From 49693da854388487d3d5e248a4d900dfe4b2afd7 Mon Sep 17 00:00:00 2001 From: cgd Date: Fri, 9 Jul 1993 09:40:07 +0000 Subject: [PATCH] update for better FP routines, from AT&T & elsewhere --- lib/libc/stdio/scanf.3 | 14 +- lib/libc/stdio/vfprintf.c | 631 +++------ lib/libc/stdio/vfscanf.c | 12 +- lib/libc/stdlib/Makefile.inc | 6 +- lib/libc/stdlib/atof.c | 2 +- lib/libc/stdlib/strtod.c | 2410 ++++++++++++++++++++++++++++++++++ 6 files changed, 2633 insertions(+), 442 deletions(-) create mode 100644 lib/libc/stdlib/strtod.c diff --git a/lib/libc/stdio/scanf.3 b/lib/libc/stdio/scanf.3 index ff88e476b00a..4eb387724748 100644 --- a/lib/libc/stdio/scanf.3 +++ b/lib/libc/stdio/scanf.3 @@ -33,9 +33,9 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)scanf.3 6.11 (Berkeley) 6/29/91 +.\" @(#)scanf.3 6.14 (Berkeley) 1/8/93 .\" -.Dd June 29, 1991 +.Dd January 8, 1993 .Dt SCANF 3 .Os .Sh NAME @@ -393,6 +393,7 @@ the number of conversions which were successfully completed is returned. .Sh SEE ALSO .Xr strtol 3 , .Xr strtoul 3 , +.Xr strtod 3 , .Xr getc 3 , .Xr printf 3 .Sh STANDARDS @@ -418,3 +419,12 @@ and conversions is unfortunate. .Pp All of the backwards compatibility formats will be removed in the future. +.Pp +Numerical strings are truncated to 512 characters; for example, +.Cm %f +and +.Cm %d +are implicitly +.Cm %512f +and +.Cm %512d . diff --git a/lib/libc/stdio/vfprintf.c b/lib/libc/stdio/vfprintf.c index 587a2af3af29..8d064c696c2e 100644 --- a/lib/libc/stdio/vfprintf.c +++ b/lib/libc/stdio/vfprintf.c @@ -35,7 +35,7 @@ */ #if defined(LIBC_SCCS) && !defined(lint) -static char sccsid[] = "@(#)vfprintf.c 5.47 (Berkeley) 3/22/91"; +static char sccsid[] = "@(#)vfprintf.c 5.50 (Berkeley) 12/16/92"; #endif /* LIBC_SCCS and not lint */ /* @@ -45,100 +45,22 @@ static char sccsid[] = "@(#)vfprintf.c 5.47 (Berkeley) 3/22/91"; */ #include -#include + #include +#include #include + #if __STDC__ #include #else #include #endif + #include "local.h" #include "fvwrite.h" -/* - * Define FLOATING_POINT to get floating point. - * Define CSH to get a csh-specific version (grr). - */ -#ifndef CSH +/* Define FLOATING_POINT to get floating point. */ #define FLOATING_POINT -#endif - -/* end of configuration stuff */ - - -#ifdef CSH -/* - * C shell hacks. Ick, gag. - */ -#undef BUFSIZ -#include "sh.h" - -#if __STDC__ -int -printf(const char *fmt, ...) { - FILE f; - va_list ap; - int ret; - - va_start(ap, fmt); - f._flags = __SWR; - f._write = NULL; - ret = vfprintf(&f, fmt, ap); - va_end(ap); - return ret; -} -#else -int -printf(fmt, args) - char *fmt; -{ - FILE f; - - f._flags = __SWR; - f._write = NULL; - return (vfprintf(&f, fmt, &args)); -} -#endif - -int -__sprint(fp, uio) - FILE *fp; - register struct __suio *uio; -{ - register char *p; - register int n, ch, iovcnt; - register struct __siov *iov; - - /* must allow sprintf to work, might as well allow others too */ - if (fp->_write || fp->_flags & __SSTR) { - if (uio->uio_resid == 0) { - uio->uio_iovcnt = 0; - return (0); - } - n = __sfvwrite(fp, uio); - uio->uio_resid = 0; - uio->uio_iovcnt = 0; - return (n); - } - iov = uio->uio_iov; - for (iovcnt = uio->uio_iovcnt; --iovcnt >= 0; iov++) { - for (p = iov->iov_base, n = iov->iov_len; --n >= 0;) { -#ifdef CSHPUTCHAR - ch = *p++; - CSHPUTCHAR; /* this horrid macro uses `ch' */ -#else -#undef putchar - putchar(*p++); -#endif - } - } - uio->uio_resid = 0; - uio->uio_iovcnt = 0; - return (0); -} - -#else /* CSH */ /* * Flush out all the vectors defined by the given uio, @@ -196,16 +118,16 @@ __sbprintf(fp, fmt, ap) return (ret); } -#endif /* CSH */ - #ifdef FLOATING_POINT +#include #include "floatio.h" #define BUF (MAXEXP+MAXFRACT+1) /* + decimal point */ #define DEFPREC 6 -static int cvt(); +static char *cvt __P((double, int, int, char *, int *, int, int *)); +static int exponent __P((char *, int, int)); #else /* no FLOATING_POINT */ @@ -224,22 +146,20 @@ static int cvt(); /* * Flags used during conversion. */ -#define LONGINT 0x01 /* long integer */ -#define LONGDBL 0x02 /* long double; unimplemented */ -#define SHORTINT 0x04 /* short integer */ -#define ALT 0x08 /* alternate form */ -#define LADJUST 0x10 /* left adjustment */ -#define ZEROPAD 0x20 /* zero (as opposed to blank) pad */ -#define HEXPREFIX 0x40 /* add 0x or 0X prefix */ - +#define ALT 0x001 /* alternate form */ +#define HEXPREFIX 0x002 /* add 0x or 0X prefix */ +#define LADJUST 0x004 /* left adjustment */ +#define LONGDBL 0x008 /* long double; unimplemented */ +#define LONGINT 0x010 /* long integer */ +#define QUADINT 0x020 /* quad integer */ +#define SHORTINT 0x040 /* short integer */ +#define ZEROPAD 0x080 /* zero (as opposed to blank) pad */ +#define FPT 0x100 /* Floating point number */ int vfprintf(fp, fmt0, ap) FILE *fp; const char *fmt0; -#if tahoe - register /* technically illegal, since we do not know what type va_list is */ -#endif - _VA_LIST_ ap; + va_list ap; { register char *fmt; /* format string */ register int ch; /* character from fmt */ @@ -254,9 +174,18 @@ vfprintf(fp, fmt0, ap) #ifdef FLOATING_POINT char softsign; /* temporary negative sign for floats */ double _double; /* double precision arguments %[eEfgG] */ - int fpprec; /* `extra' floating precision in [eEfgG] */ + int expt; /* integer value of exponent */ + int expsize; /* character count for expstr */ + int ndig; /* actual number of digits returned by cvt */ + char expstr[7]; /* buffer for exponent string */ #endif - u_long _ulong; /* integer arguments %[diouxX] */ + +#ifdef __GNUC__ /* gcc has builtin quad type (long long) SOS */ +#define quad_t long long +#define u_quad_t unsigned long long +#endif + + u_quad_t _uquad; /* integer arguments %[diouxX] */ enum { OCT, DEC, HEX } base;/* base for [diouxX] conversion */ int dprec; /* a copy of prec if [diouxX], 0 otherwise */ int fieldsz; /* field size expanded by sign, etc */ @@ -270,9 +199,9 @@ vfprintf(fp, fmt0, ap) char ox[2]; /* space for 0x hex-prefix */ /* - * Choose PADSIZE to trade efficiency vs size. If larger - * printf fields occur frequently, increase PADSIZE (and make - * the initialisers below longer). + * Choose PADSIZE to trade efficiency vs. size. If larger printf + * fields occur frequently, increase PADSIZE and make the initialisers + * below longer. */ #define PADSIZE 16 /* pad chunk size */ static char blanks[PADSIZE] = @@ -315,15 +244,16 @@ vfprintf(fp, fmt0, ap) * argument extraction methods. */ #define SARG() \ - (flags&LONGINT ? va_arg(ap, long) : \ + (flags&QUADINT ? va_arg(ap, quad_t) : \ + flags&LONGINT ? va_arg(ap, long) : \ flags&SHORTINT ? (long)(short)va_arg(ap, int) : \ (long)va_arg(ap, int)) #define UARG() \ - (flags&LONGINT ? va_arg(ap, u_long) : \ + (flags&QUADINT ? va_arg(ap, u_quad_t) : \ + flags&LONGINT ? va_arg(ap, u_long) : \ flags&SHORTINT ? (u_long)(u_short)va_arg(ap, int) : \ (u_long)va_arg(ap, u_int)) -#ifndef CSH /* sorry, fprintf(read_only_file, "") returns EOF, not 0 */ if (cantwrite(fp)) return (EOF); @@ -332,7 +262,6 @@ vfprintf(fp, fmt0, ap) if ((fp->_flags & (__SNBF|__SWR|__SRW)) == (__SNBF|__SWR) && fp->_file >= 0) return (__sbprintf(fp, fmt0, ap)); -#endif /* CSH */ fmt = (char *)fmt0; uio.uio_iov = iovp = iov; @@ -356,9 +285,6 @@ vfprintf(fp, fmt0, ap) flags = 0; dprec = 0; -#ifdef FLOATING_POINT - fpprec = 0; -#endif width = 0; prec = -1; sign = '\0'; @@ -435,6 +361,9 @@ reswitch: switch (ch) { case 'l': flags |= LONGINT; goto rflag; + case 'q': + flags |= QUADINT; + goto rflag; case 'c': *(cp = buf) = va_arg(ap, int); size = 1; @@ -445,20 +374,28 @@ reswitch: switch (ch) { /*FALLTHROUGH*/ case 'd': case 'i': - _ulong = SARG(); - if ((long)_ulong < 0) { - _ulong = -_ulong; + _uquad = SARG(); + if ((quad_t)_uquad < 0) { + _uquad = -_uquad; sign = '-'; } base = DEC; goto number; #ifdef FLOATING_POINT - case 'e': + case 'e': /* anomalous precision */ case 'E': - case 'f': + prec = (prec == -1) ? + DEFPREC + 1 : prec + 1; + /* FALLTHROUGH */ + goto fp_begin; + case 'f': /* always print trailing zeroes */ + if (prec != 0) + flags |= ALT; case 'g': case 'G': - _double = va_arg(ap, double); + if (prec == -1) + prec = DEFPREC; +fp_begin: _double = va_arg(ap, double); /* do this before tricky precision changes */ if (isinf(_double)) { if (_double < 0) @@ -472,35 +409,44 @@ reswitch: switch (ch) { size = 3; break; } - /* - * don't do unrealistic precision; just pad it with - * zeroes later, so buffer size stays rational. - */ - if (prec > MAXFRACT) { - if (ch != 'g' && ch != 'G' || (flags&ALT)) - fpprec = prec - MAXFRACT; - prec = MAXFRACT; - } else if (prec == -1) - prec = DEFPREC; - /* - * cvt may have to round up before the "start" of - * its buffer, i.e. ``intf("%.2f", (double)9.999);''; - * if the first character is still NUL, it did. - * softsign avoids negative 0 if _double < 0 but - * no significant digits will be shown. - */ - cp = buf; - *cp = '\0'; - size = cvt(_double, prec, flags, &softsign, ch, - cp, buf + sizeof(buf)); + flags |= FPT; + cp = cvt(_double, prec, flags, &softsign, + &expt, ch, &ndig); + if (ch == 'g' || ch == 'G') { + if (expt <= -4 || expt > prec) + ch = (ch == 'g') ? 