/* real.c - implementation of REAL_ARITHMETIC, REAL_VALUE_ATOF, and support for XFmode IEEE extended real floating point arithmetic. Contributed by Stephen L. Moshier (moshier@world.std.com). Copyright (C) 1993 Free Software Foundation, Inc. This file is part of GNU CC. GNU CC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. GNU CC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GNU CC; see the file COPYING. If not, write to the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */ #include #include #include "config.h" #include "tree.h" #ifndef errno extern int errno; #endif /* To enable support of XFmode extended real floating point, define LONG_DOUBLE_TYPE_SIZE 96 in the tm.h file (m68k.h or i386.h). To support cross compilation between IEEE, VAX and IBM floating point formats, define REAL_ARITHMETIC in the tm.h file. In either case the machine files (tm.h) must not contain any code that tries to use host floating point arithmetic to convert REAL_VALUE_TYPEs from `double' to `float', pass them to fprintf, etc. In cross-compile situations a REAL_VALUE_TYPE may not be intelligible to the host computer's native arithmetic. The emulator defaults to the host's floating point format so that its decimal conversion functions can be used if desired (see real.h). The first part of this file interfaces gcc to ieee.c, which is a floating point arithmetic suite that was not written with gcc in mind. The interface is followed by ieee.c itself and related items. Avoid changing ieee.c unless you have suitable test programs available. A special version of the PARANOIA floating point arithmetic tester, modified for this purpose, can be found on usc.edu : /pub/C-numanal/ieeetest.zoo. Some tutorial information on ieee.c is given in my book: S. L. Moshier, _Methods and Programs for Mathematical Functions_, Prentice-Hall or Simon & Schuster Int'l, 1989. A library of XFmode elementary transcendental functions can be obtained by ftp from research.att.com: netlib/cephes/ldouble.shar.Z */ /* Type of computer arithmetic. * Only one of DEC, IBM, MIEEE, IBMPC, or UNK should get defined. */ /* `MIEEE' refers generically to big-endian IEEE floating-point data structure. This definition should work in SFmode `float' type and DFmode `double' type on virtually all big-endian IEEE machines. If LONG_DOUBLE_TYPE_SIZE has been defined to be 96, then MIEEE also invokes the particular XFmode (`long double' type) data structure used by the Motorola 680x0 series processors. `IBMPC' refers generally to little-endian IEEE machines. In this case, if LONG_DOUBLE_TYPE_SIZE has been defined to be 96, then IBMPC also invokes the particular XFmode `long double' data structure used by the Intel 80x86 series processors. `DEC' refers specifically to the Digital Equipment Corp PDP-11 and VAX floating point data structure. This model currently supports no type wider than DFmode. `IBM' refers specifically to the IBM System/370 and compatible floating point data structure. This model currently supports no type wider than DFmode. The IBM conversions were contributed by frank@atom.ansto.gov.au (Frank Crawford). If LONG_DOUBLE_TYPE_SIZE = 64 (the default, unless tm.h defines it) then `long double' and `double' are both implemented, but they both mean DFmode. In this case, the software floating-point support available here is activated by writing #define REAL_ARITHMETIC in tm.h. The case LONG_DOUBLE_TYPE_SIZE = 128 activates TFmode support and may deactivate XFmode since `long double' is used to refer to both modes. The macros FLOAT_WORDS_BIG_ENDIAN, HOST_FLOAT_WORDS_BIG_ENDIAN, contributed by Richard Earnshaw , separate the floating point unit's endian-ness from that of the integer addressing. This permits one to define a big-endian FPU on a little-endian machine (e.g., ARM). An extension to BYTES_BIG_ENDIAN may be required for some machines in the future. These optional macros may be defined in tm.h. In real.h, they default to WORDS_BIG_ENDIAN, etc., so there is no need to define them for any normal host or target machine on which the floats and the integers have the same endian-ness. */ /* The following converts gcc macros into the ones used by this file. */ /* REAL_ARITHMETIC defined means that macros in real.h are defined to call emulator functions. */ #ifdef REAL_ARITHMETIC #if TARGET_FLOAT_FORMAT == VAX_FLOAT_FORMAT /* PDP-11, Pro350, VAX: */ #define DEC 1 #else /* it's not VAX */ #if TARGET_FLOAT_FORMAT == IBM_FLOAT_FORMAT /* IBM System/370 style */ #define IBM 1 #else /* it's also not an IBM */ #if TARGET_FLOAT_FORMAT == IEEE_FLOAT_FORMAT #if FLOAT_WORDS_BIG_ENDIAN /* Motorola IEEE, high order words come first (Sun workstation): */ #define MIEEE 1 #else /* not big-endian */ /* Intel IEEE, low order words come first: */ #define IBMPC 1 #endif /* big-endian */ #else /* it's not IEEE either */ /* UNKnown arithmetic. We don't support this and can't go on. */ unknown arithmetic type #define UNK 1 #endif /* not IEEE */ #endif /* not IBM */ #endif /* not VAX */ #else /* REAL_ARITHMETIC not defined means that the *host's* data structure will be used. It may differ by endian-ness from the target machine's structure and will get its ends swapped accordingly (but not here). Probably only the decimal <-> binary functions in this file will actually be used in this case. */ #if HOST_FLOAT_FORMAT == VAX_FLOAT_FORMAT #define DEC 1 #else /* it's not VAX */ #if HOST_FLOAT_FORMAT == IBM_FLOAT_FORMAT /* IBM System/370 style */ #define IBM 1 #else /* it's also not an IBM */ #if HOST_FLOAT_FORMAT == IEEE_FLOAT_FORMAT #if HOST_FLOAT_WORDS_BIG_ENDIAN #define MIEEE 1 #else /* not big-endian */ #define IBMPC 1 #endif /* big-endian */ #else /* it's not IEEE either */ unknown arithmetic type #define UNK 1 #endif /* not IEEE */ #endif /* not IBM */ #endif /* not VAX */ #endif /* REAL_ARITHMETIC not defined */ /* Define INFINITY for support of infinity. Define NANS for support of Not-a-Number's (NaN's). */ #if !defined(DEC) && !defined(IBM) #define INFINITY #define NANS #endif /* Support of NaNs requires support of infinity. */ #ifdef NANS #ifndef INFINITY #define INFINITY #endif #endif /* Find a host integer type that is at least 16 bits wide, and another type at least twice whatever that size is. */ #if HOST_BITS_PER_CHAR >= 16 #define EMUSHORT char #define EMUSHORT_SIZE HOST_BITS_PER_CHAR #define EMULONG_SIZE (2 * HOST_BITS_PER_CHAR) #else #if HOST_BITS_PER_SHORT >= 16 #define EMUSHORT short #define EMUSHORT_SIZE HOST_BITS_PER_SHORT #define EMULONG_SIZE (2 * HOST_BITS_PER_SHORT) #else #if HOST_BITS_PER_INT >= 16 #define EMUSHORT int #define EMUSHORT_SIZE HOST_BITS_PER_INT #define EMULONG_SIZE (2 * HOST_BITS_PER_INT) #else #if HOST_BITS_PER_LONG >= 16 #define EMUSHORT long #define EMUSHORT_SIZE HOST_BITS_PER_LONG #define EMULONG_SIZE (2 * HOST_BITS_PER_LONG) #else /* You will have to modify this program to have a smaller unit size. */ #define EMU_NON_COMPILE #endif #endif #endif #endif #if HOST_BITS_PER_SHORT >= EMULONG_SIZE #define EMULONG short #else #if HOST_BITS_PER_INT >= EMULONG_SIZE #define EMULONG int #else #if HOST_BITS_PER_LONG >= EMULONG_SIZE #define EMULONG long #else #if HOST_BITS_PER_LONG_LONG >= EMULONG_SIZE #define EMULONG long long int #else /* You will have to modify this program to have a smaller unit size. */ #define EMU_NON_COMPILE #endif #endif #endif #endif /* The host interface doesn't work if no 16-bit size exists. */ #if EMUSHORT_SIZE != 16 #define EMU_NON_COMPILE #endif /* OK to continue compilation. */ #ifndef EMU_NON_COMPILE /* Construct macros to translate between REAL_VALUE_TYPE and e type. In GET_REAL and PUT_REAL, r and e are pointers. A REAL_VALUE_TYPE is guaranteed to occupy contiguous locations in memory, with no holes. */ #if LONG_DOUBLE_TYPE_SIZE == 96 /* Number of 16 bit words in external e type format */ #define NE 6 #define MAXDECEXP 4932 #define MINDECEXP -4956 #define GET_REAL(r,e) bcopy (r, e, 2*NE) #define PUT_REAL(e,r) bcopy (e, r, 2*NE) #else /* no XFmode */ #if LONG_DOUBLE_TYPE_SIZE == 128 #define NE 10 #define MAXDECEXP 4932 #define MINDECEXP -4977 #define GET_REAL(r,e) bcopy (r, e, 2*NE) #define PUT_REAL(e,r) bcopy (e, r, 2*NE) #else #define NE 6 #define MAXDECEXP 4932 #define MINDECEXP -4956 #ifdef REAL_ARITHMETIC /* Emulator uses target format internally but host stores it in host endian-ness. */ #if HOST_FLOAT_WORDS_BIG_ENDIAN == FLOAT_WORDS_BIG_ENDIAN #define GET_REAL(r,e) e53toe ((r), (e)) #define PUT_REAL(e,r) etoe53 ((e), (r)) #else /* endian-ness differs */ /* emulator uses target endian-ness internally */ #define GET_REAL(r,e) \ do { EMUSHORT w[4]; \ w[3] = ((EMUSHORT *) r)[0]; \ w[2] = ((EMUSHORT *) r)[1]; \ w[1] = ((EMUSHORT *) r)[2]; \ w[0] = ((EMUSHORT *) r)[3]; \ e53toe (w, (e)); } while (0) #define PUT_REAL(e,r) \ do { EMUSHORT w[4]; \ etoe53 ((e), w); \ *((EMUSHORT *) r) = w[3]; \ *((EMUSHORT *) r + 1) = w[2]; \ *((EMUSHORT *) r + 2) = w[1]; \ *((EMUSHORT *) r + 3) = w[0]; } while (0) #endif /* endian-ness differs */ #else /* not REAL_ARITHMETIC */ /* emulator uses host format */ #define GET_REAL(r,e) e53toe ((r), (e)) #define PUT_REAL(e,r) etoe53 ((e), (r)) #endif /* not REAL_ARITHMETIC */ #endif /* not TFmode */ #endif /* no XFmode */ /* 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) void warning (); extern int extra_warnings; int ecmp (), enormlz (), eshift (); int eisneg (), eisinf (), eisnan (), eiisinf (), eiisnan (); void eadd (), esub (), emul (), ediv (); void eshup1 (), eshup8 (), eshup6 (), eshdn1 (), eshdn8 (), eshdn6 (); void eabs (), eneg (), emov (), eclear (), einfin (), efloor (); void eldexp (), efrexp (), eifrac (), euifrac (), ltoe (), ultoe (); void ereal_to_decimal (), eiinfin (), einan (); void esqrt (), elog (), eexp (), etanh (), epow (); void asctoe (), asctoe24 (), asctoe53 (), asctoe64 (), asctoe113 (); void etoasc (), e24toasc (), e53toasc (), e64toasc (), e113toasc (); void etoe64 (), etoe53 (), etoe24 (), e64toe (), e53toe (), e24toe (); void etoe113 (), e113toe (); void mtherr (), make_nan (); void enan (); extern unsigned EMUSHORT ezero[], ehalf[], eone[], etwo[]; extern unsigned EMUSHORT elog2[], esqrt2[]; /* Copy 32-bit numbers obtained from array containing 16-bit numbers, swapping ends if required, into output array of longs. The result is normally passed to fprintf by the ASM_OUTPUT_ macros. */ void endian (e, x, mode) unsigned EMUSHORT e[]; long x[]; enum machine_mode mode; { unsigned long th, t; #if FLOAT_WORDS_BIG_ENDIAN switch (mode) { case TFmode: /* Swap halfwords in the fourth long. */ th = (unsigned long) e[6] & 0xffff; t = (unsigned long) e[7] & 0xffff; t |= th << 16; x[3] = (long) t; case XFmode: /* Swap halfwords in the third long. */ th = (unsigned long) e[4] & 0xffff; t = (unsigned long) e[5] & 0xffff; t |= th << 16; x[2] = (long) t; /* fall into the double case */ case DFmode: /* swap halfwords in the second word */ th = (unsigned long) e[2] & 0xffff; t = (unsigned long) e[3] & 0xffff; t |= th << 16; x[1] = (long) t; /* fall into the float case */ case SFmode: /* swap halfwords in the first word */ th = (unsigned long) e[0] & 0xffff; t = (unsigned long) e[1] & 0xffff; t |= th << 16; x[0] = t; break; default: abort (); } #else /* Pack the output array without swapping. */ switch (mode) { case TFmode: /* Pack the fourth long. */ th = (unsigned long) e[7] & 0xffff; t = (unsigned long) e[6] & 0xffff; t |= th << 16; x[3] = (long) t; case XFmode: /* Pack the third long. Each element of the input REAL_VALUE_TYPE array has 16 useful bits in it. */ th = (unsigned long) e[5] & 0xffff; t = (unsigned long) e[4] & 0xffff; t |= th << 16; x[2] = (long) t; /* fall into the double case */ case DFmode: /* pack the second long */ th = (unsigned long) e[3] & 0xffff; t = (unsigned long) e[2] & 0xffff; t |= th << 16; x[1] = (long) t; /* fall into the float case */ case SFmode: /* pack the first long */ th = (unsigned long) e[1] & 0xffff; t = (unsigned long) e[0] & 0xffff; t |= th << 16; x[0] = t; break; default: abort (); } #endif } /* This is the implementation of the REAL_ARITHMETIC macro. */ void earith (value, icode, r1, r2) REAL_VALUE_TYPE *value; int icode; REAL_VALUE_TYPE *r1; REAL_VALUE_TYPE *r2; { unsigned EMUSHORT d1[NE], d2[NE], v[NE]; enum tree_code code; GET_REAL (r1, d1); GET_REAL (r2, d2); #ifdef NANS /* Return NaN input back to the caller. */ if (eisnan (d1)) { PUT_REAL (d1, value); return; } if (eisnan (d2)) { PUT_REAL (d2, value); return; } #endif code = (enum tree_code) icode; switch (code) { case PLUS_EXPR: eadd (d2, d1, v); break; case MINUS_EXPR: esub (d2, d1, v); /* d1 - d2 */ break; case MULT_EXPR: emul (d2, d1, v); break; case RDIV_EXPR: #ifndef REAL_INFINITY if (ecmp (d2, ezero) == 0) { #ifdef NANS enan (v); break; #else abort (); #endif } #endif ediv (d2, d1, v); /* d1/d2 */ break; case MIN_EXPR: /* min (d1,d2) */ if (ecmp (d1, d2) < 0) emov (d1, v); else emov (d2, v); break; case MAX_EXPR: /* max (d1,d2) */ if (ecmp (d1, d2) > 0) emov (d1, v); else emov (d2, v); break; default: emov (ezero, v); break; } PUT_REAL (v, value); } /* Truncate REAL_VALUE_TYPE toward zero to signed HOST_WIDE_INT * implements REAL_VALUE_RNDZINT (x) (etrunci (x)) */ REAL_VALUE_TYPE etrunci (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT f[NE], g[NE]; REAL_VALUE_TYPE r; HOST_WIDE_INT l; GET_REAL (&x, g); #ifdef NANS if (eisnan (g)) return (x); #endif eifrac (g, &l, f); ltoe (&l, g); PUT_REAL (g, &r); return (r); } /* Truncate REAL_VALUE_TYPE toward zero to unsigned HOST_WIDE_INT * implements REAL_VALUE_UNSIGNED_RNDZINT (x) (etruncui (x)) */ REAL_VALUE_TYPE etruncui (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT f[NE], g[NE]; REAL_VALUE_TYPE r; unsigned HOST_WIDE_INT l; GET_REAL (&x, g); #ifdef NANS if (eisnan (g)) return (x); #endif euifrac (g, &l, f); ultoe (&l, g); PUT_REAL (g, &r); return (r); } /* This is the REAL_VALUE_ATOF function. * It converts a decimal string to binary, rounding off * as indicated by the machine_mode argument. Then it * promotes the rounded value to REAL_VALUE_TYPE. */ REAL_VALUE_TYPE ereal_atof (s, t) char *s; enum machine_mode t; { unsigned EMUSHORT tem[NE], e[NE]; REAL_VALUE_TYPE r; switch (t) { case SFmode: asctoe24 (s, tem); e24toe (tem, e); break; case DFmode: asctoe53 (s, tem); e53toe (tem, e); break; case XFmode: asctoe64 (s, tem); e64toe (tem, e); break; case TFmode: asctoe113 (s, tem); e113toe (tem, e); break; default: asctoe (s, e); } PUT_REAL (e, &r); return (r); } /* Expansion of REAL_NEGATE. */ REAL_VALUE_TYPE ereal_negate (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT e[NE]; REAL_VALUE_TYPE r; GET_REAL (&x, e); #ifdef NANS if (eisnan (e)) return (x); #endif eneg (e); PUT_REAL (e, &r); return (r); } /* Round real toward zero to HOST_WIDE_INT * implements REAL_VALUE_FIX (x). */ HOST_WIDE_INT efixi (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT f[NE], g[NE]; HOST_WIDE_INT l; GET_REAL (&x, f); #ifdef NANS if (eisnan (f)) { warning ("conversion from NaN to int"); return (-1); } #endif eifrac (f, &l, g); return l; } /* Round real toward zero to unsigned HOST_WIDE_INT * implements REAL_VALUE_UNSIGNED_FIX (x). * Negative input returns zero. */ unsigned HOST_WIDE_INT efixui (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT f[NE], g[NE]; unsigned HOST_WIDE_INT l; GET_REAL (&x, f); #ifdef NANS if (eisnan (f)) { warning ("conversion from NaN to unsigned int"); return (-1); } #endif euifrac (f, &l, g); return l; } /* REAL_VALUE_FROM_INT macro. */ void ereal_from_int (d, i, j) REAL_VALUE_TYPE *d; HOST_WIDE_INT i, j; { unsigned EMUSHORT df[NE], dg[NE]; HOST_WIDE_INT low, high; int sign; sign = 0; low = i; if ((high = j) < 0) { sign = 1; /* complement and add 1 */ high = ~high; if (low) low = -low; else high += 1; } eldexp (eone, HOST_BITS_PER_WIDE_INT, df); ultoe (&high, dg); emul (dg, df, dg); ultoe (&low, df); eadd (df, dg, dg); if (sign) eneg (dg); PUT_REAL (dg, d); } /* REAL_VALUE_FROM_UNSIGNED_INT macro. */ void ereal_from_uint (d, i, j) REAL_VALUE_TYPE *d; unsigned HOST_WIDE_INT i, j; { unsigned EMUSHORT df[NE], dg[NE]; unsigned HOST_WIDE_INT low, high; low = i; high = j; eldexp (eone, HOST_BITS_PER_WIDE_INT, df); ultoe (&high, dg); emul (dg, df, dg); ultoe (&low, df); eadd (df, dg, dg); PUT_REAL (dg, d); } /* REAL_VALUE_TO_INT macro */ void ereal_to_int (low, high, rr) HOST_WIDE_INT *low, *high; REAL_VALUE_TYPE rr; { unsigned EMUSHORT d[NE], df[NE], dg[NE], dh[NE]; int s; GET_REAL (&rr, d); #ifdef NANS if (eisnan (d)) { warning ("conversion from NaN to int"); *low = -1; *high = -1; return; } #endif /* convert positive value */ s = 0; if (eisneg (d)) { eneg (d); s = 1; } eldexp (eone, HOST_BITS_PER_WIDE_INT, df); ediv (df, d, dg); /* dg = d / 2^32 is the high word */ euifrac (dg, high, dh); emul (df, dh, dg); /* fractional part is the low word */ euifrac (dg, low, dh); if (s) { /* complement and add 1 */ *high = ~(*high); if (*low) *low = -(*low); else *high += 1; } } /* REAL_VALUE_LDEXP macro. */ REAL_VALUE_TYPE ereal_ldexp (x, n) REAL_VALUE_TYPE x; int n; { unsigned EMUSHORT e[NE], y[NE]; REAL_VALUE_TYPE r; GET_REAL (&x, e); #ifdef NANS if (eisnan (e)) return (x); #endif eldexp (e, n, y); PUT_REAL (y, &r); return (r); } /* These routines are conditionally compiled because functions * of the same names may be defined in fold-const.c. */ #ifdef REAL_ARITHMETIC /* Check for infinity in a REAL_VALUE_TYPE. */ int target_isinf (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT e[NE]; #ifdef INFINITY GET_REAL (&x, e); return (eisinf (e)); #else return 0; #endif } /* Check whether a REAL_VALUE_TYPE item is a NaN. */ int target_isnan (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT e[NE]; #ifdef NANS GET_REAL (&x, e); return (eisnan (e)); #else return (0); #endif } /* Check for a negative REAL_VALUE_TYPE number. * this means strictly less than zero, not -0. */ int target_negative (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT e[NE]; GET_REAL (&x, e); if (ecmp (e, ezero) == -1) return (1); return (0); } /* Expansion of REAL_VALUE_TRUNCATE. * The result is in floating point, rounded to nearest or even. */ REAL_VALUE_TYPE real_value_truncate (mode, arg) enum machine_mode mode; REAL_VALUE_TYPE arg; { unsigned EMUSHORT e[NE], t[NE]; REAL_VALUE_TYPE r; GET_REAL (&arg, e); #ifdef NANS if (eisnan (e)) return (arg); #endif eclear (t); switch (mode) { case TFmode: etoe113 (e, t); e113toe (t, t); break; case XFmode: etoe64 (e, t); e64toe (t, t); break; case DFmode: etoe53 (e, t); e53toe (t, t); break; case SFmode: etoe24 (e, t); e24toe (t, t); break; case SImode: r = etrunci (arg); return (r); default: abort (); } PUT_REAL (t, &r); return (r); } #endif /* REAL_ARITHMETIC defined */ /* Used for debugging--print the value of R in human-readable format on stderr. */ void debug_real (r) REAL_VALUE_TYPE r; { char dstr[30]; REAL_VALUE_TO_DECIMAL (r, "%.20g", dstr); fprintf (stderr, "%s", dstr); } /* Target values are arrays of host longs. A long is guaranteed to be at least 32 bits wide. */ /* 128-bit long double */ void etartdouble (r, l) REAL_VALUE_TYPE r; long l[]; { unsigned EMUSHORT e[NE]; GET_REAL (&r, e); etoe113 (e, e); endian (e, l, TFmode); } /* 80-bit long double */ void etarldouble (r, l) REAL_VALUE_TYPE r; long l[]; { unsigned EMUSHORT e[NE]; GET_REAL (&r, e); etoe64 (e, e); endian (e, l, XFmode); } void etardouble (r, l) REAL_VALUE_TYPE r; long l[]; { unsigned EMUSHORT e[NE]; GET_REAL (&r, e); etoe53 (e, e); endian (e, l, DFmode); } long etarsingle (r) REAL_VALUE_TYPE r; { unsigned EMUSHORT e[NE]; unsigned long l; GET_REAL (&r, e); etoe24 (e, e); endian (e, &l, SFmode); return ((long) l); } void ereal_to_decimal (x, s) REAL_VALUE_TYPE x; char *s; { unsigned EMUSHORT e[NE]; GET_REAL (&x, e); etoasc (e, s, 20); } int ereal_cmp (x, y) REAL_VALUE_TYPE x, y; { unsigned EMUSHORT ex[NE], ey[NE]; GET_REAL (&x, ex); GET_REAL (&y, ey); return (ecmp (ex, ey)); } int ereal_isneg (x) REAL_VALUE_TYPE x; { unsigned EMUSHORT ex[NE]; GET_REAL (&x, ex); return (eisneg (ex)); } /* End of