libdecnumber/dpd/decimal128.c - rust-lang/gcc - Git at Google

 /* Decimal 128-bit format module for the decNumber C Library.
    Copyright (C) 2005-2021 Free Software Foundation, Inc.
    Contributed by IBM Corporation.  Author Mike Cowlishaw.

    This file is part of GCC.

    GCC 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 3, or (at your option) any later
    version.

    GCC 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.

 Under Section 7 of GPL version 3, you are granted additional
 permissions described in the GCC Runtime Library Exception, version
 3.1, as published by the Free Software Foundation.

 You should have received a copy of the GNU General Public License and
 a copy of the GCC Runtime Library Exception along with this program;
 see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
 <http://www.gnu.org/licenses/>.  */

 /* ------------------------------------------------------------------ */
 /* Decimal 128-bit format module				      */
 /* ------------------------------------------------------------------ */
 /* This module comprises the routines for decimal128 format numbers.  */
 /* Conversions are supplied to and from decNumber and String.	      */
 /*								      */
 /* This is used when decNumber provides operations, either for all    */
 /* operations or as a proxy between decNumber and decSingle.	      */
 /*								      */
 /* Error handling is the same as decNumber (qv.).		      */
 /* ------------------------------------------------------------------ */
 #include <string.h>	      /* [for memset/memcpy] */
 #include <stdio.h>	      /* [for printf] */

 #include "dconfig.h"          /* GCC definitions */
 #define  DECNUMDIGITS 34      /* make decNumbers with space for 34 */
 #include "decNumber.h"	      /* base number library */
 #include "decNumberLocal.h"   /* decNumber local types, etc. */
 #include "decimal128.h"       /* our primary include */

 /* Utility routines and tables [in decimal64.c] */
 extern const uInt   COMBEXP[32], COMBMSD[32];
 extern const uShort DPD2BIN[1024];
 extern const uShort BIN2DPD[1000];	/* [not used] */
 extern const uByte  BIN2CHAR[4001];

 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
 extern void decDigitsToDPD(const decNumber *, uInt *, Int);

 #if DECTRACE || DECCHECK
 void decimal128Show(const decimal128 *);	  /* for debug */
 extern void decNumberShow(const decNumber *);	  /* .. */
 #endif

 /* Useful macro */
 /* Clear a structure (e.g., a decNumber) */
 #define DEC_clear(d) memset(d, 0, sizeof(*d))

 /* ------------------------------------------------------------------ */
 /* decimal128FromNumber -- convert decNumber to decimal128	      */
 /*								      */
 /*   ds is the target decimal128				      */
 /*   dn is the source number (assumed valid)			      */
 /*   set is the context, used only for reporting errors 	      */
 /*								      */
 /* The set argument is used only for status reporting and for the     */
 /* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
 /* digits or an overflow is detected).	If the exponent is out of the */
 /* valid range then Overflow or Underflow will be raised.	      */
 /* After Underflow a subnormal result is possible.		      */
 /*								      */
 /* DEC_Clamped is set if the number has to be 'folded down' to fit,   */
 /* by reducing its exponent and multiplying the coefficient by a      */
 /* power of ten, or if the exponent on a zero had to be clamped.      */
 /* ------------------------------------------------------------------ */
 decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn,
 				  decContext *set) {
   uInt status=0;		   /* status accumulator */
   Int ae;			   /* adjusted exponent */
   decNumber  dw;		   /* work */
   decContext dc;		   /* .. */
   uInt comb, exp;		   /* .. */
   uInt uiwork;			   /* for macros */
   uInt targar[4]={0,0,0,0};	   /* target 128-bit */
   #define targhi targar[3]	   /* name the word with the sign */
   #define targmh targar[2]	   /* name the words */
   #define targml targar[1]	   /* .. */
   #define targlo targar[0]	   /* .. */

   /* If the number has too many digits, or the exponent could be */
   /* out of range then reduce the number under the appropriate */
   /* constraints.  This could push the number to Infinity or zero, */
   /* so this check and rounding must be done before generating the */
   /* decimal128] */
   ae=dn->exponent+dn->digits-1; 	     /* [0 if special] */
   if (dn->digits>DECIMAL128_Pmax	     /* too many digits */
    || ae>DECIMAL128_Emax		     /* likely overflow */
    || ae<DECIMAL128_Emin) {		     /* likely underflow */
     decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */
     dc.round=set->round;		     /* use supplied rounding */
     decNumberPlus(&dw, dn, &dc);	     /* (round and check) */
     /* [this changes -0 to 0, so enforce the sign...] */
     dw.bits|=dn->bits&DECNEG;
     status=dc.status;			     /* save status */
     dn=&dw;				     /* use the work number */
     } /* maybe out of range */

   if (dn->bits&DECSPECIAL) {			  /* a special value */
     if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
      else {					  /* sNaN or qNaN */
       if ((*dn->lsu!=0 || dn->digits>1) 	  /* non-zero coefficient */
        && (dn->digits<DECIMAL128_Pmax)) {	  /* coefficient fits */
 	decDigitsToDPD(dn, targar, 0);
 	}
       if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
        else targhi|=DECIMAL_sNaN<<24;
       } /* a NaN */
     } /* special */

    else { /* is finite */
     if (decNumberIsZero(dn)) {		     /* is a zero */
       /* set and clamp exponent */
       if (dn->exponent<-DECIMAL128_Bias) {
 	exp=0;				     /* low clamp */
 	status|=DEC_Clamped;
 	}
        else {
 	exp=dn->exponent+DECIMAL128_Bias;    /* bias exponent */
 	if (exp>DECIMAL128_Ehigh) {	     /* top clamp */
 	  exp=DECIMAL128_Ehigh;
 	  status|=DEC_Clamped;
 	  }
 	}
       comb=(exp>>9) & 0x18;		/* msd=0, exp top 2 bits .. */
       }
      else {				/* non-zero finite number */
       uInt msd; 			/* work */
       Int pad=0;			/* coefficient pad digits */

