix strtod multiple-precision division bug (bug 26137) [committed]

Message ID alpine.DEB.2.21.2006302304230.31826@digraph.polyomino.org.uk
State New
Headers show
Series
  • Fix strtod multiple-precision division bug (bug 26137) [committed]
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Commit Message

Joseph Myers June 30, 2020, 11:04 p.m.
Bug 26137 reports spurious "inexact" exceptions from strtod, on 32-bit
systems only, for a decimal argument that is exactly 1 + 2^-32.  In
fact the same issue also appears for 1 + 2^-64 and 1 + 2^-96 as
arguments to strtof128 on 32-bit systems, and 1 + 2^-64 as an argument
to strtof128 on 64-bit systems.  In FE_DOWNWARD or FE_TOWARDZERO mode,
the return value is also incorrect.

The problem is in the multiple-precision division logic used in the
case of dividing by a denominator that occupies at least three GMP
limbs.  There was a comment "The division does not work if the upper
limb of the two-limb mumerator is greater than the denominator.", but
in fact there were problems for the case of equality (that is, where
the high limbs are equal, offset by some multiple of the GMP limb
size) as well.  In such cases, the code used "quot = ~(mp_limb_t) 0;"
(with subsequent correction if that is an overestimate), because
udiv_qrnnd does not support the case of equality, but it's possible
for the shifted numerator to be greater than or equal to the
denominator, in which case that is an underestimate.  To avoid that,
this patch changes the ">" condition to ">=", meaning the first
division is done with a zero high word.

The tests added are all 1 + 2^-n for n from 1 to 113 except for those
that were already present in tst-strtod-round-data.

Tested for x86_64 and x86.

---

Committed.


-- 
Joseph S. Myers
joseph@codesourcery.com

Comments

Andreas Schwab July 1, 2020, 7:24 a.m. | #1
On Jun 30 2020, Joseph Myers wrote:

> +	     numerator is greater or equal to than the denominator.  */


greater than or equal to

Andreas.

-- 
Andreas Schwab, schwab@linux-m68k.org
GPG Key fingerprint = 7578 EB47 D4E5 4D69 2510  2552 DF73 E780 A9DA AEC1
"And now for something completely different."
Joseph Myers July 1, 2020, 2:54 p.m. | #2
On Wed, 1 Jul 2020, Andreas Schwab wrote:

> On Jun 30 2020, Joseph Myers wrote:

> 

> > +	     numerator is greater or equal to than the denominator.  */

> 

> greater than or equal to


Thanks, fixed.

-- 
Joseph S. Myers
joseph@codesourcery.com

Patch

diff --git a/stdlib/strtod_l.c b/stdlib/strtod_l.c
index a3836fc12e..158da787a2 100644
--- a/stdlib/strtod_l.c
+++ b/stdlib/strtod_l.c
@@ -1648,8 +1648,8 @@  ____STRTOF_INTERNAL (const STRING_TYPE *nptr, STRING_TYPE **endptr, int group,
 	  d1 = den[densize - 2];
 
 	  /* The division does not work if the upper limb of the two-limb
-	     numerator is greater than the denominator.  */
-	  if (__mpn_cmp (num, &den[densize - numsize], numsize) > 0)
+	     numerator is greater or equal to than the denominator.  */
+	  if (__mpn_cmp (num, &den[densize - numsize], numsize) >= 0)
 	    num[numsize++] = 0;
 
