Sun Jun 30 13:48:26 EDT 1991:
  dtoa.c: adjust dtoa to allow negative ndigits for modes 3,5,7,9
(fixed-point mode); fix rounding bug in these modes when the input
d (to be converted) satisfies 10^-(ndigits+1) <= |d| < 10^-ndigits ,
i.e., when the result, before rounding, would be empty but might
round to one digit.  Adjust the decpt returned in these modes when
the result is empty (i.e., when |d| <= 5 * 10^-ndigits).

Tue Jul  2 21:44:00 EDT 1991
  Correct an inefficiency introduced 2 days ago in dtoa's handling of
integers in modes 0, 1.

Mon Sep  9 23:29:38 EDT 1991
  dtoa.c: remove superfluous declaration of size_t.

Sun Oct  6 15:34:15 EDT 1991
  dtoa.c: fix another bug in modes 3,5,7,9 when the result, before
rounding, would be empty, but rounds to one digit: *decpt was low by
one.

Sat Jan 18 12:30:04 EST 1992
  dtoa.c: add some #ifdef KR_headers lines relevant only if IBM is
defined; for input decimal strings representing numbers too large, have
strtod return HUGE_VAL only if __STDC__ is defined; otherwise have it
return +-Infinity for IEEE arithmetic, +- the largest machine number
for IBM and VAX arithmetic.  (If __STDC__ is not defined, HUGE_VAL may
not be defined either, or it may be wrong.)

Mon Apr 27 23:13:43 EDT 1992
  dtoa.c: tweak strtod (one-line addition) so the end-pointer = start
pointer when the input has, e.g., only white space.

Thu May  7 18:04:46 EDT 1992
  dtoa.c: adjust treatment of exponent field (in strtod) to behave
reasonably with huge numbers and 16-bit ints.

Fri Jun 19 08:29:02 EDT 1992
  dtoa.c: fix a botch in placement of #ifdef __cplusplus (which only
matters if you're using a C++ compiler).

Wed Oct 21 11:23:07 EDT 1992
  dtoa.c: add #ifdef Bad_float_h lines for systems with missing or
inferior float.h .

Thu Apr 22 07:54:48 EDT 1993
  dtoa.c: change < to <= in line 2059:
<	for(result_k = 0; sizeof(Bigint) - sizeof(unsigned long) + j < i;
---
>	for(result_k = 0; sizeof(Bigint) - sizeof(unsigned long) + j <= i;
With 32-bit ints, the former could give too small a block for the return
value when, e.g., mode = 2 or 4 and ndigits = 24 (16 for 16-bit ints).

Mon Jun 21 12:56:42 EDT 1993
  dtoa.c: tweak to work with 32-bit ints and 64-bit longs
when compiled with -DLong=int .

Wed Jan 26 11:09:16 EST 1994
  dtoa.c: fix bug in strtod's handling of numbers with very
negative exponents (e.g. 1.8826e-512), which should underflow to 0;
fix storage leak in strtod with underflows and overflows near
the underflow and overflow thresholds.

Mon Feb 28 11:37:30 EST 1994
  dtoa.c:
85a86,89
>  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
>  *	if memory is available and otherwise does something you deem
>  *	appropriate.  If MALLOC is undefined, malloc will be invoked
>  *	directly -- and assumed always to succeed.
87a92,95
> #ifndef MALLOC
> #define MALLOC malloc
> #endif
>
352c360
< 		rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(Long));
---
> 		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));

Thu Mar  3 16:56:39 EST 1994
  dtoa.c: if MALLOC is #defined, declare it.

Wed Jan  4 15:45:34 EST 1995
  dtoa.c: add CONST qualification to tens, bigtens, tinytens (for use
on embedded systems with little spare RAM).

Fri Mar  1 08:55:39 EST 1996
  g_fmt.c: honor the sign of 0 and return the first argument (buf).

Sat Jul  6 07:59:28 EDT 1996
  dtoa.c: cosmetic changes: "ULong" rather than "unsigned Long";
update comments to reflect AT&T breakup.

Mon Aug  5 23:31:24 EDT 1996
  dtoa.c: add comment about invoking _control87(PC_53, MCW_PC)
(or the equivalent) on 80x87 machines before calling strtod or dtoa.

Tue Dec 17 15:01:56 EST 1996
  dtoa.c: new #define possibilities: #define INFNAN_CHECK to have
strtod check (case insensitively) for "Infinity" and "NaN" on machines
with IEEE arithmetic; #define MULTIPLE_THREADS if the system offers
preemptively scheduled multiple threads, in which case you must supply
routines ACQUIRE_DTOA_LOCK(n) and FREE_DTOA_LOCK(n) (n = 0 or 1).
New void freedtoa(char*) for freeing values returned by dtoa; use of
freedtoa() is required if MULTIPLE_THREADS is #defined, and is merely
recommended otherwise.
  g_fmt.c: adjusted to invoke freedtoa().

Wed Feb 12 00:40:01 EST 1997
  dtoa.c: strtod: on IEEE systems, scale to avoid intermediate
underflows when the result does not underflow; compiling with
-DNO_IEEE_Scale restores the old logic.  Fix a bug, revealed by
input string 2.2250738585072012e-308, in treating input just less
than the smallest normalized number.  (The bug introduced an extra
ULP of error in this special case.)

Tue May 12 11:13:04 EDT 1998
  dtoa.c: strtod: fix a glitch introduced with the scaling of 19970212
that caused one-bit rounding errors in certain denormal numbers, such
as 8.44291197326099e-309, which was read as 8.442911973260987e-309.
Remove #ifdef Unsigned_Shifts logic in favor of unsigned arithmetic.
Unless compiled with -DNO_LONG_LONG, use 64-bit arithmetic where
possible.

Fri May 15 07:49:07 EDT 1998
  dtoa.c: strtod: fix another glitch with scaling to avoid underflow
with IEEE arithmetic, again revealed by the input string
2.2250738585072012e-308, which was rounded to the largest denormal
rather than the smallest normal double precision number.

Wed Aug  5 23:27:26 EDT 1998
  gdtoa.tar.gz: tweaks in response to comments from Shawn C. Sheridan
(with no effect on the resulting .o files except when strtod.c is
compiled with -DNO_ERRNO); bigtens --> bigtens_D2A (a symbol meant
to be private to gdtoa.a).