REAL_ARITHMETIC interface */ /* 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) ASCII string to specified precision * e24toe (&f, e) IEEE single precision to e type * e53toe (&d, e) IEEE double precision to e type * e64toe (&d, e) IEEE long double precision to e type * e113toe (&d, e) 128-bit 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) c = b / a * efloor (a, b) truncate to integer, toward -infinity * efrexp (a, exp, s) extract exponent and significand * eifrac (e, &l, frac) e to HOST_WIDE_INT and e type fraction * euifrac (e, &l, frac) e to unsigned HOST_WIDE_INT and e type fraction * einfin (e) 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) c = b * a * eneg (e) e = -e * eround (a, b) b = nearest integer value to a * esub (a, b, c) 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) 80-bit long double to ASCII string * e113toasc (&d, str, n) 128-bit long double to ASCII string * etoasc (e, str, n) 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) HOST_WIDE_INT to e type * ultoe (&l, e) unsigned HOST_WIDE_INT 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 * * * 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) divide significands, bi = bi / ai * emdnorm (ai,l,s,exp) normalize and round off * emovi (a, ai) convert external a to internal ai * emovo (ai, a) convert internal ai to external a * emovz (ai, bi) bi = ai, low guard word of bi = 0 * emulm (ai, bi) 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 * eiisinf (ai) 1 if infinite * eiisnan (ai) 1 if a NaN * einan (ai) set ai = NaN * eiinfin (ai) set ai = infinity * * * The result is always normalized and rounded to NI-4 word precision * after each arithmetic operation. * * Exception flags are NOT fully supported. * * Signaling NaN's are NOT supported; they are treated the same * as quiet NaN's. * * Define INFINITY 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. * * Denormals are always supported here where appropriate (e.g., not * for conversion to DEC numbers). * */ /* 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 (Intel 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 or MIEEE 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 INVALID 7 /* NaN-producing operation */ /* e type constants used by high precision check routines */ #if LONG_DOUBLE_TYPE_SIZE == 128 /* 0.0 */ unsigned EMUSHORT ezero[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,}; extern unsigned EMUSHORT ezero[]; /* 5.0E-1 */ unsigned EMUSHORT ehalf[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,}; extern unsigned EMUSHORT ehalf[]; /* 1.0E0 */ unsigned EMUSHORT eone[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,}; extern unsigned EMUSHORT eone[]; /* 2.0E0 */ unsigned EMUSHORT etwo[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,}; extern unsigned EMUSHORT etwo[]; /* 3.2E1 */ unsigned EMUSHORT e32[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,}; extern unsigned EMUSHORT e32[]; /* 6.93147180559945309417232121458176568075500134360255E-1 */ unsigned EMUSHORT elog2[NE] = {0x40f3, 0xf6af, 0x03f2, 0xb398, 0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,}; extern unsigned EMUSHORT elog2[]; /* 1.41421356237309504880168872420969807856967187537695E0 */ unsigned EMUSHORT esqrt2[NE] = {0x1d6f, 0xbe9f, 0x754a, 0x89b3, 0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,}; extern unsigned EMUSHORT esqrt2[]; /* 3.14159265358979323846264338327950288419716939937511E0 */ unsigned EMUSHORT epi[NE] = {0x2902, 0x1cd1, 0x80dc, 0x628b, 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,}; extern unsigned EMUSHORT epi[]; #else /* LONG_DOUBLE_TYPE_SIZE is other than 128 */ unsigned EMUSHORT ezero[NE] = {0, 0000000, 0000000, 0000000, 0000000, 0000000,}; unsigned EMUSHORT ehalf[NE] = {0, 0000000, 0000000, 0000000, 0100000, 0x3ffe,}; unsigned EMUSHORT eone[NE] = {0, 0000000, 0000000, 0000000, 0100000, 0x3fff,}; unsigned EMUSHORT etwo[NE] = {0, 0000000, 0000000, 0000000, 0100000, 0040000,}; unsigned EMUSHORT e32[NE] = {0, 0000000, 0000000, 0000000, 0100000, 0040004,}; unsigned EMUSHORT elog2[NE] = {0xc9e4, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,}; unsigned EMUSHORT esqrt2[NE] = {0x597e, 0x6484, 0174736, 0171463, 0132404, 0x3fff,}; unsigned EMUSHORT epi[NE] = {0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,}; #endif /* Control register for rounding precision. * This can be set to 113 (if NE=10), 80 (if NE=6), 64, 56, 53, or 24 bits. */ int rndprc = NBITS; extern int rndprc; void eaddm (), esubm (), emdnorm (), asctoeg (); static void toe24 (), toe53 (), toe64 (), toe113 (); void eremain (), einit (), eiremain (); int ecmpm (), edivm (), emulm (); void emovi (), emovo (), emovz (), ecleaz (), ecleazs (), eadd1 (); #ifdef DEC void etodec (), todec (), dectoe (); #endif #ifdef IBM void etoibm (), toibm (), ibmtoe (); #endif void einit () { } /* ; Clear out entire external format number. ; ; unsigned EMUSHORT x[]; ; eclear (x); */ void eclear (x) register unsigned EMUSHORT *x; { register int i; for (i = 0; i < NE; i++) *x++ = 0; } /* Move external format number from a to b. * * emov (a, b); */ void emov (a, b) register unsigned EMUSHORT *a, *b; { register int i; for (i = 0; i < NE; i++) *b++ = *a++; } /* ; Absolute value of external format number ; ; EMUSHORT x[NE]; ; eabs (x); */ void eabs (x) unsigned EMUSHORT x[]; /* x is the memory address of a short */ { x[NE - 1] &= 0x7fff; /* sign is top bit of last word of external format */ } /* ; Negate external format number ; ; unsigned EMUSHORT x[NE]; ; eneg (x); */ void eneg (x) unsigned EMUSHORT x[]; { #ifdef NANS if (eisnan (x)) return; #endif x[NE - 1] ^= 0x8000; /* Toggle the sign bit */ } /* Return 1 if external format number is negative, * else return zero, including when it is a NaN. */ int eisneg (x) unsigned EMUSHORT x[]; { #ifdef NANS if (eisnan (x)) return (0); #endif if (x[NE - 1] & 0x8000) return (1); else return (0); } /* Return 1 if external format number is infinity. * else return zero. */ int eisinf (x) unsigned EMUSHORT x[]; { #ifdef NANS if (eisnan (x)) return (0); #endif if ((x[NE - 1] & 0x7fff) == 0x7fff) return (1); else return (0); } /* Check if e-type number is not a number. The bit pattern is one that we defined, so we know for sure how to detect it. */ int eisnan (x) unsigned EMUSHORT x[]; { #ifdef NANS int i; /* NaN has maximum exponent */ if ((x[NE - 1] & 0x7fff) != 0x7fff) return (0); /* ... and non-zero significand field. */ for (i = 0; i < NE - 1; i++) { if (*x++ != 0) return (1); } #endif return (0); } /* Fill external format number with infinity pattern (IEEE) or largest possible number (non-IEEE). */ void einfin (x) register unsigned EMUSHORT *x; { register int i; #ifdef INFINITY for (i = 0; i < NE - 1; i++) *x++ = 0; *x |= 32767; #else for (i = 0; i < NE - 1; i++) *x++ = 0xffff; *x |= 32766; if (rndprc < NBITS) { if (rndprc == 113) { *(x - 9) = 0; *(x - 8) = 0; } if (rndprc == 64) { *(x - 5) = 0; } if (rndprc == 53) { *(x - 4) = 0xf800; } else { *(x - 4) = 0; *(x - 3) = 0; *(x - 2) = 0xff00; } } #endif } /* Output an e-type NaN. This generates Intel's quiet NaN pattern for extended real. The exponent is 7fff, the leading mantissa word is c000. */ void enan (x) register unsigned EMUSHORT *x; { register int i; for (i = 0; i < NE - 2; i++) *x++ = 0; *x++ = 0xc000; *x = 0x7fff; } /* Move in external format number, * converting it to internal format. */ void emovi (a, b) unsigned EMUSHORT *a, *b; { register unsigned EMUSHORT *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 < NI; i++) *q++ = *p--; return; } #endif for (i = 2; i < NI; i++) *q++ = 0; return; } #endif /* clear high guard word */ *q++ = 0; /* move in the significand */ for (i = 0; i < NE - 1; i++) *q++ = *p--; /* clear low guard word */ *q = 0; } /* Move internal format number out, * converting it to external format. */ void emovo (a, b) unsigned EMUSHORT *a, *b; { register unsigned EMUSHORT *p, *q; unsigned EMUSHORT i; p = a; q = b + (NE - 1); /* point to output exponent */ /* combine sign and exponent */ i = *p++; if (i) *q-- = *p++ | 0x8000; else *q-- = *p++; #ifdef INFINITY if (*(p - 1) == 0x7fff) { #ifdef NANS if (eiisnan (a)) { enan (b); return; } #endif einfin (b); return; } #endif /* skip over guard word */ ++p; /* move the significand */ for (i = 0; i < NE - 1; i++) *q-- = *p++; } /* Clear out internal format number. */ void ecleaz (xi) register unsigned EMUSHORT *xi; { register int i; for (i = 0; i < NI; i++) *xi++ = 0; } /* same, but don't touch the sign. */ void ecleazs (xi) register unsigned EMUSHORT *xi; { register int i; ++xi; for (i = 0; i < NI - 1; i++) *xi++ = 0; } /* Move internal format number from a to b. */ void emovz (a, b) register unsigned EMUSHORT *a, *b; { register int i; for (i = 0; i < NI - 1; i++) *b++ = *a++; /* clear low guard word */ *b = 0; } /* Generate internal format NaN. The explicit pattern for this is maximum exponent and top two significand bits set. */ void einan (x) unsigned EMUSHORT x[]; { ecleaz (x); x[E] = 0x7fff; x[M + 1] = 0xc000; } /* Return nonzero if internal format number is a NaN. */ int eiisnan (x) unsigned EMUSHORT x[]; { int i; if ((x[E] & 0x7fff) == 0x7fff) { for (i = M + 1; i < NI; i++) { if (x[i] != 0) return (1); } } return (0); } /* Fill internal format number with infinity pattern. This has maximum exponent and significand all zeros. */ void eiinfin (x) unsigned EMUSHORT x[]; { ecleaz (x); x[E] = 0x7fff; } /* Return nonzero if internal format number is infinite. */ int eiisinf (x) unsigned EMUSHORT x[]; { #ifdef NANS if (eiisnan (x)) return (0); #endif if ((x[E] & 0x7fff) == 0x7fff) return (1); return (0); } /* ; Compare significands of numbers in internal format. ; Guard words are included in the comparison. ; ; unsigned EMUSHORT a[NI], b[NI]; ; cmpm (a, b); ; ; for the significands: ; returns +1 if a > b ; 0 if a == b ; -1 if a < b */ int ecmpm (a, b) register unsigned EMUSHORT *a, *b; { int i; a += M; /* skip up to significand area */ b += M; for (i = M; i < NI; i++) { if (*a++ != *b++) goto difrnt; } return (0); difrnt: if (*(--a) > *(--b)) return (1); else return (-1); } /* ; Shift significand down by 1 bit */ void eshdn1 (x) register unsigned EMUSHORT *x; { register unsigned EMUSHORT bits; int i; x += M; /* point to significand area */ bits = 0; for (i = M; i < NI; i++) { if (*x & 1) bits |= 1; *x >>= 1; if (bits & 2) *x |= 0x8000; bits <<= 1; ++x; } } /* ; Shift significand up by 1 bit */ void eshup1 (x) register unsigned EMUSHORT *x; { register unsigned EMUSHORT bits; int i; x += NI - 1; bits = 0; for (i = M; i < NI; i++) { if (*x & 0x8000) bits |= 1; *x <<= 1; if (bits & 2) *x |= 1; bits <<= 1; --x; } } /* ; Shift significand down by 8 bits */ void eshdn8 (x) register unsigned EMUSHORT *x; { register unsigned EMUSHORT newbyt, oldbyt; int i; x += M; oldbyt = 0; for (i = M; i < NI; i++) { newbyt = *x << 8; *x >>= 8; *x |= oldbyt; oldbyt = newbyt; ++x; } } /* ; Shift significand up by 8 bits */ void eshup8 (x) register unsigned EMUSHORT *x; { int i; register unsigned EMUSHORT newbyt, oldbyt; x += NI - 1; oldbyt = 0; for (i = M; i < NI; i++) { newbyt = *x >> 8; *x <<= 8; *x |= oldbyt; oldbyt = newbyt; --x; } } /* ; Shift significand up by 16 bits */ void eshup6 (x) register unsigned EMUSHORT *x; { int i; register unsigned EMUSHORT *p; p = x + M; x += M + 1; for (i = M; i < NI - 1; i++) *p++ = *x++; *p = 0; } /* ; Shift significand down by 16 bits */ void eshdn6 (x) register unsigned EMUSHORT *x; { int i; register unsigned EMUSHORT *p; x += NI - 1; p = x + 1; for (i = M; i < NI - 1; i++) *(--p) = *(--x); *(--p) = 0; } /* ; Add significands ; x + y replaces y */ void eaddm (x, y) unsigned EMUSHORT *x, *y; { register unsigned EMULONG a; int i; unsigned int carry; x += NI - 1; y += NI - 1; carry = 0; for (i = M; i < NI; i++) { a = (unsigned EMULONG) (*x) + (unsigned EMULONG) (*y) + carry; if (a & 0x10000) carry = 1; else carry = 0; *y = (unsigned EMUSHORT) a; --x; --y; } } /* ; Subtract significands ; y - x replaces y */ void esubm (x, y) unsigned EMUSHORT *x, *y; { unsigned EMULONG a; int i; unsigned int carry; x += NI - 1; y += NI - 1; carry = 0; for (i = M; i < NI; i++) { a = (unsigned EMULONG) (*y) - (unsigned EMULONG) (*x) - carry; if (a & 0x10000) carry = 1; else carry = 0; *y = (unsigned EMUSHORT) a; --x; --y; } } static unsigned EMUSHORT equot[NI]; #if 0 /* Radix 2 shift-and-add versions of multiply and divide */ /* Divide significands */ int edivm (den, num) unsigned EMUSHORT den[], num[]; { int i; register unsigned EMUSHORT *p, *q; unsigned EMUSHORT j; p = &equot[0]; *p++ = num[0]; *p++ = num[1]; for (i = M; i < NI; i++) { *p++ = 0; } /* Use faster compare and subtraction if denominator * has only 15 bits of significance. */ p = &den[M + 2]; if (*p++ == 0) { for (i = M + 3; i < NI; i++) { if (*p++ != 0) goto fulldiv; } if ((den[M + 1] & 1) != 0) goto fulldiv; eshdn1 (num); eshdn1 (den); p = &den[M + 1]; q = &num[M + 1]; for (i = 0; i < NBITS + 2; i++) { if (*p <= *q) { *q -= *p; j = 1; } else { j = 0; } eshup1 (equot); equot[NI - 2] |= j; eshup1 (num); } goto divdon; } /* The number of quotient bits to calculate is * NBITS + 1 scaling guard bit + 1 roundoff bit. */ fulldiv: p = &equot[NI - 2]; for (i = 0; i < NBITS + 2; i++) { if (ecmpm (den, num) <= 0) { esubm (den, num); j = 1; /* quotient bit = 1 */ } else j = 0; eshup1 (equot); *p |= j; eshup1 (num); } divdon: eshdn1 (equot); eshdn1 (equot); /* test for nonzero remainder after roundoff bit */ p = &num[M]; j = 0; for (i = M; i < NI; i++) { j |= *p++; } if (j) j = 1; for (i = 0; i < NI; i++) num[i] = equot[i]; return ((int) j); } /* Multiply significands */ int emulm (a, b) unsigned EMUSHORT a[], b[]; { unsigned EMUSHORT *p, *q; int i, j, k; equot[0] = b[0]; equot[1] = b[1]; for (i = M; i < NI; i++) equot[i] = 0; p = &a[NI - 2]; k = NBITS; while (*p == 0) /* significand is not supposed to be all zero */ { eshdn6 (a); k -= 16; } if ((*p & 0xff) == 0) { eshdn8 (a); k -= 8; } q = &equot[NI - 1]; j = 0; for (i = 0; i < k; i++) { if (*p & 1) eaddm (b, equot); /* remember if there were any nonzero bits shifted out */ if (*q & 1) j |= 1; eshdn1 (a); eshdn1 (equot); } for (i = 0; i < NI; i++) b[i] = equot[i]; /* return flag for lost nonzero bits */ return (j); } #else /* Radix 65536 versions of multiply and divide */ /* Multiply significand of e-type number b by 16-bit quantity a, e-type result to c. */ void m16m (a, b, c) unsigned short a; unsigned short b[], c[]; { register unsigned short *pp; register unsigned long carry; unsigned short *ps; unsigned short p[NI]; unsigned long aa, m; int i; aa = a; pp = &p[NI-2]; *pp++ = 0; *pp = 0; ps = &b[NI-1]; for (i=M+1; i> 16) + (m >> 16) + *pp; *pp = (unsigned short)carry; *(pp-1) = carry >> 16; } } for (i=M; i 0) { tquot -= 1; esubm (den, tprod); if (ecmpm (tprod, num) > 0) { tquot -= 1; esubm (den, tprod); } } esubm (tprod, num); equot[i] = tquot; eshup6(num); } /* test for nonzero remainder after roundoff bit */ p = &num[M]; j = 0; for (i=M; i NBITS) { ecleazs (s); return; } #endif exp -= j; #ifndef INFINITY if (exp >= 32767L) goto overf; #else if ((j > NBITS) && (exp < 32767)) { ecleazs (s); return; } #endif if (exp < 0L) { if (exp > (EMULONG) (-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 (rndprc != rlast) { ecleaz (rbit); switch (rndprc) { default: case NBITS: rw = NI - 1; /* low guard word */ rmsk = 0xffff; rmbit = 0x8000; re = rw - 1; rebit = 1; break; case 113: rw = 10; rmsk = 0x7fff; rmbit = 0x4000; rebit = 0x8000; re = rw; break; case 64: rw = 7; rmsk = 0xffff; rmbit = 0x8000; re = rw - 1; rebit = 1; break; /* For DEC or IBM arithmetic */ case 56: rw = 6; rmsk = 0xff; rmbit = 0x80; rebit = 0x100; re = rw; break; case 53: rw = 6; rmsk = 0x7ff; rmbit = 0x0400; rebit = 0x800; re = rw; break; case 24: rw = 4; rmsk = 0xff; rmbit = 0x80; rebit = 0x100; re = rw; break; } rbit[re] = rebit; rlast = rndprc; } /* Shift down 1 temporarily if the data structure has an implied most significant bit and the number is denormal. */ if ((exp <= 0) && (rndprc != 64) && (rndprc != NBITS)) { lost |= s[NI - 1] & 1; eshdn1 (s); } /* Clear out all bits below the rounding bit, remembering in r if any were nonzero. */ r = s[rw] & rmsk; if (rndprc < NBITS) { i = rw + 1; while (i < NI) { if (s[i]) r |= 1; s[i] = 0; ++i; } } s[rw] &= ~rmsk; if ((r & rmbit) != 0) { if (r == rmbit) { if (lost == 0) { /* round to even */ if ((s[re] & rebit) == 0) goto mddone; } else { if (subflg != 0) goto mddone; } } eaddm (rbit, s); } mddone: if ((exp <= 0) && (rndprc != 64) && (rndprc != NBITS)) { 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; i < NI - 1; i++) s[i] = 0; if (extra_warnings) warning ("floating point overflow"); #else s[1] = 32766; s[2] = 0; for (i = M + 1; i < NI - 1; i++) s[i] = 0xffff; s[NI - 1] = 0; if ((rndprc < 64) || (rndprc == 113)) { s[rw] &= ~rmsk; if (rndprc == 24) { s[5] = 0; s[6] = 0; } } #endif return; } if (exp < 0) s[1] = 0; else s[1] = (unsigned EMUSHORT) exp; } /* ; Subtract external format numbers. ; ; unsigned EMUSHORT a[NE], b[NE], c[NE]; ; esub (a, b, c); c = b - a */ static int subflg = 0; void esub (a, b, c) unsigned EMUSHORT *a, *b, *c; { #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", INVALID); enan (c); return; } #endif subflg = 1; eadd1 (a, b, c); } /* ; Add. ; ; unsigned EMUSHORT a[NE], b[NE], c[NE]; ; eadd (a, b, c); c = b + a */ void eadd (a, b, c) unsigned EMUSHORT *a, *b, *c; { #ifdef NANS /* NaN plus anything is a NaN. */ if (eisnan (a)) { emov (a, c); return; } if (eisnan (b)) { emov (b, c); return; } /* Infinity minus infinity is a NaN. Test for adding infinities of opposite signs. */ if (eisinf (a) && eisinf (b) && ((eisneg (a) ^ eisneg (b)) != 0)) { mtherr ("esub", INVALID); enan (c); return; } #endif subflg = 0; eadd1 (a, b, c); } void eadd1 (a, b, c) unsigned EMUSHORT *a, *b, *c; { unsigned EMUSHORT ai[NI], bi[NI], ci[NI]; int i, lost, j, k; EMULONG 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 < (EMULONG) (-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 < NI - 1; j++) { if (bi[j] != 0) { /* This could overflow, but let emovo take care of that. */ ltb += 1; break; } } bi[E] = (unsigned EMUSHORT) ltb; goto done; } if (i > 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); done: emovo (bi, c); } /* ; Divide. ; ; unsigned EMUSHORT a[NE], b[NE], c[NE]; ; ediv (a, b, c); c = b / a */ void ediv (a, b, c) unsigned EMUSHORT *a, *b, *c; { unsigned EMUSHORT ai[NI], bi[NI]; int i; EMULONG 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", INVALID); enan (c); 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); return; } /* Anything else over infinity is zero. */ 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 < NI - 1; i++) { if (bi[i] != 0) { ltb -= enormlz (bi); goto dnzro1; } } eclear (c); return; } dnzro1: if (ai[E] == 0) { /* possible divide by zero */ for (i = 1; i < NI - 1; i++) { if (ai[i] != 0) { lta -= enormlz (ai); goto dnzro2; } } if (ai[0] == bi[0]) *(c + (NE - 1)) = 0; else *(c + (NE - 1)) = 0x8000; /* Divide by zero is not an invalid operation. It is a divide-by-zero operation! */ einfin (c); mtherr ("ediv", SING); return; } dnzro2: i = edivm (ai, bi); /* calculate exponent */ lt = ltb - lta + EXONE; emdnorm (bi, i, 0, lt, 64); /* set the sign */ if (ai[0] == bi[0]) bi[0] = 0; else bi[0] = 0Xffff; emovo (bi, c); } /* ; Multiply. ; ; unsigned EMUSHORT a[NE], b[NE], c[NE]; ; emul (a, b, c); c = b * a */ void emul (a, b, c) unsigned EMUSHORT *a, *b, *c; { unsigned EMUSHORT ai[NI], bi[NI]; int i, j; EMULONG lt, lta, ltb; #ifdef NANS /* NaN times anything is the same NaN. */ if (eisnan (a)) { emov (a, c); return; } if (eisnan (b)) { emov (b, c); return; } /* Zero times infinity is a NaN. */ if ((eisinf (a) && (ecmp (b, ezero) == 0)) || (eisinf (b) && (ecmp (a, ezero) == 0))) { mtherr ("emul", INVALID); enan (c); return; } #endif /* Infinity times anything else is infinity. */ #ifdef INFINITY if (eisinf (a) || eisinf (b)) { if (eisneg (a) ^ eisneg (b)) *(c + (NE - 1)) = 0x8000; else *(c + (NE - 1)) = 0; einfin (c); return; } #endif emovi (a, ai); emovi (b, bi); lta = ai[E]; ltb = bi[E]; if (ai[E] == 0) { for (i = 1; i < NI - 1; i++) { if (ai[i] != 0) { lta -= enormlz (ai); goto mnzer1; } } eclear (c); return; } mnzer1: if (bi[E] == 0) { for (i = 1; i < NI - 1; i++) { if (bi[i] != 0) { ltb -= enormlz (bi); goto mnzer2; } } eclear (c); return; } mnzer2: /* Multiply significands */ j = emulm (ai, bi); /* calculate exponent */ lt = lta + ltb - (EXONE - 1); emdnorm (bi, j, 0, lt, 64); /* calculate sign of product */ if (ai[0] == bi[0]) bi[0] = 0; else bi[0] = 0xffff; emovo (bi, c); } /* ; Convert IEEE double precision to e type ; double d; ; unsigned EMUSHORT x[N+2]; ; e53toe (&d, x); */ void e53toe (pe, y) unsigned EMUSHORT *pe, *y; { #ifdef DEC dectoe (pe, y); /* see etodec.c */ #else #ifdef IBM ibmtoe (pe, y, DFmode); #else register unsigned EMUSHORT r; register unsigned EMUSHORT *e, *p; unsigned EMUSHORT yy[NI]; int denorm, k; e = pe; denorm = 0; /* flag if denormalized number */ ecleaz (yy); #ifdef IBMPC e += 3; #endif r = *e; yy[0] = 0; if (r & 0x8000) yy[0] = 0xffff; yy[M] = (r & 0x0f) | 0x10; r &= ~0x800f; /* strip sign and 4 significand bits */ #ifdef INFINITY if (r == 0x7ff0) { #ifdef NANS #ifdef IBMPC if (((pe[3] & 0xf) != 0) || (pe[2] != 0) || (pe[1] != 0) || (pe[0] != 0)) { enan (y); return; } #else if (((pe[0] & 0xf) != 0) || (pe[1] != 0) || (pe[2] != 0) || (pe[3] != 0)) { enan (y); return; } #endif #endif /* NANS */ eclear (y); einfin (y); if (yy[0]) eneg (y); return; } #endif /* INFINITY */ r >>= 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); #endif #ifdef MIEEE ++e; *p++ = *e++; *p++ = *e++; *p++ = *e++; #endif eshift (yy, -5); if (denorm) { /* if zero exponent, then normalize the significand */ if ((k = enormlz (yy)) > NBITS) ecleazs (yy); else yy[E] -= (unsigned EMUSHORT) (k - 1); } emovo (yy, y); #endif /* not IBM */ #endif /* not DEC */ } void e64toe (pe, y) unsigned EMUSHORT *pe, *y; { unsigned EMUSHORT yy[NI]; unsigned EMUSHORT *e, *p, *q; int i; e = pe; p = yy; for (i = 0; i < NE - 5; i++) *p++ = 0; #ifdef IBMPC for (i = 0; i < 5; i++) *p++ = *e++; #endif /* This precision is not ordinarily supported on DEC or IBM. */ #ifdef DEC for (i = 0; i < 5; i++) *p++ = *e++; #endif #ifdef IBM p = &yy[0] + (NE - 1); *p-- = *e++; ++e; for (i = 0; i < 5; i++) *p-- = *e++; #endif #ifdef MIEEE p = &yy[0] + (NE - 1); *p-- = *e++; ++e; for (i = 0; i < 4; i++) *p-- = *e++; #endif p = yy; q = y; #ifdef INFINITY if (*p == 0x7fff) { #ifdef NANS #ifdef IBMPC for (i = 0; i < 4; i++) { if (pe[i] != 0) { enan (y); return; } } #else for (i = 1; i <= 4; i++) { if (pe[i] != 0) { enan (y); return; } } #endif #endif /* NANS */ eclear (y); einfin (y); if (*p & 0x8000) eneg (y); return; } #endif /* INFINITY */ for (i = 0; i < NE; i++) *q++ = *p++; } void e113toe (pe, y) unsigned EMUSHORT *pe, *y; { register unsigned EMUSHORT r; unsigned EMUSHORT *e, *p; unsigned EMUSHORT 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); return; } } #else for (i = 1; i < 8; i++) { if (pe[i] != 0) { enan (y); return; } } #endif #endif /* NANS */ eclear (y); einfin (y); if (yy[0]) eneg (y); return; } #endif /* INFINITY */ yy[E] = r; p = &yy[M + 1]; #ifdef IBMPC for (i = 0; i < 7; i++) *p++ = *(--e); #endif #ifdef MIEEE ++e; for (i = 0; i < 7; i++) *p++ = *e++; #endif /* 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); } /* ; Convert IEEE single precision to e type ; float d; ; unsigned EMUSHORT x[N+2]; ; dtox (&d, x); */ void e24toe (pe, y) unsigned EMUSHORT *pe, *y; { #ifdef IBM ibmtoe (pe, y, SFmode); #else register unsigned EMUSHORT r; register unsigned EMUSHORT *e, *p; unsigned EMUSHORT 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); return; } #else if (((pe[1] & 0x7f) != 0) || (pe[0] != 0)) { enan (y); return; } #endif #endif /* NANS */ eclear (y); einfin (y); if (yy[0]) eneg (y); return; } #endif /* INFINITY */ 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 eshift (yy, -8); if (denorm) { /* if zero exponent, then normalize the significand */ if ((k = enormlz (yy)) > NBITS) ecleazs (yy); else yy[E] -= (unsigned EMUSHORT) (k - 1); } emovo (yy, y); #endif /* not IBM */ } void etoe113 (x, e) unsigned EMUSHORT *x, *e; { unsigned EMUSHORT xi[NI]; EMULONG exp; int rndsav; #ifdef NANS if (eisnan (x)) { make_nan (e, TFmode); return; } #endif emovi (x, xi); exp = (EMULONG) xi[E]; #ifdef INFINITY if (eisinf (x)) goto nonorm; #endif /* round off to nearest or even */ rndsav = rndprc; rndprc = 113; emdnorm (xi, 0, 0, exp, 64); rndprc = rndsav; nonorm: toe113 (xi, e); } /* move out internal format to ieee long double */ static void toe113 (a, b) unsigned EMUSHORT *a, *b; { register unsigned EMUSHORT *p, *q; unsigned EMUSHORT i; #ifdef NANS if (eiisnan (a)) { make_nan (b, TFmode); 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 } void etoe64 (x, e) unsigned EMUSHORT *x, *e; { unsigned EMUSHORT xi[NI]; EMULONG exp; int rndsav; #ifdef NANS if (eisnan (x)) { make_nan (e, XFmode); return; } #endif emovi (x, xi); /* adjust exponent for offset */ exp = (EMULONG) xi[E]; #ifdef INFINITY if (eisinf (x)) goto nonorm; #endif /* round off to nearest or even */ rndsav = rndprc; rndprc = 64; emdnorm (xi, 0, 0, exp, 64); rndprc = rndsav; nonorm: toe64 (xi, e); } /* move out internal format to ieee long double */ static void toe64 (a, b) unsigned EMUSHORT *a, *b; { register unsigned EMUSHORT *p, *q; unsigned EMUSHORT i; #ifdef NANS if (eiisnan (a)) { make_nan (b, XFmode); return; } #endif p = a; #if defined(MIEEE) || defined(IBM) q = b; #else q = b + 4; /* point to output exponent */ #if LONG_DOUBLE_TYPE_SIZE == 96 /* Clear the last two bytes of 12-byte Intel format */ *(q+1) = 0; #endif #endif /* combine sign and exponent */ i = *p++; #if defined(MIEEE) || defined(IBM) if (i) *q++ = *p++ | 0x8000; else *q++ = *p++; *q++ = 0; #else if (i) *q-- = *p++ | 0x8000; else *q-- = *p++; #endif /* skip over guard word */ ++p; /* move the significand */ #if defined(MIEEE) || defined(IBM) for (i = 0; i < 4; i++) *q++ = *p++; #else for (i = 0; i < 4; i++) *q-- = *p++; #endif } /* ; e type to IEEE double precision ; double d; ; unsigned EMUSHORT x[NE]; ; etoe53 (x, &d); */ #ifdef DEC void etoe53 (x, e) unsigned EMUSHORT *x, *e; { etodec (x, e); /* see etodec.c */ } static void toe53 (x, y) unsigned EMUSHORT *x, *y; { todec (x, y); } #else #ifdef IBM void etoe53 (x, e) unsigned EMUSHORT *x, *e; { etoibm (x, e, DFmode); } static void toe53 (x, y) unsigned EMUSHORT *x, *y; { toibm (x, y, DFmode); } #else /* it's neither DEC nor IBM */ void etoe53 (x, e) unsigned EMUSHORT *x, *e; { unsigned EMUSHORT xi[NI]; EMULONG exp; int rndsav; #ifdef NANS if (eisnan (x)) { make_nan (e, DFmode); return; } #endif emovi (x, xi); /* adjust exponent for offsets */ exp = (EMULONG) xi[E] - (EXONE - 0x3ff); #ifdef INFINITY if (eisinf (x)) goto nonorm; #endif /* round off to nearest or even */ rndsav = rndprc; rndprc = 53; emdnorm (xi, 0, 0, exp, 64); rndprc = rndsav; nonorm: toe53 (xi, e); } static void toe53 (x, y) unsigned EMUSHORT *x, *y; { unsigned EMUSHORT i; unsigned EMUSHORT *p; #ifdef NANS if (eiisnan (x)) { make_nan (y, DFmode); return; } #endif p = &x[0]; #ifdef IBMPC 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; #endif #ifdef MIEEE ++y; *y++ = 0; *y++ = 0; *y++ = 0; #endif #else *y |= (unsigned EMUSHORT) 0x7fef; #ifdef IBMPC *(--y) = 0xffff; *(--y) = 0xffff; *(--y) = 0xffff; #endif #ifdef MIEEE ++y; *y++ = 0xffff; *y++ = 0xffff; *y++ = 0xffff; #endif #endif return; } if (i == 0) { eshift (x, 4); } else { i <<= 4; eshift (x, 5); } i |= *p++ & (unsigned EMUSHORT) 0x0f; /* *p = xi[M] */ *y |= (unsigned EMUSHORT) i; /* high order output already has sign bit set */ #ifdef IBMPC *(--y) = *p++; *(--y) = *p++; *(--y) = *p; #endif #ifdef MIEEE ++y; *y++ = *p++; *y++ = *p++; *y++ = *p++; #endif } #endif /* not IBM */ #endif /* not DEC */ /* ; e type to IEEE single precision ; float d; ; unsigned EMUSHORT x[N+2]; ; xtod (x, &d); */ #ifdef IBM void etoe24 (x, e) unsigned EMUSHORT *x, *e; { etoibm (x, e, SFmode); } static void toe24 (x, y) unsigned EMUSHORT *x, *y; { toibm (x, y, SFmode); } #else void etoe24 (x, e) unsigned EMUSHORT *x, *e; { EMULONG exp; unsigned EMUSHORT xi[NI]; int rndsav; #ifdef NANS if (eisnan (x)) { make_nan (e, SFmode); return; } #endif emovi (x, xi); /* adjust exponent for offsets */ exp = (EMULONG) xi[E] - (EXONE - 0177); #ifdef INFINITY if (eisinf (x)) goto nonorm; #endif /* round off to nearest or even */ rndsav = rndprc; rndprc = 24; emdnorm (xi, 0, 0, exp, 64); rndprc = rndsav; nonorm: toe24 (xi, e); } static void toe24 (x, y) unsigned EMUSHORT *x, *y; { unsigned EMUSHORT i; unsigned EMUSHORT *p; #ifdef NANS if (eiisnan (x)) { make_nan (y, SFmode); 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++; /* Handle overflow cases. */ if (i >= 255) { #ifdef INFINITY *y |= (unsigned EMUSHORT) 0x7f80; #ifdef IBMPC *(--y) = 0; #endif #ifdef DEC *(--y) = 0; #endif #ifdef MIEEE ++y; *y = 0; #endif #else /* no INFINITY */ *y |= (unsigned EMUSHORT) 0x7f7f; #ifdef IBMPC *(--y) = 0xffff; #endif #ifdef DEC *(--y) = 0xffff; #endif #ifdef MIEEE ++y; *y = 0xffff; #endif #ifdef ERANGE errno = ERANGE; #endif #endif /* no INFINITY */ return; } if (i == 0) { eshift (x, 7); } else { i <<= 7; eshift (x, 8); } i |= *p++ & (unsigned EMUSHORT) 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 /* not IBM */ /* Compare two e type numbers. * * unsigned EMUSHORT 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. */ int ecmp (a, b) unsigned EMUSHORT *a, *b; { unsigned EMUSHORT ai[NI], bi[NI]; register unsigned EMUSHORT *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 < NI - 1; i++) { if (ai[i] != 0) goto nzro; if (bi[i] != 0) goto nzro; } return (0); nzro: if (*p == 0) return (1); else return (-1); } /* both are the same sign */ if (*p == 0) msign = 1; else msign = -1; i = NI - 1; do { if (*p++ != *q++) { goto diff; } } while (--i > 0); return (0); /* equality */ diff: if (*(--p) > *(--q)) return (msign); /* p