       /* the dn is known to fit, but it may need to be padded */
       exp=(uInt)(dn->exponent+DECIMAL128_Bias);    /* bias exponent */
       if (exp>DECIMAL128_Ehigh) {		   /* fold-down case */
 	pad=exp-DECIMAL128_Ehigh;
 	exp=DECIMAL128_Ehigh;			   /* [to maximum] */
 	status|=DEC_Clamped;
 	}

       /* [fastpath for common case is not a win, here] */
       decDigitsToDPD(dn, targar, pad);
       /* save and clear the top digit */
       msd=targhi>>14;
       targhi&=0x00003fff;

       /* create the combination field */
       if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);
 	     else comb=((exp>>9) & 0x18) | msd;
       }
     targhi|=comb<<26;		   /* add combination field .. */
     targhi|=(exp&0xfff)<<14;	   /* .. and exponent continuation */
     } /* finite */

   if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */

   /* now write to storage; this is endian */
   if (DECLITEND) {
     /* lo -> hi */
     UBFROMUI(d128->bytes,    targlo);
     UBFROMUI(d128->bytes+4,  targml);
     UBFROMUI(d128->bytes+8,  targmh);
     UBFROMUI(d128->bytes+12, targhi);
     }
    else {
     /* hi -> lo */
     UBFROMUI(d128->bytes,    targhi);
     UBFROMUI(d128->bytes+4,  targmh);
     UBFROMUI(d128->bytes+8,  targml);
     UBFROMUI(d128->bytes+12, targlo);
     }

   if (status!=0) decContextSetStatus(set, status); /* pass on status */
   /* decimal128Show(d128); */
   return d128;
   } /* decimal128FromNumber */

 /* ------------------------------------------------------------------ */
 /* decimal128ToNumber -- convert decimal128 to decNumber	      */
 /*   d128 is the source decimal128				      */
 /*   dn is the target number, with appropriate space		      */
 /* No error is possible.					      */
 /* ------------------------------------------------------------------ */
 decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) {
   uInt msd;			   /* coefficient MSD */
   uInt exp;			   /* exponent top two bits */
   uInt comb;			   /* combination field */
   Int  need;			   /* work */
   uInt uiwork;			   /* for macros */
   uInt sourar[4];		   /* source 128-bit */
   #define sourhi sourar[3]	   /* name the word with the sign */
   #define sourmh sourar[2]	   /* and the mid-high word */
   #define sourml sourar[1]	   /* and the mod-low word */
   #define sourlo sourar[0]	   /* and the lowest word */

   /* load source from storage; this is endian */
   if (DECLITEND) {
     sourlo=UBTOUI(d128->bytes	); /* directly load the low int */
     sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
     sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
     sourhi=UBTOUI(d128->bytes+12); /* then the high int */
     }
    else {
     sourhi=UBTOUI(d128->bytes	); /* directly load the high int */
     sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
     sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
     sourlo=UBTOUI(d128->bytes+12); /* then the low int */
     }

   comb=(sourhi>>26)&0x1f;	   /* combination field */

   decNumberZero(dn);		   /* clean number */
   if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */

   msd=COMBMSD[comb];		   /* decode the combination field */
   exp=COMBEXP[comb];		   /* .. */

   if (exp==3) { 		   /* is a special */
     if (msd==0) {
       dn->bits|=DECINF;
       return dn;		   /* no coefficient needed */
       }
     else if (sourhi&0x02000000) dn->bits|=DECSNAN;
     else dn->bits|=DECNAN;
     msd=0;			   /* no top digit */
     }
    else {			   /* is a finite number */
     dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
     }

   /* get the coefficient */
   sourhi&=0x00003fff;		   /* clean coefficient continuation */
   if (msd) {			   /* non-zero msd */
     sourhi|=msd<<14;		   /* prefix to coefficient */
     need=12;			   /* process 12 declets */
     }
    else { /* msd=0 */
     if (sourhi) need=11;	   /* declets to process */
      else if (sourmh) need=10;
      else if (sourml) need=7;
      else if (sourlo) need=4;
      else return dn;		   /* easy: coefficient is 0 */
     } /*msd=0 */

   decDigitsFromDPD(dn, sourar, need);	/* process declets */
   /* decNumberShow(dn); */
   return dn;
   } /* decimal128ToNumber */

 /* ------------------------------------------------------------------ */
 /* to-scientific-string -- conversion to numeric string 	      */
 /* to-engineering-string -- conversion to numeric string	      */
 /*								      */
 /*   decimal128ToString(d128, string);				      */
 /*   decimal128ToEngString(d128, string);			      */
 /*								      */
 /*  d128 is the decimal128 format number to convert		      */
 /*  string is the string where the result will be laid out	      */
 /*								      */
 /*  string must be at least 24 characters			      */
 /*								      */
 /*  No error is possible, and no status can be set.		      */
 /* ------------------------------------------------------------------ */
 char * decimal128ToEngString(const decimal128 *d128, char *string){
   decNumber dn; 			/* work */
   decimal128ToNumber(d128, &dn);
   decNumberToEngString(&dn, string);
   return string;
   } /* decimal128ToEngString */

 char * decimal128ToString(const decimal128 *d128, char *string){
   uInt msd;			   /* coefficient MSD */
   Int  exp;			   /* exponent top two bits or full */
   uInt comb;			   /* combination field */
   char *cstart; 		   /* coefficient start */
   char *c;			   /* output pointer in string */
   const uByte *u;		   /* work */
   char *s, *t;			   /* .. (source, target) */
   Int  dpd;			   /* .. */
   Int  pre, e;			   /* .. */
   uInt uiwork;			   /* for macros */

   uInt sourar[4];		   /* source 128-bit */
   #define sourhi sourar[3]	   /* name the word with the sign */
   #define sourmh sourar[2]	   /* and the mid-high word */
   #define sourml sourar[1]	   /* and the mod-low word */
   #define sourlo sourar[0]	   /* and the lowest word */