Sat Sep 12 17:05:15 EDT 1998
  gdtoa.tar.gz: more changes in response to comments from Shawn C.
Sheridan (including repair of a glitch in g_ffmt.c).  For consistency
and possible convenience, there are some new functions and some name
changes to existing ones:
	Old	New
	---	g_xLfmt
	strtoQ	strtopQ
	---	strtopd
	strtodd	strtopdd
	---	strtopf
	strtox	strtopx
	---	strtopxL
	---	strtorxL
	---	strtoIxL
Functions strtopd and strtopf are variations of strtod and strtof,
respectively, which write their results to their final (pointer)
arguments.  Functions strtorf and strtord are now analogous to the
other strtor* functions in that they now have a final pointer
argument to which they write their results, and they return the
int value they get from strtodg.
  The xL family (g_xLfmt, strto[Irp]xL) is a variation of the old x
family (for 80-bit IEEE double-extended precision) that assumes the
storage layout of the Motorola 68881's double-extended format:  80
interesting bits stored in 3 unsigned 32-bit ints (with a "hole", 16
zero bits, in the word that holds the sign and exponent).  The x
family now deals with 80-bit (5 unsigned 16-bit ints) rather than
96-bit arrays (3 unsigned 32-bit ints) that hold its 80-bit
double-extended values.  (This relaxes the alignment requirements of
the x family and results in strto[Ipr]x writing 80 rather than 96 bits
to their final arguments.)
  Each g_*fmt routine now returns a pointer to the null character
that terminates the strings it writes, rather than a pointer to
the beginning of that string (the first argument).  These routines
still return 0 (NULL) if the first argument is too short.
  The second argument to g_dfmt is now pointer (to a double) rather
than a double value.

Thu Oct 29 21:54:00 EST 1998
  dtoa.c: Fix bug in strtod under -DSudden_Underflow and (the default)
-DAvoid_Underflow: some numbers that should have suffered sudden
underflow were scaled inappropriately (giving nonzero return values).
Example: "1e-320" gave -3.6304123742133376e+280 rather than 0.

Mon Nov  2 15:41:16 EST 1998
  dtoa.c: tweak to remove LL suffixes from numeric constants (for
compilers that offer a 64-bit long long type but do not recognize the
LL constants prescribed by C9x, the proposed update to the ANSI/ISO C
standard).  Thanks to Earl Chew for pointing out the existence of such
compilers.
  gdtoa.tar.gz: renamed gdtoa.tgz and updated to incorporate the above
changes (of 29 Oct. and 2 Nov. 1998) to dtoa.c.

Thu Mar 25 17:56:44 EST 1999
  dtoa.c, gdtoa.tgz: fix a bug in strtod's reading of 4.9e-324:
it returned 0 rather than the smallest denormal.

Mon Apr 12 10:39:25 EDT 1999
  gdtoa.tgz: test/ftest.c: change %.7g to %.8g throughout.

Fri Aug 20 19:17:52 EDT 1999
  gdtoa.tgz: gdtoa.c: fix two bugs reported by David Chase (thanks!):
1. An adjustment for denormalized numbers around 503 was off by one.
2. A check for "The special case" around line 551 omitted the condition
that we not be at the bottom of the exponent range.

Mon Sep 13 10:53:34 EDT 1999
  dtoa.c: computationally invisible tweak for the benefit of people
who actually read the code:

2671c2671
< 		 && word0(d) & Exp_mask
---
> 		 && word0(d) & (Exp_mask & Exp_mask << 1)

I.e., in dtoa(), the "special case" does not arise for the smallest
normalized IEEE double.  Thanks to Waldemar Horwat for pointing this
out and suggesting the modified test above.  Also, some tweaks for
compilation with -DKR_headers.
  gdtoa.tgz: gdtoa.c: analogous change:

552c552
< 		if (bbits == 1 && be0 > fpi->emin) {
---
> 		if (bbits == 1 && be0 > fpi->emin + 1) {

This has no effect on the g*fmt.c routines, but might affect the
computation of the shortest decimal string that rounds to the
smallest normalized floating-point number of other precisions.
  gdota.tgz: test/d.out test/dI.out test/dd.out: updated to reflect
previous changes (of 19990820); test/*.c: most test programs modified
to permit #hex input.  See the comments.

Fri Sep 17 01:39:25 EDT 1999
  Try again to update dtoa.c: somehow dtoa.c got put back to a version
from 3 years ago after this "changes" file was updated on 13 Sept. 1999.
One more tweak to omit a warning on some systems:
2671c2671
<		 && word0(d) & (Exp_mask & Exp_mask << 1)
---
>		 && word0(d) & (Exp_mask & ~Exp_msk1)
Plus changes to avoid trouble with aggressively optimizing compilers
(e.g., gcc 2.95.1 under -O2).  On some systems, these changes do not
affect the resulting machine code; on others, the old way of viewing
a double as a pair of ULongs is available with -DYES_ALIAS.

Tue Sep 21 09:21:25 EDT 1999
  gdtoa.tgz: changes analogous to those of 17 Sept. 1999 to dtoa.c to
avoid trouble with aggressively optimizing compilers.

Wed Dec 15 13:14:38 EST 1999
  dtoa.c: tweak to bypass a bug with HUGE_VAL on HP systems.

Mon Jan 17 18:32:52 EST 2000
  dtoa.c and gdtoa.tgz: strtod: set errno = ERANGE on all inputs that
underflow to zero (not just those sufficiently less than the smallest
positive denormalized number).
  gdtoa.tgz: README: point out that compiling with -DNO_ERRNO inhibits
errno assignments (by strtod and the core converter, strtodg).

Tue Jan 18 16:35:31 EST 2000
  dtoa.c and gdtoa.tgz: strtod: modify the test inserted yesterday so
it may work correctly with buggy 80x87 compilers.  (The change matters,
e.g., to Microsoft Visual C++ 4.2 and 6.0.)