'e' : 'E'; + else + ch = 'g'; + } + if (ch <= 'e') { /* 'e' or 'E' fmt */ + --expt; + expsize = exponent(expstr, expt, ch); + size = expsize + ndig; + if (ndig > 1 || flags & ALT) + ++size; + } else if (ch == 'f') { /* f fmt */ + if (expt > 0) { + size = expt; + if (prec || flags & ALT) + size += prec + 1; + } else /* "0.X" */ + size = prec + 2; + } else if (expt >= ndig) { /* fixed g fmt */ + size = expt; + if (flags & ALT) + ++size; + } else + size = ndig + (expt > 0 ? + 1 : 2 - expt); + if (softsign) sign = '-'; - if (*cp == '\0') - cp++; break; #endif /* FLOATING_POINT */ case 'n': - if (flags & LONGINT) + if (flags & QUADINT) + *va_arg(ap, quad_t *) = ret; + else if (flags & LONGINT) *va_arg(ap, long *) = ret; else if (flags & SHORTINT) *va_arg(ap, short *) = ret; @@ -511,7 +457,7 @@ reswitch: switch (ch) { flags |= LONGINT; /*FALLTHROUGH*/ case 'o': - _ulong = UARG(); + _uquad = UARG(); base = OCT; goto nosign; case 'p': @@ -523,7 +469,7 @@ reswitch: switch (ch) { * -- ANSI X3J11 */ /* NOSTRICT */ - _ulong = (u_long)va_arg(ap, void *); + _uquad = (u_quad_t)va_arg(ap, void *); base = HEX; xdigs = "0123456789abcdef"; flags |= HEXPREFIX; @@ -554,7 +500,7 @@ reswitch: switch (ch) { flags |= LONGINT; /*FALLTHROUGH*/ case 'u': - _ulong = UARG(); + _uquad = UARG(); base = DEC; goto nosign; case 'X': @@ -562,10 +508,10 @@ reswitch: switch (ch) { goto hex; case 'x': xdigs = "0123456789abcdef"; -hex: _ulong = UARG(); +hex: _uquad = UARG(); base = HEX; /* leading 0x/X only if non-zero */ - if (flags & ALT && _ulong != 0) + if (flags & ALT && _uquad != 0) flags |= HEXPREFIX; /* unsigned conversions */ @@ -584,18 +530,18 @@ number: if ((dprec = prec) >= 0) * -- ANSI X3J11 */ cp = buf + BUF; - if (_ulong != 0 || prec != 0) { + if (_uquad != 0 || prec != 0) { /* - * unsigned mod is hard, and unsigned mod + * Unsigned mod is hard, and unsigned mod * by a constant is easier than that by * a variable; hence this switch. */ switch (base) { case OCT: do { - *--cp = to_char(_ulong & 7); - _ulong >>= 3; - } while (_ulong); + *--cp = to_char(_uquad & 7); + _uquad >>= 3; + } while (_uquad); /* handle octal leading 0 */ if (flags & ALT && *cp != '0') *--cp = '0'; @@ -603,18 +549,18 @@ number: if ((dprec = prec) >= 0) case DEC: /* many numbers are 1 digit */ - while (_ulong >= 10) { - *--cp = to_char(_ulong % 10); - _ulong /= 10; + while (_uquad >= 10) { + *--cp = to_char(_uquad % 10); + _uquad /= 10; } - *--cp = to_char(_ulong); + *--cp = to_char(_uquad); break; case HEX: do { - *--cp = xdigs[_ulong & 15]; - _ulong >>= 4; - } while (_ulong); + *--cp = xdigs[_uquad & 15]; + _uquad >>= 4; + } while (_uquad); break; default: @@ -638,28 +584,20 @@ number: if ((dprec = prec) >= 0) } /* - * All reasonable formats wind up here. At this point, - * `cp' points to a string which (if not flags&LADJUST) - * should be padded out to `width' places. If - * flags&ZEROPAD, it should first be prefixed by any - * sign or other prefix; otherwise, it should be blank - * padded before the prefix is emitted. After any - * left-hand padding and prefixing, emit zeroes - * required by a decimal [diouxX] precision, then print - * the string proper, then emit zeroes required by any - * leftover floating precision; finally, if LADJUST, - * pad with blanks. + * All reasonable formats wind up here. At this point, `cp' + * points to a string which (if not flags&LADJUST) should be + * padded out to `width' places. If flags&ZEROPAD, it should + * first be prefixed by any sign or other prefix; otherwise, + * it should be blank padded before the prefix is emitted. + * After any left-hand padding and prefixing, emit zeroes + * required by a decimal [diouxX] precision, then print the + * string proper, then emit zeroes required by any leftover + * floating precision; finally, if LADJUST, pad with blanks. + * + * Compute actual size, so we know how much to pad. + * fieldsz excludes decimal prec; realsz includes it. */ - - /* - * compute actual size, so we know how much to pad. - * fieldsz excludes decimal prec; realsz includes it - */ -#ifdef FLOATING_POINT - fieldsz = size + fpprec; -#else fieldsz = size; -#endif if (sign) fieldsz++; else if (flags & HEXPREFIX) @@ -687,13 +625,53 @@ number: if ((dprec = prec) >= 0) PAD(dprec - fieldsz, zeroes); /* the string or number proper */ - PRINT(cp, size); - #ifdef FLOATING_POINT - /* trailing f.p. zeroes */ - PAD(fpprec, zeroes); + if ((flags & FPT) == 0) { + PRINT(cp, size); + } else { /* glue together f_p fragments */ + if (ch >= 'f') { /* 'f' or 'g' */ + if (_double == 0) { + /* kludge for __dtoa irregularity */ + if (prec == 0 || + (flags & ALT) == 0) { + PRINT("0", 1); + } else { + PRINT("0.", 2); + PAD(ndig - 1, zeroes); + } + } else if (expt <= 0) { + PRINT("0.", 2); + PAD(-expt, zeroes); + PRINT(cp, ndig); + } else if (expt >= ndig) { + PRINT(cp, ndig); + PAD(expt - ndig, zeroes); + if (flags & ALT) + PRINT(".", 1); + } else { + PRINT(cp, expt); + cp += expt; + PRINT(".", 1); + PRINT(cp, ndig-expt); + } + } else { /* 'e' or 'E' */ + if (ndig > 1 || flags & ALT) { + ox[0] = *cp++; + ox[1] = '.'; + PRINT(ox, 2); + if (_double || flags & ALT == 0) { + PRINT(cp, ndig-1); + } else /* 0.[0..] */ + /* __dtoa irregularity */ + PAD(ndig - 1, zeroes); + } else /* XeYYY */ + PRINT(cp, 1); + PRINT(expstr, expsize); + } + } +#else + PRINT(cp, size); #endif - /* left-adjusting padding (always blank) */ if (flags & LADJUST) PAD(width - realsz, blanks); @@ -711,257 +689,54 @@ error: } #ifdef FLOATING_POINT -#include -static char *exponent(); -static char *round(); +extern char *__dtoa __P((double, int, int, int *, int *, char **)); + +static char * +cvt(value, ndigits, flags, sign, decpt, ch, length) + double value; + int ndigits, flags, *decpt, ch, *length; + char *sign; +{ + int mode, dsgn; + char *digits, *bp, *rve; + + if (ch == 'f') + mode = 3; + else { + mode = 2; + } + if (value < 0) { + value = -value; + *sign = '-'; + } else + *sign = '\000'; + digits = __dtoa(value, mode, ndigits, decpt, &dsgn, &rve); + if (flags & ALT) { /* Print trailing zeros */ + bp = digits + ndigits; + if (ch == 'f') { + if (*digits == '0' && value) + *decpt = -ndigits + 1; + bp += *decpt; + } + if (value == 0) /* kludge for __dtoa irregularity */ + rve = bp; + while (rve < bp) + *rve++ = '0'; + } + *length = rve - digits; + return (digits); +} static int -cvt(number, prec, flags, signp, fmtch, startp, endp) - double number; - register int prec; - int flags; - char *signp; - int fmtch; - char *startp, *endp; +exponent(p0, exp, fmtch) + char *p0; + int exp, fmtch; { register char *p, *t; - register double fract; - int dotrim, expcnt, gformat; - double integer, tmp; - - dotrim = expcnt = gformat = 0; - if (number < 0) { - number = -number; - *signp = '-'; - } else - *signp = 0; - - fract = modf(number, &integer); - - /* get an extra slot for rounding. */ - t = ++startp; - - /* - * get integer portion of number; put into the end of the buffer; the - * .01 is added for modf(356.0 / 10, &integer) returning .59999999... - */ - for (p = endp - 1; integer; ++expcnt) { - tmp = modf(integer / 10, &integer); - *p-- = to_char((int)((tmp + .01) * 10)); - } - switch (fmtch) { - case 'f': - /* reverse integer into beginning of buffer */ - if (expcnt) - for (; ++p < endp; *t++ = *p); - else - *t++ = '0'; - /* - * if precision required or alternate flag set, add in a - * decimal point. - */ - if (prec || flags&ALT) - *t++ = '.'; - /* if requires more precision and some fraction left */ - if (fract) { - if (prec) - do { - fract = modf(fract * 10, &tmp); - *t++ = to_char((int)tmp); - } while (--prec && fract); - if (fract) - startp = round(fract, (int *)NULL, startp, - t - 1, (char)0, signp); - } - for (; prec--; *t++ = '0'); - break; - case 'e': - case 'E': -eformat: if (expcnt) { - *t++ = *++p; - if (prec || flags&ALT) - *t++ = '.'; - /* if requires more precision and some integer left */ - for (; prec && ++p < endp; --prec) - *t++ = *p; - /* - * if done precision and more of the integer component, - * round using it; adjust fract so we don't re-round - * later. - */ - if (!prec && ++p < endp) { - fract = 0; - startp = round((double)0, &expcnt, startp, - t - 1, *p, signp); - } - /* adjust expcnt for digit in front of decimal */ - --expcnt; - } - /* until first fractional digit, decrement exponent */ - else if (fract) { - /* adjust expcnt for digit in front of decimal */ - for (expcnt = -1;; --expcnt) { - fract = modf(fract * 10, &tmp); - if (tmp) - break; - } - *t++ = to_char((int)tmp); - if (prec || flags&ALT) - *t++ = '.'; - } - else { - *t++ = '0'; - if (prec || flags&ALT) - *t++ = '.'; - } - /* if requires more precision and some fraction left */ - if (fract) { - if (prec) - do { - fract = modf(fract * 10, &tmp); - *t++ = to_char((int)tmp); - } while (--prec && fract); - if (fract) - startp = round(fract, &expcnt, startp, - t - 1, (char)0, signp); - } - /* if requires more precision */ - for (; prec--; *t++ = '0'); - - /* unless alternate flag, trim any g/G format trailing 0's */ - if (gformat && !