   /* load source from storage; this is endian */
   if (DECLITEND) {
     sourlo=UBTOUI(d128->bytes	); /* directly load the low int */
     sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
     sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
     sourhi=UBTOUI(d128->bytes+12); /* then the high int */
     }
    else {
     sourhi=UBTOUI(d128->bytes	); /* directly load the high int */
     sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
     sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
     sourlo=UBTOUI(d128->bytes+12); /* then the low int */
     }

   c=string;			   /* where result will go */
   if (((Int)sourhi)<0) *c++='-';   /* handle sign */

   comb=(sourhi>>26)&0x1f;	   /* combination field */
   msd=COMBMSD[comb];		   /* decode the combination field */
   exp=COMBEXP[comb];		   /* .. */

   if (exp==3) {
     if (msd==0) {		   /* infinity */
       strcpy(c,   "Inf");
       strcpy(c+3, "inity");
       return string;		   /* easy */
       }
     if (sourhi&0x02000000) *c++='s'; /* sNaN */
     strcpy(c, "NaN");		   /* complete word */
     c+=3;			   /* step past */
     if (sourlo==0 && sourml==0 && sourmh==0
      && (sourhi&0x0003ffff)==0) return string; /* zero payload */
     /* otherwise drop through to add integer; set correct exp */
     exp=0; msd=0;		   /* setup for following code */
     }
    else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */

   /* convert 34 digits of significand to characters */
   cstart=c;			   /* save start of coefficient */
   if (msd) *c++='0'+(char)msd;	   /* non-zero most significant digit */

   /* Now decode the declets.  After extracting each one, it is */
   /* decoded to binary and then to a 4-char sequence by table lookup; */
   /* the 4-chars are a 1-char length (significant digits, except 000 */
   /* has length 0).  This allows us to left-align the first declet */
   /* with non-zero content, then remaining ones are full 3-char */
   /* length.  We use fixed-length memcpys because variable-length */
   /* causes a subroutine call in GCC.  (These are length 4 for speed */
   /* and are safe because the array has an extra terminator byte.) */
   #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; 		  \
 		   if (c!=cstart) {memcpy(c, u+1, 4); c+=3;}	  \
 		    else if (*u)  {memcpy(c, u+4-*u, 4); c+=*u;}
   dpd=(sourhi>>4)&0x3ff;		     /* declet 1 */
   dpd2char;
   dpd=((sourhi&0xf)<<6) | (sourmh>>26);      /* declet 2 */
   dpd2char;
   dpd=(sourmh>>16)&0x3ff;		     /* declet 3 */
   dpd2char;
   dpd=(sourmh>>6)&0x3ff;		     /* declet 4 */
   dpd2char;
   dpd=((sourmh&0x3f)<<4) | (sourml>>28);     /* declet 5 */
   dpd2char;
   dpd=(sourml>>18)&0x3ff;		     /* declet 6 */
   dpd2char;
   dpd=(sourml>>8)&0x3ff;		     /* declet 7 */
   dpd2char;
   dpd=((sourml&0xff)<<2) | (sourlo>>30);     /* declet 8 */
   dpd2char;
   dpd=(sourlo>>20)&0x3ff;		     /* declet 9 */
   dpd2char;
   dpd=(sourlo>>10)&0x3ff;		     /* declet 10 */
   dpd2char;
   dpd=(sourlo)&0x3ff;			     /* declet 11 */
   dpd2char;

   if (c==cstart) *c++='0';	   /* all zeros -- make 0 */

   if (exp==0) { 		   /* integer or NaN case -- easy */
     *c='\0';			   /* terminate */
     return string;
     }

   /* non-0 exponent */
   e=0;				   /* assume no E */
   pre=c-cstart+exp;
   /* [here, pre-exp is the digits count (==1 for zero)] */
   if (exp>0 || pre<-5) {	   /* need exponential form */
     e=pre-1;			   /* calculate E value */
     pre=1;			   /* assume one digit before '.' */
     } /* exponential form */

   /* modify the coefficient, adding 0s, '.', and E+nn as needed */
   s=c-1;			   /* source (LSD) */
   if (pre>0) {			   /* ddd.ddd (plain), perhaps with E */
     char *dotat=cstart+pre;
     if (dotat<c) {		   /* if embedded dot needed... */
       t=c;				/* target */
       for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
       *t='.';				/* insert the dot */
       c++;				/* length increased by one */
       }

