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- /* 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
- * 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 long integer and e type fraction
- * euifrac( e, &l, frac ) e to unsigned long integer 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 ) 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 ) long (32 bit) integer to e type
- * ultoe( &l, e ) unsigned long (32 bit) integer to e type
- * eisneg( e ) 1 if sign bit of e != 0, else 0
- * eisinf( e ) 1 if e has maximum exponent (non-IEEE)
- * or is infinite (IEEE)
- * eisnan( e ) 1 if e is a NaN
- * esqrt( a, b ) b = square root of a
- *
- *
- * Routines for internal format numbers
- *
- * eaddm( ai, bi ) add significands, bi = bi + ai
- * ecleaz(ei) ei = 0
- * ecleazs(ei) set ei = 0 but leave its sign alone
- * ecmpm( ai, bi ) compare significands, return 1, 0, or -1
- * edivm( ai, bi ) 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
- *
- *
- * The result is always normalized and rounded to NI-4 word precision
- * after each arithmetic operation.
- *
- * Exception flags are NOT fully supported.
- *
- * Define INFINITY in mconf.h for support of infinity; otherwise a
- * saturation arithmetic is implemented.
- *
- * Define NANS for support of Not-a-Number items; otherwise the
- * arithmetic will never produce a NaN output, and might be confused
- * by a NaN input.
- * If NaN's are supported, the output of ecmp(a,b) is -2 if
- * either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
- * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
- * if in doubt.
- * Signaling NaN's are NOT supported; they are treated the same
- * as quiet NaN's.
- *
- * Denormals are always supported here where appropriate (e.g., not
- * for conversion to DEC numbers).
- */
- /*
- * Revision history:
- *
- * 5 Jan 84 PDP-11 assembly language version
- * 2 Mar 86 fixed bug in asctoq()
- * 6 Dec 86 C language version
- * 30 Aug 88 100 digit version, improved rounding
- * 15 May 92 80-bit long double support
- *
- * Author: S. L. Moshier.
- */
- #include <stdio.h>
- /* #include "\usr\include\stdio.h" */
- #include "ehead.h"
- #include "mconf.h"
- /* Change UNK into something else. */
- #ifdef UNK
- #undef UNK
- #define IBMPC 1
- #endif
- /* NaN's require infinity support. */
- #ifdef NANS
- #ifndef INFINITY
- #define INFINITY
- #endif
- #endif
- /* This handles 64-bit long ints. */
- #define LONGBITS (8 * sizeof(long))
- /* Control register for rounding precision.
- * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
- */
- int rndprc = NBITS;
- extern int rndprc;
- void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
- static void toe24(), toe53(), toe64(), toe113();
- void eremain(), einit(), eiremain();
- int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
- void emovi(), emovo(), emovz(), ecleaz(), eadd1();
- void etodec(), todec(), dectoe();
- int eisnan(), eiisnan();
- void einit()
- {
- }
- /*
- ; Clear out entire external format number.
- ;
- ; unsigned short x[];
- ; eclear( x );
- */
- void eclear( x )
- register unsigned short *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 short *a, *b;
- {
- register int i;
- for( i=0; i<NE; i++ )
- *b++ = *a++;
- }
- /*
- ; Absolute value of external format number
- ;
- ; short x[NE];
- ; eabs( x );
- */
- void eabs(x)
- unsigned short 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 short x[NE];
- ; eneg( x );
- */
- void eneg(x)
- unsigned short 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.
- */
- int eisneg(x)
- unsigned short 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 has maximum possible exponent,
- * else return zero.
- */
- int eisinf(x)
- unsigned short x[];
- {
- if( (x[NE-1] & 0x7fff) == 0x7fff )
- {
- #ifdef NANS
- if( eisnan(x) )
- return( 0 );
- #endif
- return( 1 );
- }
- else
- return( 0 );
- }
- /* Check if e-type number is not a number.
- */
- int eisnan(x)
- unsigned short 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 entire number, including exponent and significand, with
- ; largest possible number. These programs implement a saturation
- ; value that is an ordinary, legal number. A special value
- ; "infinity" may also be implemented; this would require tests
- ; for that value and implementation of special rules for arithmetic
- ; operations involving inifinity.
- */
- void einfin(x)
- register unsigned short *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
- }
- /* Move in external format number,
- * converting it to internal format.
- */
- void emovi( a, b )
- unsigned short *a, *b;
- {
- register unsigned short *p, *q;
- int i;
- q = b;
- p = a + (NE-1); /* point to last word of external number */
- /* get the sign bit */
- if( *p & 0x8000 )
- *q++ = 0xffff;
- else
- *q++ = 0;
- /* get the exponent */
- *q = *p--;
- *q++ &= 0x7fff; /* delete the sign bit */
- #ifdef INFINITY
- if( (*(q-1) & 0x7fff) == 0x7fff )
- {
- #ifdef NANS
- if( eisnan(a) )
- {
- *q++ = 0;
- for( i=3; i<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 short *a, *b;
- {
- register unsigned short *p, *q;
- unsigned short 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, NBITS );
- 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 short *xi;
- {
- register int i;
- for( i=0; i<NI; i++ )
- *xi++ = 0;
- }
- /* same, but don't touch the sign. */
- void ecleazs( xi )
- register unsigned short *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 short *a, *b;
- {
- register int i;
- for( i=0; i<NI-1; i++ )
- *b++ = *a++;
- /* clear low guard word */
- *b = 0;
- }
- /* Return nonzero if internal format number is a NaN.
- */
- int eiisnan (x)
- unsigned short x[];
- {
- int i;
- if( (x[E] & 0x7fff) == 0x7fff )
- {
- for( i=M+1; i<NI; i++ )
- {
- if( x[i] != 0 )
- return(1);
- }
- }
- return(0);
- }
- #ifdef INFINITY
- /* Return nonzero if internal format number is infinite. */
- static int
- eiisinf (x)
- unsigned short x[];
- {
- #ifdef NANS
- if (eiisnan (x))
- return (0);
- #endif
- if ((x[E] & 0x7fff) == 0x7fff)
- return (1);
- return (0);
- }
- #endif
- /*
- ; Compare significands of numbers in internal format.
- ; Guard words are included in the comparison.
