a

libc/strtod.c

@@ -0,0 +1,532 @@
+#include <u.h>
+#include <libc.h>
+#include <ctype.h>
+
+/*
+ * 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
+	Bias		= 1022,
+	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 ulong
+umuldiv(ulong a, ulong b, ulong c)
+{
+	double d;
+
+	d = ((double)a * (double)b) / (double)c;
+	if(d >= 4294967295.)
+		d = 4294967295.;
+	return d;
+}
+
+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*);
+static	void	divby(char*, int*, int);
+
+typedef	struct	Tab	Tab;
+struct	Tab
+{
+	int	bp;
+	int	siz;
+	char*	cmp;
+};
+
+double
+strtod(char *as, char **aas)
+{
+	int na, ona, ex, dp, bp, c, i, flag, state;
+	ulong low[Prec], hig[Prec], mid[Prec], num, den;
+	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=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 = 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-Nmant/3)	/* actually -Nmant*log(2)/log(10), but Nmant/3 close enough */
+		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);
+	a[na] = 0;
+
+	/*
+	 * very small numbers are represented using
+	 * bp = -Bias+1.  adjust accordingly.
+	 */
+	if(bp < -Bias+1){
+		ona = na;
+		divby(a, &na, -bp-Bias+1);
+		if(na < ona){
+			memmove(a+ona-na, a, na);
+			memset(a, '0', ona-na);
+			na = ona;
+		}
+		a[na] = 0;
+		bp = -Bias+1;
+	}
+
+	/* close approx by naive conversion */
+	num = 0;
+	den = 1;
+	for(i=0; i<9 && (c=a[i]); i++) {
+		num = num*10 + (c-'0');
+		den *= 10;
+	}
+	low[0] = umuldiv(num, One, den);
+	hig[0] = umuldiv(num+1, One, den);
+	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);
+	}
+	d = 0;
+	for(i=0; i<Prec; i++)
+		d = d*One + mid[i];
+	if(flag & Fsign)
+		d = -d;
+	d = ldexp(d, bp - Prec*Nbits);
+	return d;
+
+ret0:
+	return 0;
+
+retnan:
+	return __NaN();
+
+retinf:
+	if(flag & Fsign)
+		return __Inf(-1);
+	return __Inf(+1);
+}
+
+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:;
+	}
+	return 0;
+}
+
+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 void
+divby(char *a, int *na, int b)
+{
+	while(b > 9){
+		_divby(a, na, 9);
+		a[*na] = 0;
+		b -= 9;
+	}
+	if(b > 0)
+		_divby(a, na, b);
+}
+
+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 >= nelem(tab1))
+		d = 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 >= nelem(tab2))
+		d = 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;
+}