Subversion Repositories planix.SVN

#include <u.h>

#include <libc.h>

#include "fmtdef.h"

static ulong

umuldiv(ulong a, ulong b, ulong c)

{

	double d;

	d = ((double)a * (double)b) / (double)c;

	if(d >= 4294967295.)

		d = 4294967295.;

	return (ulong)d;

}

/*

 * This routine will convert to arbitrary precision

 * floating point entirely in multi-precision fixed.

 * The answer is the closest floating point number to

 * the given decimal number. Exactly half way are

 * rounded ala ieee rules.

 * Method is to scale input decimal between .500 and .999...

 * with external power of 2, then binary search for the

 * closest mantissa to this decimal number.

 * Nmant is is the required precision. (53 for ieee dp)

 * Nbits is the max number of bits/word. (must be <= 28)

 * Prec is calculated - the number of words of fixed mantissa.

 */

enum

{

	Nbits	= 28,				/* bits safely represented in a ulong */

	Nmant	= 53,				/* bits of precision required */

	Prec	= (Nmant+Nbits+1)/Nbits,	/* words of Nbits each to represent mantissa */

	Sigbit	= 1<<(Prec*Nbits-Nmant),	/* first significant bit of Prec-th word */

	Ndig	= 1500,

	One	= (ulong)(1<<Nbits),

	Half	= (ulong)(One>>1),

	Maxe	= 310,

	Fsign	= 1<<0,		/* found - */

	Fesign	= 1<<1,		/* found e- */

	Fdpoint	= 1<<2,		/* found . */

	S0	= 0,		/* _		_S0	+S1	#S2	.S3 */

	S1,			/* _+		#S2	.S3 */

	S2,			/* _+#		#S2	.S4	eS5 */

	S3,			/* _+.		#S4 */

	S4,			/* _+#.#	#S4	eS5 */

	S5,			/* _+#.#e	+S6	#S7 */

	S6,			/* _+#.#e+	#S7 */

	S7,			/* _+#.#e+#	#S7 */

};

static	int	xcmp(char*, char*);

static	int	fpcmp(char*, ulong*);

static	void	frnorm(ulong*);

static	void	divascii(char*, int*, int*, int*);

static	void	mulascii(char*, int*, int*, int*);

typedef	struct	Tab	Tab;

struct	Tab

{

	int	bp;

	int	siz;

	char*	cmp;

};

#ifndef ERANGE

#define ERANGE 12345

#endif

double

fmtstrtod(const char *as, char **aas)

{

	int na, ex, dp, bp, c, i, flag, state;

	ulong low[Prec], hig[Prec], mid[Prec];

	double d;

	char *s, a[Ndig];

	flag = 0;	/* Fsign, Fesign, Fdpoint */

	na = 0;		/* number of digits of a[] */

	dp = 0;		/* na of decimal point */

	ex = 0;		/* exonent */

	state = S0;

	for(s=(char*)as;; s++) {

		c = *s;

		if(c >= '0' && c <= '9') {

			switch(state) {

			case S0:

			case S1:

			case S2:

				state = S2;

				break;

			case S3:

			case S4:

				state = S4;

				break;

			case S5:

			case S6:

			case S7:

				state = S7;

				ex = ex*10 + (c-'0');

				continue;

			}

			if(na == 0 && c == '0') {

				dp--;

				continue;

			}

			if(na < Ndig-50)

				a[na++] = c;

			continue;

		}

		switch(c) {

		case '\t':

		case '\n':

		case '\v':

		case '\f':

		case '\r':

		case ' ':

			if(state == S0)

				continue;

			break;

		case '-':

			if(state == S0)

				flag |= Fsign;

			else

				flag |= Fesign;

		case '+':

			if(state == S0)

				state = S1;

			else

			if(state == S5)

				state = S6;

			else

				break;	/* syntax */

			continue;

		case '.':

			flag |= Fdpoint;

			dp = na;

			if(state == S0 || state == S1) {

				state = S3;

				continue;

			}

			if(state == S2) {

				state = S4;

				continue;

			}

			break;

		case 'e':

		case 'E':

			if(state == S2 || state == S4) {

				state = S5;

				continue;