- ;
- ; unsigned short 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 short *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 short *x;
- {
- register unsigned short 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 short *x;
- {
- register unsigned short 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 short *x;
- {
- register unsigned short 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 short *x;
- {
- int i;
- register unsigned short 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 short *x;
- {
- int i;
- register unsigned short *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 short *x;
- {
- int i;
- register unsigned short *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 short *x, *y;
- {
- register unsigned long a;
- int i;
- unsigned int carry;
- x += NI-1;
- y += NI-1;
- carry = 0;
- for( i=M; i<NI; i++ )
- {
- a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
- if( a & 0x10000 )
- carry = 1;
- else
- carry = 0;
- *y = (unsigned short )a;
- --x;
- --y;
- }
- }
- /*
- ; Subtract significands
- ; y - x replaces y
- */
- void esubm( x, y )
- unsigned short *x, *y;
- {
- unsigned long a;
- int i;
- unsigned int carry;
- x += NI-1;
- y += NI-1;
- carry = 0;
- for( i=M; i<NI; i++ )
- {
- a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
- if( a & 0x10000 )
- carry = 1;
- else
- carry = 0;
- *y = (unsigned short )a;
- --x;
- --y;
- }
- }
- /* Divide significands */
- static unsigned short equot[NI] = {0}; /* was static */
- #if 0
- int edivm( den, num )
- unsigned short den[], num[];
- {
- int i;
- register unsigned short *p, *q;
- unsigned short 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 short a[], b[];
- {
- unsigned short *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
- /* 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<NI; i++ )
- {
- if( *ps == 0 )
- {
- --ps;
- --pp;
- *(pp-1) = 0;
- }
- else
- {
- m = (unsigned long) aa * *ps--;
- carry = (m & 0xffff) + *pp;
- *pp-- = (unsigned short )carry;
- carry = (carry >> 16) + (m >> 16) + *pp;
- *pp = (unsigned short )carry;
- *(pp-1) = carry >> 16;
- }
- }
- for( i=M; i<NI; i++ )
- c[i] = p[i];
- }
- /* Divide significands. Neither the numerator nor the denominator
- is permitted to have its high guard word nonzero. */
- int edivm( den, num )
- unsigned short den[], num[];
- {
- int i;
- register unsigned short *p;
- unsigned long tnum;
- unsigned short j, tdenm, tquot;
- unsigned short tprod[NI+1];
- p = &equot[0];
- *p++ = num[0];
- *p++ = num[1];
- for( i=M; i<NI; i++ )
- {
- *p++ = 0;
- }
- eshdn1( num );
- tdenm = den[M+1];
- for( i=M; i<NI; i++ )
- {
- /* Find trial quotient digit (the radix is 65536). */
- tnum = (((unsigned long) num[M]) << 16) + num[M+1];
- /* Do not execute the divide instruction if it will overflow. */
- if( (tdenm * 0xffffL) < tnum )
- tquot = 0xffff;
- else
- tquot = tnum / tdenm;
- /* Prove that the divide worked. */
- /*
- tcheck = (unsigned long )tquot * tdenm;
- if( tnum - tcheck > tdenm )
- tquot = 0xffff;
- */
- /* Multiply denominator by trial quotient digit. */
- m16m( tquot, den, tprod );
- /* The quotient digit may have been overestimated. */
- if( ecmpm( tprod, num ) > 0 )
- {
- tquot -= 1;
- esubm( den, tprod );
- if( ecmpm( tprod, num ) > 0 )
- {
- tquot -= 1;
- esubm( den, tprod );
- }
- }
- /*
- if( ecmpm( tprod, num ) > 0 )
- {
- eshow( "tprod", tprod );
- eshow( "num ", num );
- printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
- tnum, den[M+1], tquot );
- }
- */
- esubm( tprod, num );
- /*
- if( ecmpm( num, den ) >= 0 )
- {
- eshow( "num ", num );
- eshow( "den ", den );
- printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
- tnum, den[M+1], tquot );
- }
- */
- equot[i] = tquot;
- eshup6(num);
- }
- /* test for nonzero remainder after roundoff bit */
- p = &num[M];
- j = 0;
- for( i=M; 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 short a[], b[];
- {
- unsigned short *p, *q;
- unsigned short pprod[NI];
- unsigned short j;
- int i;
- equot[0] = b[0];
- equot[1] = b[1];
- for( i=M; i<NI; i++ )
- equot[i] = 0;
- j = 0;
- p = &a[NI-1];
- q = &equot[NI-1];
- for( i=M+1; i<NI; i++ )
- {
- if( *p == 0 )
- {
- --p;
- }
- else
- {
- m16m( *p--, b, pprod );
- eaddm(pprod, equot);
- }
- j |= *q;
- eshdn6(equot);
- }
- for( i=0; i<NI; i++ )
- b[i] = equot[i];
- /* return flag for lost nonzero bits */
- return( (int)j );
- }
- /*
- eshow(str, x)
- char *str;
- unsigned short *x;
- {
- int i;
- printf( "%s ", str );
- for( i=0; i<NI; i++ )
- printf( "%04x ", *x++ );
- printf( "\n" );
- }
- */
- #endif
- /*
- * Normalize and round off.
- *
- * The internal format number to be rounded is "s".
- * Input "lost" indicates whether the number is exact.
- * This is the so-called sticky bit.
- *
- * Input "subflg" indicates whether the number was obtained
- * by a subtraction operation. In that case if lost is nonzero
- * then the number is slightly smaller than indicated.
- *
- * Input "exp" is the biased exponent, which may be negative.
- * the exponent field of "s" is ignored but is replaced by
- * "exp" as adjusted by normalization and rounding.
- *
- * Input "rcntrl" is the rounding control.
