diff --git a/newlib/ChangeLog b/newlib/ChangeLog index 2544b4e48..e1e2f35e0 100644 --- a/newlib/ChangeLog +++ b/newlib/ChangeLog @@ -1,3 +1,17 @@ +2000-12-06 Jeff Johnston + + * libc/stdlib/Makefile.am: Added ldtoa.c to list of sources. + * libc/stdlib/Makefile.in: Regenerated. + * libc/stdio/floatio.h: Added suitable MAXEXP for long double. + * libc/stdio/vfieeefp.h: Added long double bit structures. + * libc/stdio/vfprintf.c[WANT_IO_LONG_DBL]: Added long double support. + [WANT_IO_LONG_DBL](isinfl, isnanl): New static long double routines. + (exponent): Changed expbuf to reasonable maximum instead of MAXEXP. + * libc/stdio/vfscanf.c[WANT_IO_LONG_DBL]: Added long double support. + * libc/stdlib/ldtoa.c: New file containing _ldtoa_r and + _strtold routines used for conversions between character + and long double. + Wed Dec 6 12:01:00 2000 Corinna Vinschen * libc/include/stdlib.h: Add declarations for `mkstemp' and `mktemp'. diff --git a/newlib/libc/stdio/floatio.h b/newlib/libc/stdio/floatio.h index d9577b2b2..496721b88 100644 --- a/newlib/libc/stdio/floatio.h +++ b/newlib/libc/stdio/floatio.h @@ -21,7 +21,12 @@ * Floating point scanf/printf (input/output) definitions. */ +#ifdef _NO_LONGDBL /* 11-bit exponent (VAX G floating point) is 308 decimal digits */ #define MAXEXP 308 +#else /* !_NO_LONGDBL */ +/* 15-bit exponent (Intel extended floating point) is 4932 decimal digits */ +#define MAXEXP 4932 +#endif /* !_NO_LONGDBL */ /* 128 bit fraction takes up 39 decimal digits; max reasonable precision */ #define MAXFRACT 39 diff --git a/newlib/libc/stdio/vfieeefp.h b/newlib/libc/stdio/vfieeefp.h index 6843d5f47..de0267223 100644 --- a/newlib/libc/stdio/vfieeefp.h +++ b/newlib/libc/stdio/vfieeefp.h @@ -57,6 +57,85 @@ Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. #endif +#ifdef WANT_IO_LONG_DBL +/* If we are going to examine or modify specific bits in a long double using + the lword0 or lwordx macros, then we must wrap the long double inside + a union. This is necessary to avoid undefined behavior according to + the ANSI C spec. */ + +#ifdef IEEE_8087 +#if LDBL_MANT_DIG == 24 +struct ldieee +{ + unsigned manh:23; + unsigned exp:8; + unsigned sign:1; +} +#elif LDBL_MANT_DIG == 53 +struct ldieee +{ + unsigned manl:20; + unsigned manh:32; + unsigned exp:11; + unsigned sign:1; +} +#elif LDBL_MANT_DIG == 64 +struct ldieee +{ + unsigned manl:32; + unsigned manh:32; + unsigned exp:15; + unsigned sign:1; +}; +#elif LDBL_MANT_DIG > 64 +struct ldieee +{ + unsigned manl3:16; + unsigned manl2:32; + unsigned manl:32; + unsigned manh:32; + unsigned exp:15; + unsigned sign:1; +}; +#endif /* LDBL_MANT_DIG */ +#else /* !IEEE_8087 */ +#if LDBL_MANT_DIG == 24 +struct ldieee +{ + unsigned sign:1; + unsigned exp:8; + unsigned manh:23; +} +#elif LDBL_MANT_DIG == 53 +struct ldieee +{ + unsigned sign:1; + unsigned exp:11; + unsigned manh:32; + unsigned manl:20; +} +#elif LDBL_MANT_DIG == 64 +struct ldieee +{ + unsigned sign:1; + unsigned exp:15; + unsigned manh:32; + unsigned manl:32; +} +#elif LDBL_MANT_DIG > 64 +struct ldieee +{ + unsigned sign:1; + unsigned exp:15; + unsigned manh:32; + unsigned manl:32; + unsigned manl2:32; + unsigned manl3;16; +}; +#endif /* LDBL_MANT_DIG */ +#endif /* !IEEE_8087 */ +#endif /* WANT_IO_LONG_DBL */ + /* If we are going to examine or modify specific bits in a double using the word0 and/or word1 macros, then we must wrap the double inside a union. This is necessary to avoid undefined behavior according to diff --git a/newlib/libc/stdio/vfprintf.c b/newlib/libc/stdio/vfprintf.c index 117f7eb80..ea458467d 100644 --- a/newlib/libc/stdio/vfprintf.c +++ b/newlib/libc/stdio/vfprintf.c @@ -174,6 +174,14 @@ static char *rcsid = "$Id$"; #include "fvwrite.h" #include "vfieeefp.h" +/* Currently a test is made to see if long double processing is warranted. + This could be changed in the future should the _ldtoa_r code be + preferred over _dtoa_r. */ +#define _NO_LONGDBL +#if defined WANT_IO_LONG_DBL && (LDBL_MANT_DIG > DBL_MANT_DIG) +#undef _NO_LONGDBL +#endif + /* * Flush out all the vectors defined by the given uio, * then reset it so that it can be reused. @@ -240,7 +248,14 @@ __sbprintf(fp, fmt, ap) #define BUF (MAXEXP+MAXFRACT+1) /* + decimal point */ #define DEFPREC 6 +#ifdef _NO_LONGDBL static char *cvt _PARAMS((struct _reent *, double, int, int, char *, int *, int, int *)); +#else +static char *cvt _PARAMS((struct _reent *, _LONG_DOUBLE, int, int, char *, int *, int, int *)); +static int isinfl _PARAMS((_LONG_DOUBLE *)); +static int isnanl _PARAMS((_LONG_DOUBLE *)); +#endif + static int exponent _PARAMS((char *, int, int)); #else /* no FLOATING_POINT */ @@ -263,7 +278,7 @@ static int exponent _PARAMS((char *, int, int)); #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 LONGDBL 0x008 /* long double */ #define LONGINT 0x010 /* long integer */ #define QUADINT 0x020 /* quad integer */ #define SHORTINT 0x040 /* short integer */ @@ -301,9 +316,13 @@ _DEFUN (_VFPRINTF_R, (data, fp, fmt0, ap), #ifdef FLOATING_POINT char *decimal_point = localeconv()->decimal_point; char softsign; /* temporary negative sign for floats */ - double _double; /* double precision arguments %[eEfgG] */ +#ifdef _NO_LONGDBL + double _fpvalue; /* floating point arguments %[eEfgG] */ +#else + _LONG_DOUBLE _fpvalue; /* floating point arguments %[eEfgG] */ +#endif int expt; /* integer value of exponent */ - int expsize; /* character count for expstr */ + int expsize = 0; /* character count for expstr */ int ndig; /* actual number of digits returned by cvt */ char expstr[7]; /* buffer for exponent string */ #endif @@ -322,7 +341,7 @@ _DEFUN (_VFPRINTF_R, (data, fp, fmt0, ap), int dprec; /* a copy of prec if [diouxX], 0 otherwise */ int realsz; /* field size expanded by dprec */ int size; /* size of converted field or string */ - char *xdigs; /* digits for [xX] conversion */ + char *xdigs = NULL; /* digits for [xX] conversion */ #define NIOV 8 struct __suio uio; /* output information: summary */ struct __siov iov[NIOV];/* ... and individual io vectors */ @@ -553,29 +572,55 @@ reswitch: switch (ch) { prec = 1; } +#ifdef _NO_LONGDBL if (flags & LONGDBL) { - _double = (double) va_arg(ap, long double); + _fpvalue = (double) va_arg(ap, _LONG_DOUBLE); } else { - _double = va_arg(ap, double); + _fpvalue = va_arg(ap, double); } /* do this before tricky precision changes */ - if (isinf(_double)) { - if (_double < 0) + if (isinf(_fpvalue)) { + if (_fpvalue < 0) sign = '-'; cp = "Inf"; size = 3; break; } - if (isnan(_double)) { + if (isnan(_fpvalue)) { cp = "NaN"; size = 3; break; } +#else /* !_NO_LONGDBL */ + + if (flags & LONGDBL) { + _fpvalue = va_arg(ap, _LONG_DOUBLE); + } else { + _fpvalue = (_LONG_DOUBLE)va_arg(ap, double); + } + + /* do this before tricky precision changes */ + if (isinfl(&_fpvalue)) { + if (_fpvalue < 0) + sign = '-'; + cp = "Inf"; + size = 3; + break; + } + if (isnanl(&_fpvalue)) { + cp = "NaN"; + size = 3; + break; + } +#endif /* !_NO_LONGDBL */ + flags |= FPT; - cp = cvt(data, _double, prec, flags, &softsign, + + cp = cvt(data, _fpvalue, prec, flags, &softsign, &expt, ch, &ndig); + if (ch == 'g' || ch == 'G') { if (expt <= -4 || expt > prec) ch = (ch == 'g') ? 'e' : 'E'; @@ -796,7 +841,7 @@ number: if ((dprec = prec) >= 0) PRINT(cp, size); } else { /* glue together f_p fragments */ if (ch >= 'f') { /* 'f' or 'g' */ - if (_double == 0) { + if (_fpvalue == 0) { /* kludge for __dtoa irregularity */ PRINT("0", 1); if (expt < ndig || (flags & ALT) != 0) { @@ -826,7 +871,7 @@ number: if ((dprec = prec) >= 0) ox[0] = *cp++; ox[1] = '.'; PRINT(ox, 2); - if (_double) { + if (_fpvalue) { PRINT(cp, ndig-1); } else /* 0.[0..] */ /* __dtoa irregularity */ @@ -857,19 +902,60 @@ error: #ifdef FLOATING_POINT +#ifdef _NO_LONGDBL extern char *_dtoa_r _PARAMS((struct _reent *, double, int, int, int *, int *, char **)); +#else +extern char *_ldtoa_r _PARAMS((struct _reent *, _LONG_DOUBLE, int, + int, int *, int *, char **)); +#undef word0 +#define word0(x) ldword0(x) + +static int +isinfl (value) + _LONG_DOUBLE *value; +{ + struct ldieee *ldptr; + + ldptr = (struct ldieee *)value; + + if (ldptr->exp == 0x7fff && !