is bigger */ else return (-msign); /* p is littler */ } /* Find nearest integer to x = floor (x + 0.5) * * unsigned EMUSHORT x[NE], y[NE] * eround (x, y); */ void eround (x, y) unsigned EMUSHORT *x, *y; { eadd (ehalf, x, y); efloor (y, y); } /* ; convert HOST_WIDE_INT to e type ; ; HOST_WIDE_INT l; ; unsigned EMUSHORT x[NE]; ; ltoe (&l, x); ; note &l is the memory address of l */ void ltoe (lp, y) HOST_WIDE_INT *lp; unsigned EMUSHORT *y; { unsigned EMUSHORT yi[NI]; unsigned HOST_WIDE_INT ll; int k; ecleaz (yi); if (*lp < 0) { /* make it positive */ ll = (unsigned HOST_WIDE_INT) (-(*lp)); yi[0] = 0xffff; /* put correct sign in the e type number */ } else { ll = (unsigned HOST_WIDE_INT) (*lp); } /* move the long integer to yi significand area */ #if HOST_BITS_PER_WIDE_INT == 64 yi[M] = (unsigned EMUSHORT) (ll >> 48); yi[M + 1] = (unsigned EMUSHORT) (ll >> 32); yi[M + 2] = (unsigned EMUSHORT) (ll >> 16); yi[M + 3] = (unsigned EMUSHORT) ll; yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */ #else yi[M] = (unsigned EMUSHORT) (ll >> 16); yi[M + 1] = (unsigned EMUSHORT) ll; yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */ #endif if ((k = enormlz (yi)) > NBITS)/* normalize the significand */ ecleaz (yi); /* it was zero */ else yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */ emovo (yi, y); /* output the answer */ } /* ; convert unsigned HOST_WIDE_INT to e type ; ; unsigned HOST_WIDE_INT l; ; unsigned EMUSHORT x[NE]; ; ltox (&l, x); ; note &l is the memory address of l */ void ultoe (lp, y) unsigned HOST_WIDE_INT *lp; unsigned EMUSHORT *y; { unsigned EMUSHORT yi[NI]; unsigned HOST_WIDE_INT ll; int k; ecleaz (yi); ll = *lp; /* move the long integer to ayi significand area */ #if HOST_BITS_PER_WIDE_INT == 64 yi[M] = (unsigned EMUSHORT) (ll >> 48); yi[M + 1] = (unsigned EMUSHORT) (ll >> 32); yi[M + 2] = (unsigned EMUSHORT) (ll >> 16); yi[M + 3] = (unsigned EMUSHORT) ll; yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */ #else yi[M] = (unsigned EMUSHORT) (ll >> 16); yi[M + 1] = (unsigned EMUSHORT) ll; yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */ #endif if ((k = enormlz (yi)) > NBITS)/* normalize the significand */ ecleaz (yi); /* it was zero */ else yi[E] -= (unsigned EMUSHORT) k; /* subtract shift count from exponent */ emovo (yi, y); /* output the answer */ } /* ; Find signed HOST_WIDE_INT integer and floating point fractional parts ; HOST_WIDE_INT i; ; unsigned EMUSHORT x[NE], frac[NE]; ; xifrac (x, &i, frac); The integer output has the sign of the input. The fraction is the positive fractional part of abs (x). */ void eifrac (x, i, frac) unsigned EMUSHORT *x; HOST_WIDE_INT *i; unsigned EMUSHORT *frac; { unsigned EMUSHORT xi[NI]; int j, k; unsigned HOST_WIDE_INT ll; emovi (x, xi); k = (int) xi[E] - (EXONE - 1); if (k <= 0) { /* if exponent <= 0, integer = 0 and real output is fraction */ *i = 0L; emovo (xi, frac); return; } if (k > (HOST_BITS_PER_WIDE_INT - 1)) { /* long integer overflow: output large integer and correct fraction */ if (xi[0]) *i = ((unsigned HOST_WIDE_INT) 1) << (HOST_BITS_PER_WIDE_INT - 1); else *i = (((unsigned HOST_WIDE_INT) 1) << (HOST_BITS_PER_WIDE_INT - 1)) - 1; eshift (xi, k); if (extra_warnings) warning ("overflow on truncation to integer"); } else if (k > 16) { /* Shift more than 16 bits: first shift up k-16 mod 16, then shift up by 16's. */ j = k - ((k >> 4) << 4); eshift (xi, j); ll = xi[M]; k -= j; do { eshup6 (xi); ll = (ll << 16) | xi[M]; } while ((k -= 16) > 0); *i = ll; if (xi[0]) *i = -(*i); } else { /* shift not more than 16 bits */ eshift (xi, k); *i = (HOST_WIDE_INT) xi[M] & 0xffff; if (xi[0]) *i = -(*i); } xi[0] = 0; xi[E] = EXONE - 1; xi[M] = 0; if ((k = enormlz (xi)) > NBITS) ecleaz (xi); else xi[E] -= (unsigned EMUSHORT) k; emovo (xi, frac); } /* Find unsigned HOST_WIDE_INT integer and floating point fractional parts. A negative e type input yields integer output = 0 but correct fraction. */ void euifrac (x, i, frac) unsigned EMUSHORT *x; unsigned HOST_WIDE_INT *i; unsigned EMUSHORT *frac; { unsigned HOST_WIDE_INT ll; unsigned EMUSHORT xi[NI]; int j, k; emovi (x, xi); k = (int) xi[E] - (EXONE - 1); if (k <= 0) { /* if exponent <= 0, integer = 0 and argument is fraction */ *i = 0L; emovo (xi, frac); return; } if (k > HOST_BITS_PER_WIDE_INT) { /* Long integer overflow: output large integer and correct fraction. Note, the BSD microvax compiler says that ~(0UL) is a syntax error. */ *i = ~(0L); eshift (xi, k); if (extra_warnings) warning ("overflow on truncation to unsigned integer"); } else if (k > 16) { /* Shift more than 16 bits: first shift up k-16 mod 16, then shift up by 16's. */ j = k - ((k >> 4) << 4); eshift (xi, j); ll = xi[M]; k -= j; do { eshup6 (xi); ll = (ll << 16) | xi[M]; } while ((k -= 16) > 0); *i = ll; } else { /* shift not more than 16 bits */ eshift (xi, k); *i = (HOST_WIDE_INT) xi[M] & 0xffff; } if (xi[0]) /* A negative value yields unsigned integer 0. */ *i = 0L; xi[0] = 0; xi[E] = EXONE - 1; xi[M] = 0; if ((k = enormlz (xi)) > NBITS) ecleaz (xi); else xi[E] -= (unsigned EMUSHORT) k; emovo (xi, frac); } /* ; Shift significand ; ; Shifts significand area up or down by the number of bits ; given by the variable sc. */ int eshift (x, sc) unsigned EMUSHORT *x; int sc; { unsigned EMUSHORT lost; unsigned EMUSHORT *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. */ int enormlz (x) unsigned EMUSHORT x[]; { register unsigned EMUSHORT *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) { 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 LONG_DOUBLE_TYPE_SIZE == 128 static unsigned EMUSHORT 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 EMUSHORT 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 /* LONG_DOUBLE_TYPE_SIZE is other than 128 */ static unsigned EMUSHORT 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 EMUSHORT 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 void e24toasc (x, string, ndigs) unsigned EMUSHORT x[]; char *string; int ndigs; { unsigned EMUSHORT w[NI]; e24toe (x, w); etoasc (w, string, ndigs); } void e53toasc (x, string, ndigs) unsigned EMUSHORT x[]; char *string; int ndigs; { unsigned EMUSHORT w[NI]; e53toe (x, w); etoasc (w, string, ndigs); } void e64toasc (x, string, ndigs) unsigned EMUSHORT x[]; char *string; int ndigs; { unsigned EMUSHORT w[NI]; e64toe (x, w); etoasc (w, string, ndigs); } void e113toasc (x, string, ndigs) unsigned EMUSHORT x[]; char *string; int ndigs; { unsigned EMUSHORT w[NI]; e113toe (x, w); etoasc (w, string, ndigs); } static char wstring[80]; /* working storage for ASCII output */ void etoasc (x, string, ndigs) unsigned EMUSHORT x[]; char *string; int ndigs; { EMUSHORT digit; unsigned EMUSHORT y[NI], t[NI], u[NI], w[NI]; unsigned EMUSHORT *p, *r, *ten; unsigned EMUSHORT sign; int i, j, k, expon, rndsav; char *s, *ss; unsigned EMUSHORT m; rndsav = rndprc; ss = string; s = wstring; *ss = '\0'; *s = '\0'; #ifdef NANS if (eisnan (x)) { sprintf (wstring, " NaN "); goto bxit; } #endif 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 < NE - 1; k++) { if (y[k] != 0) goto tnzro; /* denormalized number */ } goto isone; /* legal all zeros */ } tnzro: /* Test for infinity. */ if (y[NE - 1] == 0x7fff) { if (sign) sprintf (wstring, " -Infinity "); else sprintf (wstring, " Infinity "); goto bxit; } /* Test for exponent nonzero but significand denormalized. * This is an error condition. */ if ((y[NE - 1] != 0) && ((y[NE - 2] & 0x8000) == 0)) { mtherr ("etoasc", DOMAIN); sprintf (wstring, "NaN"); goto bxit; } /* Compare to 1.0 */ i = ecmp (eone, y); if (i == 0) goto isone; if (i == -2) abort (); if (i < 0) { /* Number is greater than 1 */ /* Convert significand to an integer and strip trailing decimal zeros. */ emov (y, u); u[NE - 1] = EXONE + NBITS - 1; p = &etens[NTEN - 4][0]; m = 16; do { ediv (p, u, t); efloor (t, w); for (j = 0; j < NE - 1; j++) { if (t[j] != w[j]) goto noint; } emov (t, u); expon += (int) m; noint: p += NE; m >>= 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]; /* An unordered compare result shouldn't happen here. */ while (ecmp (ten, u) <= 0) { if (ecmp (p, u) <= 0) { ediv (p, u, u); emul (p, t, t); 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); expon -= 1; } } else { emovi (y, w); for (i = 0; i < NDEC + 1; i++) { if ((w[NI - 1] & 0x7) != 0) break; /* multiply by 10 */ emovz (w, u); eshdn1 (u); eshdn1 (u); eaddm (w, u); u[1] += 3; while (u[2] != 0) { eshdn1 (u); u[1] += 1; } if (u[NI - 1] != 0) break; if (eone[NE - 1] <= u[1]) break; emovz (u, w); expon -= 1; } emovo (w, y); } k = -MAXP; p = &emtens[0][0]; r = &etens[0][0]; emov (y, w); emov (eone, t); while (ecmp (eone, w) > 0) { if (ecmp (p, w) >= 0) { emul (r, w, w); emul (r, t, t); expon += k; } k /= 2; if (k == 0) break; p += NE; r += NE; } ediv (t, eone, t); } isone: /* Find the first (leading) digit. */ emovi (t, w); emovz (w, t); emovi (y, w); emovz (w, y); eiremain (t, y); 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); digit = equot[NI - 1]; expon -= 1; } s = wstring; if (sign) *s++ = '-'; else *s++ = ' '; /* Examine number of digits requested by caller. */ 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; } 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); *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); 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 (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: /* if (expon >= 0) sprintf (ss, "e+%d", expon); else sprintf (ss, "e%d", expon); */ sprintf (ss, "e%d", expon); bxit: rndprc = rndsav; /* copy out the working string */ s = string; ss = wstring; while (*ss == ' ') /* strip possible leading space */ ++ss; while ((*s++ = *ss++) != '\0') ; } /* ; 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); */ /* ASCII to single */ void asctoe24 (s, y) char *s; unsigned EMUSHORT *y; { asctoeg (s, y, 24); } /* ASCII to double */ void asctoe53 (s, y) char *s; unsigned EMUSHORT *y; { #if defined(DEC) || defined(IBM) asctoeg (s, y, 56); #else asctoeg (s, y, 53); #endif } /* ASCII