- */
- static int rlast = -1;
- static int rw = 0;
- static unsigned short rmsk = 0;
- static unsigned short rmbit = 0;
- static unsigned short rebit = 0;
- static int re = 0;
- static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0};
- void emdnorm( s, lost, subflg, exp, rcntrl )
- unsigned short s[];
- int lost;
- int subflg;
- long exp;
- int rcntrl;
- {
- int i, j;
- unsigned short r;
- /* Normalize */
- j = enormlz( s );
- /* a blank significand could mean either zero or infinity. */
- #ifndef INFINITY
- if( j > NBITS )
- {
- ecleazs( s );
- return;
- }
- #endif
- exp -= j;
- #ifndef INFINITY
- if( exp >= 32767L )
- goto overf;
- #else
- if( (j > NBITS) && (exp < 32767L) )
- {
- ecleazs( s );
- return;
- }
- #endif
- if( exp < 0L )
- {
- if( exp > (long )(-NBITS-1) )
- {
- j = (int )exp;
- i = eshift( s, j );
- if( i )
- lost = 1;
- }
- else
- {
- ecleazs( s );
- return;
- }
- }
- /* Round off, unless told not to by rcntrl. */
- if( rcntrl == 0 )
- goto mdfin;
- /* Set up rounding parameters if the control register changed. */
- if( rndprc != rlast )
- {
- ecleaz( rbit );
- switch( rndprc )
- {
- default:
- case NBITS:
- rw = NI-1; /* low guard word */
- rmsk = 0xffff;
- rmbit = 0x8000;
- rebit = 1;
- re = rw - 1;
- break;
- case 113:
- rw = 10;
- rmsk = 0x7fff;
- rmbit = 0x4000;
- rebit = 0x8000;
- re = rw;
- break;
- case 64:
- rw = 7;
- rmsk = 0xffff;
- rmbit = 0x8000;
- rebit = 1;
- re = rw-1;
- break;
- /* For DEC 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.
- * For rndprc = 64 or NBITS, there is no implied bit.
- * But Intel long double denormals lose one bit of significance even so.
- */
- #if IBMPC
- if( (exp <= 0) && (rndprc != NBITS) )
- #else
- if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
- #endif
- {
- lost |= s[NI-1] & 1;
- eshdn1(s);
- }
- /* Clear out all bits below the rounding bit,
- * remembering in r if any were nonzero.
- */
- r = s[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 IBMPC
- if( (exp <= 0) && (rndprc != NBITS) )
- #else
- if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
- #endif
- {
- eshup1(s);
- }
- if( s[2] != 0 )
- { /* overflow on roundoff */
- eshdn1(s);
- exp += 1;
- }
- mdfin:
- s[NI-1] = 0;
- if( exp >= 32767L )
- {
- #ifndef INFINITY
- overf:
- #endif
- #ifdef INFINITY
- s[1] = 32767;
- for( i=2; i<NI-1; i++ )
- s[i] = 0;
- #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 short )exp;
- }
- /*
- ; Subtract external format numbers.
- ;
- ; unsigned short a[NE], b[NE], c[NE];
- ; esub( a, b, c ); c = b - a
- */
- static int subflg = 0;
- void esub( a, b, c )
- unsigned short *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", DOMAIN );
- enan( c, NBITS );
- return;
- }
- #endif
- subflg = 1;
- eadd1( a, b, c );
- }
- /*
- ; Add.
- ;
- ; unsigned short a[NE], b[NE], c[NE];
- ; eadd( a, b, c ); c = b + a
- */
- void eadd( a, b, c )
- unsigned short *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( "eadd", DOMAIN );
- enan( c, NBITS );
- return;
- }
- #endif
- subflg = 0;
- eadd1( a, b, c );
- }
- void eadd1( a, b, c )
- unsigned short *a, *b, *c;
- {
- unsigned short ai[NI], bi[NI], ci[NI];
- int i, lost, j, k;
- long lt, lta, ltb;
- #ifdef INFINITY
- if( eisinf(a) )
- {
- emov(a,c);
- if( subflg )
- eneg(c);
- return;
- }
- if( eisinf(b) )
- {
- emov(b,c);
- return;
- }
- #endif
- emovi( a, ai );
- emovi( b, bi );
- if( subflg )
- ai[0] = ~ai[0];
- /* compare exponents */
- lta = ai[E];
- ltb = bi[E];
- lt = lta - ltb;
- if( lt > 0L )
- { /* put the larger number in bi */
- emovz( bi, ci );
- emovz( ai, bi );
- emovz( ci, ai );
- ltb = bi[E];
- lt = -lt;
- }
- lost = 0;
- if( lt != 0L )
- {
- if( lt < (long )(-NBITS-1) )
- goto done; /* answer same as larger addend */
- k = (int )lt;
- lost = eshift( ai, k ); /* shift the smaller number down */
- }
- else
- {
- /* exponents were the same, so must compare significands */
- i = ecmpm( ai, bi );
- if( i == 0 )
- { /* the numbers are identical in magnitude */
- /* if different signs, result is zero */
- if( ai[0] != bi[0] )
- {
- eclear(c);
- return;
- }
- /* if same sign, result is double */
- /* double denomalized tiny number */
- if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) )
- {
- eshup1( bi );
- goto done;
- }
- /* add 1 to exponent unless both are zero! */
- for( j=1; j<NI-1; j++ )
- {
- if( bi[j] != 0 )
- {
- /* This could overflow, but let emovo take care of that. */
- ltb += 1;
- break;
- }
- }
- bi[E] = (unsigned short )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 short a[NE], b[NE], c[NE];
- ; ediv( a, b, c ); c = b / a
- */
- void ediv( a, b, c )
- unsigned short *a, *b, *c;
- {
- unsigned short ai[NI], bi[NI];
- int i;
- long lt, lta, ltb;
- #ifdef NANS
- /* Return any NaN input. */
- if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
- if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