(ldptr->manh & 0x7fffffff) && !ldptr->manl) + return 1; + return 0; +} + +static int +isnanl (value) + _LONG_DOUBLE *value; +{ + struct ldieee *ldptr; + + ldptr = (struct ldieee *)value; + + if (ldptr->exp == 0x7fff && ((ldptr->manh & 0x7fffffff) || ldptr->manl)) + return 1; + return 0; +} +#endif static char * cvt(data, value, ndigits, flags, sign, decpt, ch, length) struct _reent *data; +#ifdef _NO_LONGDBL double value; +#else + _LONG_DOUBLE value; +#endif int ndigits, flags, *decpt, ch, *length; char *sign; { int mode, dsgn; char *digits, *bp, *rve; +#ifdef _NO_LONGDBL union double_union tmp; +#else + struct ldieee *ldptr; +#endif if (ch == 'f') { mode = 3; /* ndigits after the decimal point */ @@ -884,13 +970,27 @@ cvt(data, value, ndigits, flags, sign, decpt, ch, length) mode = 2; /* ndigits significant digits */ } +#ifdef _NO_LONGDBL tmp.d = value; + if (word0(tmp) & Sign_bit) { /* this will check for < 0 and -0.0 */ value = -value; *sign = '-'; } else *sign = '\000'; + digits = _dtoa_r(data, value, mode, ndigits, decpt, &dsgn, &rve); +#else /* !_NO_LONGDBL */ + ldptr = (struct ldieee *)&value; + if (ldptr->sign) { /* this will check for < 0 and -0.0 */ + value = -value; + *sign = '-'; + } else + *sign = '\000'; + + digits = _ldtoa_r(data, value, mode, ndigits, decpt, &dsgn, &rve); +#endif /* !_NO_LONGDBL */ + if ((ch != 'g' && ch != 'G') || flags & ALT) { /* Print trailing zeros */ bp = digits + ndigits; if (ch == 'f') { @@ -913,7 +1013,7 @@ exponent(p0, exp, fmtch) int exp, fmtch; { register char *p, *t; - char expbuf[MAXEXP]; + char expbuf[40]; p = p0; *p++ = fmtch; @@ -923,13 +1023,13 @@ exponent(p0, exp, fmtch) } else *p++ = '+'; - t = expbuf + MAXEXP; + t = expbuf + 40; if (exp > 9) { do { *--t = to_char(exp % 10); } while ((exp /= 10) > 9); *--t = to_char(exp); - for (; t < expbuf + MAXEXP; *p++ = *t++); + for (; t < expbuf + 40; *p++ = *t++); } else { *p++ = '0'; diff --git a/newlib/libc/stdio/vfscanf.c b/newlib/libc/stdio/vfscanf.c index 7e88f1202..cc0f26d3c 100644 --- a/newlib/libc/stdio/vfscanf.c +++ b/newlib/libc/stdio/vfscanf.c @@ -34,6 +34,17 @@ #endif #ifdef FLOATING_POINT +#include + +/* Currently a test is made to see if long double processing is warranted. + This could be changed in the future should the _ldtoa_r code be + preferred over _dtoa_r. */ +#define _NO_LONGDBL +#if defined WANT_IO_LONG_DBL && (LDBL_MANT_DIG > DBL_MANT_DIG) +#undef _NO_LONGDBL +extern _LONG_DOUBLE _strtold _PARAMS((char *s, char **sptr)); +#endif + #include "floatio.h" #define BUF (MAXEXP+MAXFRACT+3) /* 3 = sign + decimal point + NUL */ /* An upper bound for how long a long prints in decimal. 4 / 13 approximates @@ -48,7 +59,7 @@ */ #define LONG 0x01 /* l: long or double */ -#define LONGDBL 0x02 /* L: long double; unimplemented */ +#define LONGDBL 0x02 /* L: long double */ #define SHORT 0x04 /* h: short */ #define SUPPRESS 0x08 /* suppress assignment */ #define POINTER 0x10 /* weird %p pointer (`fake hex') */ @@ -372,7 +383,7 @@ __svfscanf (fp, fmt0, ap) for (;;) { - if ((n = fp->_r) < width) + if ((n = fp->_r) < (int)width) { sum += n; width -= n; @@ -683,8 +694,9 @@ __svfscanf (fp, fmt0, ap) However, ANSI / ISO C makes no such stipulation; we have to get exact results even when there is an unreasonable amount of leading zeroes. */ - long leading_zeroes, zeroes, exp_adjust; - char *exp_start; + long leading_zeroes = 0; + long zeroes, exp_adjust; + char *exp_start = NULL; #ifdef hardway if (width == 0 || width > sizeof (buf) - 1) width = sizeof (buf) - 1; @@ -808,7 +820,11 @@ __svfscanf (fp, fmt0, ap) } if ((flags & SUPPRESS) == 0) { +#ifdef _NO_LONGDBL double res; +#else /* !_NO_LONG_DBL */ + long double res; +#endif /* !_NO_LONG_DBL */ long new_exp; *p = 0; @@ -829,7 +845,11 @@ __svfscanf (fp, fmt0, ap) exp_start = buf + sizeof (buf) - MAX_LONG_LEN - 1; sprintf (exp_start, "e%ld", new_exp); } +#ifdef _NO_LONG_DBL res = atof (buf); +#else /* !_NO_LONG_DBL */ + res = _strtold (buf, NULL); +#endif /* !_NO_LONG_DBL */ if (flags & LONG) { dp = va_arg (ap, double *); diff --git a/newlib/libc/stdlib/Makefile.am b/newlib/libc/stdlib/Makefile.am index f33550fc7..e6d60dbc3 100644 --- a/newlib/libc/stdlib/Makefile.am +++ b/newlib/libc/stdlib/Makefile.am @@ -34,6 +34,7 @@ lib_a_SOURCES = \ getopt.c \ labs.c \ ldiv.c \ + ldtoa.c \ malign.c \ malloc.c \ mblen.c \ @@ -157,6 +158,7 @@ doc: $(CHEWOUT_FILES) CLEANFILES = $(CHEWOUT_FILES) *.ref dtoa.o: dtoa.c mprec.h +ldtoa.o: ldtoa.c mprec.h ecvtbuf.o: ecvtbuf.c mprec.h mbtowc_r.o: mbtowc_r.c mbctype.h $(COMPILE) -c -fshort-enums $(srcdir)/mbtowc_r.c -o $@ diff --git a/newlib/libc/stdlib/Makefile.in b/newlib/libc/stdlib/Makefile.in index 82664b3b6..8274e6c88 100644 --- a/newlib/libc/stdlib/Makefile.in +++ b/newlib/libc/stdlib/Makefile.in @@ -116,6 +116,7 @@ lib_a_SOURCES = \ getopt.c \ labs.c \ ldiv.c \ + ldtoa.c \ malign.c \ malloc.c \ mblen.c \ @@ -212,11 +213,12 @@ malloptr.o lib_a_OBJECTS = __adjust.o __exp10.o __ten_mu.o abort.o abs.o assert.o \ atexit.o atof.o atoff.o atoi.o atol.o bsearch.o calloc.o div.o dtoa.o \ dtoastub.o ecvtbuf.o efgcvt.o environ.o envlock.o eprintf.o exit.o \ -getenv.o getenv_r.o getopt.o labs.o ldiv.o malign.o malloc.o mblen.o \ -mblen_r.o mbstowcs.o mbstowcs_r.o mbtowc.o mbtowc_r.o mlock.o mprec.o \ -msize.o mstats.o mtrim.o putenv.o putenv_r.o qsort.o rand.o rand_r.o \ -realloc.o setenv.o setenv_r.o strdup.o strdup_r.o strtod.o strtol.o \ -strtoul.o system.o valloc.o wcstombs.o wcstombs_r.o wctomb.o wctomb_r.o +getenv.o getenv_r.o getopt.o labs.o ldiv.o ldtoa.o malign.o malloc.o \ +mblen.o mblen_r.o mbstowcs.o mbstowcs_r.o mbtowc.o mbtowc_r.o mlock.o \ +mprec.o msize.o mstats.o mtrim.o putenv.o putenv_r.o qsort.o rand.o \ +rand_r.o realloc.o setenv.o setenv_r.o strdup.o strdup_r.o strtod.o \ +strtol.o strtoul.o system.o valloc.o wcstombs.o wcstombs_r.o wctomb.o \ +wctomb_r.o CFLAGS = @CFLAGS@ COMPILE = $(CC) $(DEFS) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CFLAGS) $(CFLAGS) CCLD = $(CC) @@ -226,7 +228,7 @@ DIST_COMMON = Makefile.am Makefile.in DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST) -TAR = tar +TAR = gtar GZIP_ENV = --best SOURCES = $(lib_a_SOURCES) OBJECTS = $(lib_a_OBJECTS) @@ -312,7 +314,7 @@ distdir: $(DISTFILES) @for file in $(DISTFILES); do \ if test -f $$file; then d=.; else d=$(srcdir); fi; \ if test -d $$d/$$file; then \ - cp -pr $$/$$file $(distdir)/$$file; \ + cp -pr $$d/$$file $(distdir)/$$file; \ else \ test -f $(distdir)/$$file \ || ln $$d/$$file $(distdir)/$$file 2> /dev/null \ @@ -436,6 +438,7 @@ doc: $(CHEWOUT_FILES) cat $(srcdir)/stdlib.tex >> $(TARGETDOC) dtoa.o: dtoa.c mprec.h +ldtoa.o: ldtoa.c mprec.h ecvtbuf.o: ecvtbuf.c mprec.h mbtowc_r.o: mbtowc_r.c mbctype.h $(COMPILE) -c -fshort-enums $(srcdir)/mbtowc_r.c -o $@ diff --git a/newlib/libc/stdlib/ldtoa.c b/newlib/libc/stdlib/ldtoa.c new file mode 100644 index 000000000..c6e63774e --- /dev/null +++ b/newlib/libc/stdlib/ldtoa.c @@ -0,0 +1,3667 @@ + + /* Extended precision arithmetic functions for long double I/O. + * This program has been placed in the public domain. + */ + +#include <_ansi.h> +#include +#include +#include +#include +#include "mprec.h" + +/* These are the externally visible entries. */ +/* linux name: long double _IO_strtold (char *, char **); */ +long double _strtold (char *, char **); +char * _ldtoa_r (struct _reent *, long double, int, int, int *, int *, char **); +#if 0 +void _IO_ldtostr(long double *, char *, int, int, char); +#endif + + /* Number of 16 bit words in external x type format */ + #define NE 10 + + /* Number of 16 bit words in internal format */ + #define NI (NE+3) + + /* Array offset to exponent */ + #define E 1 + + /* Array offset to high guard word */ + #define M 2 + + /* Number of bits of precision */ + #define NBITS ((NI-4)*16) + + /* Maximum number of decimal digits in ASCII conversion + * = NBITS*log10(2) + */ + #define NDEC (NBITS*8/27) + + /* The exponent of 1.0 */ + #define EXONE (0x3fff) + +/* Control structure for long doublue conversion including rounding precision values. + * rndprc can be set to 80 (if NE=6), 64, 56, 53, or 24 bits. + */ +typedef struct +{ + int rlast; + int rndprc; + int rw; + int re; + int outexpon; + unsigned short rmsk; + unsigned short rmbit; + unsigned short rebit; + unsigned short rbit[NI]; + unsigned short equot[NI]; +} LDPARMS; + +static void esub(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp); +static void emul(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp); +static void ediv(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp); +static int ecmp(short unsigned int *a, short unsigned int *b); +static int enormlz(short unsigned int *x); +static int eshift(short unsigned int *x, int sc); +static void eshup1(register short unsigned int *x); +static