 	  if (numsize < densize)
diff --git a/stdlib/tst-strtod-round-data b/stdlib/tst-strtod-round-data
index 8a898ddb0e..84ab705709 100644
--- a/stdlib/tst-strtod-round-data
+++ b/stdlib/tst-strtod-round-data
@@ -155,3 +155,113 @@ 
 -179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137215
 -1189731495357231765085759326628007130763444687096510237472674821233261358180483686904488595472612039915115437484839309258897667381308687426274524698341565006080871634366004897522143251619531446845952345709482135847036647464830984784714280967845614138476044338404886122905286855313236158695999885790106357018120815363320780964323712757164290613406875202417365323950267880089067517372270610835647545755780793431622213451903817859630690311343850657539360649645193283178291767658965405285113556134369793281725888015908414675289832538063419234888599898980623114025121674472051872439321323198402942705341366951274739014593816898288994445173400364617928377138074411345791848573595077170437644191743889644885377684738322240608239079061399475675334739784016491742621485229014847672335977897158397334226349734811441653077758250988926030894789604676153104257260141806823027588003441951455327701598071281589597169413965608439504983171255062282026626200048042149808200002060993433681237623857880627479727072877482838438705048034164633337013385405998040701908662387301605018188262573723766279240798931717708807901740265407930976419648877869604017517691938687988088008944251258826969688364194133945780157844364946052713655454906327187428531895100278695119323496808703630436193927592692344820812834297364478686862064169042458555136532055050508189891866846863799917647547291371573500701015197559097453040033031520683518216494195636696077748110598284901343611469214274121810495077979275556645164983850062051066517084647369464036640569339464837172183352956873912042640003611618789278195710052094562761306703551840330110645101995435167626688669627763820604342480357906415354212732946756073006907088870496125050068156659252761297664065498347492661798824062312210409274584565587264846417650160123175874034726261957289081466197651553830744424709698634753627770356227126145052549125229448040149114795681359875968512808575244271871455454084894986155020794806980939215658055319165641681105966454159951476908583129721503298816585142073061480888021769818338417129396878371459575846052583142928447249703698548125295775920936450022651427249949580708203966082847550921891152133321048011973883636577825533325988852156325439335021315312134081390451021255363707903495916963125924201167877190108935255914539488216897117943269373608639074472792751116715127106396425081353553137213552890539802602978645319795100976432939091924660228878912900654210118287298298707382159717184569540515403029173307292454391789568674219640761451173600617752186991913366837033887201582071625868247133104513315097274713442728340606642890406496636104443217752811227470029162858093727701049646499540220983981932786613204254226464243689610107429923197638681545837561773535568984536053627234424277105760924864023781629665526314910906960488073475217005121136311870439925762508666032566213750416695719919674223210606724721373471234021613540712188239909701971943944347480314217903886317767779921539892177334344368907550318800833546852344370327089284147501640589448482001254237386680074457341910933774891959681016516069106149905572425810895586938833067490204900368624166301968553005687040285095450484840073528643826570403767157286512380255109954518857013476588189300004138849715883139866071547574816476727635116435462804401112711392529180570794193422686818353212799068972247697191474268157912195973794192807298886952361100880264258801320928040011928153970801130741339550003299015924978259936974358726286143980520112454369271114083747919007803406596321353417004068869443405472140675963640997405009225803505672726465095506267339268892424364561897661906898424186770491035344080399248327097911712881140170384182058601614758284200750183500329358499691864066590539660709069537381601887679046657759654588001937117771344698326428792622894338016112445533539447087462049763409147542099248815521395929388007711172017894897793706604273480985161028815458787911160979113422433557549170905442026397275695283207305331845419990749347810524006194197200591652147867193696254337864981603833146354201700628817947177518115217674352016511172347727727075220056177748218928597158346744541337107358427757919660562583883823262178961691787226118865632764934288772405859754877759869235530653929937901193611669007472354746360764601872442031379944139824366828698790212922996174192728625891720057612509349100482545964152046477925114446500732164109099345259799455690095576788686397487061948854749024863607921857834205793797188834779656273479112388585706424836379072355410286787018527401653934219888361061949671961055068686961468019035629749424086587195041004404915266476272761070511568387063401264136517237211409916458796347624949215904533937210937520465798300175408017538862312719042361037129338896586028150046596078872444365564480545689033575955702988396719744528212984142578483954005084264327730840985420021409069485412320805268520094146798876110414583170390473982488899228091818213934288295679717369943152460447027290669964066815
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diff --git a/stdlib/tst-strtod-round-data.h b/stdlib/tst-strtod-round-data.h
index 5ac25f7b29..8899d15f9b 100644
--- a/stdlib/tst-strtod-round-data.h
+++ b/stdlib/tst-strtod-round-data.h
@@ -11972,4 +11972,3469 @@  static const struct test tests[] = {
 	0x1p+1024, false,
 	0x1p+1024, false,
 	0x1.0000000000000000000000000001p+1024, false),
+  TEST ("1.5",
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	true,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false,
+	0x1.8p+0, false),
+  TEST ("1.25",
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	true,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false,
+	0x1.4p+0, false),
+  TEST ("1.125",
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	true,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false,
+	0x1.2p+0, false),
+  TEST ("1.0625",
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	true,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false,
+	0x1.1p+0, false),
+  TEST ("1.03125",
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	true,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false,
+	0x1.08p+0, false),
+  TEST ("1.015625",
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	true,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false,
+	0x1.04p+0, false),
+  TEST ("1.0078125",
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	true,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false,
+	0x1.02p+0, false),
+  TEST ("1.00390625",
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	true,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false,
+	0x1.01p+0, false),
+  TEST ("1.001953125",
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	true,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false,
+	0x1.008p+0, false),
+  TEST ("1.0009765625",
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	true,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false,
+	0x1.004p+0, false),
+  TEST ("1.00048828125",
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	true,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false,