Thu Nov  2 21:00:45 EST 2000
  dtoa.c and gdtoa.tgz:
1. Fix bug in test for exact half-way cases of denormalized numbers
   (without -DNO_IEEE_Scale).
2. Compilation with -DNO_ERRNO prevents strtod from assigning
   errno = ERANGE when the result overflows or underflows to 0.
3. With IEEE arithmetic and no -DNO_IEEE_Scale, adjust scaling so
   ulp(d) never returns a denormalized number.  This and other tweaks
   permit strtod and dtoa to work correctly on machines that flush
   underflows to zero but otherwise use IEEE arithmetic without
   Sudden_Underflow being #defined (and with strtod simply returning 0
   instead of denormalized numbers).
4. Compilations with -DUSE_LOCALE causes strtod to use the current
   locale's decimal_point value.
5. Under compilations with -DINFNAN_CHECK, strtod and strtodg (case
   insensitively) treat "inf" the same as "infinity" and, unless
   compiled with -DNo_Hex_NaN, accept "nan(x)", where x is a string of
   hexadecimal digits and spaces, as a NaN whose value is constructed
   from x (as explained in comments near the top of dtoa.c and in
   gdtoaimp.h).
6. The default PRIVATE_MEM is increased slightly (to 2304), and comments
   near the top of dtoa.c provide more discussion of PRIVATE_MEM.
7. Meanings of dtoa modes 4,5,8,9 changed.  See comments in dtoa.c and
   gdtoa.c; modes 4 and 5 may now provide shorter strings that round
   (in round-nearest mode) to the given double value.  (Paxson's
   testbase program is unhappy with this new rounding, as it can
   introduce an error of more than one base-10 ulp when 17 or more
   decimal digits are requested.)
8. With IEEE arithmetic, compilation with -DHonor_FLT_ROUNDS causes
   strtod and dtoa to round according to FLT_ROUNDS:
	0 ==> towards 0,
	1 ==> nearest,
	2 ==> towards +Infinity,
	3 ==> towards -Infinity.
9. With IEEE arithmetic, compilation with -DSET_INEXACT causes extra
   computation (and sometimes slower conversions in dtoa and strtod,
   particularly for dtoa in cases where otherwise some simple floating-
   point computations would suffice) to set the IEEE inexact flag
   correctly.  As comments in dtoa.c explain in more detail, this
   requires compilation in an environment (such as #include "dtoa.c"
   in suitable source) that provides
		int get_inexact(void);
		void clear_inexact(void);
10. On input "-x", return 0 rather than -0.

gdtoa.tgz: gethex.c: adjust logic for reading hex constants to accord
with current wording of the C99 standard.  Previously, I thought hex
constants read by strtod and friends had to have either a decimal point
or an exponent field; p. 307 of the C99 standard states that both are
optional.  Because of the complexity of this reading, it is available
only in the variant of strtod that appears in gdtoa.tgz.

strtodg (gdtoa.tgz): New return value STRTOG_NaNbits (with
STRTOG_NoNumber renumbered).  Allow STRTOG_Neg bit in strtodg returns
for STRTOG_NaN and STRTOG_NaNbits.

gdtoa.tgz: Fix uninitialized variable bug in g_Qfmt.c's handling of NaNs.

Mon Nov 13 14:00:05 EST 2000
  gdtoa.tgz: strtodg:  fix a storage leak and an apparently rare infinite
loop with a boundary case of directed rounding.  Example input to
gdtoa/test/Qtest where the loop bug bit:
	r 3
	35184372088831.999999999999999999999999999999999999
This was revealed by testbase for quad precision Solaris arithmetic;
it did not show up in several other testbase configurations.

Wed Feb  7 12:56:11 EST 2001
  dtoa.c:  fix bug (possible infinite loop, e.g., with
2.47032822920623272e-324) introduced 20001113 in handling the special
case of a power of 2 to be rounded down one ulp.  Add test (required
by changes of 20001113) for the extra special case of 2^-1075 (half
the smallest denormal).
  gdtoa.tgz: corresponding adjustments to strtod.c and strtodg.c.

Tue Mar 13 00:46:09 EST 2001
  gdtoa.tgz: gdtoa/strtodg.c: fix bug in handling values exactly half
an ulp less than the smallest normal floating-point number;
gdtoa/*test.c: fix glitch in handling "n ..." lines (intended to
change "ndig").

Wed Mar  6 10:13:52 EST 2002
  gdtoa.tgz:  add gdtoa/test/strtodt.c and gdtoa/test/testnos3 to test
strtod on hard cases posted by Fred Tydeman to comp.arch.arithmetic on
26 Feb. 1996.  Add comment to gdtoa/README about strtod requiring true
IEEE arithmetic (with 53-bit rounding precision on 80x87 chips).
In gdtoa/test, automate selection of expected output files [xQ]*.out.

Wed Mar  5 10:35:41 EST 2003
  gdtoa.tgz:  fix a bug in strtod's handling of 0-valued 0x... "decimal"
strings.  A fault was possible.  Thanks to David Shultz for reporting
this bug.

Tue Mar 18 09:38:28 EST 2003
  gdtoa.tgz:  fix a glitch in strtodg.c with -DUSE_LOCALE; add #ifdef
USE_LOCALE lines to g__fmt.c (to affect binary --> decimal conversions
via the g*fmt routines), and add comments about -DUSE_LOCALE to README.
In short, compiling strtod.c, strtodg.c, and g__fmt.c with -DUSE_LOCALE
causes them to determine the decimal-point character from the current
locale.  (Otherwise it is '.'.)

Fri Mar 21 16:36:27 EST 2003
  gdtoa.tgz:  gethex.c: add #ifdef USE_LOCAL logic; strtod.c: fix a
glitch in handling 0x... input (the return from gethex was ignored).

Wed Mar 26 15:35:10 EST 2003
  gdtoa.tgz:  gethex.c:  pedantic (and normally invisible) change:
use unsigned char for decimalpoint variable (under -DUSE_LOCALE).

Sat Jan 17 23:58:52 MST 2004
  gdtoa.tgz:  gethex.c:  supply missing parens in test for whether a
denormal result should be zero, correct logic for rounding up when the
result is denormal, and when returning zero or Infinity, set *bp = 0;
strtod.c:  switch on gethex(...)  & STRTOG_Retmask rather than just on
gethex(), and only copybits(..., bb) when bb is nonzero.  This
mattered for underflows and overflows in 0x notation.

Thu Mar 25 22:34:56 MST 2004
 dtoa.c and gdtoa.c/misc.c:  change "(!x & 1)" to "(!x)" to avoid
confusion by human readers -- the object code is unaffected (with
reasonable compilers).

Mon Apr 12 00:44:22 MDT 2004
 dtoa.c and gdtoa.tar.gz:  update contact info. for dmg and correct
page numbers in comment on Steele & White (1990).
 gdtoa.tgz:  add strtodnrp.c for a variant of strtod that is slower
but does not require 53-bit rounding precision on Intel IA32 systems.