- /* Zero over zero, or infinity over infinity, is a NaN. */
- if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0))
- || (eisinf (a) && eisinf (b)) )
- {
- mtherr( "ediv", DOMAIN );
- enan( c, NBITS );
- return;
- }
- #endif
- /* Infinity over anything else is infinity. */
- #ifdef INFINITY
- if( eisinf(b) )
- {
- if( eisneg(a) ^ eisneg(b) )
- *(c+(NE-1)) = 0x8000;
- else
- *(c+(NE-1)) = 0;
- einfin(c);
- return;
- }
- if( eisinf(a) )
- {
- eclear(c);
- return;
- }
- #endif
- emovi( a, ai );
- emovi( b, bi );
- lta = ai[E];
- ltb = bi[E];
- if( bi[E] == 0 )
- { /* See if numerator is zero. */
- for( i=1; i<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;
- 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 short a[NE], b[NE], c[NE];
- ; emul( a, b, c ); c = b * a
- */
- void emul( a, b, c )
- unsigned short *a, *b, *c;
- {
- unsigned short ai[NI], bi[NI];
- int i, j;
- long 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", DOMAIN );
- enan( c, NBITS );
- 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 short x[N+2];
- ; e53toe( &d, x );
- */
- void e53toe( pe, y )
- unsigned short *pe, *y;
- {
- #ifdef DEC
- dectoe( pe, y ); /* see etodec.c */
- #else
- register unsigned short r;
- register unsigned short *p, *e;
- unsigned short yy[NI];
- int denorm, k;
- e = pe;
- denorm = 0; /* flag if denormalized number */
- ecleaz(yy);
- #ifdef IBMPC
- e += 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, NBITS );
- return;
- }
- #else
- if( ((pe[0] & 0xf) != 0) || (pe[1] != 0)
- || (pe[2] != 0) || (pe[3] != 0) )
- {
- enan( y, NBITS );
- return;
- }
- #endif
- #endif /* NANS */
- eclear( y );
- einfin( y );
- if( yy[0] )
- eneg(y);
- return;
- }
- #endif
- 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
- (void )eshift( yy, -5 );
- if( denorm )
- { /* if zero exponent, then normalize the significand */
- if( (k = enormlz(yy)) > NBITS )
- ecleazs(yy);
- else
- yy[E] -= (unsigned short )(k-1);
- }
- emovo( yy, y );
- #endif /* not DEC */
- }
- void e64toe( pe, y )
- unsigned short *pe, *y;
- {
- unsigned short yy[NI];
- unsigned short *p, *q, *e;
- 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
- #ifdef DEC
- 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
- #ifdef IBMPC
- /* For Intel long double, shift denormal significand up 1
- -- but only if the top significand bit is zero. */
- if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
- {
- unsigned short temp[NI+1];
- emovi(yy, temp);
- eshup1(temp);
- emovo(temp,y);
- return;
- }
- #endif
- #ifdef INFINITY
- /* Point to the exponent field. */
- p = &yy[NE-1];
- if( *p == 0x7fff )
- {
- #ifdef NANS
- #ifdef IBMPC
- for( i=0; i<4; i++ )
- {
- if((i != 3 && pe[i] != 0)
- /* Check for Intel long double infinity pattern. */
- || (i == 3 && pe[i] != 0x8000))
- {
- enan( y, NBITS );
- return;
- }
- }
- #else
- for( i=1; i<=4; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
- #endif
- #endif /* NANS */
- eclear( y );
- einfin( y );
- if( *p & 0x8000 )
- eneg(y);
- return;
- }
- #endif
- p = yy;
- q = y;
- for( i=0; i<NE; i++ )
- *q++ = *p++;
- }
- void e113toe(pe,y)
- unsigned short *pe, *y;
- {
- register unsigned short r;
- unsigned short *e, *p;
- unsigned short yy[NI];
- int denorm, i;
- e = pe;
- denorm = 0;
- ecleaz(yy);
- #ifdef IBMPC
- e += 7;
- #endif
- r = *e;
- yy[0] = 0;
- if( r & 0x8000 )
- yy[0] = 0xffff;
- r &= 0x7fff;
- #ifdef INFINITY
- if( r == 0x7fff )
- {
- #ifdef NANS
- #ifdef IBMPC
- for( i=0; i<7; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
- #else
- for( i=1; i<8; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
- #endif
- #endif /* NANS */
- eclear( y );
- einfin( y );
- if( *e & 0x8000 )
- eneg(y);
- return;
- }
- #endif /* INFINITY */
- yy[E] = r;
- p = &yy[M + 1];
- #ifdef IBMPC
- for( i=0; i<7; i++ )
- *p++ = *(--e);
- #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 short x[N+2];
- ; dtox( &d, x );
- */
- void e24toe( pe, y )
- unsigned short *pe, *y;
- {
- register unsigned short r;
- register unsigned short *p, *e;
- unsigned short yy[NI];
- int denorm, k;
- e = pe;
- denorm = 0; /* flag if denormalized number */
- ecleaz(yy);
- #ifdef IBMPC
- e += 1;
- #endif
- #ifdef DEC
- e += 1;
- #endif
- r = *e;
- yy[0] = 0;
- if( r & 0x8000 )
- yy[0] = 0xffff;
- yy[M] = (r & 0x7f) | 0200;
- r &= ~0x807f; /* strip sign and 7 significand bits */
- #ifdef INFINITY
- if( r == 0x7f80 )
- {
- #ifdef NANS
- #ifdef MIEEE
- if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) )
- {
- enan( y, NBITS );
- return;
- }
- #else
- if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) )
- {
- enan( y, NBITS );
- return;
- }
- #endif
- #endif /* NANS */
- eclear( y );
- einfin( y );
- if( yy[0] )
- eneg(y);
- return;
- }
- #endif
- r >>= 7;
- /* If zero exponent, then the significand is denormalized.