void eshup8(register short unsigned int *x); +static void eshup6(register short unsigned int *x); +static void eshdn1(register short unsigned int *x); +static void eshdn8(register short unsigned int *x); +static void eshdn6(register short unsigned int *x); +static void eneg(short unsigned int *x); +static void emov(register short unsigned int *a, register short unsigned int *b); +static void eclear(register short unsigned int *x); +static void einfin(register short unsigned int *x, register LDPARMS *ldp); +static void efloor(short unsigned int *x, short unsigned int *y, LDPARMS *ldp); +static void etoasc(short unsigned int *x, char *string, int ndigs, int outformat, LDPARMS *ldp); +#if LDBL_MANT_DIG == 24 +static void e24toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp); +#elif LDBL_MANT_DIG == 53 +static void e53toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp); +#elif LDBL_MANT_DIG == 64 +static void e64toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp); +#else +static void e113toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp); +#endif + +/* econst.c */ +/* e type constants used by high precision check routines */ + +#if NE == 10 +/* 0.0 */ +static unsigned short ezero[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,}; + +/* 1.0E0 */ +static unsigned short eone[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,}; + +#else + +/* 0.0 */ +static unsigned short ezero[NE] = { +0, 0000000,0000000,0000000,0000000,0000000,}; +/* 1.0E0 */ +static unsigned short eone[NE] = { +0, 0000000,0000000,0000000,0100000,0x3fff,}; + +#endif + +/* Debugging routine for displaying errors */ +#ifdef DEBUG +/* Notice: the order of appearance of the following + * messages is bound to the error codes defined + * in mconf.h. + */ +static char *ermsg[7] = { +"unknown", /* error code 0 */ +"domain", /* error code 1 */ +"singularity", /* et seq. */ +"overflow", +"underflow", +"total loss of precision", +"partial loss of precision" +}; +#define mtherr(name, code) printf( "\n%s %s error\n", name, ermsg[code] ); +#else +#define mtherr(name, code) +#endif + +/* ieee.c + * + * Extended precision IEEE binary floating point arithmetic routines + * + * Numbers are stored in C language as arrays of 16-bit unsigned + * short integers. The arguments of the routines are pointers to + * the arrays. + * + * + * External e type data structure, simulates Intel 8087 chip + * temporary real format but possibly with a larger significand: + * + * NE-1 significand words (least significant word first, + * most significant bit is normally set) + * exponent (value = EXONE for 1.0, + * top bit is the sign) + * + * + * Internal data structure of a number (a "word" is 16 bits): + * + * ei[0] sign word (0 for positive, 0xffff for negative) + * ei[1] biased exponent (value = EXONE for the number 1.0) + * ei[2] high guard word (always zero after normalization) + * ei[3] + * to ei[NI-2] significand (NI-4 significand words, + * most significant word first, + * most significant bit is set) + * ei[NI-1] low guard word (0x8000 bit is rounding place) + * + * + * + * Routines for external format numbers + * + * asctoe( string, e ) ASCII string to extended double e type + * asctoe64( string, &d ) ASCII string to long double + * asctoe53( string, &d ) ASCII string to double + * asctoe24( string, &f ) ASCII string to single + * asctoeg( string, e, prec, ldp ) ASCII string to specified precision + * e24toe( &f, e, ldp ) IEEE single precision to e type + * e53toe( &d, e, ldp ) IEEE double precision to e type + * e64toe( &d, e, ldp ) IEEE long double precision to e type + * e113toe( &d, e, ldp ) IEEE long double precision to e type + * eabs(e) absolute value + * eadd( a, b, c ) c = b + a + * eclear(e) e = 0 + * ecmp (a, b) Returns 1 if a > b, 0 if a == b, + * -1 if a < b, -2 if either a or b is a NaN. + * ediv( a, b, c, ldp ) c = b / a + * efloor( a, b, ldp ) truncate to integer, toward -infinity + * efrexp( a, exp, s ) extract exponent and significand + * eifrac( e, &l, frac ) e to long integer and e type fraction + * euifrac( e, &l, frac ) e to unsigned long integer and e type fraction + * einfin( e, ldp ) set e to infinity, leaving its sign alone + * eldexp( a, n, b ) multiply by 2**n + * emov( a, b ) b = a + * emul( a, b, c, ldp ) c = b * a + * eneg(e) e = -e + * eround( a, b ) b = nearest integer value to a + * esub( a, b, c, ldp ) c = b - a + * e24toasc( &f, str, n ) single to ASCII string, n digits after decimal + * e53toasc( &d, str, n ) double to ASCII string, n digits after decimal + * e64toasc( &d, str, n ) long double to ASCII string + * etoasc(e,str,n,fmt,ldp)e to ASCII string, n digits after decimal + * etoe24( e, &f ) convert e type to IEEE single precision + * etoe53( e, &d ) convert e type to IEEE double precision + * etoe64( e, &d ) convert e type to IEEE long double precision + * ltoe( &l, e ) long (32 bit) integer to e type + * ultoe( &l, e ) unsigned long (32 bit) integer to e type + * eisneg( e ) 1 if sign bit of e != 0, else 0 + * eisinf( e ) 1 if e has maximum exponent (non-IEEE) + * or is infinite (IEEE) + * eisnan( e ) 1 if e is a NaN + * esqrt( a, b ) b = square root of a + * + * + * Routines for internal format numbers + * + * eaddm( ai, bi ) add significands, bi = bi + ai + * ecleaz(ei) ei = 0 + * ecleazs(ei) set ei = 0 but leave its sign alone + * ecmpm( ai, bi ) compare significands, return 1, 0, or -1 + * edivm( ai, bi, ldp ) divide significands, bi = bi / ai + * emdnorm(ai,l,s,exp,ldp) normalize and round off + * emovi( a, ai ) convert external a to internal ai + * emovo( ai, a, ldp ) convert internal ai to external a + * emovz( ai, bi ) bi = ai, low guard word of bi = 0 + * emulm( ai, bi, ldp ) multiply significands, bi = bi * ai + * enormlz(ei) left-justify the significand + * eshdn1( ai ) shift significand and guards down 1 bit + * eshdn8( ai ) shift down 8 bits + * eshdn6( ai ) shift down 16 bits + * eshift( ai, n ) shift ai n bits up (or down if n < 0) + * eshup1( ai ) shift significand and guards up 1 bit + * eshup8( ai ) shift up 8 bits + * eshup6( ai ) shift up 16 bits + * esubm( ai, bi ) subtract significands, bi = bi - ai + * + * + * The result is always normalized and rounded to NI-4 word precision + * after each arithmetic operation. + * + * Exception flags are NOT fully supported. + * + * Define INFINITY in mconf.h for support of infinity; otherwise a + * saturation arithmetic is implemented. + * + * Define NANS for support of Not-a-Number items; otherwise the + * arithmetic will never produce a NaN output, and might be confused + * by a NaN input. + * If NaN's are supported, the output of ecmp(a,b) is -2 if + * either a or b is a NaN. This means asking if(ecmp(a,b) < 0) + * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than + * if in doubt. + * Signaling NaN's are NOT supported; they are treated the same + * as quiet NaN's. + * + * Denormals are always supported here where appropriate (e.g., not + * for conversion to DEC numbers). + */ + +/* + * Revision history: + * + * 5 Jan 84 PDP-11 assembly language version + * 6 Dec 86 C language version + * 30 Aug 88 100 digit version, improved rounding + * 15 May 92 80-bit long double support + * 22 Nov 00 Revised to fit into newlib by Jeff Johnston + * + * Author: S. L. Moshier. + * + * Copyright (c) 1984,2000 S.L. Moshier + * + * 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, THE AUTHOR MAKES NO REPRESENTATION + * OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS + * SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + */ + +#include +/* #include "\usr\include\stdio.h" */ +/*#include "ehead.h"*/ +/*#include "mconf.h"*/ +/* mconf.h + * + * Common include file for math routines + * + * + * + * SYNOPSIS: + * + * #include "mconf.h" + * + * + * + * DESCRIPTION: + * + * This file contains definitions for error codes that are + * passed to the common error handling routine mtherr() + * (which see). + * + * The file also includes a conditional assembly definition + * for the type of computer arithmetic (IEEE, DEC, Motorola + * IEEE, or UNKnown). + * + * For Digital Equipment PDP-11 and VAX computers, certain + * IBM systems, and others that use numbers with a 56-bit + * significand, the symbol DEC should be defined. In this + * mode, most floating point constants are given as arrays + * of octal integers to eliminate decimal to binary conversion + * errors that might be introduced by the compiler. + * + * For computers, such