Tue Apr 13 00:28:14 MDT 2004
 gdtoa.tgz: strtod.c: fix glitch when both INFNAN_CHECK and No_Hex_NaN
are #defined.  Thanks to David Mendenhall for pointing this bug out.

Wed Jan  5 22:39:17 MST 2005
  gdtoa.tgz:
    gethex.c:  fix the bug reported by Stefan Farfeleder of ignoring a
binary-exponent-part if the converted number is zero.
    strto[pr]x.c: fix bug reported by Stefan Farfeleder in setting the
exponent of denormals (which should be 0, not 1).
    g_xfmt.c: fix a corresponding bug with denormals.
    strtodg.c: fix a bug under IBM (base 16) arithemtic reported
by Greg Alexander:  a correction to the binary exponent for changes to
the exponent of a native double value for avoiding overflow had to be
multiplied by 4 ("e2 <<= 2;").
    Various files: minor tweaks for portability.

Sat Jan 15 15:36:03 MST 2005
  gdtoa.tgz: gethex.c:  fix a glitch introduced last week (and reported
by Stefan Farfelder) with 0x forms with no nonzero digits before the "."
character, e.g., 0x.1 (which was rendered as 0 rather than .0625).
  gdtoa.tgz: many files: add automatic computation of gd_qnan.h for
giving the system-dependent format of a quiet NaN (the one generated
for Infinity - Infinity).  Tweak test/makefile so differences in the
spelling of Infinity ("INF" or "Inf" on some systems) do not matter.
Fix bug in strtod.c and strtodg.c under which, e.g., -.nan was read
as NaN rather than unacceptable input (causing return 0).  Adjust
comments in README about nan(...).  Fix glitch in test/dt.c.

Sun Jan 16 18:22:13 MST 2005
  gdtoa.tgz: strtodg.c: fix long-standing bug in handling input
that rounds up to 2^nbits, e.g., strtof("16777215.5").  Thanks to
Edward Moy for reporting this problem.
  gdtoa.tgz: Fix some bugs with -DJust_16.

Thu Sep 22 22:40:16 MDT 2005
gdtoa.tgz:
  strtod.c: unless prevented by -DNO_FENV_H, include C99's fenv.h
and with hex input, get the current rounding mode from fegetround().
With decimal input, strtod honors the rounding mode automatically.
Thanks to David Schultz (das at FreeBSD dot ORG) for pointing
  strtodg.c: fix a bug with handling numbers very near the largest
possible one, which were sometimes incorrectly converted to Infinity.
Thanks to Edward Moy (emoy at apple dot com) for pointing this out.
  g_Qfmt.c: change strcpy to strcp.  Thanks to J. T. Conklin
(jtc at acorntoolworks dot com) for pointing this out.
  test/xtest.c:  fix some subscript bugs.
  test/x.ou0, test/x.ou1, test/xL.: update in response to the above fix to
test/xtest.c.
  test/makefile:  add -lm to some link lines (needed for fegetround).

Sun Jan 21 20:26:44 MST 2007
gdtoa.tgz:
  strtodg.c:  fix a botch in the test of whether to increase rvbits
before terminating the big for(;;) loop with dsign true:  change
	if (hi0bits(rvb->x[(rvb->wds - 1) >> kshift])
			!= j)
		rvbits++;
to
	if (hi0bits(rvb->x[rvb->wds - 1]) != j)
		rvbits++;
Example of input where this bug bit:  1.9e27.  Thanks to Edward Moy
<emoy@apple.com> for providing this example.  Also, simplify the
preceding computation of j.
  test/README:  add comment that strtodt needs to operate with 53-bit
rounding precision on Intel x86 systems, and add a pointer to Paxson's
paper.

Sat Mar 15 11:44:31 MDT 2008
  dtoa.c and gdtoa.tgz:  with -DINFNAN_CHECK and without
-DGDOTA_NON_PEDANTIC_NANCHECK, conform to the ill-advised prescription
in the C99 standard of consuming (...)  in "nan(...)"  even when ...
is not of the expected form.  Allow an optional 0x or 0X to precede
the string of hex digits in the expected form of ... .
  gdtoa.tgz: gethex.c: have, e.g., strtod("0xyz",&se) set se to "xyz".
Previously it was incorrectly set to "0xyz".

Thu Aug 28 22:37:35 MDT 2008
  dtoa.c and gdtoa.tgz:  Fix a bug in strtod when compiled with
-DHonor_FLT_ROUNDS:  in rounding modes other than "to nearest",
strtod looped on input larger than and within a factor of 2 of
the largest finite floating-point number.  Since FLT_ROUNDS is buggy
on some (Linux) systems in that it does not reflect calls on
fesetround(), when Honor_FLT_ROUNDS is #defined, get the curren
rounding mode from fegetround() rather than FLT_ROUNDS, unless
Trust_FLT_ROUNDS is also #defined.
  gdtoa/test/getround.c in gdtoa.tgz: simply report the current
rounding mode when the input line is "r" by itself.  (Previously it
did so, but also complained of invalid input.)
  gdtoa/gethex.c: fix an off-by-one bug in a rounding test; detect and
deal with huge exponents (positive or negative).  This affected the
reading of hexadecimal floating-point values (0x...).  Also set errno
to ERANGE on out-of-range values (unless compiled with -DNO_ERRNO).
  gdtoa/strtod.c: adjust scaling of tinytens[4] (as in dtoa.c) to
avoid double rounding when dealing with numbers near the bottom of
the exponent range.

Sat Aug 30 23:37:07 MDT 2008
  gdtoa/gethex.c: ensure *bp is set to something (NULL if nothing else).
  Bring gdtoa/xsum0.out and gdtoa/test/xsum0.out up to date.