     /* finally add the E-part, if needed; it will never be 0, and has */
     /* a maximum length of 4 digits */
     if (e!=0) {
       *c++='E'; 		   /* starts with E */
       *c++='+'; 		   /* assume positive */
       if (e<0) {
 	*(c-1)='-';		   /* oops, need '-' */
 	e=-e;			   /* uInt, please */
 	}
       if (e<1000) {		   /* 3 (or fewer) digits case */
 	u=&BIN2CHAR[e*4];	   /* -> length byte */
 	memcpy(c, u+4-*u, 4);	   /* copy fixed 4 characters [is safe] */
 	c+=*u;			   /* bump pointer appropriately */
 	}
        else {			   /* 4-digits */
 	Int thou=((e>>3)*1049)>>17; /* e/1000 */
 	Int rem=e-(1000*thou);	    /* e%1000 */
 	*c++='0'+(char)thou;
 	u=&BIN2CHAR[rem*4];	   /* -> length byte */
 	memcpy(c, u+1, 4);	   /* copy fixed 3+1 characters [is safe] */
 	c+=3;			   /* bump pointer, always 3 digits */
 	}
       }
     *c='\0';			   /* add terminator */
     /*printf("res %s\n", string); */
     return string;
     } /* pre>0 */

   /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
   t=c+1-pre;
   *(t+1)='\0';				/* can add terminator now */
   for (; s>=cstart; s--, t--) *t=*s;	/* shift whole coefficient right */
   c=cstart;
   *c++='0';				/* always starts with 0. */
   *c++='.';
   for (; pre<0; pre++) *c++='0';	/* add any 0's after '.' */
   /*printf("res %s\n", string); */
   return string;
   } /* decimal128ToString */

 /* ------------------------------------------------------------------ */
 /* to-number -- conversion from numeric string			      */
 /*								      */
 /*   decimal128FromString(result, string, set); 		      */
 /*								      */
 /*  result  is the decimal128 format number which gets the result of  */
 /*	    the conversion					      */
 /*  *string is the character string which should contain a valid      */
 /*	    number (which may be a special value)		      */
 /*  set     is the context					      */
 /*								      */
 /* The context is supplied to this routine is used for error handling */
 /* (setting of status and traps) and for the rounding mode, only.     */
 /* If an error occurs, the result will be a valid decimal128 NaN.     */
 /* ------------------------------------------------------------------ */
 decimal128 * decimal128FromString(decimal128 *result, const char *string,
 				  decContext *set) {
   decContext dc;			     /* work */
   decNumber dn; 			     /* .. */

   decContextDefault(&dc, DEC_INIT_DECIMAL128); /* no traps, please */
   dc.round=set->round;			       /* use supplied rounding */

   decNumberFromString(&dn, string, &dc);     /* will round if needed */
   decimal128FromNumber(result, &dn, &dc);
   if (dc.status!=0) {			     /* something happened */
     decContextSetStatus(set, dc.status);     /* .. pass it on */
     }
   return result;
   } /* decimal128FromString */

 /* ------------------------------------------------------------------ */
 /* decimal128IsCanonical -- test whether encoding is canonical	      */
 /*   d128 is the source decimal128				      */
 /*   returns 1 if the encoding of d128 is canonical, 0 otherwise      */
 /* No error is possible.					      */
 /* ------------------------------------------------------------------ */
 uInt decimal128IsCanonical(const decimal128 *d128) {
   decNumber dn; 			/* work */
   decimal128 canon;			 /* .. */
   decContext dc;			/* .. */
   decContextDefault(&dc, DEC_INIT_DECIMAL128);
   decimal128ToNumber(d128, &dn);
   decimal128FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
   return memcmp(d128, &canon, DECIMAL128_Bytes)==0;
   } /* decimal128IsCanonical */

 /* ------------------------------------------------------------------ */
 /* decimal128Canonical -- copy an encoding, ensuring it is canonical  */
 /*   d128 is the source decimal128				      */
 /*   result is the target (may be the same decimal128)		      */
 /*   returns result						      */
 /* No error is possible.					      */
 /* ------------------------------------------------------------------ */
 decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) {
   decNumber dn; 			/* work */
   decContext dc;			/* .. */
   decContextDefault(&dc, DEC_INIT_DECIMAL128);
   decimal128ToNumber(d128, &dn);
   decimal128FromNumber(result, &dn, &dc);/* result will now be canonical */
   return result;
   } /* decimal128Canonical */

 #if DECTRACE || DECCHECK
 /* Macros for accessing decimal128 fields.  These assume the argument
    is a reference (pointer) to the decimal128 structure, and the
    decimal128 is in network byte order (big-endian) */
 /* Get sign */
 #define decimal128Sign(d)	((unsigned)(d)->bytes[0]>>7)

 /* Get combination field */
 #define decimal128Comb(d)	(((d)->bytes[0] & 0x7c)>>2)

 /* Get exponent continuation [does not remove bias] */
 #define decimal128ExpCon(d)	((((d)->bytes[0] & 0x03)<<10)	      \
 			      | ((unsigned)(d)->bytes[1]<<2)	      \
 			      | ((unsigned)(d)->bytes[2]>>6))

 /* Set sign [this assumes sign previously 0] */
 #define decimal128SetSign(d, b) {				      \
   (d)->bytes[0]|=((unsigned)(b)<<7);}

 /* Set exponent continuation [does not apply bias] */
 /* This assumes range has been checked and exponent previously 0; */
 /* type of exponent must be unsigned */
 #define decimal128SetExpCon(d, e) {				      \
   (d)->bytes[0]|=(uByte)((e)>>10);				      \
   (d)->bytes[1] =(uByte)(((e)&0x3fc)>>2);			      \
   (d)->bytes[2]|=(uByte)(((e)&0x03)<<6);}

 /* ------------------------------------------------------------------ */
 /* decimal128Show -- display a decimal128 in hexadecimal [debug aid]  */
 /*   d128 -- the number to show 				      */
 /* ------------------------------------------------------------------ */
 /* Also shows sign/cob/expconfields extracted */
 void decimal128Show(const decimal128 *d128) {
   char buf[DECIMAL128_Bytes*2+1];
   Int i, j=0;

   if (DECLITEND) {
     for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
       sprintf(&buf[j], "%02x", d128->bytes[15-i]);
       }
     printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
 	   d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,
 	   ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)|
 	   (d128->bytes[13]>>6));
     }
    else {
     for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
       sprintf(&buf[j], "%02x", d128->bytes[i]);
       }
     printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
 	   decimal128Sign(d128), decimal128Comb(d128),
 	   decimal128ExpCon(d128));
     }
   } /* decimal128Show */
 #endif
	/* Decimal 128-bit format module for the decNumber C Library.
	Copyright (C) 2005-2021 Free Software Foundation, Inc.
	Contributed by IBM Corporation. Author Mike Cowlishaw.