(flags&ALT)) { - while (t > startp && *--t == '0'); - if (*t == '.') - --t; - ++t; - } - t = exponent(t, expcnt, fmtch); - break; - case 'g': - case 'G': - /* a precision of 0 is treated as a precision of 1. */ - if (!prec) - ++prec; - /* - * ``The style used depends on the value converted; style e - * will be used only if the exponent resulting from the - * conversion is less than -4 or greater than the precision.'' - * -- ANSI X3J11 - */ - if (expcnt > prec || !expcnt && fract && fract < .0001) { - /* - * g/G format counts "significant digits, not digits of - * precision; for the e/E format, this just causes an - * off-by-one problem, i.e. g/G considers the digit - * before the decimal point significant and e/E doesn't - * count it as precision. - */ - --prec; - fmtch -= 2; /* G->E, g->e */ - gformat = 1; - goto eformat; - } - /* - * reverse integer into beginning of buffer, - * note, decrement precision - */ - if (expcnt) - for (; ++p < endp; *t++ = *p, --prec); - else - *t++ = '0'; - /* - * if precision required or alternate flag set, add in a - * decimal point. If no digits yet, add in leading 0. - */ - if (prec || flags&ALT) { - dotrim = 1; - *t++ = '.'; - } - else - dotrim = 0; - /* if requires more precision and some fraction left */ - if (fract) { - if (prec) { - do { - fract = modf(fract * 10, &tmp); - *t++ = to_char((int)tmp); - } while(!tmp); - while (--prec && fract) { - fract = modf(fract * 10, &tmp); - *t++ = to_char((int)tmp); - } - } - if (fract) - startp = round(fract, (int *)NULL, startp, - t - 1, (char)0, signp); - } - /* alternate format, adds 0's for precision, else trim 0's */ - if (flags&ALT) - for (; prec--; *t++ = '0'); - else if (dotrim) { - while (t > startp && *--t == '0'); - if (*t != '.') - ++t; - } - } - return (t - startp); -} - -static char * -round(fract, exp, start, end, ch, signp) - double fract; - int *exp; - register char *start, *end; - char ch, *signp; -{ - double tmp; - - if (fract) - (void)modf(fract * 10, &tmp); - else - tmp = to_digit(ch); - if (tmp > 4) - for (;; --end) { - if (*end == '.') - --end; - if (++*end <= '9') - break; - *end = '0'; - if (end == start) { - if (exp) { /* e/E; increment exponent */ - *end = '1'; - ++*exp; - } - else { /* f; add extra digit */ - *--end = '1'; - --start; - } - break; - } - } - /* ``"%.3f", (double)-0.0004'' gives you a negative 0. */ - else if (*signp == '-') - for (;; --end) { - if (*end == '.') - --end; - if (*end != '0') - break; - if (end == start) - *signp = 0; - } - return (start); -} - -static char * -exponent(p, exp, fmtch) - register char *p; - register int exp; - int fmtch; -{ - register char *t; char expbuf[MAXEXP]; + p = p0; *p++ = fmtch; if (exp < 0) { exp = -exp; @@ -981,6 +756,6 @@ exponent(p, exp, fmtch) *p++ = '0'; *p++ = to_char(exp); } - return (p); + return (p - p0); } #endif /* FLOATING_POINT */ diff --git a/lib/libc/stdio/vfscanf.c b/lib/libc/stdio/vfscanf.c index 102cfca986a7..43d1981aff88 100644 --- a/lib/libc/stdio/vfscanf.c +++ b/lib/libc/stdio/vfscanf.c @@ -35,7 +35,7 @@ */ #if defined(LIBC_SCCS) && !defined(lint) -static char sccsid[] = "@(#)vfscanf.c 5.6 (Berkeley) 2/24/91"; +static char sccsid[] = "@(#)vfscanf.c 5.7 (Berkeley) 12/14/92"; #endif /* LIBC_SCCS and not lint */ #include @@ -50,12 +50,8 @@ static char sccsid[] = "@(#)vfscanf.c 5.6 (Berkeley) 2/24/91"; #define FLOATING_POINT -#ifdef FLOATING_POINT #include "floatio.h" -#define BUF (MAXEXP+MAXFRACT+3) /* 3 = sign + decimal point + NUL */ -#else -#define BUF 40 -#endif +#define BUF 513 /* Maximum length of numeric string. */ /* * Flags used during conversion. @@ -101,7 +97,7 @@ static u_char *__sccl(); __svfscanf(fp, fmt0, ap) register FILE *fp; char const *fmt0; - _VA_LIST_ ap; + va_list ap; { register u_char *fmt = (u_char *)fmt0; register int c; /* character from format, or conversion */ @@ -635,7 +631,7 @@ literal: double res; *p = 0; - res = atof(buf); + res = strtod(buf, (char **) NULL); if (flags & LONG) *va_arg(ap, double *) = res; else diff --git a/lib/libc/stdlib/Makefile.inc b/lib/libc/stdlib/Makefile.inc index 658eba2d9933..27ec7ca07a85 100644 --- a/lib/libc/stdlib/Makefile.inc +++ b/lib/libc/stdlib/Makefile.inc @@ -3,10 +3,10 @@ # stdlib sources .PATH: ${.CURDIR}/${MACHINE}/stdlib ${.CURDIR}/stdlib -SRCS+= abort.c atexit.c atoi.c atol.c bsearch.c calloc.c div.c exit.c \ +SRCS+= abort.c atexit.c atoi.c atof.c atol.c bsearch.c calloc.c div.c exit.c \ getenv.c getopt.c heapsort.c labs.c ldiv.c malloc.c multibyte.c \ - putenv.c qsort.c radixsort.c rand.c random.c setenv.c strtol.c \ - strtoul.c system.c + putenv.c qsort.c radixsort.c rand.c random.c setenv.c strtod.c \ + strtol.c strtoul.c system.c .if (${MACHINE} == "hp300") SRCS+= abs.s atof.c diff --git a/lib/libc/stdlib/atof.c b/lib/libc/stdlib/atof.c index 8c7c3598714b..c3577abfa275 100644 --- a/lib/libc/stdlib/atof.c +++ b/lib/libc/stdlib/atof.c @@ -32,7 +32,7 @@ */ #if defined(LIBC_SCCS) && !defined(lint) -static char sccsid[] = "@(#)atof.c 5.2 (Berkeley) 6/1/90"; +static char sccsid[] = "@(#)atof.c 5.3 (Berkeley) 1/8/93"; #endif /* LIBC_SCCS and not lint */ #include diff --git a/lib/libc/stdlib/strtod.c b/lib/libc/stdlib/strtod.c new file mode 100644 index 000000000000..26bd80d2e882 --- /dev/null +++ b/lib/libc/stdlib/strtod.c @@ -0,0 +1,2410 @@ +#if defined(LIBC_SCCS) && !defined(lint) +static char sccsid[] = "@(#)strtod.c 5.1 (Berkeley) 11/13/92"; +#endif /* LIBC_SCCS and not lint */ + +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991 by AT&T. + * + * 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 AT&T 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 + AT&T Bell Laboratories, Room 2C-463 + 600 Mountain Avenue + Murray Hill, NJ 07974-2070 + U.S.A. + dmg@research.att.com or research!dmg + */ + +/* 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 address. + * #define Sudden_Underflow for IEEE-format machines without gradual + * underflow (i.e., that flush to zero on underflow). + * #define IBM for IBM mainframe-style floating-point arithmetic. + * #define VAX for VAX-style floating-point arithmetic. + * #define Unsigned_Shifts if >> does treats its left operand as unsigned. + * #define No_leftright to omit left-right logic in fast floating-point + * computation of dtoa. + * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. + * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines + * that use extended-precision instructions to compute rounded + * products and quotients) with IBM. + * #define ROUND_BIASED for IEEE-format with biased rounding. + * #define Inaccurate_Divide for IEEE-format with correctly rounded + * products but inaccurate quotients, e.g., for Intel i860. + * #define Just_16 to store 16 bits per 32-bit long when doing high-precision + * integer arithmetic. Whether this speeds things up or slows things + * down depends on the machine and the number being converted. + * #define KR_headers for old-style C function headers. + * #define Bad_float_h if your system lacks a float.h or if it does not + * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, + * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. + */ + +#define IEEE_8087 + +#ifdef DEBUG +#include "stdio.h" +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} +#endif + +#ifdef __cplusplus +#include "malloc.h" +#include "memory.h" +#else +#ifndef KR_headers +#include "stdlib.h" +#include "string.h" +#else +#include "malloc.h" +#include "memory.h" +#endif +#endif + +#include "errno.h" +#ifdef Bad_float_h +#undef __STDC__ +#ifdef IEEE_MC68k +#define IEEE_ARITHMETIC +#endif +#ifdef IEEE_8087 +#define IEEE_ARITHMETIC +#endif +#ifdef IEEE_ARITHMETIC +#define DBL_DIG 15 +#define DBL_MAX_10_EXP 308 +#define DBL_MAX_EXP 1024 +#define FLT_RADIX 2 +#define FLT_ROUNDS 1 +#define DBL_MAX 1.7976931348623157e+308 +#endif + +#ifdef IBM +#define DBL_DIG 16 +#define DBL_MAX_10_EXP 75 +#define DBL_MAX_EXP 63 +#define FLT_RADIX 16 +#define FLT_ROUNDS 0 +#define DBL_MAX 7.2370055773322621e+75 +#endif + +#ifdef VAX +#define DBL_DIG 16 +#define DBL_MAX_10_EXP 38 +#define DBL_MAX_EXP 127 +#define FLT_RADIX 2 +#define FLT_ROUNDS 1 +#define DBL_MAX 1.7014118346046923e+38 +#endif + +#ifndef LONG_MAX +#define LONG_MAX 2147483647 +#endif +#else +#include "float.h" +#endif +#ifndef __MATH_H__ +#include "math.h" +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +#ifndef CONST +#ifdef KR_headers +#define CONST /* blank */ +#else +#define CONST const +#endif +#endif + +#ifdef Unsigned_Shifts +#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000; +#else +#define Sign_Extend(a,b) /*no-op*/ +#endif + +#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 +Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. +#endif + +#ifdef IEEE_8087 +#define word0(x) ((unsigned long *)&x)[1] +#define word1(x) ((unsigned long *)&x)[0] +#else +#define word0(x) ((unsigned long *)&x)[0] +#define word1(x) ((unsigned long *)&x)[1] +#endif + +/* The following definition of Storeinc is appropriate for MIPS processors. + * An alternative that might be better on some machines is + * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) + */ +#if defined(IEEE_8087) + defined(VAX) +#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ +((unsigned short *)a)[0] = (unsigned short)c, a++) +#else +#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ +((unsigned short *)a)[1] = (unsigned short)c, a++) +#endif + +/* #define P DBL_MANT_DIG */ +/* Ten_pmax = floor(P*log(2)/log(5)) */ +/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ +/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ +/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ + +#if defined(IEEE_8087) + defined(IEEE_MC68k) +#define Exp_shift 20 +#define Exp_shift1 20 +#define Exp_msk1 0x100000 +#define Exp_msk11 0x100000 +#define Exp_mask 0x7ff00000 +#define P 53 +#define Bias 1023 +#define IEEE_Arith +#define Emin (-1022) +#define Exp_1 0x3ff00000 +#define Exp_11 0x3ff00000 +#define Ebits 11 +#define Frac_mask 0xfffff +#define Frac_mask1 0xfffff +#define Ten_pmax 22 +#define Bletch 0x10 +#define Bndry_mask 0xfffff +#define Bndry_mask1 0xfffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 1 +#define Tiny0 0 +#define Tiny1 1 +#define Quick_max 14 +#define Int_max 14 +#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */ +#else +#undef Sudden_Underflow +#define Sudden_Underflow +#ifdef IBM +#define Exp_shift 24 +#define Exp_shift1 24 +#define Exp_msk1 0x1000000 +#define Exp_msk11 0x1000000 +#define Exp_mask 0x7f000000 +#define P 14 +#define Bias 65 +#define Exp_1 0x41000000 +#define Exp_11 0x41000000 +#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ +#define Frac_mask 0xffffff +#define Frac_mask1 0xffffff +#define Bletch 4 +#define Ten_pmax 22 +#define Bndry_mask 0xefffff +#define Bndry_mask1 0xffffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 4 +#define Tiny0 0x100000 +#define Tiny1 0 +#define Quick_max 14 +#define Int_max 15 +#else /* VAX */ +#define Exp_shift 23 +#define Exp_shift1 7 +#define Exp_msk1 0x80 +#define Exp_msk11 0x800000 +#define Exp_mask 0x7f80 +#define P 56 +#define Bias 129 +#define Exp_1 0x40800000 +#define Exp_11 0x4080 +#define Ebits 8 +#define Frac_mask 0x7fffff +#define Frac_mask1 0xffff007f +#define Ten_pmax 24 +#define Bletch 2 +#define Bndry_mask 0xffff007f +#define Bndry_mask1 0xffff007f +#define LSB 0x10000 +#define Sign_bit 0x8000 +#define Log2P 1 +#define Tiny0 0x80 +#define Tiny1 0 +#define Quick_max 15 +#define Int_max 15 +#endif +#endif + +#ifndef IEEE_Arith +#define ROUND_BIASED +#endif + +#ifdef RND_PRODQUOT +#define rounded_product(a,b) a = rnd_prod(a, b) +#define rounded_quotient(a,b) a = rnd_quot(a, b) +#ifdef KR_headers +extern double rnd_prod(), rnd_quot(); +#else +extern double rnd_prod(double, double), rnd_quot(double, double); +#endif +#else +#define rounded_product(a,b) a *= b +#define rounded_quotient(a,b) a /= b +#endif + +#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) +#define Big1 0xffffffff + +#ifndef Just_16 +/* When Pack_32 is not defined, we store 16 bits per 32-bit long. + * This makes some inner loops simpler and sometimes saves work + * during multiplications, but it often seems to make things slightly + * slower. Hence the default is now to store 32 bits per long. + */ +#ifndef Pack_32 +#define Pack_32 +#endif +#endif + +#define Kmax 15 + +#ifdef __cplusplus +extern "C" double strtod(const char *s00, char **se); +extern "C" char *dtoa(double d, int mode, int ndigits, + int *decpt, int *sign, char **rve); +#endif + + struct +Bigint { + struct Bigint *next; + int k, maxwds, sign, wds; + unsigned long x[1]; +}; + + typedef struct Bigint Bigint; + + static Bigint *freelist[Kmax+1]; + + static Bigint * +Balloc +#ifdef KR_headers + (k) int k; +#else + (int k) +#endif +{ + int x; + Bigint *rv; + + if (rv = freelist[k]) { + freelist[k] = rv->next; + } else { + x = 1 << k; + rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(long)); + rv->k = k; + rv->maxwds = x; + } + rv->sign = rv->wds = 0; + return rv; +} + + static void +Bfree +#ifdef KR_headers + (v) Bigint *v; +#else + (Bigint *v) +#endif +{ + if (v) { + v->next = freelist[v->k]; + freelist[v->k] = v; + } +} + +#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ +y->wds*sizeof(long) + 2*sizeof(int)) + + static Bigint * +multadd +#ifdef KR_headers + (b, m, a) Bigint *b; int m, a; +#else + (Bigint *b, int m, int a) /* multiply by m and add a */ +#endif +{ + int i, wds; + unsigned long *x, y; +#ifdef Pack_32 + unsigned long xi, z; +#endif + Bigint *b1; + + wds = b->wds; + x = b->x; + i = 0; + do { +#ifdef Pack_32 + xi = *x; + y = (xi & 0xffff) * m + a; + z = (xi >> 16) * m + (y >> 16); + a = (int)(z >> 16); + *x++ = (z << 16) + (y & 0xffff); +#else + y = *x * m + a; + a = (int)(y >> 16); + *x++ = y & 0xffff; +#endif + } while (++i < wds); + if (a) { + if (wds >= b->maxwds) { + b1 = Balloc(b->k+1); + Bcopy(b1, b); + Bfree(b); + b = b1; + } + b->x[wds++] = a; + b->wds = wds; + } + return b; +} + + static Bigint * +s2b +#ifdef KR_headers + (s, nd0, nd, y9) CONST char *s; int nd0, nd; unsigned long y9; +#else + (CONST char *s, int nd0, int nd, unsigned long y9) +#endif +{ + Bigint *b; + int i, k; + long x, y; + + x = (nd + 8) / 9; + for (k = 0, y = 1; x > y; y <<= 1, k++) ; +#ifdef Pack_32 + b = Balloc(k); + b->x[0] = y9; + b->wds = 1; +#else + b = Balloc(k+1); + b->x[0] = y9 & 0xffff; + b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; +#endif + + i = 9; + if (9 < nd0) { + s += 9; + do + b = multadd(b, 10, *s++ - '0'); + while (++i < nd0); + s++; + } else + s += 10; + for (; i < nd; i++) + b = multadd(b, 10, *s++ - '0'); + return b; +} + + static int +hi0bits +#ifdef KR_headers + (x) register unsigned long x; +#else + (register unsigned long x) +#endif +{ + register int k = 0; + + if (!(x & 0xffff0000)) { + k = 16; + x <<= 16; + } + if (!(x & 0xff000000)) { + k += 8; + x <<= 8; + } + if (!(x & 0xf0000000)) { + k += 4; + x <<= 4; + } + if (!(x & 0xc0000000)) { + k += 2; + x <<= 2; + } + if (!(x & 0x80000000)) { + k++; + if (!(x & 0x40000000)) + return 32; + } + return k; +} + + static int +lo0bits +#ifdef KR_headers + (y) unsigned long *y; +#else + (unsigned long *y) +#endif +{ + register int k; + register unsigned long x = *y; + + if (x & 7) { + if (x & 1) + return 0; + if (x & 2) { + *y = x >> 1; + return 1; + } + *y = x >> 2; + return 2; + } + k = 0; + if (!(x & 0xffff)) { + k = 16; + x >>= 16; + } + if (!(x & 0xff)) { + k += 8; + x >>= 8; + } + if (!(x & 0xf)) { + k += 4; + x >>= 4; + } + if (!(x & 0x3)) { + k += 2; + x >>= 2; + } + if (!