Tue Sep  9 22:08:30 MDT 2008
  gdtoa/strto*.c and gdtoa/*fmt.c:  if compiled with -DUSE_LOCALE, use
the current locale's decimal point character string.
  gdtoa/gdtoa.c: trim trailing zeros in a missed case (e.g., ndigits = 6
on 1020302).
  dtoa.c and gdtoa/strtod.c: on systems with IEEE arithmetic (and without
NO_ERRNO being defined) set ERANGE for denormal values as well as real
underflows.
  gdtoa/strtodg.c:  fix an off-by-one bug in rounding to the largest
representable magnitude when nbits is a multiple of 32.
  gdtoa/*fmt.c and gdtoa/gdtoa.h:  bufsize changed from unsigned to size_t.
  gdtoaimp.h, *fmt.c:  change in calling sequence to internal g__fmt(),
which now explicitly checks bufsize.
  Relevant routines (see README) honor the current rounding mode if
compiled with -DHonor_FLT_ROUNDS on IEEE-arithmetic systems that provide
the C99 fegetround() function.
  gdtoa/test/getround.c can optionally be compiled with
-DHonor_FLT_ROUNDS and/or -DUSE_MY_LOCALE for manual testing of gdtoa.a
compiled with -DHonor_FLT_ROUNDS or -DUSE_LOCALE.

Fri Oct 10 20:07:15 MDT 2008
  gdtoa/gethex.c:  fix a bug reading hexadecimal floating-point values
starting with "0xd" for a nonzero digit d (such as "0x1.0002p3").  The
bug caused the values to be read as zero with endptr set incorrectly.

Tue Oct 28 00:14:08 MDT 2008
  gdtoa/strtod.c: fix a comment glitch (with commented {}).

Tue Nov 11 23:05:25 MST 2008
  gdtoa:  fix a glitch in the strto* routines when compiled with
-DUSE_LOCALE and the locale's decimal-point string is two or more
characters long.  Wrong conversions were then possible.

Fri Dec  5 18:20:36 MST 2008
  gdtoa.tgz: fix bugs with reading C99-style hexadecimal floating-point
values when compiled with -DPack_16; on IEEE-arithmetic systems, make
INFNAN_CHECK the default unless NO_INFNAN_CHECK is #defined.  (This is
consistent with dtoa.c, which has worked this way for a while.)
  dtoa.c:  add recognition of C99-style hexadecimal floating-point
values (unless compiled with NO_HEX_FP is #defined).

Thu Dec 11 23:10:23 MST 2008
  dtoa.c: omit an unused variable.

Fri Jan  2 22:45:33 MST 2009
  dtoa.c: tweak to banish some compiler warnings.

Sun Mar  1 20:57:22 MST 2009
  dtoa.c, gdtoa/{g__fmt.c, gethex.c, strtod.c, strtodg.c}: change malloc
to MALLOC.
  dtoa.c and gdtoa/gdtoaimp.h and gdtoa/misc.c:  reduce Kmax, and use
MALLOC and FREE or free for huge blocks, which are possible only in
pathological cases, such as dtoa calls in mode 3 with thousands of
digits requested, or strtod() calls with thousand of digits.  For the
latter case, I have an alternate approach that runs much faster
and uses less memory, but finding time to get it ready for distribution
may take a while.

Mon Mar 16 00:32:43 MDT 2009
  dtoa.c:  Fix a bug under -DUSE_LOCALE in handling "decimal point"
strings more than one character long.
  dtoa.c and gdtoa/misc.c:  Remove a buggy test activated with
-DDEBUG.
  dtoa.c and gdtoa/gdtoa.c: simplify logic for "4 leading 0 bits".
  dtoa.c:  Add logic (that can be disabled with -DNO_STRTOD_BIGCOMP
and that) to strtod for more efficiently handling a very long input
string.  It proceeds by initially truncating the input string, then if
necessary comparing the whole string with a decimal expansion to
decide close cases.  This logic is only used for input more than
STRTOD_DIGLIM digits long (default 40), and for now only applies to
IEEE arithmetic (for want of other kinds of platforms on which to run
tests).  This only appears worthwhile for absurdly long input strings,
so a corresponding update to gdtoa does not seem warranted.
  dtoa.c, gdtoa.tgz:  tweaks (mostly adding unnecessary parens) to
silence "gcc -Wall" warnings.  Aside from a couple of minor changes
to banish erroneous warnings about uninitialized variables, the tweaks
do not affect the generated object code.

Sat Apr 11 23:25:58 MDT 2009
  dtoa.c: fix glitch in compiling with -DNo_Hex_NaN and the bug of
accepting (e.g.) ".nan" or ".inf" as NaN or Infinity.
  gdtoa.tgz: tweaks to silence warnings from "gcc -Wstrict-aliasing=2";
update xsum0.out files.

Sun Apr 19 23:40:24 MDT 2009
  dtoa.c, gdtoa/misc.c:  do not attempt to allocate large memory blocks
from the private memory pool (which was an unlikely event, but a bug).
  gdtoa/strtopx.c, gdtoa/strtopxL.c, gdtoa/strtorx.c, gdtoa/strtorxL.c:
supply explicit bit for Infinity.  Note that the Q routines (which do
not supply this bit) are appropriate for Sparc quad precision (probably
known as long double with most current compilers).

Wed Dec  9 08:14:52 MST 2009
  gdtoa.tgz:  add gdtoa/printf.c* and modify makefile so "make Printf"
adds a printf to gdtoa.a (to be accessed with #include "stdio1.h" to
get gdtoa/stdio1.h, which you might install in some standard place).
On Intel/AMD i386, x86_64, and Sparc systems, this adds formats %La,
%Le, %Lf and %Lg to handle long double.  On x86_64 systems, it also
adds %Lqa, %Lqe, %Lqf and %Lqg to handle 128-bit bit types (called
__float128 by gcc and _Quad by the Intel compiler).  In gdtoa/test,
"make pf_test" tests this printf (provided the system is an i386,
x86_64, or Sparc system).  On x86_64 systems, "make pf_testLq" tests
the %Lq...  formats (briefly).

Mon Jan 11 22:25:17 MST 2010
  dtoa.c: fix a minor performance bug and, under compilation with -DDEBUG,
an erroneous error message "oversize b in quorem" in strtod's processing
of some input that underflows to zero.  Also fix a bug in bigcomp()'s
handling of numbers that will scale to denormal values.  The increments
that bigcomp applied were ignoring the effects of denormalization.