	This file is part of GCC.

	GCC 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 3, or (at your option) any later
	version.

	GCC 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.

	Under Section 7 of GPL version 3, you are granted additional
	permissions described in the GCC Runtime Library Exception, version
	3.1, as published by the Free Software Foundation.

	You should have received a copy of the GNU General Public License and
	a copy of the GCC Runtime Library Exception along with this program;
	see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
	<http://www.gnu.org/licenses/>. */

	/* ------------------------------------------------------------------ */
	/* Decimal 128-bit format module */
	/* ------------------------------------------------------------------ */
	/* This module comprises the routines for decimal128 format numbers. */
	/* Conversions are supplied to and from decNumber and String. */
	/* */
	/* This is used when decNumber provides operations, either for all */
	/* operations or as a proxy between decNumber and decSingle. */
	/* */
	/* Error handling is the same as decNumber (qv.). */
	/* ------------------------------------------------------------------ */
	#include <string.h> /* [for memset/memcpy] */
	#include <stdio.h> /* [for printf] */

	#include "dconfig.h" /* GCC definitions */
	#define DECNUMDIGITS 34 /* make decNumbers with space for 34 */
	#include "decNumber.h" /* base number library */
	#include "decNumberLocal.h" /* decNumber local types, etc. */
	#include "decimal128.h" /* our primary include */

	/* Utility routines and tables [in decimal64.c] */
	extern const uInt COMBEXP[32], COMBMSD[32];
	extern const uShort DPD2BIN[1024];
	extern const uShort BIN2DPD[1000]; /* [not used] */
	extern const uByte BIN2CHAR[4001];

	extern void decDigitsFromDPD(decNumber , const uInt , Int);
	extern void decDigitsToDPD(const decNumber , uInt , Int);

	#if DECTRACE \|\| DECCHECK
	void decimal128Show(const decimal128 ); / for debug */
	extern void decNumberShow(const decNumber ); / .. */
	#endif

	/* Useful macro */
	/* Clear a structure (e.g., a decNumber) */
	#define DEC_clear(d) memset(d, 0, sizeof(*d))

	/* ------------------------------------------------------------------ */
	/* decimal128FromNumber -- convert decNumber to decimal128 */
	/* */
	/* ds is the target decimal128 */
	/* dn is the source number (assumed valid) */
	/* set is the context, used only for reporting errors */
	/* */
	/* The set argument is used only for status reporting and for the */
	/* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
	/* digits or an overflow is detected). If the exponent is out of the */
	/* valid range then Overflow or Underflow will be raised. */
	/* After Underflow a subnormal result is possible. */
	/* */
	/* DEC_Clamped is set if the number has to be 'folded down' to fit, */
	/* by reducing its exponent and multiplying the coefficient by a */
	/* power of ten, or if the exponent on a zero had to be clamped. */
	/* ------------------------------------------------------------------ */
	decimal128 * decimal128FromNumber(decimal128 d128, const decNumber dn,
	decContext *set) {
	uInt status=0; /* status accumulator */
	Int ae; /* adjusted exponent */
	decNumber dw; /* work */
	decContext dc; /* .. */
	uInt comb, exp; /* .. */
	uInt uiwork; /* for macros */
	uInt targar[4]={0,0,0,0}; /* target 128-bit */
	#define targhi targar[3] /* name the word with the sign */
	#define targmh targar[2] /* name the words */
	#define targml targar[1] /* .. */
	#define targlo targar[0] /* .. */

	/* If the number has too many digits, or the exponent could be */
	/* out of range then reduce the number under the appropriate */
	/* constraints. This could push the number to Infinity or zero, */
	/* so this check and rounding must be done before generating the */
	/* decimal128] */
	ae=dn->exponent+dn->digits-1; /* [0 if special] */
	if (dn->digits>DECIMAL128_Pmax /* too many digits */
	\|\| ae>DECIMAL128_Emax /* likely overflow */
	\|\| ae<DECIMAL128_Emin) { /* likely underflow */
	decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */
	dc.round=set->round; /* use supplied rounding */
	decNumberPlus(&dw, dn, &dc); /* (round and check) */
	/* [this changes -0 to 0, so enforce the sign...] */
	dw.bits\|=dn->bits&DECNEG;
	status=dc.status; /* save status */
	dn=&dw; /* use the work number */
	} /* maybe out of range */

	if (dn->bits&DECSPECIAL) { /* a special value */
	if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
	else { /* sNaN or qNaN */
	if ((dn->lsu!=0 \|\| dn->digits>1) / non-zero coefficient */
	&& (dn->digits<DECIMAL128_Pmax)) { /* coefficient fits */
	decDigitsToDPD(dn, targar, 0);
	}
	if (dn->bits&DECNAN) targhi\|=DECIMAL_NaN<<24;
	else targhi\|=DECIMAL_sNaN<<24;
	} /* a NaN */
	} /* special */

	else { /* is finite */
	if (decNumberIsZero(dn)) { /* is a zero */
	/* set and clamp exponent */
	if (dn->exponent<-DECIMAL128_Bias) {
	exp=0; /* low clamp */
	status\|=DEC_Clamped;
	}
	else {
	exp=dn->exponent+DECIMAL128_Bias; /* bias exponent */
	if (exp>DECIMAL128_Ehigh) { /* top clamp */
	exp=DECIMAL128_Ehigh;
	status\|=DEC_Clamped;
	}
	}
	comb=(exp>>9) & 0x18; /* msd=0, exp top 2 bits .. */
	}
	else { /* non-zero finite number */
	uInt msd; /* work */
	Int pad=0; /* coefficient pad digits */