as IBM PC, that follow the IEEE + * Standard for Binary Floating Point Arithmetic (ANSI/IEEE + * Std 754-1985), the symbol IBMPC should be defined. These + * numbers have 53-bit significands. In this mode, constants + * are provided as arrays of hexadecimal 16 bit integers. + * + * To accommodate other types of computer arithmetic, all + * constants are also provided in a normal decimal radix + * which one can hope are correctly converted to a suitable + * format by the available C language compiler. To invoke + * this mode, the symbol UNK is defined. + * + * An important difference among these modes is a predefined + * set of machine arithmetic constants for each. The numbers + * MACHEP (the machine roundoff error), MAXNUM (largest number + * represented), and several other parameters are preset by + * the configuration symbol. Check the file const.c to + * ensure that these values are correct for your computer. + * + * For ANSI C compatibility, define ANSIC equal to 1. Currently + * this affects only the atan2() function and others that use it. + */ + +/* Constant definitions for math error conditions + */ + +#define DOMAIN 1 /* argument domain error */ +#define SING 2 /* argument singularity */ +#define OVERFLOW 3 /* overflow range error */ +#define UNDERFLOW 4 /* underflow range error */ +#define TLOSS 5 /* total loss of precision */ +#define PLOSS 6 /* partial loss of precision */ + +#define EDOM 33 +#define ERANGE 34 + +typedef struct + { + double r; + double i; + }cmplx; + +/* Type of computer arithmetic */ + +#ifndef DEC +#ifdef __IEEE_LITTLE_ENDIAN +#define IBMPC 1 +#else /* !__IEEE_LITTLE_ENDIAN */ +#define MIEEE 1 +#endif /* !__IEEE_LITTLE_ENDIAN */ +#endif /* !DEC */ + +/* Define 1 for ANSI C atan2() function + * See atan.c and clog.c. + */ +#define ANSIC 1 + +/*define VOLATILE volatile*/ +#define VOLATILE + +#define NANS +#define INFINITY + +/* NaN's require infinity support. */ +#ifdef NANS +#ifndef INFINITY +#define INFINITY +#endif +#endif + +/* This handles 64-bit long ints. */ +#define LONGBITS (8 * sizeof(long)) + + +static void eaddm(short unsigned int *x, short unsigned int *y); +static void esubm(short unsigned int *x, short unsigned int *y); +static void emdnorm(short unsigned int *s, int lost, int subflg, long int exp, int rcntrl, LDPARMS *ldp); +static int asctoeg(char *ss, short unsigned int *y, int oprec, LDPARMS *ldp); +static void enan(short unsigned int *nan, int size); +#if LDBL_MANT_DIG == 24 +static void toe24(short unsigned int *x, short unsigned int *y); +#elif LDBL_MANT_DIG == 53 +static void toe53(short unsigned int *x, short unsigned int *y); +#elif LDBL_MANT_DIG == 64 +static void toe64(short unsigned int *a, short unsigned int *b); +#else +static void toe113(short unsigned int *a, short unsigned int *b); +#endif +static void eiremain(short unsigned int *den, short unsigned int *num, LDPARMS *ldp); +static int ecmpm(register short unsigned int *a, register short unsigned int *b); +static int edivm(short unsigned int *den, short unsigned int *num, LDPARMS *ldp); +static int emulm(short unsigned int *a, short unsigned int *b, LDPARMS *ldp); +static int eisneg(short unsigned int *x); +static int eisinf(short unsigned int *x); +static void emovi(short unsigned int *a, short unsigned int *b); +static void emovo(short unsigned int *a, short unsigned int *b, LDPARMS *ldp); +static void emovz(register short unsigned int *a, register short unsigned int *b); +static void ecleaz(register short unsigned int *xi); +static void eadd1(short unsigned int *a, short unsigned int *b, short unsigned int *c, int subflg, LDPARMS *ldp); +static int eisnan(short unsigned int *x); +static int eiisnan(short unsigned int *x); + +#ifdef DEC +static void etodec(), todec(), dectoe(); +#endif + +/* +; Clear out entire external format number. +; +; unsigned short x[]; +; eclear( x ); +*/ + +static void eclear(register short unsigned int *x) +{ +register int i; + +for( i=0; irndprc < NBITS ) + { + if (ldp->rndprc == 113) + { + *(x - 9) = 0; + *(x - 8) = 0; + } + if( ldp->rndprc == 64 ) + { + *(x-5) = 0; + } + if( ldp->rndprc == 53 ) + { + *(x-4) = 0xf800; + } + else + { + *(x-4) = 0; + *(x-3) = 0; + *(x-2) = 0xff00; + } + } +#endif +} + +/* Move in external format number, + * converting it to internal format. + */ +static void emovi(short unsigned int *a, short unsigned int *b) +{ +register unsigned short *p, *q; +int i; + +q = b; +p = a + (NE-1); /* point to last word of external number */ +/* get the sign bit */ +if( *p & 0x8000 ) + *q++ = 0xffff; +else + *q++ = 0; +/* get the exponent */ +*q = *p--; +*q++ &= 0x7fff; /* delete the sign bit */ +#ifdef INFINITY +if( (*(q-1) & 0x7fff) == 0x7fff ) + { +#ifdef NANS + if( eisnan(a) ) + { + *q++ = 0; + for( i=3; i b +; 0 if a == b +; -1 if a < b +*/ +static int ecmpm(register short unsigned int *a, register short unsigned int *b) +{ +int i; + +a += M; /* skip up to significand area */ +b += M; +for( i=M; i *(--b) ) + return(1); +else + return(-1); +} + + +/* +; Shift significand down by 1 bit +*/ + +static void eshdn1(register short unsigned int *x) +{ +register unsigned short bits; +int i; + +x += M; /* point to significand area */ + +bits = 0; +for( i=M; i>= 1; + if( bits & 2 ) + *x |= 0x8000; + bits <<= 1; + ++x; + } +} + + + +/* +; Shift significand up by 1 bit +*/ + +static void eshup1(register short unsigned int *x) +{ +register unsigned short bits; +int i; + +x += NI-1; +bits = 0; + +for( i=M; i>= 8; + *x |= oldbyt; + oldbyt = newbyt; + ++x; + } +} + +/* +; Shift significand up by 8 bits +*/ + +static void eshup8(register short unsigned int *x) +{ +int i; +register unsigned short newbyt, oldbyt; + +x += NI-1; +oldbyt = 0; + +for( i=M; i> 8; + *x <<= 8; + *x |= oldbyt; + oldbyt = newbyt; + --x; + } +} + +/* +; Shift significand up by 16 bits +*/ + +static void eshup6(register short unsigned int *x) +{ +int i; +register unsigned short *p; + +p = x + M; +x += M + 1; + +for( i=M; i> 16) + (m >> 16) + *pp; + *pp = (unsigned short )carry; + *(pp-1) = carry >> 16; + } + } +for( i=M; iequot; + +p = &equot[0]; +*p++ = num[0]; +*p++ = num[1]; + +for( i=M; i tdenm ) + tquot = 0xffff; +*/ + /* Multiply denominator by trial quotient digit. */ + m16m( tquot, den, tprod ); + /* The quotient digit may have been overestimated. */ + if( ecmpm( tprod, num ) > 0 ) + { + tquot -= 1; + esubm( den, tprod ); + if( ecmpm( tprod, num ) > 0 ) + { + tquot -= 1; + esubm( den, tprod ); + } + } +/* + if( ecmpm( tprod, num ) > 0 ) + { + eshow( "tprod", tprod ); + eshow( "num ", num ); + printf( "tnum = %08lx, tden = %04x, tquot = %04x\n", + tnum, den[M+1], tquot ); + } +*/ + esubm( tprod, num ); +/* + if( ecmpm( num, den ) >= 0 ) + { + eshow( "num ", num ); + eshow( "den ", den ); + printf( "tnum = %08lx, tden = %04x, tquot = %04x\n", + tnum, den[M+1], tquot ); + } +*/ + equot[i] = tquot; + eshup6(num); + } +/* test for nonzero remainder after roundoff bit */ +p = &num[M]; +j = 0; +for( i=M; iequot; + +equot[0] = b[0]; +equot[1] = b[1]; +for( i=M; i NBITS ) + { + ecleazs( s ); + return; + } +#endif +exp -= j; +#ifndef INFINITY +if( exp >= 32767L ) + goto overf; +#else +if( (j > NBITS) && (exp < 32767L) ) + { + ecleazs( s ); + return; + } +#endif +if( exp < 0L ) + { + if( exp > (long )(-NBITS-1) ) + { + j = (int )exp; + i = eshift( s, j ); + if( i ) + lost = 1; + } + else + { + ecleazs( s ); + return; + } + } +/* Round off, unless told not to by rcntrl. */ +if( rcntrl == 0 ) + goto mdfin; +/* Set up rounding parameters if the control register changed. */ +if( ldp->rndprc != ldp->rlast ) + { + ecleaz( ldp->rbit ); + switch( ldp->rndprc ) + { + default: + case NBITS: + ldp->rw = NI-1; /* low guard word */ + ldp->rmsk = 0xffff; + ldp->rmbit = 0x8000; + ldp->rebit = 1; + ldp->re = ldp->rw - 1; + break; + case 113: + ldp->rw = 10; + ldp->rmsk = 0x7fff; + ldp->rmbit = 0x4000; + ldp->rebit = 0x8000; + ldp->re = ldp->rw; + break; + case 64: + ldp->rw = 7; + ldp->rmsk = 0xffff; + ldp->rmbit = 0x8000; + ldp->rebit = 1; + ldp->re = ldp->rw-1; + break; +/* For DEC arithmetic */ + case 56: + ldp->rw = 6; + ldp->rmsk = 0xff; + ldp->rmbit = 0x80; + ldp->rebit = 0x100; + ldp->re = ldp->rw; + break; + case 53: + ldp->rw = 6; + ldp->rmsk = 0x7ff; + ldp->rmbit = 0x0400; + ldp->rebit = 0x800; + ldp->re = ldp->rw; + break; + case 24: + ldp->rw = 4; + ldp->rmsk = 0xff; + ldp->rmbit = 0x80; + ldp->rebit = 0x100; + ldp->re = ldp->rw; + break; + } + ldp->rbit[ldp->re] = ldp->rebit; + ldp->rlast = ldp->rndprc; + } + +/* Shift down 1 temporarily if the data structure has an implied + * most significant bit and the number is denormal. + * For rndprc = 64 or NBITS, there is no implied bit. + * But Intel long double denormals lose one bit of significance even so. + */ +#if IBMPC +if( (exp <= 0) && (ldp->rndprc != NBITS) ) +#else +if( (exp <= 0) && (ldp->rndprc != 64) && (ldp->rndprc != NBITS) ) +#endif + { + lost |= s[NI-1] & 1; + eshdn1(s); + } +/* Clear out all bits below the rounding bit, + * remembering in r if any were nonzero. + */ +r = s[ldp->rw] & ldp->rmsk; +if( ldp->rndprc < NBITS ) + { + i = ldp->rw + 1; + while( i < NI ) + { + if( s[i] ) + r |= 1; + s[i] = 0; + ++i; + } + } +s[ldp->rw] &= ~ldp->rmsk; +if( (r & ldp->rmbit) != 0 ) + { + if( r == ldp->rmbit ) + { + if( lost == 0 ) + { /* round to even */ + if( (s[ldp->re] & ldp->rebit) == 0 ) + goto mddone; + } + else + { + if( subflg != 0 ) + goto mddone; + } + } + eaddm( ldp->rbit, s ); + } +mddone: +#if IBMPC +if( (exp <= 0) && (ldp->rndprc != NBITS) ) +#else +if( (exp <= 0) && (ldp->rndprc != 64) && (ldp->rndprc != NBITS) ) +#endif + { + eshup1(s); + } +if( s[2] != 0 ) + { /* overflow on roundoff */ + eshdn1(s); + exp += 1; + } +mdfin: +s[NI-1] = 0; +if( exp >= 32767L ) + { +#ifndef INFINITY +overf: +#endif +#ifdef INFINITY + s[1] = 32767; + for( i=2; irndprc < 64) || (ldp->rndprc == 113) ) + { + s[ldp->rw] &= ~ldp->rmsk; + if( ldp->rndprc == 24 ) + { + s[5] = 0; + s[6] = 0; + } + } +#endif + return; + } +if( exp < 0 ) + s[1] = 0; +else + s[1] = (unsigned short )exp; +} + + + +/* +; Subtract external format numbers. +; +; unsigned short a[NE], b[NE], c[NE]; +; LDPARMS *ldp; +; esub( a, b, c, ldp ); c = b - a +*/ + +static void esub(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp) +{ + +#ifdef NANS +if( eisnan(a) ) + { + emov (a, c); + return; + } +if( eisnan(b) ) + { + emov(b,c); + return; + } +/* Infinity minus infinity is a NaN. + * Test for subtracting infinities of the same sign. + */ +if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0)) + { + mtherr( "esub", DOMAIN ); + enan( c, NBITS ); + return; + } +#endif +eadd1( a, b, c, 1, ldp ); +} + + + +static void eadd1(short unsigned int *a, short unsigned int *b, short unsigned int *c, int subflg, LDPARMS *ldp) +{ +unsigned short ai[NI], bi[NI], ci[NI]; +int i, lost, j, k; +long lt, lta, ltb; + +#ifdef INFINITY +if( eisinf(a) ) + { + emov(a,c); + if( subflg ) + eneg(c); + return; + } +if( eisinf(b) ) + { + emov(b,c); + return; + } +#endif +emovi( a, ai ); +emovi( b, bi ); +if( subflg ) + ai[0] = ~ai[0]; + +/* compare exponents */ +lta = ai[E]; +ltb = bi[E]; +lt = lta - ltb; +if( lt > 0L ) + { /* put the larger number in bi */ + emovz( bi, ci ); + emovz( ai, bi ); + emovz( ci, ai ); + ltb = bi[E]; + lt = -lt; + } +lost = 0; +if( lt != 0L ) + { + if( lt < (long )(-NBITS-1) ) + goto done; /* answer same as larger addend */ + k = (int )lt; + lost = eshift( ai, k ); /* shift the smaller number down */ + } +else + { +/* exponents were the same, so must compare significands */ + i = ecmpm( ai, bi ); + if( i == 0 ) + { /* the numbers are identical in magnitude */ + /* if different signs, result is zero */ + if( ai[0] != bi[0] ) + { + eclear(c); + return; + } + /* if same sign, result is double */ + /* double denomalized tiny number */ + if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) ) + { + eshup1( bi ); + goto done; + } + /* add 1 to exponent unless both are zero! */ + for( j=1; j 0 ) + { /* put the larger number in bi */ + emovz( bi, ci ); + emovz( ai, bi ); + emovz( ci, ai ); + } + } +if( ai[0] == bi[0] ) + { + eaddm( ai, bi ); + subflg = 0; + } +else + { + esubm( ai, bi ); + subflg = 1; + } +emdnorm( bi, lost, subflg, ltb, 64, ldp ); + +done: +emovo( bi, c, ldp ); +} + + + +/* +; Divide. +; +; unsigned short a[NE], b[NE], c[NE]; +; LDPARMS *ldp; +; ediv( a, b, c, ldp ); c = b / a +*/ +static void ediv(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp) +{ +unsigned short ai[NI], bi[NI]; +int i; +long lt, lta, ltb; + +#ifdef NANS +/* Return any NaN input. */ +if( eisnan(a) ) + { + emov(a,c); + return; + } +if( eisnan(b) ) + { + emov(b,c); + return; + } +/* Zero over zero, or infinity over infinity, is a NaN. */ +if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0)) + || (eisinf (a) && eisinf (b)) ) + { + mtherr( "ediv", DOMAIN ); + enan( c, NBITS ); + return; + } +#endif +/* Infinity over anything else is infinity. */ +#ifdef INFINITY +if( eisinf(b) ) + { + if( eisneg(a) ^ eisneg(b) ) + *(c+(NE-1)) = 0x8000; + else + *(c+(NE-1)) = 0; + einfin(c, ldp); + return; + } +if( eisinf(a) ) + { + eclear(c); + return; + } +#endif +emovi( a, ai ); +emovi( b, bi ); +lta = ai[E]; +ltb = bi[E]; +if( bi[E] == 0 ) + { /* See if numerator is zero. */ + for( i=1; i 64 +static void e113toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp) +{ +register unsigned short r; +unsigned short *e, *p; +unsigned short yy[NI]; +int denorm, i; + +e = pe; +denorm = 0; +ecleaz(yy); +#ifdef IBMPC +e += 7; +#endif +r = *e; +yy[0] = 0; +if( r & 0x8000 ) + yy[0] = 0xffff; +r &= 0x7fff; +#ifdef INFINITY +if( r == 0x7fff ) + { +#ifdef NANS +#ifdef IBMPC + for( i=0; i<7; i++ ) + { + if( pe[i] != 0 ) + { + enan( y, NBITS ); + return; + } + } +#else /* !IBMPC */ + for( i=1; i<8; i++ ) + { + if( pe[i] != 0 ) + { + enan( y, NBITS ); + return; + } + } +#endif /* !IBMPC */ +#endif /* NANS */ + eclear( y ); + einfin( y ); + if( *e & 0x8000 ) + eneg(y); + return; + } +#endif /* INFINITY */ +yy[E] = r; +p = &yy[M + 1]; +#ifdef IBMPC +for( i=0; i<7; i++ ) + *p++ = *(--e); +#else /* IBMPC */ +++e; +for( i=0; i<7; i++ ) + *p++ = *e++; +#endif /* IBMPC */ +/* If denormal, remove the implied bit; else shift down 1. */ +if( r == 0 ) + { + yy[M] = 0; + } +else + { + yy[M] = 1; + eshift( yy, -1 ); + } +emovo(yy,y,ldp); +} + +/* move out internal format to ieee long double */ +static void toe113(short unsigned int *a, short unsigned int *b) +{ +register unsigned short *p, *q; +unsigned short i; + +#ifdef NANS +if( eiisnan(a) ) + { + enan( b, 113 ); + return; + } +#endif +p = a; +#ifdef MIEEE +q = b; +#else +q = b + 7; /* point to output exponent */ +#endif + +/* If not denormal, delete the implied bit. */ +if( a[E] != 0 ) + { + eshup1 (a); + } +/* combine sign and exponent */ +i = *p++; +#ifdef MIEEE +if( i ) + *q++ = *p++ | 0x8000; +else + *q++ = *p++; +#else +if( i ) + *q-- = *p++ | 0x8000; +else + *q-- = *p++; +#endif +/* skip over guard word */ +++p; +/* move the significand */ +#ifdef MIEEE +for (i = 0; i < 7; i++) + *q++ = *p++; +#else +for (i = 0; i < 7; i++) + *q-- = *p++; +#endif +} +#endif /* LDBL_MANT_DIG > 64 */ + + +#if LDBL_MANT_DIG == 64 +static void e64toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp) +{ +unsigned short yy[NI]; +unsigned short *p, *q, *e; +int i; + +e = pe; +p = yy; + +for( i=0; i>= 4; +/* If zero exponent, then the significand is denormalized. + * So, take back the understood high significand bit. */ +if( r == 0 ) + { + denorm = 1; + yy[M] &= ~0x10; + } +r += EXONE - 01777; +yy[E] = r; +p = &yy[M+1]; +#ifdef IBMPC +*p++ = *(--e); +*p++ = *(--e); +*p++ = *(--e); +#else /* !IBMPC */ +++e; +*p++ = *e++; +*p++ = *e++; +*p++ = *e++; +#endif /* !IBMPC */ +(void )eshift( yy, -5 ); +if( denorm ) + { /* if zero exponent, then normalize the significand */ + if( (k = enormlz(yy)) > NBITS ) + ecleazs(yy); + else + yy[E] -= (unsigned short )(k-1); + } +emovo( yy, y, ldp ); +#endif /* !DEC */ +} + +/* +; e type to IEEE double precision +; double d; +; unsigned short x[NE]; +; etoe53( x, &d ); +*/ + +#ifdef DEC + +static void etoe53( x, e ) +unsigned short *x, *e; +{ +etodec( x, e ); /* see etodec.c */ +} + +static void toe53( x, y ) +unsigned short *x, *y; +{ +todec( x, y ); +} + +#else + +static void toe53(short unsigned int *x, short unsigned int *y) +{ +unsigned short i; +unsigned short *p; + + +#ifdef NANS +if( eiisnan(x) ) + { + enan( y, 53 ); + return; + } +#endif +p = &x[0]; +#ifdef IBMPC +y += 3; +#endif +#ifdef DEC +y += 3; +#endif +*y = 0; /* output high order */ +if( *p++ ) + *y = 0x8000; /* output sign bit */ + +i = *p++; +if( i >= (unsigned int )2047 ) + { /* Saturate at largest number less than infinity. */ +#ifdef INFINITY + *y |= 0x7ff0; +#ifdef IBMPC + *(--y) = 0; + *(--y) = 0; + *(--y) = 0; +#else /* !IBMPC */ + ++y; + *y++ = 0; + *y++ = 0; + *y++ = 0; +#endif /* IBMPC */ +#else /* !INFINITY */ + *y |= (unsigned short )0x7fef; +#ifdef IBMPC + *(--y) = 