Sat Jan 23 00:25:54 MST 2010
  dtoa.c:  Fix some glitches in recently introduced changes meant to
speed up returns in pedantic cases.  In quorem, adjust #ifdef DEBUG
stuff so it does not complain when bigcomp() calls quorem on input
near the smallest representable number and rounding up by a bit causes
a quorem return > 9 (which in this case is not a bug).  Fix a memory
leak in the unlikely case of overflow only being detected after some
high-precision integer computations.  Fix an off-by-one bug in
handling a large number of digits with a few nonzero digits, followed
by many zeros, and then some nonzero digits.  (This does not happen
with sensible input.)  Fix an off-by-one bug in a recently introduced
quick test for underflow (i.e., zero result) on input at the bottom of
the exponent range.  Thanks to Mark Dickinson for pointing these bugs
out.

  dtoa.c and gdtoa/strtod.c:  Fix an obscure bug in strtod's handling
of some inputs of many digits at the bottom of the exponent range:
results were sometimes off by a bit when gdtoa/strtod.c or dtoa.c was
compiled without -DNO_IEEE_SCALE and, for dtoa.c, when compiled with
-DNO_STRTOD_BIGCOMP.

  gdtoa/test/testnos3: add some examples that went wrong before
the present changes.

Sat Jan 23 23:29:02 MST 2010
  dtoa.c: more tweaks relevant only to absurd input.

Tue Feb  2 23:05:34 MST 2010
  dtoa.c: add test for setting errno = ERANGE when input of many digits
is rounded to Infinity or underflows to zero.  Fix a memory leak in
such instances.
  gdtoa/strtod.c: make some corresponding changes.

Wed Jul  7 09:25:46 MDT 2010
  dtoa.c:  adjust to use bigcomp when necessary when compiled with
-DHonor_FLT_ROUNDS (and without -DNO_STRTOD_BIGCOMP), and the rounding
mode is torwards +Infinity.  An input (supplied by Rick Regan
<exploringbinary@gmail.com>) where this matters is
1.100000000000000088817841970012523233890533447265626
  gdtoa/strtod.c:  fix errors (introduced 20090411) when compiled
with -DHonor_FLT_ROUNDS.

Wed Sep 15 09:00:26 MDT 2010
  dtoa.c, gdtoa/dtoa.c, gdtoa/gdtoa.c:  fix bugs with -DROUND_BIASED
pointed out by Jay Foad.

Mon Sep 27 13:43:30 MDT 2010
  gdtoa/gdtoa.c: fix a glitch (not revealed by compilation) in the
changes of 15 Sept. 2010.

Fri Nov  5 13:02:41 MDT 2010
  dtoa.c:  fix a bug related to bigcomp:  decimal strings with all
zeros before the decimal point more than 40 significant digits that
required use of bigcomp might be converted very incorrectly.
Example: .010000000000000000057612911342378542997169 .
Thanks to Rick Regan <exploringbinary@gmail.com> for reporting the
symptoms and providing an example.

20110304:
  dtoa.c, gdtoa/gdtoaimp.h, gdtoa/strtod.c:  if
ROUND_BIASED_without_Round_Up is #defined, assume ROUND_BIASED and
omit the quick computation that would use ordinary arithmetic to
compute the correctly rounded result with one rounding error.  If you
want biased rounding with IEEE-style format "double" and will operate
with rounding toward +Infinity, it suffices to #define ROUND_BIASED
(and thus retain the quick computation when it is appropriate).
  gdtoa/gdtoa.h: change default Long from long to int (with the goal
of portability when compiling without -DLong=... specified).  On some
64-bit systems, long is a 64-bit type; we need a 32-bit type here.
  dtoa.c, gdtoa/gdtoa.c: fix a glith with ndigits with mode = 4 at
the bottom of the exponent range, e.g., 1e-323.

20110321:
  dtoa.c, gdtoaimp.h: add comment that defining No_leftright will
sometimes cause dtoa (or gdtoa) modes 4 and 5 to be treated the
same as modes 2 and 3, respectively (and thus not work as intended).

20110428:
  dtoa.c: fix a glitch under compilation with Honor_FLT_ROUNDS and
NO_HEX_FP #defined.

20111102:
  gdota.tgz: add field int_max to struct FPI and adjust gdtoa.c and
*fmt.c so gdtoa.c tests against fpi->int_max rather than Int_max.
This only affects some conversions by g_ffmt.c, which in some cases
produced too many digits, such as the case added to the end of
tests/testnos.

20120417
  dtoa.c:  augment a test in bigcomp() to correctly compare a long
input string of digits with a computed string after all of the
input string has otherwise been processed.  This matters only
rarely; a string for which it matters (reported by Herman Geza) is
1.8254370818746402660437411213933955878019332885742187 .

20120423
  dtoa.c:  add a comment that gcc's -ffast-math flag disables IEEE
arithmetic (whence dtoa and strtod may not function right if you
use this flag or related flags).

20121220
  dtoa.c and gdtoa.tgz:  to avoid a possible one-time race when
Infinity or NaN appear in decimal->binary conversions done in parallel
threads, replace hexdig_init() with static initialization.

20121223
  gdtoa.tgz:  add variants g_ddfmt_p(), g_dfmt_p(), g_ffmt_p(),
g_Qfmt_p(), g_xfmt_p(), and g_xLfmt_p() of g_ddfmt(), g_dfmt(),
g_ffmt(), g_Qfmt(), g_xfmt(), and g_xLfmt(), respectively, that
have an additional final int argument that governs details of
the rendering of Infinity and NaN.  For more details, see the
updated README.

20130129
  dtoa.c:  fix an obscure memory leak in gethex().  (See the
new ret_tinyf label.)  Thanks to avernar@gmail.com for pointing
this issue out.

20131122
  dtoa.c:  fix a possible glitch with strtod in deciding whether a
decimal value less in absolute value than the smallest denormal should
be rounded to zero.  (The fix is to force use of bigcomp() when at the
bottom of the exponent range and we otherwise would have returned 0.)
Thanks to Rick Regan <exploringbinary@gmail.com> for sending an
example that illustrated the bug.

20131209
  dtoa.c, gdtoa.tgz: when strtod computes its starting approximation,
allow z to involve one more digit for IEEE arithmetic and two more
digits for IBM-mainframe and VAX arithmetics.  Thanks to Walter Qian
(water.qian@gmail.com) for suggesting this change, which makes some
conversions faster.

20150112
  dtoa.c: "ifdef KR_headers" stuff removed; modifications to
"#ifdef MULTIPLE_THREADS":  function
	void set_max_dtoa_threads(unsigned int n);
is provided and
	unsigned int dtoa_get_threadno(void);
is expected to be available to return the current thread number.
After set_max_dtoa_threads(n), calls on strtod and dtoa by
threads with thread numbers < n avoid calls on ACQUIRE_DTOA_LOCK
and FREE_DTOA_LOCK by keeping thread-specific copies of entities
for which changes by other threads would otherwise cause trouble.
See the updated comments in dtoa.c about MULTIPLE_THREADS.