- * So, take back the understood high significand bit. */
- if( r == 0 )
- {
- denorm = 1;
- yy[M] &= ~0200;
- }
- r += EXONE - 0177;
- yy[E] = r;
- p = &yy[M+1];
- #ifdef IBMPC
- *p++ = *(--e);
- #endif
- #ifdef DEC
- *p++ = *(--e);
- #endif
- #ifdef MIEEE
- ++e;
- *p++ = *e++;
- #endif
- (void )eshift( yy, -8 );
- if( denorm )
- { /* if zero exponent, then normalize the significand */
- if( (k = enormlz(yy)) > NBITS )
- ecleazs(yy);
- else
- yy[E] -= (unsigned short )(k-1);
- }
- emovo( yy, y );
- }
- void etoe113(x,e)
- unsigned short *x, *e;
- {
- unsigned short xi[NI];
- long exp;
- int rndsav;
- #ifdef NANS
- if( eisnan(x) )
- {
- enan( e, 113 );
- return;
- }
- #endif
- emovi( x, xi );
- exp = (long )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 short *a, *b;
- {
- register unsigned short *p, *q;
- unsigned short i;
- #ifdef NANS
- if( eiisnan(a) )
- {
- enan( b, 113 );
- return;
- }
- #endif
- p = a;
- #ifdef MIEEE
- q = b;
- #else
- q = b + 7; /* point to output exponent */
- #endif
- /* If not denormal, delete the implied bit. */
- if( a[E] != 0 )
- {
- eshup1 (a);
- }
- /* combine sign and exponent */
- i = *p++;
- #ifdef MIEEE
- if( i )
- *q++ = *p++ | 0x8000;
- else
- *q++ = *p++;
- #else
- if( i )
- *q-- = *p++ | 0x8000;
- else
- *q-- = *p++;
- #endif
- /* skip over guard word */
- ++p;
- /* move the significand */
- #ifdef MIEEE
- for (i = 0; i < 7; i++)
- *q++ = *p++;
- #else
- for (i = 0; i < 7; i++)
- *q-- = *p++;
- #endif
- }
- void etoe64( x, e )
- unsigned short *x, *e;
- {
- unsigned short xi[NI];
- long exp;
- int rndsav;
- #ifdef NANS
- if( eisnan(x) )
- {
- enan( e, 64 );
- return;
- }
- #endif
- emovi( x, xi );
- exp = (long )xi[E]; /* adjust exponent for offset */
- #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 short *a, *b;
- {
- register unsigned short *p, *q;
- unsigned short i;
- #ifdef NANS
- if( eiisnan(a) )
- {
- enan( b, 64 );
- return;
- }
- #endif
- #ifdef IBMPC
- /* Shift Intel denormal significand down 1. */
- if( a[E] == 0 )
- eshdn1(a);
- #endif
- p = a;
- #ifdef MIEEE
- q = b;
- #else
- q = b + 4; /* point to output exponent */
- #if 1
- /* NOTE: if data type is 96 bits wide, clear the last word here. */
- *(q+1)= 0;
- #endif
- #endif
- /* combine sign and exponent */
- i = *p++;
- #ifdef MIEEE
- 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 */
- #ifdef MIEEE
- for( i=0; i<4; i++ )
- *q++ = *p++;
- #else
- #ifdef INFINITY
- if (eiisinf (a))
- {
- /* Intel long double infinity. */
- *q-- = 0x8000;
- *q-- = 0;
- *q-- = 0;
- *q = 0;
- return;
- }
- #endif
- for( i=0; i<4; i++ )
- *q-- = *p++;
- #endif
- }
- /*
- ; e type to IEEE double precision
- ; double d;
- ; unsigned short x[NE];
- ; etoe53( x, &d );
- */
- #ifdef DEC
- void etoe53( x, e )
- unsigned short *x, *e;
- {
- etodec( x, e ); /* see etodec.c */
- }
- static void toe53( x, y )
- unsigned short *x, *y;
- {
- todec( x, y );
- }
- #else
- void etoe53( x, e )
- unsigned short *x, *e;
- {
- unsigned short xi[NI];
- long exp;
- int rndsav;
- #ifdef NANS
- if( eisnan(x) )
- {
- enan( e, 53 );
- return;
- }
- #endif
- emovi( x, xi );
- exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */
- #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 short *x, *y;
- {
- unsigned short i;
- unsigned short *p;
- #ifdef NANS
- if( eiisnan(x) )
- {
- enan( y, 53 );
- return;
- }
- #endif
- p = &x[0];
- #ifdef IBMPC
- y += 3;
- #endif
- *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 short )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 )
- {
- (void )eshift( x, 4 );
- }
- else
- {
- i <<= 4;
- (void )eshift( x, 5 );
- }
- i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */
- *y |= (unsigned short )i; /* high order output already has sign bit set */
- #ifdef IBMPC
- *(--y) = *p++;
- *(--y) = *p++;
- *(--y) = *p;
- #endif
- #ifdef MIEEE
- ++y;
- *y++ = *p++;
- *y++ = *p++;
- *y++ = *p++;
- #endif
- }
- #endif /* not DEC */
- /*
- ; e type to IEEE single precision
- ; float d;
- ; unsigned short x[N+2];
- ; xtod( x, &d );
- */
- void etoe24( x, e )
- unsigned short *x, *e;
- {
- long exp;
- unsigned short xi[NI];
- int rndsav;
- #ifdef NANS
- if( eisnan(x) )
- {
- enan( e, 24 );
- return;
- }
- #endif
- emovi( x, xi );
- exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */
- #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 short *x, *y;
- {
- unsigned short i;
- unsigned short *p;
- #ifdef NANS
- if( eiisnan(x) )
- {
- enan( y, 24 );
- return;
- }
- #endif
- p = &x[0];
- #ifdef IBMPC
- y += 1;
- #endif
- #ifdef DEC
- y += 1;
- #endif
- *y = 0; /* output high order */
- if( *p++ )
- *y = 0x8000; /* output sign bit */
- i = *p++;
- if( i >= 255 )
- { /* Saturate at largest number less than infinity. */
- #ifdef INFINITY
- *y |= (unsigned short )0x7f80;
- #ifdef IBMPC
- *(--y) = 0;
- #endif
- #ifdef DEC
- *(--y) = 0;
- #endif
- #ifdef MIEEE
- ++y;
- *y = 0;
- #endif
- #else
- *y |= (unsigned short )0x7f7f;
- #ifdef IBMPC
- *(--y) = 0xffff;
- #endif
- #ifdef DEC
- *(--y) = 0xffff;
- #endif
- #ifdef MIEEE
- ++y;
- *y = 0xffff;
- #endif
- #endif
- return;
- }
- if( i == 0 )
- {
- (void )eshift( x, 7 );
- }
- else
- {
- i <<= 7;
- (void )eshift( x, 8 );
- }
- i |= *p++ & (unsigned short )0x7f; /* *p = xi[M] */
- *y |= i; /* high order output already has sign bit set */
- #ifdef IBMPC
- *(--y) = *p;
- #endif
- #ifdef DEC
- *(--y) = *p;
- #endif
- #ifdef MIEEE
- ++y;
- *y = *p;
- #endif
- }
- /* Compare two e type numbers.
- *
- * unsigned short a[NE], b[NE];
- * ecmp( a, b );
- *
- * returns +1 if a > b
- * 0 if a == b
- * -1 if a < b
- * -2 if either a or b is a NaN.