+	0x1.002p+0, false),
+  TEST ("1.000244140625",
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	true,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false,
+	0x1.001p+0, false),
+  TEST ("1.0001220703125",
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	true,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false,
+	0x1.0008p+0, false),
+  TEST ("1.00006103515625",
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	true,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false,
+	0x1.0004p+0, false),
+  TEST ("1.000030517578125",
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	true,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false,
+	0x1.0002p+0, false),
+  TEST ("1.0000152587890625",
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	true,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false,
+	0x1.0001p+0, false),
+  TEST ("1.00000762939453125",
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	true,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false,
+	0x1.00008p+0, false),
+  TEST ("1.000003814697265625",
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	true,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false,
+	0x1.00004p+0, false),
+  TEST ("1.0000019073486328125",
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	true,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false,
+	0x1.00002p+0, false),
+  TEST ("1.00000095367431640625",
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	true,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false,
+	0x1.00001p+0, false),
+  TEST ("1.000000476837158203125",
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	true,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false,
+	0x1.000008p+0, false),
+  TEST ("1.0000000298023223876953125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	true,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false,
+	0x1.0000008p+0, false),
+  TEST ("1.00000001490116119384765625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	true,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false,
+	0x1.0000004p+0, false),
+  TEST ("1.000000007450580596923828125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	true,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false,
+	0x1.0000002p+0, false),
+  TEST ("1.0000000037252902984619140625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	true,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false,
+	0x1.0000001p+0, false),
+  TEST ("1.00000000186264514923095703125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	true,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false,
+	0x1.00000008p+0, false),
+  TEST ("1.000000000931322574615478515625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	true,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false,
+	0x1.00000004p+0, false),
+  TEST ("1.0000000004656612873077392578125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	true,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false,
+	0x1.00000002p+0, false),
+  TEST ("1.00000000023283064365386962890625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	true,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false,
+	0x1.00000001p+0, false),
+  TEST ("1.000000000116415321826934814453125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	true,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false,
+	0x1.000000008p+0, false),
+  TEST ("1.0000000000582076609134674072265625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	true,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false,
+	0x1.000000004p+0, false),
+  TEST ("1.00000000002910383045673370361328125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	true,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false,
+	0x1.000000002p+0, false),
+  TEST ("1.000000000014551915228366851806640625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	true,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false,
+	0x1.000000001p+0, false),
+  TEST ("1.0000000000072759576141834259033203125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	true,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false,
+	0x1.0000000008p+0, false),
+  TEST ("1.00000000000363797880709171295166015625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	true,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false,
+	0x1.0000000004p+0, false),
+  TEST ("1.000000000001818989403545856475830078125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	true,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false,
+	0x1.0000000002p+0, false),
+  TEST ("1.0000000000009094947017729282379150390625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	true,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false,
+	0x1.0000000001p+0, false),
+  TEST ("1.00000000000045474735088646411895751953125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	true,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	true,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	true,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	true,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false,
+	0x1.00000000008p+0, false),
+  TEST ("1.000000000000227373675443232059478759765625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	true,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	true,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	true,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	true,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false,
+	0x1.00000000004p+0, false),
+  TEST ("1.0000000000001136868377216160297393798828125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	true,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	true,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	true,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	true,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false,
+	0x1.00000000002p+0, false),
+  TEST ("1.00000000000005684341886080801486968994140625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	true,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	true,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	true,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	true,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false,
+	0x1.00000000001p+0, false),
+  TEST ("1.000000000000028421709430404007434844970703125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	true,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	true,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	true,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	true,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false,
+	0x1.000000000008p+0, false),
+  TEST ("1.0000000000000142108547152020037174224853515625",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
+	true,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	true,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	true,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	true,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	true,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false,
+	0x1.000000000004p+0, false),
+  TEST ("1.00000000000000710542735760100185871124267578125",
+	false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1p+0, false,
+	0x1.000002p+0, false,
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