	/* the dn is known to fit, but it may need to be padded */
	exp=(uInt)(dn->exponent+DECIMAL128_Bias); /* bias exponent */
	if (exp>DECIMAL128_Ehigh) { /* fold-down case */
	pad=exp-DECIMAL128_Ehigh;
	exp=DECIMAL128_Ehigh; /* [to maximum] */
	status\|=DEC_Clamped;
	}

	/* [fastpath for common case is not a win, here] */
	decDigitsToDPD(dn, targar, pad);
	/* save and clear the top digit */
	msd=targhi>>14;
	targhi&=0x00003fff;

	/* create the combination field */
	if (msd>=8) comb=0x18 \| ((exp>>11) & 0x06) \| (msd & 0x01);
	else comb=((exp>>9) & 0x18) \| msd;
	}
	targhi\|=comb<<26; /* add combination field .. */
	targhi\|=(exp&0xfff)<<14; /* .. and exponent continuation */
	} /* finite */

	if (dn->bits&DECNEG) targhi\|=0x80000000; /* add sign bit */

	/* now write to storage; this is endian */
	if (DECLITEND) {
	/* lo -> hi */
	UBFROMUI(d128->bytes, targlo);
	UBFROMUI(d128->bytes+4, targml);
	UBFROMUI(d128->bytes+8, targmh);
	UBFROMUI(d128->bytes+12, targhi);
	}
	else {
	/* hi -> lo */
	UBFROMUI(d128->bytes, targhi);
	UBFROMUI(d128->bytes+4, targmh);
	UBFROMUI(d128->bytes+8, targml);
	UBFROMUI(d128->bytes+12, targlo);
	}

	if (status!=0) decContextSetStatus(set, status); /* pass on status */
	/* decimal128Show(d128); */
	return d128;
	} /* decimal128FromNumber */

	/* ------------------------------------------------------------------ */
	/* decimal128ToNumber -- convert decimal128 to decNumber */
	/* d128 is the source decimal128 */
	/* dn is the target number, with appropriate space */
	/* No error is possible. */
	/* ------------------------------------------------------------------ */
	decNumber * decimal128ToNumber(const decimal128 d128, decNumber dn) {
	uInt msd; /* coefficient MSD */
	uInt exp; /* exponent top two bits */
	uInt comb; /* combination field */
	Int need; /* work */
	uInt uiwork; /* for macros */
	uInt sourar[4]; /* source 128-bit */
	#define sourhi sourar[3] /* name the word with the sign */
	#define sourmh sourar[2] /* and the mid-high word */
	#define sourml sourar[1] /* and the mod-low word */
	#define sourlo sourar[0] /* and the lowest word */

	/* load source from storage; this is endian */
	if (DECLITEND) {
	sourlo=UBTOUI(d128->bytes ); /* directly load the low int */
	sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
	sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
	sourhi=UBTOUI(d128->bytes+12); /* then the high int */
	}
	else {
	sourhi=UBTOUI(d128->bytes ); /* directly load the high int */
	sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
	sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
	sourlo=UBTOUI(d128->bytes+12); /* then the low int */
	}

	comb=(sourhi>>26)&0x1f; /* combination field */

	decNumberZero(dn); /* clean number */
	if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */

	msd=COMBMSD[comb]; /* decode the combination field */
	exp=COMBEXP[comb]; /* .. */

	if (exp==3) { /* is a special */
	if (msd==0) {
	dn->bits\|=DECINF;
	return dn; /* no coefficient needed */
	}
	else if (sourhi&0x02000000) dn->bits\|=DECSNAN;
	else dn->bits\|=DECNAN;
	msd=0; /* no top digit */
	}
	else { /* is a finite number */
	dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
	}

	/* get the coefficient */
	sourhi&=0x00003fff; /* clean coefficient continuation */
	if (msd) { /* non-zero msd */
	sourhi\|=msd<<14; /* prefix to coefficient */
	need=12; /* process 12 declets */
	}
	else { /* msd=0 */
	if (sourhi) need=11; /* declets to process */
	else if (sourmh) need=10;
	else if (sourml) need=7;
	else if (sourlo) need=4;
	else return dn; /* easy: coefficient is 0 */
	} /msd=0 /

	decDigitsFromDPD(dn, sourar, need); /* process declets */
	/* decNumberShow(dn); */
	return dn;
	} /* decimal128ToNumber */