- */
- int ecmp( a, b )
- unsigned short *a, *b;
- {
- unsigned short ai[NI], bi[NI];
- register unsigned short *p, *q;
- register int i;
- int msign;
- #ifdef NANS
- if (eisnan (a) || eisnan (b))
- return( -2 );
- #endif
- emovi( a, ai );
- p = ai;
- emovi( b, bi );
- q = bi;
- if( *p != *q )
- { /* the signs are different */
- /* -0 equals + 0 */
- for( i=1; i<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 short x[NE], y[NE]
- * eround( x, y );
- */
- void eround( x, y )
- unsigned short *x, *y;
- {
- eadd( ehalf, x, y );
- efloor( y, y );
- }
- /*
- ; convert long (32-bit) integer to e type
- ;
- ; long l;
- ; unsigned short x[NE];
- ; ltoe( &l, x );
- ; note &l is the memory address of l
- */
- void ltoe( lp, y )
- long *lp; /* lp is the memory address of a long integer */
- unsigned short *y; /* y is the address of a short */
- {
- unsigned short yi[NI];
- unsigned long ll;
- int k;
- ecleaz( yi );
- if( *lp < 0 )
- {
- ll = (unsigned long )( -(*lp) ); /* make it positive */
- yi[0] = 0xffff; /* put correct sign in the e type number */
- }
- else
- {
- ll = (unsigned long )( *lp );
- }
- /* move the long integer to yi significand area */
- if( sizeof(long) == 8 )
- {
- yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
- yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
- yi[M + 2] = (unsigned short) (ll >> 16);
- yi[M + 3] = (unsigned short) ll;
- yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
- }
- else
- {
- yi[M] = (unsigned short )(ll >> 16);
- yi[M+1] = (unsigned short )ll;
- yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
- }
- if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
- ecleaz( yi ); /* it was zero */
- else
- yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
- emovo( yi, y ); /* output the answer */
- }
- /*
- ; convert unsigned long (32-bit) integer to e type
- ;
- ; unsigned long l;
- ; unsigned short x[NE];
- ; ltox( &l, x );
- ; note &l is the memory address of l
- */
- void ultoe( lp, y )
- unsigned long *lp; /* lp is the memory address of a long integer */
- unsigned short *y; /* y is the address of a short */
- {
- unsigned short yi[NI];
- unsigned long ll;
- int k;
- ecleaz( yi );
- ll = *lp;
- /* move the long integer to ayi significand area */
- if( sizeof(long) == 8 )
- {
- yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
- yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
- yi[M + 2] = (unsigned short) (ll >> 16);
- yi[M + 3] = (unsigned short) ll;
- yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
- }
- else
- {
- yi[M] = (unsigned short )(ll >> 16);
- yi[M+1] = (unsigned short )ll;
- yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
- }
- if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
- ecleaz( yi ); /* it was zero */
- else
- yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
- emovo( yi, y ); /* output the answer */
- }
- /*
- ; Find long integer and fractional parts
- ; long i;
- ; unsigned short 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 short *x;
- long *i;
- unsigned short *frac;
- {
- unsigned short xi[NI];
- int j, k;
- unsigned long 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 > (8 * sizeof(long) - 1) )
- {
- /*
- ; long integer overflow: output large integer
- ; and correct fraction
- */
- j = 8 * sizeof(long) - 1;
- if( xi[0] )
- *i = (long) ((unsigned long) 1) << j;
- else
- *i = (long) (((unsigned long) (~(0L))) >> 1);
- (void )eshift( xi, k );
- }
- if( k > 16 )
- {
- /*
- Shift more than 16 bits: shift up k-16 mod 16
- then shift 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 = (long )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 short )k;
- emovo( xi, frac );
- }
- /*
- ; Find unsigned long integer and fractional parts
- ; unsigned long i;
- ; unsigned short x[NE], frac[NE];
- ; xifrac( x, &i, frac );
- A negative e type input yields integer output = 0
- but correct fraction.
- */
- void euifrac( x, i, frac )
- unsigned short *x;
- unsigned long *i;
- unsigned short *frac;
- {
- unsigned short xi[NI];
- int j, k;
- unsigned long ll;
- 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 > (8 * sizeof(long)) )
- {
- /*
- ; long integer overflow: output large integer
- ; and correct fraction
- */
- *i = ~(0L);
- (void )eshift( xi, k );
- }
- else if( k > 16 )
- {
- /*
- Shift more than 16 bits: 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 = (long )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 short )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 short *x;
- int sc;
- {
- unsigned short lost;
- unsigned short *p;
- if( sc == 0 )
- return( 0 );
- lost = 0;
- p = x + NI-1;
- if( sc < 0 )
- {
- sc = -sc;
- while( sc >= 16 )
- {
- lost |= *p; /* remember lost bits */
- eshdn6(x);
- sc -= 16;
- }
- while( sc >= 8 )
- {
- lost |= *p & 0xff;
- eshdn8(x);
- sc -= 8;
- }
- while( sc > 0 )
- {
- lost |= *p & 1;
- eshdn1(x);
- sc -= 1;
- }
- }
- else
- {
- while( sc >= 16 )
- {
- eshup6(x);
- sc -= 16;
- }
- while( sc >= 8 )
- {
- eshup8(x);
- sc -= 8;
- }
- while( sc > 0 )
- {
- eshup1(x);
- sc -= 1;
- }
- }
- if( lost )
- lost = 1;
- return( (int )lost );
- }
- /*
- ; normalize
- ;
- ; Shift normalizes the significand area pointed to by argument
- ; shift count (up = positive) is returned.
- */
- int enormlz(x)
- unsigned short x[];
- {
- register unsigned short *p;
- int sc;
- sc = 0;
- p = &x[M];
- if( *p != 0 )
- goto normdn;
- ++p;
- if( *p & 0x8000 )
- return( 0 ); /* already normalized */
- while( *p == 0 )
- {
- eshup6(x);
- sc += 16;
- /* With guard word, there are NBITS+16 bits available.
- * return true if all are zero.
- */
- if( sc > NBITS )
- return( sc );
- }
- /* see if high byte is zero */
- while( (*p & 0xff00) == 0 )
- {
- eshup8(x);
- sc += 8;
- }
- /* now shift 1 bit at a time */
- while( (*p & 0x8000) == 0)
- {
- eshup1(x);
- sc += 1;
- if( sc > (NBITS+16) )
- {
- mtherr( "enormlz", UNDERFLOW );
- return( sc );
- }
- }
- return( sc );
- /* Normalize by shifting down out of the high guard word
- of the significand */
- normdn:
- if( *p & 0xff00 )
- {
- eshdn8(x);
- sc -= 8;
- }
- while( *p != 0 )
- {
- eshdn1(x);
- sc -= 1;
- if( sc < -NBITS )
- {
- mtherr( "enormlz", OVERFLOW );
- return( sc );
- }
- }
- return( sc );
- }
- /* Convert e type number to decimal format ASCII string.