0xffff; + *(--y) = 0xffff; + *(--y) = 0xffff; +#else /* !IBMPC */ + ++y; + *y++ = 0xffff; + *y++ = 0xffff; + *y++ = 0xffff; +#endif +#endif /* !INFINITY */ + return; + } +if( i == 0 ) + { + (void )eshift( x, 4 ); + } +else + { + i <<= 4; + (void )eshift( x, 5 ); + } +i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */ +*y |= (unsigned short )i; /* high order output already has sign bit set */ +#ifdef IBMPC +*(--y) = *p++; +*(--y) = *p++; +*(--y) = *p; +#else /* !IBMPC */ +++y; +*y++ = *p++; +*y++ = *p++; +*y++ = *p++; +#endif /* !IBMPC */ +} + +#endif /* not DEC */ +#endif /* LDBL_MANT_DIG == 53 */ + +#if LDBL_MANT_DIG == 24 +/* +; Convert IEEE single precision to e type +; float d; +; unsigned short x[N+2]; +; dtox( &d, x ); +*/ +void e24toe( short unsigned int *pe, short unsigned int *y, LDPARMS *ldp ) +{ +register unsigned short r; +register unsigned short *p, *e; +unsigned short yy[NI]; +int denorm, k; + +e = pe; +denorm = 0; /* flag if denormalized number */ +ecleaz(yy); +#ifdef IBMPC +e += 1; +#endif +#ifdef DEC +e += 1; +#endif +r = *e; +yy[0] = 0; +if( r & 0x8000 ) + yy[0] = 0xffff; +yy[M] = (r & 0x7f) | 0200; +r &= ~0x807f; /* strip sign and 7 significand bits */ +#ifdef INFINITY +if( r == 0x7f80 ) + { +#ifdef NANS +#ifdef MIEEE + if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) ) + { + enan( y, NBITS ); + return; + } +#else /* !MIEEE */ + if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) ) + { + enan( y, NBITS ); + return; + } +#endif /* !MIEEE */ +#endif /* NANS */ + eclear( y ); + einfin( y ); + if( yy[0] ) + eneg(y); + return; + } +#endif +r >>= 7; +/* If zero exponent, then the significand is denormalized. + * So, take back the understood high significand bit. */ +if( r == 0 ) + { + denorm = 1; + yy[M] &= ~0200; + } +r += EXONE - 0177; +yy[E] = r; +p = &yy[M+1]; +#ifdef IBMPC +*p++ = *(--e); +#endif +#ifdef DEC +*p++ = *(--e); +#endif +#ifdef MIEEE +++e; +*p++ = *e++; +#endif +(void )eshift( yy, -8 ); +if( denorm ) + { /* if zero exponent, then normalize the significand */ + if( (k = enormlz(yy)) > NBITS ) + ecleazs(yy); + else + yy[E] -= (unsigned short )(k-1); + } +emovo( yy, y, ldp ); +} + +static void toe24(short unsigned int *x, short unsigned int *y) +{ +unsigned short i; +unsigned short *p; + +#ifdef NANS +if( eiisnan(x) ) + { + enan( y, 24 ); + return; + } +#endif +p = &x[0]; +#ifdef IBMPC +y += 1; +#endif +#ifdef DEC +y += 1; +#endif +*y = 0; /* output high order */ +if( *p++ ) + *y = 0x8000; /* output sign bit */ + +i = *p++; +if( i >= 255 ) + { /* Saturate at largest number less than infinity. */ +#ifdef INFINITY + *y |= (unsigned short )0x7f80; +#ifdef IBMPC + *(--y) = 0; +#endif +#ifdef DEC + *(--y) = 0; +#endif +#ifdef MIEEE + ++y; + *y = 0; +#endif +#else /* !INFINITY */ + *y |= (unsigned short )0x7f7f; +#ifdef IBMPC + *(--y) = 0xffff; +#endif +#ifdef DEC + *(--y) = 0xffff; +#endif +#ifdef MIEEE + ++y; + *y = 0xffff; +#endif +#endif /* !INFINITY */ + return; + } +if( i == 0 ) + { + (void )eshift( x, 7 ); + } +else + { + i <<= 7; + (void )eshift( x, 8 ); + } +i |= *p++ & (unsigned short )0x7f; /* *p = xi[M] */ +*y |= i; /* high order output already has sign bit set */ +#ifdef IBMPC +*(--y) = *p; +#endif +#ifdef DEC +*(--y) = *p; +#endif +#ifdef MIEEE +++y; +*y = *p; +#endif +} +#endif /* LDBL_MANT_DIG == 24 */ + +/* Compare two e type numbers. + * + * unsigned short a[NE], b[NE]; + * ecmp( a, b ); + * + * returns +1 if a > b + * 0 if a == b + * -1 if a < b + * -2 if either a or b is a NaN. + */ +static int ecmp(short unsigned int *a, short unsigned int *b) +{ +unsigned short ai[NI], bi[NI]; +register unsigned short *p, *q; +register int i; +int msign; + +#ifdef NANS +if (eisnan (a) || eisnan (b)) + return( -2 ); +#endif +emovi( a, ai ); +p = ai; +emovi( b, bi ); +q = bi; + +if( *p != *q ) + { /* the signs are different */ +/* -0 equals + 0 */ + for( i=1; i 0 ); + +return(0); /* equality */ + + + +diff: + +if( *(--p) > *(--q) ) + return( msign ); /* p is bigger */ +else + return( -msign ); /* p is littler */ +} + + +/* +; Shift significand +; +; Shifts significand area up or down by the number of bits +; given by the variable sc. +*/ +static int eshift(short unsigned int *x, int sc) +{ +unsigned short lost; +unsigned short *p; + +if( sc == 0 ) + return( 0 ); + +lost = 0; +p = x + NI-1; + +if( sc < 0 ) + { + sc = -sc; + while( sc >= 16 ) + { + lost |= *p; /* remember lost bits */ + eshdn6(x); + sc -= 16; + } + + while( sc >= 8 ) + { + lost |= *p & 0xff; + eshdn8(x); + sc -= 8; + } + + while( sc > 0 ) + { + lost |= *p & 1; + eshdn1(x); + sc -= 1; + } + } +else + { + while( sc >= 16 ) + { + eshup6(x); + sc -= 16; + } + + while( sc >= 8 ) + { + eshup8(x); + sc -= 8; + } + + while( sc > 0 ) + { + eshup1(x); + sc -= 1; + } + } +if( lost ) + lost = 1; +return( (int )lost ); +} + + + +/* +; normalize +; +; Shift normalizes the significand area pointed to by argument +; shift count (up = positive) is returned. +*/ +static int enormlz(short unsigned int *x) +{ +register unsigned short *p; +int sc; + +sc = 0; +p = &x[M]; +if( *p != 0 ) + goto normdn; +++p; +if( *p & 0x8000 ) + return( 0 ); /* already normalized */ +while( *p == 0 ) + { + eshup6(x); + sc += 16; +/* With guard word, there are NBITS+16 bits available. + * return true if all are zero. + */ + if( sc > NBITS ) + return( sc ); + } +/* see if high byte is zero */ +while( (*p & 0xff00) == 0 ) + { + eshup8(x); + sc += 8; + } +/* now shift 1 bit at a time */ +while( (*p & 0x8000) == 0) + { + eshup1(x); + sc += 1; + if( sc > (NBITS+16) ) + { + mtherr( "enormlz", UNDERFLOW ); + return( sc ); + } + } +return( sc ); + +/* Normalize by shifting down out of the high guard word + of the significand */ +normdn: + +if( *p & 0xff00 ) + { + eshdn8(x); + sc -= 8; + } +while( *p != 0 ) + { + eshdn1(x); + sc -= 1; + + if( sc < -NBITS ) + { + mtherr( "enormlz", OVERFLOW ); + return( sc ); + } + } +return( sc ); +} + + + + +/* Convert e type number to decimal format ASCII string. + * The constants are for 64 bit precision. + */ + +#define NTEN 12 +#define MAXP 4096 + +#if NE == 10 +static unsigned short etens[NTEN + 1][NE] = +{ + {0x6576, 0x4a92, 0x804a, 0x153f, + 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */ + {0x6a32, 0xce52, 0x329a, 0x28ce, + 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */ + {0x526c, 0x50ce, 0xf18b, 0x3d28, + 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,}, + {0x9c66, 0x58f8, 0xbc50, 0x5c54, + 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,}, + {0x851e, 0xeab7, 0x98fe, 0x901b, + 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,}, + {0x0235, 0x0137, 0x36b1, 0x336c, + 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,}, + {0x50f8, 0x25fb, 0xc76b, 0x6b71, + 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */ +}; + +static unsigned short emtens[NTEN + 1][NE] = +{ + {0x2030, 0xcffc, 0xa1c3, 0x8123, + 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */ + {0x8264, 0xd2cb, 0xf2ea, 0x12d4, + 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */ + {0xf53f, 0xf698, 0x6bd3, 0x0158, + 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,}, + {0xe731, 0x04d4, 0xe3f2, 0xd332, + 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,}, + {0xa23e, 0x5308, 0xfefb, 0x1155, + 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,}, + {0xe26d, 0xdbde, 0xd05d, 0xb3f6, + 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,}, + {0x2a20, 0x6224, 0x47b3, 0x98d7, + 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,}, + {0x0b5b, 0x4af2, 0xa581, 0x18ed, + 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,}, + {0xbf71, 0xa9b3, 0x7989, 0xbe68, + 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,}, + {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b, + 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,}, + {0xc155, 0xa4a8, 0x404e, 0x6113, + 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,}, + {0xd70a, 0x70a3, 0x0a3d, 0xa3d7, + 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,}, + {0xcccd, 0xcccc, 0xcccc, 0xcccc, + 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */ +}; +#else +static unsigned short etens[NTEN+1][NE] = { +{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */ +{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */ +{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,}, +{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,}, +{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,}, +{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,}, +{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,}, +{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,}, +{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,}, +{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,}, +{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,}, +{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,}, +{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */ +}; + +static unsigned short emtens[NTEN+1][NE] = { +{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */ +{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */ +{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,}, +{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,}, +{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,}, +{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,}, +{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,}, +{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,}, +{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,}, +{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,}, +{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,}, +{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,}, +{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */ +}; +#endif + + + +/* ASCII string outputs for unix */ + + +#if 0 +void _IO_ldtostr(x, string, ndigs, flags, fmt) +long double *x; +char *string; +int ndigs; +int flags; +char fmt; +{ +unsigned short w[NI]; +char *t, *u; +LDPARMS rnd; +LDPARMS *ldp = &rnd; + +rnd.rlast = -1; +rnd.rndprc = NBITS; + +if (sizeof(long double) == 16) + e113toe( (unsigned short *)x, w, ldp ); +else + e64toe( (unsigned short *)x, w, ldp ); + +etoasc( w, string, ndigs, -1, ldp ); +if( ndigs == 0 && flags == 0 ) + { + /* Delete the decimal point unless alternate format. */ + t = string; + while( *t != '.' ) + ++t; + u = t + 1; + while( *t != '\0' ) + *t++ = *u++; + } +if (*string == ' ') + { + t = string; + u = t + 1; + while( *t != '\0' ) + *t++ = *u++; + } +if (fmt == 'E') + { + t = string; + while( *t != 'e' ) + ++t; + *t = 'E'; + } +} + +#endif + +/* This routine will not return more than NDEC+1 digits. */ + +char * +_ldtoa_r (struct _reent *ptr, long double d, int mode, int ndigits, int *decpt, + int *sign, char **rve) +{ +unsigned short e[NI]; +char *s, *p; +int k; +LDPARMS rnd; +LDPARMS *ldp = &rnd; +char *outstr; + +rnd.rlast = -1; +rnd.rndprc = NBITS; + +/* reentrancy addition to use mprec storage pool */ +if (ptr->_result) + { + ptr->_result->_k = ptr->_result_k; + ptr->_result->_maxwds = 1 << ptr->_result_k; + Bfree (ptr, ptr->_result); + ptr->_result = 0; + } + +#if LDBL_MANT_DIG == 24 +e24toe( (unsigned short *)&d, e, ldp ); +#elif LDBL_MANT_DIG == 53 +e53toe( (unsigned short *)&d, e, ldp ); +#elif LDBL_MANT_DIG == 64 +e64toe( (unsigned short *)&d, e, ldp ); +#else +e113toe( (unsigned short *)&d, e, ldp ); +#endif + +if( eisneg(e) ) + *sign = 1; +else + *sign = 0; +/* Mode 3 is "f" format. */ +if( mode != 3 ) + ndigits -= 1; +/* Mode 0 is for %.999 format, which is supposed to give a + minimum length string that will convert back to the same binary value. + For now, just ask for 20 digits which is enough but sometimes too many. */ +if( mode == 0 ) + ndigits = 20; +/* This sanity limit must agree with the corresponding one in etoasc, to + keep straight the returned value of outexpon. */ +if( ndigits > NDEC ) + ndigits = NDEC; + +/* reentrancy addition to use mprec storage pool */ +ptr->_result = Balloc (ptr, 3); +ptr->_result_k = 3; +outstr = (char *)ptr->_result; + +etoasc( e, outstr, ndigits, mode, ldp ); +s = outstr; +if( eisinf(e) || eisnan(e) ) + { + *decpt = 9999; + goto stripspaces; + } +*decpt = ldp->outexpon + 1; + +/* Transform the string returned by etoasc into what the caller wants. */ + +/* Look for decimal point and delete it from the string. */ +s = outstr; +while( *s != '\0' ) + { + if( *s == '.' ) + goto yesdecpt; + ++s; + } +goto nodecpt; + +yesdecpt: + +/* Delete the decimal point. */ +while( *s != '\0' ) + { + *s = *(s+1); + ++s; + } + +nodecpt: + +/* Back up over the exponent field. */ +while( *s != 'E' && s > outstr) + --s; +*s = '\0'; + +stripspaces: + +/* Strip leading spaces and sign. */ +p = outstr; +while( *p == ' ' || *p == '-') + ++p; + +/* Find new end of string. */ +s = outstr; +while( (*s++ = *p++) != '\0' ) + ; +--s; + +/* Strip trailing zeros. */ +if( mode == 2 ) + k = 1; +else if( ndigits > ldp->outexpon ) + k = ndigits; +else + k = ldp->outexpon; + +while( *(s-1) == '0' && ((s - outstr) > k)) + *(--s) = '\0'; + +/* In f format, flush small off-scale values to zero. + Rounding has been taken care of by etoasc. */ +if( mode == 3 && ((ndigits + ldp->outexpon) < 0)) + { + s = outstr; + *s = '\0'; + *decpt = 0; + } + +if( rve ) + *rve = s; +return outstr; +} + +static void etoasc(short unsigned int *x, char *string, int ndigits, int outformat, LDPARMS *ldp) +{ +long digit; +unsigned short y[NI], t[NI], u[NI], w[NI]; +unsigned short *p, *r, *ten; +unsigned short sign; +int i, j, k, expon, rndsav, ndigs; +char *s, *ss; +unsigned short m; +unsigned short *equot = ldp->equot; + +ndigs = ndigits; +rndsav = ldp->rndprc; +#ifdef NANS +if( eisnan(x) ) + { + sprintf( string, " NaN " ); + expon = 9999; + goto bxit; + } +#endif +ldp->rndprc = NBITS; /* set to full precision */ +emov( x, y ); /* retain external format */ +if( y[NE-1] & 0x8000 ) + { + sign = 0xffff; + y[NE-1] &= 0x7fff; + } +else + { + sign = 0; + } +expon = 0; +ten = &etens[NTEN][0]; +emov( eone, t ); +/* Test for zero exponent */ +if( y[NE-1] == 0 ) + { + for( k=0; k>= 1; + } +while( m != 0 ); + +/* Rescale from integer significand */ + u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1); + emov( u, y ); +/* Find power of 10 */ + emov( eone, t ); + m = MAXP; + p = &etens[0][0]; + while( ecmp( ten, u ) <= 0 ) + { + if( ecmp( p, u ) <= 0 ) + { + ediv( p, u, u, ldp ); + emul( p, t, t, ldp ); + expon += (int )m; + } + m >>= 1; + if( m == 0 ) + break; + p += NE; + } + } +else + { /* Number is less than 1.0 */ +/* Pad significand with trailing decimal zeros. */ + if( y[NE-1] == 0 ) + { + while( (y[NE-2] & 0x8000) == 0 ) + { + emul( ten, y, y, ldp ); + expon -= 1; + } + } + else + { + emovi( y, w ); + for( i=0; i 0 ) + { + if( ecmp( p, w ) >= 0 ) + { + emul( r, w, w, ldp ); + emul( r, t, t, ldp ); + expon += k; + } + k /= 2; + if( k == 0 ) + break; + p += NE; + r += NE; + } + ediv( t, eone, t, ldp ); + } +isone: +/* Find the first (leading) digit. */ +emovi( t, w ); +emovz( w, t ); +emovi( y, w ); +emovz( w, y ); +eiremain( t, y, ldp ); +digit = equot[NI-1]; +while( (digit == 0) && (ecmp(y,ezero) != 0) ) + { + eshup1( y ); + emovz( y, u ); + eshup1( u ); + eshup1( u ); + eaddm( u, y ); + eiremain( t, y, ldp ); + digit = equot[NI-1]; + expon -= 1; + } +s = string; +if( sign ) + *s++ = '-'; +else + *s++ = ' '; +/* Examine number of digits requested by caller. */ +if( outformat == 3 ) + ndigs += expon; +/* +else if( ndigs < 0 ) + ndigs = 0; +*/ +if( ndigs > NDEC ) + ndigs = NDEC; +if( digit == 10 ) + { + *s++ = '1'; + *s++ = '.'; + if( ndigs > 0 ) + { + *s++ = '0'; + ndigs -= 1; + } + expon += 1; + if( ndigs < 0 ) + { + ss = s; + goto doexp; + } + } +else + { + *s++ = (char )digit + '0'; + *s++ = '.'; + } +/* Generate digits after the decimal point. */ +for( k=0; k<=ndigs; k++ ) + { +/* multiply current number by 10, without normalizing */ + eshup1( y ); + emovz( y, u ); + eshup1( u ); + eshup1( u ); + eaddm( u, y ); + eiremain( t, y, ldp ); + *s++ = (char )equot[NI-1] + '0'; + } +digit = equot[NI-1]; +--s; +ss = s; +/* round off the ASCII string */ +if( digit > 4 ) + { +/* Test for critical rounding case in ASCII output. */ + if( digit == 5 ) + { + emovo( y, t, ldp ); + if( ecmp(t,ezero) != 0 ) + goto roun; /* round to nearest */ + if( (*(s-1) & 1) == 0 ) + goto doexp; /* round to even */ + } +/* Round up and propagate carry-outs */ +roun: + --s; + k = *s & 0x7f; +/* Carry out to most significant digit? */ + if( ndigs < 0 ) + { + /* This will print like "1E-6". */ + *s = '1'; + expon += 1; + goto doexp; + } + else if( k == '.' ) + { + --s; + k = *s; + k += 1; + *s = (char )k; +/* Most significant digit carries to 10? */ + if( k > '9' ) + { + expon += 1; + *s = '1'; + } + goto doexp; + } +/* Round up and carry out from less significant digits */ + k += 1; + *s = (char )k; + if( k > '9' ) + { + *s = '0'; + goto roun; + } + } +doexp: +#ifdef __GO32__ +if( expon >= 0 ) + sprintf( ss, "e+%02d", expon ); +else + sprintf( ss, "e-%02d", -expon ); +#else + sprintf( ss, "E%d", expon ); +#endif +bxit: +ldp->rndprc = rndsav; +ldp->outexpon = expon; +} + + + + +/* +; ASCTOQ +; ASCTOQ.MAC LATEST REV: 11 JAN 84 +; SLM, 3 JAN 78 +; +; Convert ASCII string to quadruple precision floating point +; +; Numeric input is free field decimal number +; with max of 15 digits with or without +; decimal point entered as ASCII from teletype. +; Entering E after the number followed by a second +; number causes the second number to be interpreted +; as a power of 10 to be multiplied by the first number +; (i.e., "scientific" notation). +; +; Usage: +; asctoq( string, q ); +*/ + +long double _strtold (char *s, char **se) +{ + long double x; + LDPARMS rnd; + LDPARMS *ldp = &rnd; + int lenldstr; + + rnd.rlast = -1; + rnd.rndprc = NBITS; + + lenldstr = asctoeg( s, (unsigned short *)&x, LDBL_MANT_DIG, ldp ); + if (se) + *se = s + lenldstr; + return x; +} + + + +static int +asctoeg(char *ss, short unsigned int *y, int oprec, LDPARMS *ldp) +{ +unsigned short yy[NI], xt[NI], tt[NI]; +int esign, decflg, sgnflg, nexp, exp, prec, lost; +int k, trail, c, rndsav; +long lexp; +unsigned short nsign, *p; +char *sp, *s, *lstr; +int lenldstr; + +/* Copy the input string. */ +c = strlen (ss) + 2; +lstr = (char *) alloca (c); +s = ss; +lenldstr = 0; +while( *s == ' ' ) /* skip leading spaces */ + { + ++s; + ++lenldstr; + } +sp = lstr; +for( k=0; krndprc; +ldp->rndprc = NBITS; /* Set to full precision */ +lost = 0; +nsign = 0; +decflg = 0; +sgnflg = 0; +nexp = 0; +exp = 0; +prec = 0; +ecleaz( yy ); +trail = 0; + +nxtcom: +k = *s - '0'; +if( (k >= 0) && (k <= 9) ) + { +/* Ignore leading zeros */ + if( (prec == 0) && (decflg == 0) && (k == 0) ) + goto donchr; +/* Identify and strip trailing zeros after the decimal point. */ + if( (trail == 0) && (decflg != 0) ) + { + sp = s; + while( (*sp >= '0') && (*sp <= '9') ) + ++sp; +/* Check for syntax error */ + c = *sp & 0x7f; + if( (c != 'e') && (c != 'E') && (c != '\0') + && (c != '\n') && (c != '\r') && (c != ' ') + && (c != ',') ) + goto error; + --sp; + while( *sp == '0' ) + *sp-- = 'z'; + trail = 1; + if( *s == 'z' ) + goto donchr; + } +/* If enough digits were given to more than fill up the yy register, + * continuing until overflow into the high guard word yy[2] + * guarantees that there will be a roundoff bit at the top + * of the low guard word after normalization. + */ + if( yy[2] == 0 ) + { + if( decflg ) + nexp += 1; /* count digits after decimal point */ + eshup1( yy ); /* multiply current number by 10 */ + emovz( yy, xt ); + eshup1( xt ); + eshup1( xt ); + eaddm( xt, yy ); + ecleaz( xt ); + xt[NI-2] = (unsigned short )k; + eaddm( xt, yy ); + } + else + { + /* Mark any lost non-zero digit. */ + lost |= k; + /* Count lost digits before the decimal point. */ + if (decflg == 0) + nexp -= 1; + } + prec += 1; + goto donchr; + } + +switch( *s ) + { + case 'z': + break; + case 'E': + case 'e': + goto expnt; + case '.': /* decimal point */ + if( decflg ) + goto error; + ++decflg; + break; + case '-': + nsign = 0xffff; + if( sgnflg ) + goto error; + ++sgnflg; + break; + case '+': + if( sgnflg ) + goto error; + ++sgnflg; + break; + case ',': + case ' ': + case '\0': + case '\n': + case '\r': + goto daldone; + case 'i': + case 'I': + goto infinite; + default: + error: +#ifdef NANS + enan( yy, NI*16 ); +#else + mtherr( "asctoe", DOMAIN ); + ecleaz(yy); +#endif + goto aexit; + } +donchr: +++s; +goto nxtcom; + +/* Exponent interpretation */ +expnt: + +esign = 1; +exp = 0; +++s; +/* check for + or - */ +if( *s == '-' ) + { + esign = -1; + ++s; + } +if( *s == '+' ) + ++s; +while( (*s >= '0') && (*s <= '9') ) + { + exp *= 10; + exp += *s++ - '0'; + if (exp > 4977) + { + if (esign < 0) + goto zero; + else + goto infinite; + } + } +if( esign < 0 ) + exp = -exp; +if( exp > 4932 ) + { +infinite: + ecleaz(yy); + yy[E] = 0x7fff; /* infinity */ + goto aexit; + } +if( exp < -4977 ) + { +zero: + ecleaz(yy); + goto aexit; + } + +daldone: +nexp = exp - nexp; +/* Pad trailing zeros to minimize power of 10, per IEEE spec. */ +while( (nexp > 0) && (yy[2] == 0) ) + { + emovz( yy, xt ); + eshup1( xt ); + eshup1( xt ); + eaddm( yy, xt ); + eshup1( xt ); + if( xt[2] != 0 ) + break; + nexp -= 1; + emovz( xt, yy ); + } +if( (k = enormlz(yy)) > NBITS ) + { + ecleaz(yy); + goto aexit; + } +lexp = (EXONE - 1 + NBITS) - k; +emdnorm( yy, lost, 0, lexp, 64, ldp ); +/* convert to external format */ + + +/* Multiply by 10**nexp. If precision is 64 bits, + * the maximum relative error incurred in forming 10**n + * for 0 <= n <= 324 is 8.2e-20, at 10**180. + * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947. + * For 0 >= n >= -999, it is -1.55e-19 at 10**-435. + */ +lexp = yy[E]; +if( nexp == 0 ) + { + k = 0; + goto expdon; + } +esign = 1; +if( nexp < 0 ) + { + nexp = -nexp; + esign = -1; + if( nexp > 4096 ) + { /* Punt. Can't handle this without 2 divides. */ + emovi( etens[0], tt ); + lexp -= tt[E]; + k = edivm( tt, yy, ldp ); + lexp += EXONE; + nexp -= 4096; + } + } +p = &etens[NTEN][0]; +emov( eone, xt ); +exp = 1; +do + { + if( exp & nexp ) + emul( p, xt, xt, ldp ); + p -= NE; + exp = exp + exp; + } +while( exp <= MAXP ); + +emovi( xt, tt ); +if( esign < 0 ) + { + lexp -= tt[E]; + k = edivm( tt, yy, ldp ); + lexp += EXONE; + } +else + { + lexp += tt[E]; + k = emulm( tt, yy, ldp ); + lexp -= EXONE - 1; + } + +expdon: + +/* Round and convert directly to the destination type */ +if( oprec == 53 ) + lexp -= EXONE - 0x3ff; +else if( oprec == 24 ) + lexp -= EXONE - 0177; +#ifdef DEC +else if( oprec == 56 ) + lexp -= EXONE - 0201; +#endif +ldp->rndprc = oprec; +emdnorm( yy, k, 0, lexp, 64, ldp ); + +aexit: + +ldp->rndprc = rndsav; +yy[0] = nsign; +switch( oprec ) + { +#ifdef DEC + case 56: + todec( yy, y ); /* see etodec.c */ + break; +#endif +#if LDBL_MANT_DIG == 53 + case 53: + toe53( yy, y ); + break; +#elif LDBL_MANT_DIG == 24 + case 24: + toe24( yy, y ); + break; +#elif LDBL_MANT_DIG == 64 + case 64: + toe64( yy, y ); + break; +#elif LDBL_MANT_DIG == 113 + case 113: + toe113( yy, y ); + break; +#else + case NBITS: + emovo( yy, y, ldp ); + break; +#endif + } +lenldstr += s - lstr; +return lenldstr; +} + + + +/* y = largest integer not greater than x + * (truncated toward minus infinity) + * + * unsigned short x[NE], y[NE] + * LDPARMS *ldp + * + * efloor( x, y, ldp ); + */ +static unsigned short bmask[] = { +0xffff, +0xfffe, +0xfffc, +0xfff8, +0xfff0, +0xffe0, +0xffc0, +0xff80, +0xff00, +0xfe00, +0xfc00, +0xf800, +0xf000, +0xe000, +0xc000, +0x8000, +0x0000, +}; + +static void efloor(short unsigned int *x, short unsigned int *y, LDPARMS *ldp) +{ +register unsigned short *p; +int e, expon, i; +unsigned short f[NE]; + +emov( x, f ); /* leave in external format */ +expon = (int )f[NE-1]; +e = (expon & 0x7fff) - (EXONE - 1); +if( e <= 0 ) + { + eclear(y); + goto isitneg; + } +/* number of bits to clear out */ +e = NBITS - e; +emov( f, y ); +if( e <= 0 ) + return; + +p = &y[0]; +while( e >= 16 ) + { + *p++ = 0; + e -= 16; + } +/* clear the remaining bits */ +*p &= bmask[e]; +/* truncate negatives toward minus infinity */ +isitneg: + +if( (unsigned short )expon & (unsigned short )0x8000 ) + { + for( i=0; iequot; + +ld = den[E]; +ld -= enormlz( den ); +ln = num[E]; +ln -= enormlz( num ); +ecleaz( equot ); +while( ln >= ld ) + { + if( ecmpm(den,num) <= 0 ) + { + esubm(den, num); + j = 1; + } + else + { + j = 0; + } + eshup1(equot); + equot[NI-1] |= j; + eshup1(num); + ln -= 1; + } +emdnorm( num, 0, 0, ln, 0, ldp ); +} + +/* NaN bit patterns + */ +#ifdef MIEEE +static unsigned short nan113[8] = { + 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; +static unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; +static unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff}; +static unsigned short nan24[2] = {0x7fff, 0xffff}; +#else /* !MIEEE */ +static unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0x8000, 0x7fff}; +static unsigned short nan64[6] = {0, 0, 0, 0, 0xc000, 0x7fff}; +static unsigned short nan53[4] = {0, 0, 0, 0x7ff8}; +static unsigned short nan24[2] = {0, 0x7fc0}; +#endif /* !MIEEE */ + + +static void enan (short unsigned int *nan, int size) +{ +int i, n; +unsigned short *p; + +switch( size ) + { +#ifndef DEC + case 113: + n = 8; + p = nan113; + break; + + case 64: + n = 6; + p = nan64; + break; + + case 53: + n = 4; + p = nan53; + break; + + case 24: + n = 2; + p = nan24; + break; + + case NBITS: + for( i=0; i