/****************************************************************
?*
?*?The?author?of?this?software?is?David?M.?Gay.
?*
?*?Copyright?（c）?1991?2000?2001?by?Lucent?Technologies.
?*
?*?Permission?to?use?copy?modify?and?distribute?this?software?for?any
?*?purpose?without?fee?is?hereby?granted?provided?that?this?entire?notice
?*?is?included?in?all?copies?of?any?software?which?is?or?includes?a?copy
?*?or?modification?of?this?software?and?in?all?copies?of?the?supporting
?*?documentation?for?such?software.
?*
?*?THIS?SOFTWARE?IS?BEING?PROVIDED?“AS?IS“?WITHOUT?ANY?EXPRESS?OR?IMPLIED
?*?WARRANTY.??IN?PARTICULAR?NEITHER?THE?AUTHOR?NOR?LUCENT?MAKES?ANY
?*?REPRESENTATION?OR?WARRANTY?OF?ANY?KIND?CONCERNING?THE?MERCHANTABILITY
?*?OF?THIS?SOFTWARE?OR?ITS?FITNESS?FOR?ANY?PARTICULAR?PURPOSE.
?*
?***************************************************************/

/*?Please?send?bug?reports?to?David?M.?Gay?（dmg?at?acm?dot?org
?*?with?“?at?“?changed?at?“@“?and?“?dot?“?changed?to?“.“）.	*/

/*?On?a?machine?with?IEEE?extended-precision?registers?it?is
?*?necessary?to?specify?double-precision?（53-bit）?rounding?precision
?*?before?invoking?strtod?or?dtoa.??If?the?machine?uses?（the?equivalent
?*?of）?Intel?80x87?arithmetic?the?call
?*	_control87（PC_53?MCW_PC）;
?*?does?this?with?many?compilers.??Whether?this?or?another?call?is
?*?appropriate?depends?on?the?compiler;?for?this?to?work?it?may?be
?*?necessary?to?#include?“float.h“?or?another?system-dependent?header
?*?file.
?*/

/*?strtod?for?IEEE-?VAX-?and?IBM-arithmetic?machines.
?*
?*?This?strtod?returns?a?nearest?machine?number?to?the?input?decimal
?*?string?（or?sets?errno?to?ERANGE）.??With?IEEE?arithmetic?ties?are
?*?broken?by?the?IEEE?round-even?rule.??Otherwise?ties?are?broken?by
?*?biased?rounding?（add?half?and?chop）.
?*
?*?Inspired?loosely?by?William?D.?Clinger‘s?paper?“How?to?Read?Floating
?*?Point?Numbers?Accurately“?[Proc.?ACM?SIGPLAN?‘90?pp.?92-101].
?*
?*?Modifications:
?*
?*	1.?We?only?require?IEEE?IBM?or?VAX?double-precision
?*		arithmetic?（not?IEEE?double-extended）.
?*	2.?We?get?by?with?floating-point?arithmetic?in?a?case?that
?*		Clinger?missed?--?when?we‘re?computing?d?*?10^n
?*		for?a?small?integer?d?and?the?integer?n?is?not?too
?*		much?larger?than?22?（the?maximum?integer?k?for?which
?*		we?can?represent?10^k?exactly）?we?may?be?able?to
?*		compute?（d*10^k）?*?10^（e-k）?with?just?one?roundoff.
?*	3.?Rather?than?a?bit-at-a-time?adjustment?of?the?binary
?*		result?in?the?hard?case?we?use?floating-point
?*		arithmetic?to?determine?the?adjustment?to?within
?*		one?bit;?only?in?really?hard?cases?do?we?need?to
?*		compute?a?second?residual.
?*	4.?Because?of?3.?we?don‘t?need?a?large?table?of?powers?of?10
?*		for?ten-to-e?（just?some?small?tables?e.g.?of?10^k
?*		for?0?<=?k?<=?22）.
?*/

/*
?*?#define?IEEE_8087?for?IEEE-arithmetic?machines?where?the?least
?*	significant?byte?has?the?lowest?address.
?*?#define?IEEE_MC68k?for?IEEE-arithmetic?machines?where?the?most
?*	significant?byte?has?the?lowest?ad