(x & 1)) { + k++; + x >>= 1; + if (!x & 1) + return 32; + } + *y = x; + return k; +} + + static Bigint * +i2b +#ifdef KR_headers + (i) int i; +#else + (int i) +#endif +{ + Bigint *b; + + b = Balloc(1); + b->x[0] = i; + b->wds = 1; + return b; + } + + static Bigint * +mult +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + Bigint *c; + int k, wa, wb, wc; + unsigned long carry, y, z; + unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0; +#ifdef Pack_32 + unsigned long z2; +#endif + + if (a->wds < b->wds) { + c = a; + a = b; + b = c; + } + k = a->k; + wa = a->wds; + wb = b->wds; + wc = wa + wb; + if (wc > a->maxwds) + k++; + c = Balloc(k); + for (x = c->x, xa = x + wc; x < xa; x++) + *x = 0; + xa = a->x; + xae = xa + wa; + xb = b->x; + xbe = xb + wb; + xc0 = c->x; +#ifdef Pack_32 + for (; xb < xbe; xb++, xc0++) { + if (y = *xb & 0xffff) { + x = xa; + xc = xc0; + carry = 0; + do { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc(xc, z2, z); + } while (x < xae); + *xc = carry; + } + if (y = *xb >> 16) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } while (x < xae); + *xc = z2; + } + } +#else + for (; xb < xbe; xc0++) { + if (y = *xb++) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } while (x < xae); + *xc = carry; + } + } +#endif + for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; + c->wds = wc; + return c; +} + + static Bigint *p5s; + + static Bigint * +pow5mult +#ifdef KR_headers + (b, k) Bigint *b; int k; +#else + (Bigint *b, int k) +#endif +{ + Bigint *b1, *p5, *p51; + int i; + static int p05[3] = { 5, 25, 125 }; + + if (i = k & 3) + b = multadd(b, p05[i-1], 0); + + if (!(k >>= 2)) + return b; + if (!(p5 = p5s)) { + /* first time */ + p5 = p5s = i2b(625); + p5->next = 0; + } + for (;;) { + if (k & 1) { + b1 = mult(b, p5); + Bfree(b); + b = b1; + } + if (!(k >>= 1)) + break; + if (!(p51 = p5->next)) { + p51 = p5->next = mult(p5,p5); + p51->next = 0; + } + p5 = p51; + } + return b; +} + + static Bigint * +lshift +#ifdef KR_headers + (b, k) Bigint *b; int k; +#else + (Bigint *b, int k) +#endif +{ + int i, k1, n, n1; + Bigint *b1; + unsigned long *x, *x1, *xe, z; + +#ifdef Pack_32 + n = k >> 5; +#else + n = k >> 4; +#endif + k1 = b->k; + n1 = n + b->wds + 1; + for (i = b->maxwds; n1 > i; i <<= 1) + k1++; + b1 = Balloc(k1); + x1 = b1->x; + for (i = 0; i < n; i++) + *x1++ = 0; + x = b->x; + xe = x + b->wds; +#ifdef Pack_32 + if (k &= 0x1f) { + k1 = 32 - k; + z = 0; + do { + *x1++ = *x << k | z; + z = *x++ >> k1; + } while (x < xe); + if (*x1 = z) + ++n1; + } +#else + if (k &= 0xf) { + k1 = 16 - k; + z = 0; + do { + *x1++ = *x << k & 0xffff | z; + z = *x++ >> k1; + } while (x < xe); + if (*x1 = z) + ++n1; + } +#endif + else + do + *x1++ = *x++; + while (x < xe); + b1->wds = n1 - 1; + Bfree(b); + return b1; +} + + static int +cmp +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + unsigned long *xa, *xa0, *xb, *xb0; + int i, j; + + i = a->wds; + j = b->wds; +#ifdef DEBUG + if (i > 1 && !a->x[i-1]) + Bug("cmp called with a->x[a->wds-1] == 0"); + if (j > 1 && !b->x[j-1]) + Bug("cmp called with b->x[b->wds-1] == 0"); +#endif + if (i -= j) + return i; + xa0 = a->x; + xa = xa0 + j; + xb0 = b->x; + xb = xb0 + j; + for (;;) { + if (*--xa != *--xb) + return *xa < *xb ? -1 : 1; + if (xa <= xa0) + break; + } + return 0; +} + + static Bigint * +diff +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + Bigint *c; + int i, wa, wb; + long borrow, y; /* We need signed shifts here. */ + unsigned long *xa, *xae, *xb, *xbe, *xc; +#ifdef Pack_32 + long z; +#endif + + i = cmp(a,b); + if (!i) { + c = Balloc(0); + c->wds = 1; + c->x[0] = 0; + return c; + } + if (i < 0) { + c = a; + a = b; + b = c; + i = 1; + } else + i = 0; + c = Balloc(a->k); + c->sign = i; + wa = a->wds; + xa = a->x; + xae = xa + wa; + wb = b->wds; + xb = b->x; + xbe = xb + wb; + xc = c->x; + borrow = 0; +#ifdef Pack_32 + do { + y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; + borrow = z >> 16; + Sign_Extend(borrow, z); + Storeinc(xc, z, y); + } while (xb < xbe); + while (xa < xae) { + y = (*xa & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + z = (*xa++ >> 16) + borrow; + borrow = z >> 16; + Sign_Extend(borrow, z); + Storeinc(xc, z, y); + } +#else + do { + y = *xa++ - *xb++ + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *xc++ = y & 0xffff; + } while (xb < xbe); + while (xa < xae) { + y = *xa++ + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *xc++ = y & 0xffff; + } +#endif + while (!*--xc) + wa--; + c->wds = wa; + return c; +} + + static double +ulp +#ifdef KR_headers + (x) double x; +#else + (double x) +#endif +{ + register long L; + double a; + + L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; +#ifndef Sudden_Underflow + if (L > 0) { +#endif +#ifdef IBM + L |= Exp_msk1 >> 4; +#endif + word0(a) = L; + word1(a) = 0; +#ifndef Sudden_Underflow + } else { + L = -L >> Exp_shift; + if (L < Exp_shift) { + word0(a) = 0x80000 >> L; + word1(a) = 0; + } else { + word0(a) = 0; + L -= Exp_shift; + word1(a) = L >= 31 ? 1 : 1 << 31 - L; + } + } +#endif + return a; +} + + static double +b2d +#ifdef KR_headers + (a, e) Bigint *a; int *e; +#else + (Bigint *a, int *e) +#endif +{ + unsigned long *xa, *xa0, w, y, z; + int k; + double d; +#ifdef VAX + unsigned long d0, d1; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + + xa0 = a->x; + xa = xa0 + a->wds; + y = *--xa; +#ifdef DEBUG + if (!y) Bug("zero y in b2d"); +#endif + k = hi0bits(y); + *e = 32 - k; +#ifdef Pack_32 + if (k < Ebits) { + d0 = Exp_1 | y >> Ebits - k; + w = xa > xa0 ? *--xa : 0; + d1 = y << (32-Ebits) + k | w >> Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) { + d0 = Exp_1 | y << k | z >> 32 - k; + y = xa > xa0 ? *--xa : 0; + d1 = z << k | y >> 32 - k; + } else { + d0 = Exp_1 | y; + d1 = z; + } +#else + if (k < Ebits + 16) { + z = xa > xa0 ? *--xa : 0; + d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; + w = xa > xa0 ? *--xa : 0; + y = xa > xa0 ? *--xa : 0; + d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + w = xa > xa0 ? *--xa : 0; + k -= Ebits + 16; + d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; + y = xa > xa0 ? *--xa : 0; + d1 = w << k + 16 | y << k; +#endif + ret_d: +#ifdef VAX + word0(d) = d0 >> 16 | d0 << 16; + word1(d) = d1 >> 16 | d1 << 16; +#else +#undef d0 +#undef d1 +#endif + return d; +} + + static Bigint * +d2b +#ifdef KR_headers + (d, e, bits) double d; int *e, *bits; +#else + (double d, int *e, int *bits) +#endif +{ + Bigint *b; + int de, i, k; + unsigned long *x, y, z; +#ifdef VAX + unsigned long d0, d1; + d0 = word0(d) >> 16 | word0(d) << 16; + d1 = word1(d) >> 16 | word1(d) << 16; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + +#ifdef Pack_32 + b = Balloc(1); +#else + b = Balloc(2); +#endif + x = b->x; + + z = d0 & Frac_mask; + d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ +#ifdef Sudden_Underflow + de = (int)(d0 >> Exp_shift); +#ifndef IBM + z |= Exp_msk11; +#endif +#else + if (de = (int)(d0 >> Exp_shift)) + z |= Exp_msk1; +#endif +#ifdef Pack_32 + if (y = d1) { + if (k = lo0bits(&y)) { + x[0] = y | z << 32 - k; + z >>= k; + } + else + x[0] = y; + i = b->wds = (x[1] = z) ? 2 : 1; + } else { +#ifdef DEBUG + if (!z) + Bug("Zero passed to d2b"); +#endif + k = lo0bits(&z); + x[0] = z; + i = b->wds = 1; + k += 32; + } +#else + if (y = d1) { + if (k = lo0bits(&y)) + if (k >= 16) { + x[0] = y | z << 32 - k & 0xffff; + x[1] = z >> k - 16 & 0xffff; + x[2] = z >> k; + i = 2; + } else { + x[0] = y & 0xffff; + x[1] = y >> 16 | z << 16 - k & 0xffff; + x[2] = z >> k & 0xffff; + x[3] = z >> k+16; + i = 3; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16; + x[2] = z & 0xffff; + x[3] = z >> 16; + i = 3; + } + } else { +#ifdef DEBUG + if (!z) + Bug("Zero passed to d2b"); +#endif + k = lo0bits(&z); + if (k >= 16) { + x[0] = z; + i = 0; + } else { + x[0] = z & 0xffff; + x[1] = z >> 16; + i = 1; + } + k += 32; + } + while (!x[i]) + --i; + b->wds = i + 1; +#endif +#ifndef Sudden_Underflow + if (de) { +#endif +#ifdef IBM + *e = (de - Bias - (P-1) << 2) + k; + *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); +#else + *e = de - Bias - (P-1) + k; + *bits = P - k; +#endif +#ifndef Sudden_Underflow + } else { + *e = de - Bias - (P-1) + 1 + k; +#ifdef Pack_32 + *bits = 32*i - hi0bits(x[i-1]); +#else + *bits = (i+2)*16 - hi0bits(x[i]); +#endif + } +#endif + return b; +} +#undef d0 +#undef d1 + + static double +ratio +#ifdef KR_headers + (a, b) Bigint *a, *b; +#else + (Bigint *a, Bigint *b) +#endif +{ + double da, db; + int k, ka, kb; + + da = b2d(a, &ka); + db = b2d(b, &kb); +#ifdef Pack_32 + k = ka - kb + 32*(a->wds - b->wds); +#else + k = ka - kb + 16*(a->wds - b->wds); +#endif +#ifdef IBM + if (k > 0) { + word0(da) += (k >> 2)*Exp_msk1; + if (k &= 3) + da *= 1 << k; + } else { + k = -k; + word0(db) += (k >> 