to long double */ void asctoe64 (s, y) char *s; unsigned EMUSHORT *y; { asctoeg (s, y, 64); } /* ASCII to 128-bit long double */ void asctoe113 (s, y) char *s; unsigned EMUSHORT *y; { asctoeg (s, y, 113); } /* ASCII to super double */ void asctoe (s, y) char *s; unsigned EMUSHORT *y; { asctoeg (s, y, NBITS); } /* ASCII to e type, with specified rounding precision = oprec. */ void asctoeg (ss, y, oprec) char *ss; unsigned EMUSHORT *y; int oprec; { unsigned EMUSHORT yy[NI], xt[NI], tt[NI]; int esign, decflg, sgnflg, nexp, exp, prec, lost; int k, trail, c, rndsav; EMULONG lexp; unsigned EMUSHORT nsign, *p; char *sp, *s, *lstr; /* Copy the input string. */ lstr = (char *) alloca (strlen (ss) + 1); s = ss; while (*s == ' ') /* skip leading spaces */ ++s; sp = lstr; while ((*sp++ = *s++) != '\0') ; s = lstr; rndsav = rndprc; 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 EMUSHORT) 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 einan (yy); #else mtherr ("asctoe", DOMAIN); eclear (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 > -(MINDECEXP)) { if (esign < 0) goto zero; else goto infinite; } } if (esign < 0) exp = -exp; if (exp > MAXDECEXP) { infinite: ecleaz (yy); yy[E] = 0x7fff; /* infinity */ goto aexit; } if (exp < MINDECEXP) { 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); /* 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); lexp += EXONE; nexp -= 4096; } } p = &etens[NTEN][0]; emov (eone, xt); exp = 1; do { if (exp & nexp) emul (p, xt, xt); p -= NE; exp = exp + exp; } while (exp <= MAXP); emovi (xt, tt); if (esign < 0) { lexp -= tt[E]; k = edivm (tt, yy); lexp += EXONE; } else { lexp += tt[E]; k = emulm (tt, yy); lexp -= EXONE - 1; } expdon: /* Round and convert directly to the destination type */ if (oprec == 53) lexp -= EXONE - 0x3ff; #ifdef IBM else if (oprec == 24 || oprec == 56) lexp -= EXONE - (0x41 << 2); #else else if (oprec == 24) lexp -= EXONE - 0177; #endif #ifdef DEC else if (oprec == 56) lexp -= EXONE - 0201; #endif rndprc = oprec; emdnorm (yy, k, 0, lexp, 64); aexit: rndprc = rndsav; yy[0] = nsign; switch (oprec) { #ifdef DEC case 56: todec (yy, y); /* see etodec.c */ break; #endif #ifdef IBM case 56: toibm (yy, y, DFmode); break; #endif case 53: toe53 (yy, y); break; case 24: toe24 (yy, y); break; case 64: toe64 (yy, y); break; case 113: toe113 (yy, y); break; case NBITS: emovo (yy, y); break; } } /* y = largest integer not greater than x * (truncated toward minus infinity) * * unsigned EMUSHORT x[NE], y[NE] * * efloor (x, y); */ static unsigned EMUSHORT bmask[] = { 0xffff, 0xfffe, 0xfffc, 0xfff8, 0xfff0, 0xffe0, 0xffc0, 0xff80, 0xff00, 0xfe00, 0xfc00, 0xf800, 0xf000, 0xe000, 0xc000, 0x8000, 0x0000, }; void efloor (x, y) unsigned EMUSHORT x[], y[]; { register unsigned EMUSHORT *p; int e, expon, i; unsigned EMUSHORT 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 EMUSHORT) expon & (unsigned EMUSHORT) 0x8000) { for (i = 0; i < NE - 1; i++) { if (f[i] != y[i]) { esub (eone, y, y); break; } } } } /* unsigned EMUSHORT x[], s[]; * int *exp; * * efrexp (x, exp, s); * * Returns s and exp such that s * 2**exp = x and .5 <= s < 1. * For example, 1.1 = 0.55 * 2**1 * Handles denormalized numbers properly using long integer exp. */ void efrexp (x, exp, s) unsigned EMUSHORT x[]; int *exp; unsigned EMUSHORT s[]; { unsigned EMUSHORT xi[NI]; EMULONG li; emovi (x, xi); li = (EMULONG) ((EMUSHORT) xi[1]); if (li == 0) { li -= enormlz (xi); } xi[1] = 0x3ffe; emovo (xi, s); *exp = (int) (li - 0x3ffe); } /* unsigned EMUSHORT x[], y[]; * int pwr2; * * eldexp (x, pwr2, y); * * Returns y = x * 2**pwr2. */ void eldexp (x, pwr2, y) unsigned EMUSHORT x[]; int pwr2; unsigned EMUSHORT y[]; { unsigned EMUSHORT xi[NI]; EMULONG li; int i; emovi (x, xi); li = xi[1]; li += pwr2; i = 0; emdnorm (xi, i, i, li, 64); emovo (xi, y); } /* c = remainder after dividing b by a * Least significant integer quotient bits left in equot[]. */ void eremain (a, b, c) unsigned EMUSHORT a[], b[], c[]; { unsigned EMUSHORT den[NI], num[NI]; #ifdef NANS if (eisinf (b) || (ecmp (a, ezero) == 0) || eisnan (a) || eisnan (b)) { enan (c); return; } #endif if (ecmp (a, ezero) == 0) { mtherr ("eremain", SING); eclear (c); return; } emovi (a, den); emovi (b, num); eiremain (den, num); /* Sign of remainder = sign of quotient */ if (a[0] == b[0]) num[0] = 0; else num[0] = 0xffff; emovo (num, c); } void eiremain (den, num) unsigned EMUSHORT den[], num[]; { EMULONG ld, ln; unsigned EMUSHORT j; 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); } /* mtherr.c * * Library common error handling routine * * * * SYNOPSIS: * * char *fctnam; * int code; * void mtherr (); * * mtherr (fctnam, code); * * * * DESCRIPTION: * * This routine may be called to report one of the following * error conditions (in the include file mconf.h). * * Mnemonic Value Significance * * DOMAIN 1 argument domain error * SING 2 function singularity * OVERFLOW 3 overflow range error * UNDERFLOW 4 underflow range error * TLOSS 5 total loss of precision * PLOSS 6 partial loss of precision * INVALID 7 NaN - producing operation * EDOM 33 Unix domain error code * ERANGE 34 Unix range error code * * The default version of the file prints the function name, * passed to it by the pointer fctnam, followed by the * error condition. The display is directed to the standard * output device. The routine then returns to the calling * program. Users may wish to modify the program to abort by * calling exit under severe error conditions such as domain * errors. * * Since all error conditions pass control to this function, * the display may be easily changed, eliminated, or directed * to an error logging device. * * SEE ALSO: * * mconf.h * */ /* Cephes Math Library Release 2.0: April, 1987 Copyright 1984, 1987 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ /* include "mconf.h" */ /* Notice: the order of appearance of the following * messages is bound to the error codes defined * in mconf.h. */ #define NMSGS 8 static char *ermsg[NMSGS] = { "unknown", /* error code 0 */ "domain", /* error code 1 */ "singularity", /* et seq. */ "overflow", "underflow", "total loss of precision", "partial loss of precision", "invalid operation" }; int merror = 0; extern int merror; void mtherr (name, code) char *name; int code; { char errstr[80]; /* Display string passed by calling program, * which is supposed to be the name of the * function in which the error occurred. */ /* Display error message defined * by the code argument. */ if ((code <= 0) || (code >= NMSGS)) code = 0; sprintf (errstr, " %s %s error", name, ermsg[code]); if (extra_warnings) warning (errstr); /* Set global error message word */ merror = code + 1; /* Return to calling * program */ } #ifdef DEC /* Here is etodec.c . * */ /* ; convert DEC double precision to e type ; double d; ; EMUSHORT e[NE]; ; dectoe (&d, e); */ void dectoe (d, e) unsigned EMUSHORT *d; unsigned EMUSHORT *e; { unsigned EMUSHORT y[NI]; register unsigned EMUSHORT r, *p; ecleaz (y); /* start with a zero */ p = y; /* point to our number */ r = *d; /* get DEC exponent word */ if (*d & (unsigned int) 0x8000) *p = 0xffff; /* fill in our sign */ ++p; /* bump pointer to our exponent word */ r &= 0x7fff; /* strip the sign bit */ if (r == 0) /* answer = 0 if high order DEC word = 0 */ goto done; r >>= 7; /* shift exponent word down 7 bits */ r += EXONE - 0201; /* subtract DEC exponent offset */ /* add our e type exponent offset */ *p++ = r; /* to form our exponent */ r = *d++; /* now do the high order mantissa */ r &= 0177; /* strip off the DEC exponent and sign bits */ r |= 0200; /* the DEC understood high order mantissa bit */ *p++ = r; /* put result in our high guard word */ *p++ = *d++; /* fill in the rest of our mantissa */ *p++ = *d++; *p = *d; eshdn8 (y); /* shift our mantissa down 8 bits */ done: emovo (y, e); } /* ; convert e type to DEC double precision ; double d; ; EMUSHORT e[NE]; ; etodec (e, &d); */ void etodec (x, d) unsigned EMUSHORT *x, *d; { unsigned EMUSHORT xi[NI]; EMULONG exp; int rndsav; emovi (x, xi); exp = (EMULONG) xi[E] - (EXONE - 0201); /* adjust exponent for offsets */ /* round off to nearest or even */ rndsav = rndprc; rndprc = 56; emdnorm (xi, 0, 0, exp, 64); rndprc = rndsav; todec (xi, d); } void todec (x, y) unsigned EMUSHORT *x, *y; { unsigned EMUSHORT i; unsigned EMUSHORT *p; p = x; *y = 0; if (*p++) *y = 0100000; i = *p++; if (i == 0) { *y++ = 0; *y++ = 0; *y++ = 0; *y++ = 0; return; } if (i > 0377) { *y++ |= 077777; *y++ = 0xffff; *y++ = 0xffff; *y++ = 0xffff; #ifdef ERANGE errno = ERANGE; #endif return; } i &= 0377; i <<= 7; eshup8 (x); x[M] &= 0177; i |= x[M]; *y++ |= i; *y++ = x[M + 1]; *y++ = x[M + 2]; *y++ = x[M + 3]; } #endif /* DEC */ #ifdef IBM /* Here is etoibm * */ /* ; convert IBM single/double precision to e type ; single/double d; ; EMUSHORT e[NE]; ; enum machine_mode mode; SFmode/DFmode ; ibmtoe (&d, e, mode); */ void ibmtoe (d, e, mode) unsigned EMUSHORT *d; unsigned EMUSHORT *e; enum machine_mode mode; { unsigned EMUSHORT y[NI]; register unsigned EMUSHORT r, *p; int rndsav; ecleaz (y); /* start with a zero */ p = y; /* point to our number */ r = *d; /* get IBM exponent word */ if (*d & (unsigned int) 0x8000) *p = 0xffff; /* fill in our sign */ ++p; /* bump pointer to our exponent word */ r &= 0x7f00; /* strip the sign bit */ r >>= 6; /* shift exponent word down 6 bits */ /* in fact shift by 8 right and 2 left */ r += EXONE - (0x41 << 2); /* subtract IBM exponent offset */ /* add our e type exponent offset */ *p++ = r; /* to form our exponent */ *p++ = *d++ & 0xff; /* now do the high order mantissa */ /* strip off the IBM exponent and sign bits */ if (mode != SFmode) /* there are only 2 words in SFmode */ { *p++ = *d++; /* fill in the rest of our mantissa */ *p++ = *d++; } *p = *d; if (y[M] == 0 && y[M+1] == 0 && y[M+2] == 0 && y[M+3] == 0) y[0] = y[E] = 0; else y[E] -= 5 + enormlz (y); /* now normalise the mantissa */ /* handle change in RADIX */ emovo (y, e); } /* ; convert e type to