20150119
  dtoa.c:  fix a glitch (possible fault) in the updates of 20150112.

20151020
  dtoa.c:  add a test for dtoa() to return "1" under mode 4 when
converting some very small powers of 10, such as 1e-322 with
ndigits = 4 and 1e-319 with ndigits = 7 (examples provided by
jay.foad@gmail.com).

20160219
  dtoa.c: fix glitches when compiled with both MULTIPLE_THREADS and
Honor_FLT_ROUNDS #defined (a senseless combination).
  gdtoa.tgz: make changes similar to the "#ifdef MULTIPLE_THREADS"
changes to dtoa.c of 20150112.  Adjust gdtoa(...,mode,...) to assume
"round near" when mode is 0 or 1.  Make various tweaks to banish
(useless) warnings from "gcc -Wall -Wextra".  Thanks to Jarkko
Hietaniemi <jhi@iki.fi> for advocating the latter exercise (and
correcting a typo in README).

20160220
  gdtoa.tgz: in gdtoa/test, adjust dItest.c, ddtest.c, dtest,c, ftest.c
to banish pedantic warnings that appear with "gcc -O2 -Wall -Wextra"
but not with "gcc -O -Wall -Wextra".

20160307
  dtoa.c:  fix glitches with floating-point values in hexadecimal
notation:  some values that should overflow to (appropriately signed)
Infinity, such as 0x1p1025, were mishandled, and values greater than
0x1p-1075 and less than 0x1.0000000000001p-1075 where treated as zero
rather than the smallest denormal number.
  gdtoa.tgz:  fix a bug with hexadecimal input greater than the
smallest denormal and less than the smallest denormal times the
smallest number greater than one.  In round-to-nearest values, such
values should round to the smallest denormal rather than to zero.
Thanks to Albert Chan <albertmcchan@yahoo.com> for bug reports.

20160325
  dtoa.c:  fix a bug whereby dtoa(...,mode,...) with, e.g., mode = 2 or
3 could return a string with trailing zeros, contrary to specification.
An example provided by Albert Chan:  dtoa(81320560005., 2, 10,...).
  gdtoa.tgz: fix the analogous bug in gdtoa/dtoa.c and gdtoa/gdtoa.c
and apply the bug fix of 20151020 to gdtoa/dtoa.c.


20160429
  dtoa.c:  new variant dtoa_r() of dtoa(), with new trailing arguments
char *s0 and size_t s0len.  When s0len is large enough to accommodate
the desired return value (including a trailing NULL byte) and possibly
some intermediate trailing zeros, dtoa_r() returns s0.  Otherwise
dtoa_r() returns NULL, and if the call had the form
        dtoa_r(..., rve, s0, s0len)
with rve not NULL, then a subsequent call with s0len greater than
*rve - (char*)0 should succeed in returning s0.
  On systems with 64-bit integer arithmetic and IEEE arithmetic, new
logic in dtoa.c sometimes makes strtod(), dtoa(), and dtoa_r() faster
than before -- an order of magnitude or more faster in some cases.
The new logic can be suppressed by compilation with -DNO_BF96 or
-DNO_LONG_LONG.  Thanks to Albert Chan <albertmcchan@yahoo.com> for
prompting me to revisit use of 64-bit integer arithmetic here.
  dtoa.c, gdtoa.tgz (file dtoa.c):  Fix a bug with dtoa mode 0 when
Honor_FLT_ROUNDS is defined:  with some inputs and nondefault rounding
modes (e.g., 1.23 with round toward zero), the returned string was off
by one.  When the new 64-bit integer logic is used, the test in
question is very unlikely to be used.  This is another bug reported by
Albert Chan.

20160502
  dtoa.c:  add "ll" suffix to long long decimal constants (array pfive).

20160503
  dtoa.c:  fix some glitches in obscure cases; remove
"#ifdef DELAY_URES" logic, which gave wrong results in rare cases.

20160504
  dtoa.c:  fix more rarely seen bugs with dtoa()'s rounding of final
digits.

20160505
  dtoa.c:  fix some glitches in strtod() when Honor_FLT_ROUNDS is
defined:  zero was returned for some decimal values that should have
been rounded to +- the smallest denormal, and +-Infinity was returned
for some hexadecimal strings with huge values that should have been
rounded to +- the largest finite value.

20160506
  gdtoa.tgz: analogous bug fixes to those of 20160505.
  dtoa.c: fix glitches with some denormals and some directed roundings.

20160507
  dtoa.c: fix strtod overflow tests.

20160508
  dtoa.c: strtod: fix rounding bugs with some denormals and with some
strings of more than 19 digits; dtoa: fix rarely seen off-by-one bug
in the final digit with modes 2 and 3.

20160510
  dtoa.c: strtod: fix a glitch that caused some values less than the
half smallest denormal not to round to zero, and adjust a test that
in rare cases incorrectly avoided a longer computation; dtoa: fix a
glitch with -DNO_BF96 -DHonor_FLT_ROUNDS.

20160513
  dtoa.c: tighten a test that occasionally falsely indicated
sufficiency of an approximate computation.  In some difficult but
unlikely cases, the value returned by strtod was off by one bit.
Fix some tests used with directed roundings that sometimes caused
(and dota_r) modes 2 and 3 to return off-by-one values.  Thanks
to Albert Chan for providing examples.

20160514
  dtoa.c:  strtod:  tighten a variant, missed yesterday, of a test
that occasionally falsely indicated sufficiency of an approximate
computation.  Also apply to denormals a test hitherto only applied to
normal numbers for sufficiency of an approximate computation.

20160516
  dtoa.c (versions >= 20160429, without -DNO_BF96):  fix more glitches
with directed roundings.

20160518
  dtoa.c: strtod (without -DNO_BF96): minor efficiency improvement on some
inputs with more than 19 significant digits.

20160521
  dtoa.c (without -DNO_BF96):  strtod:  fix glitches with directed
rounding of denormals; dtoa and strtod:  fix some bugs with
-DSET_INEXACT.

20160523
  dtoa.c (without -DNO_BF96):  strtod:  fix a bug in rounding some
denormal values; dtoa:  fix a potential glitch with -DSET_INEXACT.
Thanks to Albert Chan for providing examples of the strtod bug.