- * The constants are for 64 bit precision.
- */
- #define NTEN 12
- #define MAXP 4096
- #if NE == 10
- static unsigned short etens[NTEN + 1][NE] =
- {
- {0x6576, 0x4a92, 0x804a, 0x153f,
- 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
- {0x6a32, 0xce52, 0x329a, 0x28ce,
- 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
- {0x526c, 0x50ce, 0xf18b, 0x3d28,
- 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
- {0x9c66, 0x58f8, 0xbc50, 0x5c54,
- 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
- {0x851e, 0xeab7, 0x98fe, 0x901b,
- 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
- {0x0235, 0x0137, 0x36b1, 0x336c,
- 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
- {0x50f8, 0x25fb, 0xc76b, 0x6b71,
- 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
- };
- static unsigned short emtens[NTEN + 1][NE] =
- {
- {0x2030, 0xcffc, 0xa1c3, 0x8123,
- 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */
- {0x8264, 0xd2cb, 0xf2ea, 0x12d4,
- 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */
- {0xf53f, 0xf698, 0x6bd3, 0x0158,
- 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
- {0xe731, 0x04d4, 0xe3f2, 0xd332,
- 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
- {0xa23e, 0x5308, 0xfefb, 0x1155,
- 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
- {0xe26d, 0xdbde, 0xd05d, 0xb3f6,
- 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
- {0x2a20, 0x6224, 0x47b3, 0x98d7,
- 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
- {0x0b5b, 0x4af2, 0xa581, 0x18ed,
- 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
- {0xbf71, 0xa9b3, 0x7989, 0xbe68,
- 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
- {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
- 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
- {0xc155, 0xa4a8, 0x404e, 0x6113,
- 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
- {0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
- 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
- {0xcccd, 0xcccc, 0xcccc, 0xcccc,
- 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */
- };
- #else
- static unsigned short etens[NTEN+1][NE] = {
- {0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
- {0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
- {0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
- {0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
- {0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
- {0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
- {0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
- {0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
- {0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
- {0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
- {0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
- {0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
- {0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
- };
- static unsigned short emtens[NTEN+1][NE] = {
- {0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */
- {0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */
- {0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,},
- {0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,},
- {0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,},
- {0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,},
- {0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,},
- {0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,},
- {0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,},
- {0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,},
- {0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,},
- {0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,},
- {0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */
- };
- #endif
- void e24toasc( x, string, ndigs )
- unsigned short x[];
- char *string;
- int ndigs;
- {
- unsigned short w[NI];
- e24toe( x, w );
- etoasc( w, string, ndigs );
- }
- void e53toasc( x, string, ndigs )
- unsigned short x[];
- char *string;
- int ndigs;
- {
- unsigned short w[NI];
- e53toe( x, w );
- etoasc( w, string, ndigs );
- }
- void e64toasc( x, string, ndigs )
- unsigned short x[];
- char *string;
- int ndigs;
- {
- unsigned short w[NI];
- e64toe( x, w );
- etoasc( w, string, ndigs );
- }
- void e113toasc (x, string, ndigs)
- unsigned short x[];
- char *string;
- int ndigs;
- {
- unsigned short w[NI];
- e113toe (x, w);
- etoasc (w, string, ndigs);
- }
- void etoasc( x, string, ndigs )
- unsigned short x[];
- char *string;
- int ndigs;
- {
- long digit;
- unsigned short y[NI], t[NI], u[NI], w[NI];
- unsigned short *p, *r, *ten;
- unsigned short sign;
- int i, j, k, expon, rndsav;
- char *s, *ss;
- unsigned short m;
- rndsav = rndprc;
- #ifdef NANS
- if( eisnan(x) )
- {
- sprintf( string, " 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( string, " -Infinity " );
- else
- sprintf( string, " 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( string, "NaN" );
- goto bxit;
- }
- /* Compare to 1.0 */
- i = ecmp( eone, y );
- if( i == 0 )
- goto isone;
- 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];
- 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 = string;
- 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;
- }
- /*
- ; 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 short *y;
- {
- asctoeg( s, y, 24 );
- }
- /* ASCII to double */
- void asctoe53( s, y )
- char *s;
- unsigned short *y;
- {
- #ifdef DEC
- asctoeg( s, y, 56 );
- #else
- asctoeg( s, y, 53 );
- #endif
- }
- /* ASCII to long double */
- void asctoe64( s, y )
- char *s;
- unsigned short *y;
- {
- asctoeg( s, y, 64 );
- }
- /* ASCII to 128-bit long double */
- void asctoe113 (s, y)
- char *s;
- unsigned short *y;
- {
- asctoeg( s, y, 113 );
- }
- /* ASCII to super double */
- void asctoe( s, y )
- char *s;
- unsigned short *y;
- {
- asctoeg( s, y, NBITS );
- }
- /* Space to make a copy of the input string: */
- static char lstr[82] = {0};
- void asctoeg( ss, y, oprec )
- char *ss;
- unsigned short *y;
- int oprec;