	/* ------------------------------------------------------------------ */
	/* to-scientific-string -- conversion to numeric string */
	/* to-engineering-string -- conversion to numeric string */
	/* */
	/* decimal128ToString(d128, string); */
	/* decimal128ToEngString(d128, string); */
	/* */
	/* d128 is the decimal128 format number to convert */
	/* string is the string where the result will be laid out */
	/* */
	/* string must be at least 24 characters */
	/* */
	/* No error is possible, and no status can be set. */
	/* ------------------------------------------------------------------ */
	char * decimal128ToEngString(const decimal128 d128, char string){
	decNumber dn; /* work */
	decimal128ToNumber(d128, &dn);
	decNumberToEngString(&dn, string);
	return string;
	} /* decimal128ToEngString */

	char * decimal128ToString(const decimal128 d128, char string){
	uInt msd; /* coefficient MSD */
	Int exp; /* exponent top two bits or full */
	uInt comb; /* combination field */
	char cstart; / coefficient start */
	char c; / output pointer in string */
	const uByte u; / work */
	char s, t; /* .. (source, target) */
	Int dpd; /* .. */
	Int pre, e; /* .. */
	uInt uiwork; /* for macros */

	uInt sourar[4]; /* source 128-bit */
	#define sourhi sourar[3] /* name the word with the sign */
	#define sourmh sourar[2] /* and the mid-high word */
	#define sourml sourar[1] /* and the mod-low word */
	#define sourlo sourar[0] /* and the lowest word */

	/* load source from storage; this is endian */
	if (DECLITEND) {
	sourlo=UBTOUI(d128->bytes ); /* directly load the low int */
	sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
	sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
	sourhi=UBTOUI(d128->bytes+12); /* then the high int */
	}
	else {
	sourhi=UBTOUI(d128->bytes ); /* directly load the high int */
	sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
	sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
	sourlo=UBTOUI(d128->bytes+12); /* then the low int */
	}

	c=string; /* where result will go */
	if (((Int)sourhi)<0) c++='-'; / handle sign */

	comb=(sourhi>>26)&0x1f; /* combination field */
	msd=COMBMSD[comb]; /* decode the combination field */
	exp=COMBEXP[comb]; /* .. */

	if (exp==3) {
	if (msd==0) { /* infinity */
	strcpy(c, "Inf");
	strcpy(c+3, "inity");
	return string; /* easy */
	}
	if (sourhi&0x02000000) c++='s'; / sNaN */
	strcpy(c, "NaN"); /* complete word */
	c+=3; /* step past */
	if (sourlo==0 && sourml==0 && sourmh==0
	&& (sourhi&0x0003ffff)==0) return string; /* zero payload */
	/* otherwise drop through to add integer; set correct exp */
	exp=0; msd=0; /* setup for following code */
	}
	else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */

	/* convert 34 digits of significand to characters */
	cstart=c; /* save start of coefficient */
	if (msd) c++='0'+(char)msd; / non-zero most significant digit */

	/* Now decode the declets. After extracting each one, it is */
	/* decoded to binary and then to a 4-char sequence by table lookup; */
	/* the 4-chars are a 1-char length (significant digits, except 000 */
	/* has length 0). This allows us to left-align the first declet */
	/* with non-zero content, then remaining ones are full 3-char */
	/* length. We use fixed-length memcpys because variable-length */
	/* causes a subroutine call in GCC. (These are length 4 for speed */
	/* and are safe because the array has an extra terminator byte.) */
	#define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
	if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
	else if (u) {memcpy(c, u+4-u, 4); c+=*u;}
	dpd=(sourhi>>4)&0x3ff; /* declet 1 */
	dpd2char;
	dpd=((sourhi&0xf)<<6) \| (sourmh>>26); /* declet 2 */
	dpd2char;
	dpd=(sourmh>>16)&0x3ff; /* declet 3 */
	dpd2char;
	dpd=(sourmh>>6)&0x3ff; /* declet 4 */
	dpd2char;
	dpd=((sourmh&0x3f)<<4) \| (sourml>>28); /* declet 5 */
	dpd2char;
	dpd=(sourml>>18)&0x3ff; /* declet 6 */
	dpd2char;
	dpd=(sourml>>8)&0x3ff; /* declet 7 */
	dpd2char;
	dpd=((sourml&0xff)<<2) \| (sourlo>>30); /* declet 8 */
	dpd2char;
	dpd=(sourlo>>20)&0x3ff; /* declet 9 */
	dpd2char;
	dpd=(sourlo>>10)&0x3ff; /* declet 10 */
	dpd2char;
	dpd=(sourlo)&0x3ff; /* declet 11 */
	dpd2char;

	if (c==cstart) c++='0'; / all zeros -- make 0 */

	if (exp==0) { /* integer or NaN case -- easy */
	c='\0'; / terminate */
	return string;
	}

	/* non-0 exponent */
	e=0; /* assume no E */
	pre=c-cstart+exp;
	/* [here, pre-exp is the digits count (==1 for zero)] */
	if (exp>0 \|\| pre<-5) { /* need exponential form */
	e=pre-1; /* calculate E value */
	pre=1; /* assume one digit before '.' */
	} /* exponential form */

	/* modify the coefficient, adding 0s, '.', and E+nn as needed */
	s=c-1; /* source (LSD) */
	if (pre>0) { /* ddd.ddd (plain), perhaps with E */
	char *dotat=cstart+pre;
	if (dotat<c) { /* if embedded dot needed... */
	t=c; /* target */
	for (; s>=dotat; s--, t--) t=s; /* open the gap; leave t at gap */
	t='.'; / insert the dot */
	c++; /* length increased by one */
	}