2)*Exp_msk1; + if (k &= 3) + db *= 1 << k; + } +#else + if (k > 0) + word0(da) += k*Exp_msk1; + else { + k = -k; + word0(db) += k*Exp_msk1; + } +#endif + return da / db; +} + + static double +tens[] = { + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, + 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, + 1e20, 1e21, 1e22 +#ifdef VAX + , 1e23, 1e24 +#endif + }; + + static double +#ifdef IEEE_Arith +bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; +static double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 }; +#define n_bigtens 5 +#else +#ifdef IBM +bigtens[] = { 1e16, 1e32, 1e64 }; +static double tinytens[] = { 1e-16, 1e-32, 1e-64 }; +#define n_bigtens 3 +#else +bigtens[] = { 1e16, 1e32 }; +static double tinytens[] = { 1e-16, 1e-32 }; +#define n_bigtens 2 +#endif +#endif + + double +strtod +#ifdef KR_headers + (s00, se) CONST char *s00; char **se; +#else + (CONST char *s00, char **se) +#endif +{ + int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, + e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; + CONST char *s, *s0, *s1; + double aadj, aadj1, adj, rv, rv0; + long L; + unsigned long y, z; + Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; + sign = nz0 = nz = 0; + rv = 0.; + for (s = s00;;s++) switch(*s) { + case '-': + sign = 1; + /* no break */ + case '+': + if (*++s) + goto break2; + /* no break */ + case 0: + s = s00; + goto ret; + case '\t': + case '\n': + case '\v': + case '\f': + case '\r': + case ' ': + continue; + default: + goto break2; + } + break2: + if (*s == '0') { + nz0 = 1; + while (*++s == '0') ; + if (!*s) + goto ret; + } + s0 = s; + y = z = 0; + for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) + if (nd < 9) + y = 10*y + c - '0'; + else if (nd < 16) + z = 10*z + c - '0'; + nd0 = nd; + if (c == '.') { + c = *++s; + if (!nd) { + for (; c == '0'; c = *++s) + nz++; + if (c > '0' && c <= '9') { + s0 = s; + nf += nz; + nz = 0; + goto have_dig; + } + goto dig_done; + } + for (; c >= '0' && c <= '9'; c = *++s) { + have_dig: + nz++; + if (c -= '0') { + nf += nz; + for (i = 1; i < nz; i++) + if (nd++ < 9) + y *= 10; + else if (nd <= DBL_DIG + 1) + z *= 10; + if (nd++ < 9) + y = 10*y + c; + else if (nd <= DBL_DIG + 1) + z = 10*z + c; + nz = 0; + } + } + } + dig_done: + e = 0; + if (c == 'e' || c == 'E') { + if (!nd && !nz && !nz0) { + s = s00; + goto ret; + } + s00 = s; + esign = 0; + switch(c = *++s) { + case '-': + esign = 1; + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while (c == '0') + c = *++s; + if (c > '0' && c <= '9') { + L = c - '0'; + s1 = s; + while ((c = *++s) >= '0' && c <= '9') + L = 10*L + c - '0'; + if (s - s1 > 8 || L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + e = 19999; /* safe for 16 bit ints */ + else + e = (int)L; + if (esign) + e = -e; + } else + e = 0; + } else + s = s00; + } + if (!nd) { + if (!nz && !nz0) + s = s00; + goto ret; + } + e1 = e -= nf; + + /* Now we have nd0 digits, starting at s0, followed by a + * decimal point, followed by nd-nd0 digits. The number we're + * after is the integer represented by those digits times + * 10**e */ + + if (!nd0) + nd0 = nd; + k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; + rv = y; + if (k > 9) + rv = tens[k - 9] * rv + z; + if (nd <= DBL_DIG +#ifndef RND_PRODQUOT + && FLT_ROUNDS == 1 +#endif + ) { + if (!e) + goto ret; + if (e > 0) { + if (e <= Ten_pmax) { +#ifdef VAX + goto vax_ovfl_check; +#else + /* rv = */ rounded_product(rv, tens[e]); + goto ret; +#endif + } + i = DBL_DIG - nd; + if (e <= Ten_pmax + i) { + /* A fancier test would sometimes let us do + * this for larger i values. + */ + e -= i; + rv *= tens[i]; +#ifdef VAX + /* VAX exponent range is so narrow we must + * worry about overflow here... + */ + vax_ovfl_check: + word0(rv) -= P*Exp_msk1; + /* rv = */ rounded_product(rv, tens[e]); + if ((word0(rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) + goto ovfl; + word0(rv) += P*Exp_msk1; +#else + /* rv = */ rounded_product(rv, tens[e]); +#endif + goto ret; + } + } +#ifndef Inaccurate_Divide + else if (e >= -Ten_pmax) { + /* rv = */ rounded_quotient(rv, tens[-e]); + goto ret; + } +#endif + } + e1 += nd - k; + + /* Get starting approximation = rv * 10**e1 */ + + if (e1 > 0) { + if (i = e1 & 15) + rv *= tens[i]; + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { + ovfl: + errno = ERANGE; +#ifdef __STDC__ + rv = HUGE_VAL; +#else + /* Can't trust HUGE_VAL */ +#ifdef IEEE_Arith + word0(rv) = Exp_mask; + word1(rv) = 0; +#else + word0(rv) = Big0; + word1(rv) = Big1; +#endif +#endif + goto ret; + } + if (e1 >>= 4) { + for (j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + rv *= bigtens[j]; + /* The last multiplication could overflow. */ + word0(rv) -= P*Exp_msk1; + rv *= bigtens[j]; + if ((z = word0(rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-P)) + goto ovfl; + if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + /* set to largest number */ + /* (Can't trust DBL_MAX) */ + word0(rv) = Big0; + word1(rv) = Big1; + } + else + word0(rv) += P*Exp_msk1; + } + } + } else if (e1 < 0) { + e1 = -e1; + if (i = e1 & 15) + rv /= tens[i]; + if (e1 &= ~15) { + e1 >>= 4; + for (j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + rv *= tinytens[j]; + /* The last multiplication could underflow. */ + rv0 = rv; + rv *= tinytens[j]; + if (!rv) { + rv = 2.*rv0; + rv *= tinytens[j]; + if (!rv) { + undfl: + rv = 0.; + errno = ERANGE; + goto ret; + } + word0(rv) = Tiny0; + word1(rv) = Tiny1; + /* The refinement below will clean + * this approximation up. + */ + } + } + } + + /* Now the hard part -- adjusting rv to the correct value.*/ + + /* Put digits into bd: true value = bd * 10^e */ + + bd0 = s2b(s0, nd0, nd, y); + + for (;;) { + bd = Balloc(bd0->k); + Bcopy(bd, bd0); + bb = d2b(rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ + bs = i2b(1); + + if (e >= 0) { + bb2 = bb5 = 0; + bd2 = bd5 = e; + } else { + bb2 = bb5 = -e; + bd2 = bd5 = 0; + } + if (bbe >= 0) + bb2 += bbe; + else + bd2 -= bbe; + bs2 = bb2; +#ifdef Sudden_Underflow +#ifdef IBM + j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); +#else + j = P + 1 - bbbits; +#endif +#else + i = bbe + bbbits - 1; /* logb(rv) */ + if (i < Emin) /* denormal */ + j = bbe + (P-Emin); + else + j = P + 1 - bbbits; +#endif + bb2 += j; + bd2 += j; + i = bb2 < bd2 ? bb2 : bd2; + if (i > bs2) + i = bs2; + if (i > 0) { + bb2 -= i; + bd2 -= i; + bs2 -= i; + } + if (bb5 > 0) { + bs = pow5mult(bs, bb5); + bb1 = mult(bs, bb); + Bfree(bb); + bb = bb1; + } + if (bb2 > 0) + bb = lshift(bb, bb2); + if (bd5 > 0) + bd = pow5mult(bd, bd5); + if (bd2 > 0) + bd = lshift(bd, bd2); + if (bs2 > 0) + bs = lshift(bs, bs2); + delta = diff(bb, bd); + dsign = delta->sign; + delta->sign = 0; + i = cmp(delta, bs); + if (i < 0) { + /* Error is less than half an ulp -- check for + * special case of mantissa a power of two. + */ + if (dsign || word1(rv) || word0(rv) & Bndry_mask) + break; + delta = lshift(delta,Log2P); + if (cmp(delta, bs) > 0) + goto drop_down; + break; + } + if (i == 0) { + /* exactly half-way between */ + if (dsign) { + if ((word0(rv) & Bndry_mask1) == Bndry_mask1 + && word1(rv) == 0xffffffff) { + /*boundary case -- increment exponent*/ + word0(rv) = (word0(rv) & Exp_mask) + + Exp_msk1 +#ifdef IBM + | Exp_msk1 >> 4 +#endif + ; + word1(rv) = 0; + break; + } + } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { + drop_down: + /* boundary case -- decrement exponent */ +#ifdef Sudden_Underflow + L = word0(rv) & Exp_mask; +#ifdef IBM + if (L < Exp_msk1) +#else + if (L <= Exp_msk1) +#endif + goto undfl; + L -= Exp_msk1; +#else + L = (word0(rv) & Exp_mask) - Exp_msk1; +#endif + word0(rv) = L | Bndry_mask1; + word1(rv) = 0xffffffff; +#ifdef IBM + goto cont; +#else + break; +#endif + } +#ifndef ROUND_BIASED + if (!