20160607
  dtoa.c (without -DNO_BF96):  strtod:  fix a rarely seen 1-bit error
converting strings of more than 19 digits.  Thanks to Albert Chan for
examples.

20160611
  dtoa.c (without -DNO_BF96):  minor performance improvement on some
strtod inputs, using truncated rather than rounded 96-bit approximate
powers of 10.  Thanks to Albert Chan for suggesting use of truncated
rather than rounded constants.

20161024
  dtoa.c: tweak for C++ compilation with MALLOC or REALLOC #defined.

20161107
  dtoa.c: make errno assignments via a macro, Set_errno(x), that by
default is "errno = x", but can be set to something else in a local
errno.h, such as "#define Set_errno(x) _set_errno(x)", which works
with some compilers on Microsoft systems, but not others, and is
not known to be necessary with any of those compilers.  Note that
a local errno.h (included in dtoa.c via #include "errno.h") probably
should #include <errno.h>.

20180411
  dtoa.c: fix glitches (compile errors) with compilation under
-DSudden_Underflow .

20180730
  strtodg.c in gdtoa.c:  fix a glitch, introduced 20160506, with some
return values of +-Infinity:  the STRTOG_Overflow bit was not set.
  strtoIg.c in gdtoa.c: undo some changes, probably of 20160506, that
caused trouble with subnormal values, such as 1.23e-320, on which
strtoId (which calls strtoIg) returned two equal values, rather than
values differing by one in the least-significant bit.
  test/dt.c:  when compiled with -DUSE_fpinit, initially invoke
fpinit_ASL() (found in the AMPL/solver interface library) to set Intel
80x87-style floating point arithmetic to 53-bit rounding precision.
  test/dtest.c: change output to say "strtord consumes" rather than
"strtod consumes".
  test/d.out: update to reflect the above change to dtest.c.

20230515
  qnan.c in gdtoa.tgz: fix a bug that bit on little-endian machines:
in the two printf statements involving subscripts _0 and _1, the
subscripts should be 0 and 1.

20230822
  dtoa.c: banish two pedantic warnings when compiled with NO_LONG_LONG
#defined.  (No change to the resulting object code.)

20231101
  dtoa.c: change
	#ifdef Check_FLT_ROUNDS
		try_quick = Rounding == 1;
	#endif
to
	#ifdef Check_FLT_ROUNDS
		try_quick = Rounding == 1;
	#else
		try_quick = 1;
	#endif
so try_quick is initialized when both USE_BF96 and SET_INEXACT are
undefined.  Thanks to Peter Hoddie <peter@moddable.com> for pointing
out the need for such a change.

20231209
  Tweak to prevent spurious diagnostics, e.g., by
UndefinedBehaviorSanitizer:  change
	s1 = s;
	while((c = *++s) >= '0' && c <= '9')
		L = 10*L + c - '0';
	if (s - s1 > 8 || L > 19999)
to
	while((c = *++s) >= '0' && c <= '9') {
		if (L <= 19999)
			L = 10*L + c - '0';
		}
	if (L > 19999)
in dtoa.c, and in strtod.c and strtodg.c in gdtoa.tgz.  Thanks to
Peter Hoddie <peter@moddable.com> for suggesting this change.

20240130
  dtoa.c and gdtoa.tgz:  Fix bug in strtod's handling of
0x1.fffffffffffffp-1023 which gave 0 rather than the expected
0x1p-1022.  Thanks to Rick Regan (exploringbinary@gmail.com) for this
example.

20240202
  dtoa.c and gdtoa.tgz:  another try: fix bug in strtod's handling of
0x1.fffffffffffffp-1023 which gave 0 rather than the expected
0x1p-1022.  The previous fix worked on that input, but broke some
other (denormal) inputs.  Thanks again to Rick Regan
(exploringbinary@gmail.com) for providing examples.

20240206
  dtoa.c and gdtoa.tgz:  yet another try:  fix bugs in strtod's
handling of hex input that should give 0x1p-1022.  The previous fixes
sometimes worked, but broke some other (denormal) inputs.  Thanks
again to Rick Regan (exploringbinary@gmail.com) for providing
examples.

20240207
  dtoa.c and gdtoa.tgz:  yesterday's fix to bugs in strtod's handling
of hex input that should give 0x1p-1022 broke rounding in other cases
of denormal input (due to a missing pair of parentheses).  Thanks
again to Rick Regan (exploringbinary@gmail.com) for providing more
examples.

20240213
  dtoa.c and gdtoa.tgz:  fixes to some other cases of hexadecimal
input; adjust recent change for compilation with -DHonor_FLT_ROUNDS
-DTrust_FLT_ROUNDS.  Thannks to Rick Regan (exploringbinary@gmail.com)
for providing more examples.

20240215
  dtoa.c and gdtoa.tgz:  fix a glitch that only matters when multiple
threads are in use.

20240221
  dtoa.c and gdtoa.tgz:  fix another glitch with nondefault rounding
modes and hexadecimal inputs near the smallest representable normal
number.

20240224
  dtoa.c and gdtoa.tgz:  fix yet another glitch with nondefault
rounding modes and hexadecimal inputs near the smallest representable
normal number.  Thanks again to Rick Regan (exploringbinary@gmail.com)
for providing another example.

20240715
  dtoa.c: Fix a bug that caused dtoa to render 6.9999999999999996e-161
as 7e-161.  The fix was removal of a couple of lines, changing
	if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp) {
		if ((ures + rb) << (1 - eulp) < ulp)
			goto Roundup;
		goto Fast_failed1;
		}
to

	if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp)
		goto Fast_failed1;
  Fix a bug that caused dtoa to render
.000491831912544516 as
.0004918319125445159 .  The fix was to add another test, changing
	if (ures < res
	|| (ures == res && dig & 1))
		goto Roundup;
to
	if (ures < res
	|| (ures == res && dig & 1)
	|| (dig == 9 && 2*ures <= ulp))
		goto Roundup;

20240718
  dtoa.c:  Tweak the change of 20240715 to fix a bug that caused dtoa
to render 6.9999999999999996e-161 as 7e-161 to allow more efficiency
in some cases:  change
	if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp)
		goto Fast_failed1;
to
	if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp) {
		if ((ures + rb) << (2 - eulp) < ulp)
			goto Roundup;
		goto Fast_failed1;
		}