			}

			break;

		}

		break;

	}

	/*

	 * clean up return char-pointer

	 */

	switch(state) {

	case S0:

		if(xcmp(s, "nan") == 0) {

			if(aas != nil)

				*aas = s+3;

			goto retnan;

		}

	case S1:

		if(xcmp(s, "infinity") == 0) {

			if(aas != nil)

				*aas = s+8;

			goto retinf;

		}

		if(xcmp(s, "inf") == 0) {

			if(aas != nil)

				*aas = s+3;

			goto retinf;

		}

	case S3:

		if(aas != nil)

			*aas = (char*)as;

		goto ret0;	/* no digits found */

	case S6:

		s--;		/* back over +- */

	case S5:

		s--;		/* back over e */

		break;

	}

	if(aas != nil)

		*aas = s;

	if(flag & Fdpoint)

	while(na > 0 && a[na-1] == '0')

		na--;

	if(na == 0)

		goto ret0;	/* zero */

	a[na] = 0;

	if(!(flag & Fdpoint))

		dp = na;

	if(flag & Fesign)

		ex = -ex;

	dp += ex;

	if(dp < -Maxe){

		errno = ERANGE;

		goto ret0;	/* underflow by exp */

	} else

	if(dp > +Maxe)

		goto retinf;	/* overflow by exp */

	/*

	 * normalize the decimal ascii number

	 * to range .[5-9][0-9]* e0

	 */

	bp = 0;		/* binary exponent */

	while(dp > 0)

		divascii(a, &na, &dp, &bp);

	while(dp < 0 || a[0] < '5')

		mulascii(a, &na, &dp, &bp);

	/* close approx by naive conversion */

	mid[0] = 0;

	mid[1] = 1;

	for(i=0; (c=a[i]); i++) {

		mid[0] = mid[0]*10 + (c-'0');

		mid[1] = mid[1]*10;

		if(i >= 8)

			break;

	}

	low[0] = umuldiv(mid[0], One, mid[1]);

	hig[0] = umuldiv(mid[0]+1, One, mid[1]);

	for(i=1; i<Prec; i++) {

		low[i] = 0;

		hig[i] = One-1;

	}

	/* binary search for closest mantissa */

	for(;;) {

		/* mid = (hig + low) / 2 */

		c = 0;

		for(i=0; i<Prec; i++) {

			mid[i] = hig[i] + low[i];

			if(c)

				mid[i] += One;

			c = mid[i] & 1;

			mid[i] >>= 1;

		}

		frnorm(mid);

		/* compare */

		c = fpcmp(a, mid);

		if(c > 0) {

			c = 1;

			for(i=0; i<Prec; i++)

				if(low[i] != mid[i]) {

					c = 0;

					low[i] = mid[i];

				}

			if(c)

				break;	/* between mid and hig */

			continue;

		}

		if(c < 0) {

			for(i=0; i<Prec; i++)

				hig[i] = mid[i];

			continue;

		}

		/* only hard part is if even/odd roundings wants to go up */

		c = mid[Prec-1] & (Sigbit-1);

		if(c == Sigbit/2 && (mid[Prec-1]&Sigbit) == 0)

			mid[Prec-1] -= c;

		break;	/* exactly mid */

	}

	/* normal rounding applies */

	c = mid[Prec-1] & (Sigbit-1);

	mid[Prec-1] -= c;

	if(c >= Sigbit/2) {

		mid[Prec-1] += Sigbit;

		frnorm(mid);

	}

	goto out;

ret0:

	return 0;

retnan:

	return __NaN();

retinf:

	/*

	 * Unix strtod requires these.  Plan 9 would return Inf(0) or Inf(-1). */

	errno = ERANGE;

	if(flag & Fsign)

		return -HUGE_VAL;

	return HUGE_VAL;

out:

	d = 0;

	for(i=0; i<Prec; i++)

		d = d*One + mid[i];

	if(flag & Fsign)

		d = -d;

	d = ldexp(d, bp - Prec*Nbits);

	if(d == 0){	/* underflow */

		errno = ERANGE;

	}

	return d;

}

static void

frnorm(ulong *f)