(word1(rv) & LSB)) + break; +#endif + if (dsign) + rv += ulp(rv); +#ifndef ROUND_BIASED + else { + rv -= ulp(rv); +#ifndef Sudden_Underflow + if (!rv) + goto undfl; +#endif + } +#endif + break; + } + if ((aadj = ratio(delta, bs)) <= 2.) { + if (dsign) + aadj = aadj1 = 1.; + else if (word1(rv) || word0(rv) & Bndry_mask) { +#ifndef Sudden_Underflow + if (word1(rv) == Tiny1 && !word0(rv)) + goto undfl; +#endif + aadj = 1.; + aadj1 = -1.; + } else { + /* special case -- power of FLT_RADIX to be */ + /* rounded down... */ + + if (aadj < 2./FLT_RADIX) + aadj = 1./FLT_RADIX; + else + aadj *= 0.5; + aadj1 = -aadj; + } + } else { + aadj *= 0.5; + aadj1 = dsign ? aadj : -aadj; +#ifdef Check_FLT_ROUNDS + switch(FLT_ROUNDS) { + case 2: /* towards +infinity */ + aadj1 -= 0.5; + break; + case 0: /* towards 0 */ + case 3: /* towards -infinity */ + aadj1 += 0.5; + } +#else + if (FLT_ROUNDS == 0) + aadj1 += 0.5; +#endif + } + y = word0(rv) & Exp_mask; + + /* Check for overflow */ + + if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { + rv0 = rv; + word0(rv) -= P*Exp_msk1; + adj = aadj1 * ulp(rv); + rv += adj; + if ((word0(rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (word0(rv0) == Big0 && word1(rv0) == Big1) + goto ovfl; + word0(rv) = Big0; + word1(rv) = Big1; + goto cont; + } else + word0(rv) += P*Exp_msk1; + } else { +#ifdef Sudden_Underflow + if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { + rv0 = rv; + word0(rv) += P*Exp_msk1; + adj = aadj1 * ulp(rv); + rv += adj; +#ifdef IBM + if ((word0(rv) & Exp_mask) < P*Exp_msk1) +#else + if ((word0(rv) & Exp_mask) <= P*Exp_msk1) +#endif + { + if (word0(rv0) == Tiny0 + && word1(rv0) == Tiny1) + goto undfl; + word0(rv) = Tiny0; + word1(rv) = Tiny1; + goto cont; + } else + word0(rv) -= P*Exp_msk1; + } else { + adj = aadj1 * ulp(rv); + rv += adj; + } +#else + /* Compute adj so that the IEEE rounding rules will + * correctly round rv + adj in some half-way cases. + * If rv * ulp(rv) is denormalized (i.e., + * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid + * trouble from bits lost to denormalization; + * example: 1.2e-307 . + */ + if (y <= (P-1)*Exp_msk1 && aadj >= 1.) { + aadj1 = (double)(int)(aadj + 0.5); + if (!dsign) + aadj1 = -aadj1; + } + adj = aadj1 * ulp(rv); + rv += adj; +#endif + } + z = word0(rv) & Exp_mask; + if (y == z) { + /* Can we stop now? */ + L = aadj; + aadj -= L; + /* The tolerances below are conservative. */ + if (dsign || word1(rv) || word0(rv) & Bndry_mask) { + if (aadj < .4999999 || aadj > .5000001) + break; + } else if (aadj < .4999999/FLT_RADIX) + break; + } + cont: + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(delta); + } + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(bd0); + Bfree(delta); + ret: + if (se) + *se = (char *)s; + return sign ? -rv : rv; +} + + static int +quorem +#ifdef KR_headers + (b, S) Bigint *b, *S; +#else + (Bigint *b, Bigint *S) +#endif +{ + int n; + long borrow, y; + unsigned long carry, q, ys; + unsigned long *bx, *bxe, *sx, *sxe; +#ifdef Pack_32 + long z; + unsigned long si, zs; +#endif + + n = S->wds; +#ifdef DEBUG + /*debug*/ if (b->wds > n) + /*debug*/ Bug("oversize b in quorem"); +#endif + if (b->wds < n) + return 0; + sx = S->x; + sxe = sx + --n; + bx = b->x; + bxe = bx + n; + q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ +#ifdef DEBUG + /*debug*/ if (q > 9) + /*debug*/ Bug("oversized quotient in quorem"); +#endif + if (q) { + borrow = 0; + carry = 0; + do { +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + z = (*bx >> 16) - (zs & 0xffff) + borrow; + borrow = z >> 16; + Sign_Extend(borrow, z); + Storeinc(bx, z, y); +#else + ys = *sx++ * q + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *bx++ = y & 0xffff; +#endif + } while (sx <= sxe); + if (!*bxe) { + bx = b->x; + while (--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + if (cmp(b, S) >= 0) { + q++; + borrow = 0; + carry = 0; + bx = b->x; + sx = S->x; + do { +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + z = (*bx >> 16) - (zs & 0xffff) + borrow; + borrow = z >> 16; + Sign_Extend(borrow, z); + Storeinc(bx, z, y); +#else + ys = *sx++ + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) + borrow; + borrow = y >> 16; + Sign_Extend(borrow, y); + *bx++ = y & 0xffff; +#endif + } while (sx <= sxe); + bx = b->x; + bxe = bx + n; + if (!*bxe) { + while (--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + return q; +} + +/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. + * + * Inspired by "How to Print Floating-Point Numbers Accurately" by + * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101]. + * + * Modifications: + * 1. Rather than iterating, we use a simple numeric overestimate + * to determine k = floor(log10(d)). We scale relevant + * quantities using O(log2(k)) rather than O(k) multiplications. + * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't + * try to generate digits strictly left to right. Instead, we + * compute with fewer bits and propagate the carry if necessary + * when rounding the final digit up. This is often faster. + * 3. Under the assumption that input will be rounded nearest, + * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. + * That is, we allow equality in stopping tests when the + * round-nearest rule will give the same floating-point value + * as would satisfaction of the stopping test with strict + * inequality. + * 4. We remove common factors of powers of 2 from relevant + * quantities. + * 5. When converting floating-point integers less than 1e16, + * we use floating-point arithmetic rather than resorting + * to multiple-precision integers. + * 6. When asked to produce fewer than 15 digits, we first try + * to get by with floating-point arithmetic; we resort to + * multiple-precision integer arithmetic only if we cannot + * guarantee that the floating-point calculation has given + * the correctly rounded result. For k requested digits and + * "uniformly" distributed input, the probability is + * something like 10^(k-15) that we must resort to the long + * calculation. + */ + +char * +__dtoa +#ifdef KR_headers + (d, mode, ndigits, decpt, sign, rve) + double d; int mode, ndigits, *decpt, *sign; char **rve; +#else + (double d, int mode, int ndigits, int *decpt, int *sign, char **rve) +#endif +{ + /* Arguments ndigits, decpt, sign are similar to those + of ecvt and fcvt; trailing zeros are suppressed from + the returned string. If not null, *rve is set to point + to the end of the return value. If d is +-Infinity or NaN, + then *decpt is set to 9999. + + mode: + 0 ==> shortest string that yields d when read in + and rounded to nearest. + 1 ==> like 0, but with Steele & White stopping rule; + e.g. with IEEE P754 arithmetic , mode 0 gives + 1e23 whereas mode 1 gives 9.999999999999999e22. + 2 ==> max(1,ndigits) significant digits. This gives a + return value similar to that of ecvt, except + that trailing zeros are suppressed. + 3 ==> through ndigits past the decimal point. This + gives a return value similar to that from fcvt, + except that trailing zeros are suppressed, and + ndigits can be negative. + 4-9 should give the same return values as 2-3, i.e., + 4 <= mode <= 9 ==> same return as mode + 2 + (mode & 1). These modes are mainly for + debugging; often they run slower but sometimes + faster than modes 2-3. + 4,5,8,9 ==> left-to-right digit generation. + 6-9 ==> don't try fast floating-point estimate + (if applicable). + + Values of mode other than 0-9 are treated as mode 0. + + Sufficient space is allocated to the return value + to hold the suppressed trailing zeros. + */ + + int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, + j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, + spec_case, try_quick; + long L; +#ifndef Sudden_Underflow + int denorm; + unsigned long x; +#endif + Bigint *b, *b1, *delta, *mlo, *mhi, *S; + double d2, ds, eps; + char *s, *s0; + static Bigint *result; + static int result_k; + + if (result) { + result->k = result_k; + result->maxwds = 1 << result_k; + Bfree(result); + result = 0; + } + + if (word0(d) & Sign_bit) { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + word0(d) &= ~Sign_bit; /* clear sign bit */ + } + else + *sign = 0; + +#if defined(IEEE_Arith) + defined(VAX) +#ifdef IEEE_Arith + if ((word0(d) & Exp_mask) == Exp_mask) +#else + if (word0(d) == 0x8000) +#endif + { + /* Infinity or NaN */ + *decpt = 9999; + s = +#ifdef IEEE_Arith + !