IBM single/double precision ; single/double d; ; EMUSHORT e[NE]; ; enum machine_mode mode; SFmode/DFmode ; etoibm (e, &d, mode); */ void etoibm (x, d, mode) unsigned EMUSHORT *x, *d; enum machine_mode mode; { unsigned EMUSHORT xi[NI]; EMULONG exp; int rndsav; emovi (x, xi); exp = (EMULONG) xi[E] - (EXONE - (0x41 << 2)); /* adjust exponent for offsets */ /* round off to nearest or even */ rndsav = rndprc; rndprc = 56; emdnorm (xi, 0, 0, exp, 64); rndprc = rndsav; toibm (xi, d, mode); } void toibm (x, y, mode) unsigned EMUSHORT *x, *y; enum machine_mode mode; { unsigned EMUSHORT i; unsigned EMUSHORT *p; int r; p = x; *y = 0; if (*p++) *y = 0x8000; i = *p++; if (i == 0) { *y++ = 0; *y++ = 0; if (mode != SFmode) { *y++ = 0; *y++ = 0; } return; } r = i & 0x3; i >>= 2; if (i > 0x7f) { *y++ |= 0x7fff; *y++ = 0xffff; if (mode != SFmode) { *y++ = 0xffff; *y++ = 0xffff; } #ifdef ERANGE errno = ERANGE; #endif return; } i &= 0x7f; *y |= (i << 8); eshift (x, r + 5); *y++ |= x[M]; *y++ = x[M + 1]; if (mode != SFmode) { *y++ = x[M + 2]; *y++ = x[M + 3]; } } #endif /* IBM */ /* Output a binary NaN bit pattern in the target machine's format. */ /* If special NaN bit patterns are required, define them in tm.h as arrays of unsigned 16-bit shorts. Otherwise, use the default patterns here. */ #ifdef TFMODE_NAN TFMODE_NAN; #else #ifdef MIEEE unsigned EMUSHORT TFnan[8] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; #endif #ifdef IBMPC unsigned EMUSHORT TFnan[8] = {0, 0, 0, 0, 0, 0, 0x8000, 0xffff}; #endif #endif #ifdef XFMODE_NAN XFMODE_NAN; #else #ifdef MIEEE unsigned EMUSHORT XFnan[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; #endif #ifdef IBMPC unsigned EMUSHORT XFnan[6] = {0, 0, 0, 0xc000, 0xffff, 0}; #endif #endif #ifdef DFMODE_NAN DFMODE_NAN; #else #ifdef MIEEE unsigned EMUSHORT DFnan[4] = {0x7fff, 0xffff, 0xffff, 0xffff}; #endif #ifdef IBMPC unsigned EMUSHORT DFnan[4] = {0, 0, 0, 0xfff8}; #endif #endif #ifdef SFMODE_NAN SFMODE_NAN; #else #ifdef MIEEE unsigned EMUSHORT SFnan[2] = {0x7fff, 0xffff}; #endif #ifdef IBMPC unsigned EMUSHORT SFnan[2] = {0, 0xffc0}; #endif #endif void make_nan (nan, mode) unsigned EMUSHORT *nan; enum machine_mode mode; { int i, n; unsigned EMUSHORT *p; n = 0; switch (mode) { /* Possibly the `reserved operand' patterns on a VAX can be used like NaN's, but probably not in the same way as IEEE. */ #if !defined(DEC) && !defined(IBM) case TFmode: n = 8; p = TFnan; break; case XFmode: n = 6; p = XFnan; break; case DFmode: n = 4; p = DFnan; break; case SFmode: n = 2; p = SFnan; break; #endif default: abort (); } for (i=0; i < n; i++) *nan++ = *p++; } /* Convert an SFmode target `float' value to a REAL_VALUE_TYPE. This is the inverse of the function `etarsingle' invoked by REAL_VALUE_TO_TARGET_SINGLE. */ REAL_VALUE_TYPE ereal_from_float (f) unsigned long f; { REAL_VALUE_TYPE r; unsigned EMUSHORT s[2]; unsigned EMUSHORT e[NE]; /* Convert 32 bit integer to array of 16 bit pieces in target machine order. This is the inverse operation to what the function `endian' does. */ #if FLOAT_WORDS_BIG_ENDIAN s[0] = (unsigned EMUSHORT) (f >> 16); s[1] = (unsigned EMUSHORT) f; #else s[0] = (unsigned EMUSHORT) f; s[1] = (unsigned EMUSHORT) (f >> 16); #endif /* Convert and promote the target float to E-type. */ e24toe (s, e); /* Output E-type to REAL_VALUE_TYPE. */ PUT_REAL (e, &r); return r; } /* Convert a DFmode target `double' value to a REAL_VALUE_TYPE. This is the inverse of the function `etardouble' invoked by REAL_VALUE_TO_TARGET_DOUBLE. The DFmode is stored as an array of long ints with 32 bits of the value per each long. The first element of the input array holds the bits that would come first in the target computer's memory. */ REAL_VALUE_TYPE ereal_from_double (d) unsigned long d[]; { REAL_VALUE_TYPE r; unsigned EMUSHORT s[4]; unsigned EMUSHORT e[NE]; /* Convert array of 32 bit pieces to equivalent array of 16 bit pieces. This is the inverse of `endian'. */ #if FLOAT_WORDS_BIG_ENDIAN s[0] = (unsigned EMUSHORT) (d[0] >> 16); s[1] = (unsigned EMUSHORT) d[0]; s[2] = (unsigned EMUSHORT) (d[1] >> 16); s[3] = (unsigned EMUSHORT) d[1]; #else s[0] = (unsigned EMUSHORT) d[0]; s[1] = (unsigned EMUSHORT) (d[0] >> 16); s[2] = (unsigned EMUSHORT) d[1]; s[3] = (unsigned EMUSHORT) (d[1] >> 16); #endif /* Convert target double to E-type. */ e53toe (s, e); /* Output E-type to REAL_VALUE_TYPE. */ PUT_REAL (e, &r); return r; } /* Convert target computer unsigned 64-bit integer to e-type. The endian-ness of DImode follows the convention for integers, so we use WORDS_BIG_ENDIAN here, not FLOAT_WORDS_BIG_ENDIAN. */ void uditoe (di, e) unsigned EMUSHORT *di; /* Address of the 64-bit int. */ unsigned EMUSHORT *e; { unsigned EMUSHORT yi[NI]; int k; ecleaz (yi); #if WORDS_BIG_ENDIAN for (k = M; k < M + 4; k++) yi[k] = *di++; #else for (k = M + 3; k >= M; k--) yi[k] = *di++; #endif yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */ if ((k = enormlz (yi)) > NBITS)/* normalize the significand */ ecleaz (yi); /* it was zero */ else yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */ emovo (yi, e); } /* Convert target computer signed 64-bit integer to e-type. */ void ditoe (di, e) unsigned EMUSHORT *di; /* Address of the 64-bit int. */ unsigned EMUSHORT *e; { unsigned EMULONG acc; unsigned EMUSHORT yi[NI]; unsigned EMUSHORT carry; int k, sign; ecleaz (yi); #if WORDS_BIG_ENDIAN for (k = M; k < M + 4; k++) yi[k] = *di++; #else for (k = M + 3; k >= M; k--) yi[k] = *di++; #endif /* Take absolute value */ sign = 0; if (yi[M] & 0x8000) { sign = 1; carry = 0; for (k = M + 3; k >= M; k--) { acc = (unsigned EMULONG) (~yi[k] & 0xffff) + carry; yi[k] = acc; carry = 0; if (acc & 0x10000) carry = 1; } } yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */ if ((k = enormlz (yi)) > NBITS)/* normalize the significand */ ecleaz (yi); /* it was zero */ else yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */ emovo (yi, e); if (sign) eneg (e); } /* Convert e-type to unsigned 64-bit int. */ void etoudi (x, i) unsigned EMUSHORT *x; unsigned EMUSHORT *i; { unsigned EMUSHORT xi[NI]; int j, k; emovi (x, xi); if (xi[0]) { xi[M] = 0; goto noshift; } k = (int) xi[E] - (EXONE - 1); if (k <= 0) { for (j = 0; j < 4; j++) *i++ = 0; return; } if (k > 64) { for (j = 0; j < 4; j++) *i++ = 0xffff; if (extra_warnings) warning ("overflow on truncation to integer"); return; } if (k > 16) { /* Shift more than 16 bits: first shift up k-16 mod 16, then shift up by 16's. */ j = k - ((k >> 4) << 4); if (j == 0) j = 16; eshift (xi, j); #if WORDS_BIG_ENDIAN *i++ = xi[M]; #else i += 3; *i-- = xi[M]; #endif k -= j; do { eshup6 (xi); #if WORDS_BIG_ENDIAN *i++ = xi[M]; #else *i-- = xi[M]; #endif } while ((k -= 16) > 0); } else { /* shift not more than 16 bits */ eshift (xi, k); noshift: #if WORDS_BIG_ENDIAN i += 3; *i-- = xi[M]; *i-- = 0; *i-- = 0; *i = 0; #else *i++ = xi[M]; *i++ = 0; *i++ = 0; *i = 0; #endif } } /* Convert e-type to signed 64-bit int. */ void etodi (x, i) unsigned EMUSHORT *x; unsigned EMUSHORT *i; { unsigned EMULONG acc; unsigned EMUSHORT xi[NI]; unsigned EMUSHORT carry; unsigned EMUSHORT *isave; int j, k; emovi (x, xi); k = (int) xi[E] - (EXONE - 1); if (k <= 0) { for (j = 0; j < 4; j++) *i++ = 0; return; } if (k > 64) { for (j = 0; j < 4; j++) *i++ = 0xffff; if (extra_warnings) warning ("overflow on truncation to integer"); return; } isave = i; if (k > 16) { /* Shift more than 16 bits: first shift up k-16 mod 16, then shift up by 16's. */ j = k - ((k >> 4) << 4); if (j == 0) j = 16; eshift (xi, j); #if WORDS_BIG_ENDIAN *i++ = xi[M]; #else i += 3; *i-- = xi[M]; #endif k -= j; do { eshup6 (xi); #if WORDS_BIG_ENDIAN *i++ = xi[M]; #else *i-- = xi[M]; #endif } while ((k -= 16) > 0); } else { /* shift not more than 16 bits */ eshift (xi, k); #if WORDS_BIG_ENDIAN i += 3; *i = xi[M]; *i-- = 0; *i-- = 0; *i = 0; #else *i++ = xi[M]; *i++ = 0; *i++ = 0; *i = 0; #endif } /* Negate if negative */ if (xi[0]) { carry = 0; #if WORDS_BIG_ENDIAN isave += 3; #endif for (k = 0; k < 4; k++) { acc = (unsigned EMULONG) (~(*isave) & 0xffff) + carry; #if WORDS_BIG_ENDIAN *isave-- = acc; #else *isave++ = acc; #endif carry = 0; if (acc & 0x10000) carry = 1; } } } /* Longhand square root routine. */ static int esqinited = 0; static unsigned short sqrndbit[NI]; void esqrt (x, y) unsigned EMUSHORT *x, *y; { unsigned EMUSHORT temp[NI], num[NI], sq[NI], xx[NI]; EMULONG m, exp; int i, j, k, n, nlups; if (esqinited == 0) { ecleaz (sqrndbit); sqrndbit[NI - 2] = 1; esqinited = 1; } /* Check for arg <= 0 */ i = ecmp (x, ezero); if (i <= 0) { #ifdef NANS if (i == -2) { enan (y); return; } #endif eclear (y); if (i < 0) mtherr ("esqrt", DOMAIN); return; } #ifdef INFINITY if (eisinf (x)) { eclear (y); einfin (y); return; } #endif /* Bring in the arg and renormalize if it is denormal. */ emovi (x, xx); m = (EMULONG) xx[1]; /* local long word exponent */ if (m == 0) m -= enormlz (xx); /* Divide exponent by 2 */ m -= 0x3ffe; exp = (unsigned short) ((m / 2) + 0x3ffe); /* Adjust if exponent odd */ if ((m & 1) != 0) { if (m > 0) exp += 1; eshdn1 (xx); } ecleaz (sq); ecleaz (num); n = 8; /* get 8 bits of result per inner loop */ nlups = rndprc; j = 0; while (nlups > 0) { /* bring in next word of arg */ if (j < NE) num[NI - 1] = xx[j + 3]; /* Do additional bit on last outer loop, for roundoff. */ if (nlups <= 8) n = nlups + 1; for (i = 0; i < n; i++) { /* Next 2 bits of arg */ eshup1 (num); eshup1 (num); /* Shift up answer */ eshup1 (sq); /* Make trial divisor */ for (k = 0; k < NI; k++) temp[k] = sq[k]; eshup1 (temp); eaddm (sqrndbit, temp); /* Subtract and insert answer bit if it goes in */ if (ecmpm (temp, num) <= 0) { esubm (temp, num); sq[NI - 2] |= 1; } } nlups -= n; j += 1; } /* Adjust for extra, roundoff loop done. */ exp += (NBITS - 1) - rndprc; /* Sticky bit = 1 if the remainder is nonzero. */ k = 0; for (i = 3; i < NI; i++) k |= (int) num[i]; /* Renormalize and round off. */ emdnorm (sq, k, 0, exp, 64); emovo (sq, y); } #endif /* EMU_NON_COMPILE not defined */