	/* finally add the E-part, if needed; it will never be 0, and has */
	/* a maximum length of 4 digits */
	if (e!=0) {
	c++='E'; / starts with E */
	c++='+'; / assume positive */
	if (e<0) {
	(c-1)='-'; / oops, need '-' */
	e=-e; /* uInt, please */
	}
	if (e<1000) { /* 3 (or fewer) digits case */
	u=&BIN2CHAR[e4]; / -> length byte */
	memcpy(c, u+4-u, 4); / copy fixed 4 characters [is safe] */
	c+=u; / bump pointer appropriately */
	}
	else { /* 4-digits */
	Int thou=((e>>3)1049)>>17; / e/1000 */
	Int rem=e-(1000thou); / e%1000 */
	*c++='0'+(char)thou;
	u=&BIN2CHAR[rem4]; / -> length byte */
	memcpy(c, u+1, 4); /* copy fixed 3+1 characters [is safe] */
	c+=3; /* bump pointer, always 3 digits */
	}
	}
	c='\0'; / add terminator */
	/printf("res %s\n", string); /
	return string;
	} /* pre>0 */

	/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
	t=c+1-pre;
	(t+1)='\0'; / can add terminator now */
	for (; s>=cstart; s--, t--) t=s; /* shift whole coefficient right */
	c=cstart;
	c++='0'; / always starts with 0. */
	*c++='.';
	for (; pre<0; pre++) c++='0'; / add any 0's after '.' */
	/printf("res %s\n", string); /
	return string;
	} /* decimal128ToString */

	/* ------------------------------------------------------------------ */
	/* to-number -- conversion from numeric string */
	/* */
	/* decimal128FromString(result, string, set); */
	/* */
	/* result is the decimal128 format number which gets the result of */
	/* the conversion */
	/* string is the character string which should contain a valid /
	/* number (which may be a special value) */
	/* set is the context */
	/* */
	/* The context is supplied to this routine is used for error handling */
	/* (setting of status and traps) and for the rounding mode, only. */
	/* If an error occurs, the result will be a valid decimal128 NaN. */
	/* ------------------------------------------------------------------ */
	decimal128 * decimal128FromString(decimal128 result, const char string,
	decContext *set) {
	decContext dc; /* work */
	decNumber dn; /* .. */

	decContextDefault(&dc, DEC_INIT_DECIMAL128); /* no traps, please */
	dc.round=set->round; /* use supplied rounding */

	decNumberFromString(&dn, string, &dc); /* will round if needed */
	decimal128FromNumber(result, &dn, &dc);
	if (dc.status!=0) { /* something happened */
	decContextSetStatus(set, dc.status); /* .. pass it on */
	}
	return result;
	} /* decimal128FromString */

	/* ------------------------------------------------------------------ */
	/* decimal128IsCanonical -- test whether encoding is canonical */
	/* d128 is the source decimal128 */
	/* returns 1 if the encoding of d128 is canonical, 0 otherwise */
	/* No error is possible. */
	/* ------------------------------------------------------------------ */
	uInt decimal128IsCanonical(const decimal128 *d128) {
	decNumber dn; /* work */
	decimal128 canon; /* .. */
	decContext dc; /* .. */
	decContextDefault(&dc, DEC_INIT_DECIMAL128);
	decimal128ToNumber(d128, &dn);
	decimal128FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
	return memcmp(d128, &canon, DECIMAL128_Bytes)==0;
	} /* decimal128IsCanonical */

	/* ------------------------------------------------------------------ */
	/* decimal128Canonical -- copy an encoding, ensuring it is canonical */
	/* d128 is the source decimal128 */
	/* result is the target (may be the same decimal128) */
	/* returns result */
	/* No error is possible. */
	/* ------------------------------------------------------------------ */
	decimal128 * decimal128Canonical(decimal128 result, const decimal128 d128) {
	decNumber dn; /* work */
	decContext dc; /* .. */
	decContextDefault(&dc, DEC_INIT_DECIMAL128);
	decimal128ToNumber(d128, &dn);
	decimal128FromNumber(result, &dn, &dc);/* result will now be canonical */
	return result;
	} /* decimal128Canonical */

	#if DECTRACE \|\| DECCHECK
	/* Macros for accessing decimal128 fields. These assume the argument
	is a reference (pointer) to the decimal128 structure, and the
	decimal128 is in network byte order (big-endian) */
	/* Get sign */
	#define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7)

	/* Get combination field */
	#define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2)

	/* Get exponent continuation [does not remove bias] */
	#define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \
	\| ((unsigned)(d)->bytes[1]<<2) \
	\| ((unsigned)(d)->bytes[2]>>6))

	/* Set sign [this assumes sign previously 0] */
	#define decimal128SetSign(d, b) { \
	(d)->bytes[0]\|=((unsigned)(b)<<7);}

	/* Set exponent continuation [does not apply bias] */
	/* This assumes range has been checked and exponent previously 0; */
	/* type of exponent must be unsigned */
	#define decimal128SetExpCon(d, e) { \
	(d)->bytes[0]\|=(uByte)((e)>>10); \
	(d)->bytes[1] =(uByte)(((e)&0x3fc)>>2); \
	(d)->bytes[2]\|=(uByte)(((e)&0x03)<<6);}

	/* ------------------------------------------------------------------ */
	/* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */
	/* d128 -- the number to show */
	/* ------------------------------------------------------------------ */
	/* Also shows sign/cob/expconfields extracted */
	void decimal128Show(const decimal128 *d128) {
	char buf[DECIMAL128_Bytes*2+1];
	Int i, j=0;

	if (DECLITEND) {
	for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
	sprintf(&buf[j], "%02x", d128->bytes[15-i]);
	}
	printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
	d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,
	((d128->bytes[15]&0x3)<<10)\|(d128->bytes[14]<<2)\|
	(d128->bytes[13]>>6));
	}
	else {
	for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
	sprintf(&buf[j], "%02x", d128->bytes[i]);
	}
	printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
	decimal128Sign(d128), decimal128Comb(d128),
	decimal128ExpCon(d128));
	}
	} /* decimal128Show */
	#endif