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" : +#endif + "NaN"; + if (rve) + *rve = +#ifdef IEEE_Arith + s[3] ? s + 8 : +#endif + s + 3; + return s; + } +#endif +#ifdef IBM + d += 0; /* normalize */ +#endif + if (!d) { + *decpt = 1; + s = "0"; + if (rve) + *rve = s + 1; + return s; + } + + b = d2b(d, &be, &bbits); +#ifdef Sudden_Underflow + i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); +#else + if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) { +#endif + d2 = d; + word0(d2) &= Frac_mask1; + word0(d2) |= Exp_11; +#ifdef IBM + if (j = 11 - hi0bits(word0(d2) & Frac_mask)) + d2 /= 1 << j; +#endif + + /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 + * log10(x) = log(x) / log(10) + * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) + * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) + * + * This suggests computing an approximation k to log10(d) by + * + * k = (i - Bias)*0.301029995663981 + * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); + * + * We want k to be too large rather than too small. + * The error in the first-order Taylor series approximation + * is in our favor, so we just round up the constant enough + * to compensate for any error in the multiplication of + * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, + * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, + * adding 1e-13 to the constant term more than suffices. + * Hence we adjust the constant term to 0.1760912590558. + * (We could get a more accurate k by invoking log10, + * but this is probably not worthwhile.) + */ + + i -= Bias; +#ifdef IBM + i <<= 2; + i += j; +#endif +#ifndef Sudden_Underflow + denorm = 0; + } else { + /* d is denormalized */ + + i = bbits + be + (Bias + (P-1) - 1); + x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32 + : word1(d) << 32 - i; + d2 = x; + word0(d2) -= 31*Exp_msk1; /* adjust exponent */ + i -= (Bias + (P-1) - 1) + 1; + denorm = 1; + } +#endif + ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; + k = (int)ds; + if (ds < 0. && ds != k) + k--; /* want k = floor(ds) */ + k_check = 1; + if (k >= 0 && k <= Ten_pmax) { + if (d < tens[k]) + k--; + k_check = 0; + } + j = bbits - i - 1; + if (j >= 0) { + b2 = 0; + s2 = j; + } else { + b2 = -j; + s2 = 0; + } + if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; + } else { + b2 -= k; + b5 = -k; + s5 = 0; + } + if (mode < 0 || mode > 9) + mode = 0; + try_quick = 1; + if (mode > 5) { + mode -= 4; + try_quick = 0; + } + leftright = 1; + switch(mode) { + case 0: + case 1: + ilim = ilim1 = -1; + i = 18; + ndigits = 0; + break; + case 2: + leftright = 0; + /* no break */ + case 4: + if (ndigits <= 0) + ndigits = 1; + ilim = ilim1 = i = ndigits; + break; + case 3: + leftright = 0; + /* no break */ + case 5: + i = ndigits + k + 1; + ilim = i; + ilim1 = i - 1; + if (i <= 0) + i = 1; + } + j = sizeof(unsigned long); + for (result_k = 0; sizeof(Bigint) - sizeof(unsigned long) + j < i; + j <<= 1) result_k++; + result = Balloc(result_k); + s = s0 = (char *)result; + + if (ilim >= 0 && ilim <= Quick_max && try_quick) { + + /* Try to get by with floating-point arithmetic. */ + + i = 0; + d2 = d; + k0 = k; + ilim0 = ilim; + ieps = 2; /* conservative */ + if (k > 0) { + ds = tens[k&0xf]; + j = k >> 4; + if (j & Bletch) { + /* prevent overflows */ + j &= Bletch - 1; + d /= bigtens[n_bigtens-1]; + ieps++; + } + for (; j; j >>= 1, i++) + if (j & 1) { + ieps++; + ds *= bigtens[i]; + } + d /= ds; + } else if (j1 = -k) { + d *= tens[j1 & 0xf]; + for (j = j1 >> 4; j; j >>= 1, i++) + if (j & 1) { + ieps++; + d *= bigtens[i]; + } + } + if (k_check && d < 1. && ilim > 0) { + if (ilim1 <= 0) + goto fast_failed; + ilim = ilim1; + k--; + d *= 10.; + ieps++; + } + eps = ieps*d + 7.; + word0(eps) -= (P-1)*Exp_msk1; + if (ilim == 0) { + S = mhi = 0; + d -= 5.; + if (d > eps) + goto one_digit; + if (d < -eps) + goto no_digits; + goto fast_failed; + } +#ifndef No_leftright + if (leftright) { + /* Use Steele & White method of only + * generating digits needed. + */ + eps = 0.5/tens[ilim-1] - eps; + for (i = 0;;) { + L = d; + d -= L; + *s++ = '0' + (int)L; + if (d < eps) + goto ret1; + if (1. - d < eps) + goto bump_up; + if (++i >= ilim) + break; + eps *= 10.; + d *= 10.; + } + } else { +#endif + /* Generate ilim digits, then fix them up. */ + eps *= tens[ilim-1]; + for (i = 1;; i++, d *= 10.) { + L = d; + d -= L; + *s++ = '0' + (int)L; + if (i == ilim) { + if (d > 0.5 + eps) + goto bump_up; + else if (d < 0.5 - eps) { + while (*--s == '0'); + s++; + goto ret1; + } + break; + } + } +#ifndef No_leftright + } +#endif + fast_failed: + s = s0; + d = d2; + k = k0; + ilim = ilim0; + } + + /* Do we have a "small" integer? */ + + if (be >= 0 && k <= Int_max) { + /* Yes. */ + ds = tens[k]; + if (ndigits < 0 && ilim <= 0) { + S = mhi = 0; + if (ilim < 0 || d <= 5*ds) + goto no_digits; + goto one_digit; + } + for (i = 1;; i++) { + L = d / ds; + d -= L*ds; +#ifdef Check_FLT_ROUNDS + /* If FLT_ROUNDS == 2, L will usually be high by 1 */ + if (d < 0) { + L--; + d += ds; + } +#endif + *s++ = '0' + (int)L; + if (i == ilim) { + d += d; + if (d > ds || d == ds && L & 1) { + bump_up: + while (*--s == '9') + if (s == s0) { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + if (!(d *= 10.)) + break; + } + goto ret1; + } + + m2 = b2; + m5 = b5; + mhi = mlo = 0; + if (leftright) { + if (mode < 2) { + i = +#ifndef Sudden_Underflow + denorm ? be + (Bias + (P-1) - 1 + 1) : +#endif +#ifdef IBM + 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); +#else + 1 + P - bbits; +#endif + } else { + j = ilim - 1; + if (m5 >= j) + m5 -= j; + else { + s5 += j -= m5; + b5 += j; + m5 = 0; + } + if ((i = ilim) < 0) { + m2 -= i; + i = 0; + } + } + b2 += i; + s2 += i; + mhi = i2b(1); + } + if (m2 > 0 && s2 > 0) { + i = m2 < s2 ? m2 : s2; + b2 -= i; + m2 -= i; + s2 -= i; + } + if (b5 > 0) { + if (leftright) { + if (m5 > 0) { + mhi = pow5mult(mhi, m5); + b1 = mult(mhi, b); + Bfree(b); + b = b1; + } + if (j = b5 - m5) + b = pow5mult(b, j); + } else + b = pow5mult(b, b5); + } + S = i2b(1); + if (s5 > 0) + S = pow5mult(S, s5); + + /* Check for special case that d is a normalized power of 2. */ + + if (mode < 2) { + if (!word1(d) && !(word0(d) & Bndry_mask) +#ifndef Sudden_Underflow + && word0(d) & Exp_mask +#endif + ) { + /* The special case */ + b2 += Log2P; + s2 += Log2P; + spec_case = 1; + } else + spec_case = 0; + } + + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + * + * Perhaps we should just compute leading 28 bits of S once + * and for all and pass them and a shift to quorem, so it + * can do shifts and ors to compute the numerator for q. + */ +#ifdef Pack_32 + if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) + i = 32 - i; +#else + if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) + i = 16 - i; +#endif + if (i > 4) { + i -= 4; + b2 += i; + m2 += i; + s2 += i; + } else if (i < 4) { + i += 28; + b2 += i; + m2 += i; + s2 += i; + } + if (b2 > 0) + b = lshift(b, b2); + if (s2 > 0) + S = lshift(S, s2); + if (k_check) { + if (cmp(b,S) < 0) { + k--; + b = multadd(b, 10, 0); /* we botched the k estimate */ + if (leftright) + mhi = multadd(mhi, 10, 0); + ilim = ilim1; + } + } + if (ilim <= 0 && mode > 2) { + if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { + /* no digits, fcvt style */ + no_digits: + k = -1 - ndigits; + goto ret; + } + one_digit: + *s++ = '1'; + k++; + goto ret; + } + if (leftright) { + if (m2 > 0) + mhi = lshift(mhi, m2); + + /* Compute mlo -- check for special case + * that d is a normalized power of 2. + */ + + mlo = mhi; + if (spec_case) { + mhi = Balloc(mhi->k); + Bcopy(mhi, mlo); + mhi = lshift(mhi, Log2P); + } + + for (i = 1;;i++) { + dig = quorem(b,S) + '0'; + /* Do we yet have the shortest decimal string + * that will round to d? + */ + j = cmp(b, mlo); + delta = diff(S, mhi); + j1 = delta->sign ? 1 : cmp(b, delta); + Bfree(delta); +#ifndef ROUND_BIASED + if (j1 == 0 && !mode && !(word1(d) & 1)) { + if (dig == '9') + goto round_9_up; + if (j > 0) + dig++; + *s++ = dig; + goto ret; + } +#endif + if (j < 0 || j == 0 && !mode +#ifndef ROUND_BIASED + && !(word1(d) & 1) +#endif + ) { + if (j1 > 0) { + b = lshift(b, 1); + j1 = cmp(b, S); + if ((j1 > 0 || j1 == 0 && dig & 1) + && dig++ == '9') + goto round_9_up; + } + *s++ = dig; + goto ret; + } + if (j1 > 0) { + if (dig == '9') { /* possible if i == 1 */ + round_9_up: + *s++ = '9'; + goto roundoff; + } + *s++ = dig + 1; + goto ret; + } + *s++ = dig; + if (i == ilim) + break; + b = multadd(b, 10, 0); + if (mlo == mhi) + mlo = mhi = multadd(mhi, 10, 0); + else { + mlo = multadd(mlo, 10, 0); + mhi = multadd(mhi, 10, 0); + } + } + } else + for (i = 1;; i++) { + *s++ = dig = quorem(b,S) + '0'; + if (i >= ilim) + break; + b = multadd(b, 10, 0); + } + + /* Round off last digit */ + + b = lshift(b, 1); + j = cmp(b, S); + if (j > 0 || j == 0 && dig & 1) { + roundoff: + while (*--s == '9') + if (s == s0) { + k++; + *s++ = '1'; + goto ret; + } + ++*s++; + } else { + while (*--s == '0'); + s++; + } + ret: + Bfree(S); + if (mhi) { + if (mlo && mlo != mhi) + Bfree(mlo); + Bfree(mhi); + } + ret1: + Bfree(b); + if (s == s0) { /* don't return empty string */ + *s++ = '0'; + k = 0; + } + *s = 0; + *decpt = k + 1; + if (rve) + *rve = s; + return s0; + } +#ifdef __cplusplus +} +#endif