- {
- unsigned short yy[NI], xt[NI], tt[NI];
- int esign, decflg, sgnflg, nexp, exp, prec, lost;
- int k, trail, c, rndsav;
- long lexp;
- unsigned short nsign, *p;
- char *sp, *s;
- /* Copy the input string. */
- s = ss;
- while( *s == ' ' ) /* skip leading spaces */
- ++s;
- sp = lstr;
- for( k=0; k<79; k++ )
- {
- if( (*sp++ = *s++) == '\0' )
- break;
- }
- *sp = '\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 short )k;
- eaddm( xt, yy );
- }
- else
- {
- /* Mark any lost non-zero digit. */
- lost |= k;
- /* Count lost digits before the decimal point. */
- if (decflg == 0)
- nexp -= 1;
- }
- prec += 1;
- goto donchr;
- }
- switch( *s )
- {
- case 'z':
- break;
- case 'E':
- case 'e':
- goto expnt;
- case '.': /* decimal point */
- if( decflg )
- goto error;
- ++decflg;
- break;
- case '-':
- nsign = 0xffff;
- if( sgnflg )
- goto error;
- ++sgnflg;
- break;
- case '+':
- if( sgnflg )
- goto error;
- ++sgnflg;
- break;
- case ',':
- case ' ':
- case '\0':
- case '\n':
- case '\r':
- goto daldone;
- case 'i':
- case 'I':
- goto infinite;
- default:
- error:
- #ifdef NANS
- enan( yy, NI*16 );
- #else
- mtherr( "asctoe", DOMAIN );
- ecleaz(yy);
- #endif
- goto aexit;
- }
- donchr:
- ++s;
- goto nxtcom;
- /* Exponent interpretation */
- expnt:
- esign = 1;
- exp = 0;
- ++s;
- /* check for + or - */
- if( *s == '-' )
- {
- esign = -1;
- ++s;
- }
- if( *s == '+' )
- ++s;
- while( (*s >= '0') && (*s <= '9') )
- {
- exp *= 10;
- exp += *s++ - '0';
- if (exp > 4977)
- {
- if (esign < 0)
- goto zero;
- else
- goto infinite;
- }
- }
- if( esign < 0 )
- exp = -exp;
- if( exp > 4932 )
- {
- infinite:
- ecleaz(yy);
- yy[E] = 0x7fff; /* infinity */
- goto aexit;
- }
- if( exp < -4977 )
- {
- zero:
- ecleaz(yy);
- goto aexit;
- }
- daldone:
- nexp = exp - nexp;
- /* Pad trailing zeros to minimize power of 10, per IEEE spec. */
- while( (nexp > 0) && (yy[2] == 0) )
- {
- emovz( yy, xt );
- eshup1( xt );
- eshup1( xt );
- eaddm( yy, xt );
- eshup1( xt );
- if( xt[2] != 0 )
- break;
- nexp -= 1;
- emovz( xt, yy );
- }
- if( (k = enormlz(yy)) > NBITS )
- {
- ecleaz(yy);
- goto aexit;
- }
- lexp = (EXONE - 1 + NBITS) - k;
- emdnorm( yy, lost, 0, lexp, 64 );
- /* 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;
- else if( oprec == 24 )
- lexp -= EXONE - 0177;
- #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
- 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 short x[NE], y[NE]
- *
- * efloor( x, y );
- */
- static unsigned short bmask[] = {
- 0xffff,
- 0xfffe,
- 0xfffc,
- 0xfff8,
- 0xfff0,
- 0xffe0,
- 0xffc0,
- 0xff80,
- 0xff00,
- 0xfe00,
- 0xfc00,
- 0xf800,
- 0xf000,
- 0xe000,
- 0xc000,
- 0x8000,
- 0x0000,
- };
- void efloor( x, y )
- unsigned short x[], y[];
- {
- register unsigned short *p;
- int e, expon, i;
- unsigned short f[NE];
- emov( x, f ); /* leave in external format */
- expon = (int )f[NE-1];
- e = (expon & 0x7fff) - (EXONE - 1);
- if( e <= 0 )
- {
- eclear(y);
- goto isitneg;
- }
- /* number of bits to clear out */
- e = NBITS - e;
- emov( f, y );
- if( e <= 0 )
- return;
- p = &y[0];
- while( e >= 16 )
- {
- *p++ = 0;
- e -= 16;
- }
- /* clear the remaining bits */
- *p &= bmask[e];
- /* truncate negatives toward minus infinity */
- isitneg:
- if( (unsigned short )expon & (unsigned short )0x8000 )
- {
- for( i=0; i<NE-1; i++ )
- {
- if( f[i] != y[i] )
- {
- esub( eone, y, y );
- break;
- }
- }
- }
- }
- /* unsigned short x[], s[];
- * long *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 short x[];
- long *exp;
- unsigned short s[];
- {
- unsigned short xi[NI];
- long li;
- emovi( x, xi );
- li = (long )((short )xi[1]);
- if( li == 0 )
- {
- li -= enormlz( xi );
- }
- xi[1] = 0x3ffe;
- emovo( xi, s );
- *exp = li - 0x3ffe;
- }
- /* unsigned short x[], y[];
- * long pwr2;
- *
- * eldexp( x, pwr2, y );
- *
- * Returns y = x * 2**pwr2.
- */
- void eldexp( x, pwr2, y )
- unsigned short x[];
- long pwr2;
- unsigned short y[];
- {
- unsigned short xi[NI];
- long 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 short a[], b[], c[];
- {
- unsigned short den[NI], num[NI];
- #ifdef NANS
- if( eisinf(b) || (ecmp(a,ezero) == 0) || eisnan(a) || eisnan(b))
- {
- enan( c, NBITS );
- 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 short den[], num[];
- {
- long ld, ln;
- unsigned short 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 );
- }
- /* NaN bit patterns
- */
- #ifdef MIEEE
- unsigned short nan113[8] = {
- 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
- unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
- unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff};
- unsigned short nan24[2] = {0x7fff, 0xffff};
- #endif
- #ifdef IBMPC
- unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff};
- unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0};
- unsigned short nan53[4] = {0, 0, 0, 0xfff8};
- unsigned short nan24[2] = {0, 0xffc0};
- #endif
- void enan (nan, size)
- unsigned short *nan;
- int size;
- {
- int i, n;
- unsigned short *p;
- switch( size )
- {
- #ifndef DEC
- case 113:
- n = 8;
- p = nan113;
- break;
- case 64:
- n = 6;
- p = nan64;
- break;
- case 53:
- n = 4;
- p = nan53;
- break;
- case 24:
- n = 2;
- p = nan24;
- break;
- case NBITS:
- for( i=0; i<NE-2; i++ )
- *nan++ = 0;
- *nan++ = 0xc000;
- *nan++ = 0x7fff;
- return;
- case NI*16:
- *nan++ = 0;
- *nan++ = 0x7fff;
- *nan++ = 0;
- *nan++ = 0xc000;
- for( i=4; i<NI; i++ )
- *nan++ = 0;
- return;
- #endif
- default:
- mtherr( "enan", DOMAIN );
- return;
- }
- for (i=0; i < n; i++)
- *nan++ = *p++;
- }
- /* Longhand square root. */
- static int esqinited = 0;
- static unsigned short sqrndbit[NI];
- void esqrt( x, y )
- short *x, *y;
- {
- unsigned short temp[NI], num[NI], sq[NI], xx[NI];
- int i, j, k, n, nlups;
- long m, exp;
- 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, NBITS);
- 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 = (long )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 );
- }
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