{

	int i, c;

	c = 0;

	for(i=Prec-1; i>0; i--) {

		f[i] += c;

		c = f[i] >> Nbits;

		f[i] &= One-1;

	}

	f[0] += c;

}

static int

fpcmp(char *a, ulong* f)

{

	ulong tf[Prec];

	int i, d, c;

	for(i=0; i<Prec; i++)

		tf[i] = f[i];

	for(;;) {

		/* tf *= 10 */

		for(i=0; i<Prec; i++)

			tf[i] = tf[i]*10;

		frnorm(tf);

		d = (tf[0] >> Nbits) + '0';

		tf[0] &= One-1;

		/* compare next digit */

		c = *a;

		if(c == 0) {

			if('0' < d)

				return -1;

			if(tf[0] != 0)

				goto cont;

			for(i=1; i<Prec; i++)

				if(tf[i] != 0)

					goto cont;

			return 0;

		}

		if(c > d)

			return +1;

		if(c < d)

			return -1;

		a++;

	cont:;

	}

}

static void

divby(char *a, int *na, int b)

{

	int n, c;

	char *p;

	p = a;

	n = 0;

	while(n>>b == 0) {

		c = *a++;

		if(c == 0) {

			while(n) {

				c = n*10;

				if(c>>b)

					break;

				n = c;

			}

			goto xx;

		}

		n = n*10 + c-'0';

		(*na)--;

	}

	for(;;) {

		c = n>>b;

		n -= c<<b;

		*p++ = c + '0';

		c = *a++;

		if(c == 0)

			break;

		n = n*10 + c-'0';

	}

	(*na)++;

xx:

	while(n) {

		n = n*10;

		c = n>>b;

		n -= c<<b;

		*p++ = c + '0';

		(*na)++;

	}

	*p = 0;

}

static	Tab	tab1[] =

{

	 1,  0, "",

	 3,  1, "7",

	 6,  2, "63",

	 9,  3, "511",

	13,  4, "8191",

	16,  5, "65535",

	19,  6, "524287",

	23,  7, "8388607",

	26,  8, "67108863",

	27,  9, "134217727",

};

static void

divascii(char *a, int *na, int *dp, int *bp)

{

	int b, d;

	Tab *t;

	d = *dp;

	if(d >= (int)(nelem(tab1)))

		d = (int)(nelem(tab1))-1;

	t = tab1 + d;

	b = t->bp;

	if(memcmp(a, t->cmp, t->siz) > 0)

		d--;

	*dp -= d;

	*bp += b;

	divby(a, na, b);

}

static void

mulby(char *a, char *p, char *q, int b)

{

	int n, c;

	n = 0;

	*p = 0;

	for(;;) {

		q--;

		if(q < a)

			break;

		c = *q - '0';

		c = (c<<b) + n;

		n = c/10;

		c -= n*10;

		p--;

		*p = c + '0';

	}

	while(n) {

		c = n;

		n = c/10;

		c -= n*10;

		p--;

		*p = c + '0';

	}

}

static	Tab	tab2[] =

{

	 1,  1, "",				/* dp = 0-0 */

	 3,  3, "125",

	 6,  5, "15625",

	 9,  7, "1953125",

	13, 10, "1220703125",

	16, 12, "152587890625",

	19, 14, "19073486328125",

	23, 17, "11920928955078125",

	26, 19, "1490116119384765625",

	27, 19, "7450580596923828125",		/* dp 8-9 */

};

static void

mulascii(char *a, int *na, int *dp, int *bp)

{

	char *p;

	int d, b;

	Tab *t;

	d = -*dp;

	if(d >= (int)(nelem(tab2)))

		d = (int)(nelem(tab2))-1;

	t = tab2 + d;

	b = t->bp;

	if(memcmp(a, t->cmp, t->siz) < 0)

		d--;

	p = a + *na;

	*bp -= b;

	*dp += d;

	*na += d;

	mulby(a, p+d, p, b);

}

static int

xcmp(char *a, char *b)

{

	int c1, c2;

	while((c1 = *b++)) {

		c2 = *a++;

		if(isupper(c2))

			c2 = tolower(c2);

		if(c1 != c2)

			return 1;

	}

	return 0;

}