Import sources from 2011-03-30 iso image

1 files changed, 1293 insertions, 0 deletions

diff --git a/sys/src/libstdio/dtoa.c b/sys/src/libstdio/dtoa.c
new file mode 100755
index 000000000..26441ded7
--- /dev/null
+++ b/sys/src/libstdio/dtoa.c
@@ -0,0 +1,1293 @@
+/* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
+/* kudos to dmg@bell-labs.com, gripes to ehg@bell-labs.com */
+
+/* Let x be the exact mathematical number defined by a decimal
+ *	string s.  Then atof(s) is the round-nearest-even IEEE
+ *	floating point value.
+ * Let y be an IEEE floating point value and let s be the string
+ *	printed as %.17g.  Then atof(s) is exactly y.
+ */
+#include <u.h>
+#include <libc.h>
+
+static Lock _dtoalk[2];
+#define ACQUIRE_DTOA_LOCK(n)	lock(&_dtoalk[n])
+#define FREE_DTOA_LOCK(n)	unlock(&_dtoalk[n])
+#define PRIVATE_mem ((2000+sizeof(double)-1)/sizeof(double))
+static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
+#define FLT_ROUNDS	1
+#define DBL_DIG		15
+#define DBL_MAX_10_EXP	308
+#define DBL_MAX_EXP	1024
+#define FLT_RADIX	2
+#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+#define fpword0(x) ((FPdbleword*)&x)->hi
+#define fpword1(x) ((FPdbleword*)&x)->lo
+/* Ten_pmax = floor(P*log(2)/log(5)) */
+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
+/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
+/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
+
+#define Exp_shift  20
+#define Exp_shift1 20
+#define Exp_msk1    0x100000
+#define Exp_msk11   0x100000
+#define Exp_mask  0x7ff00000
+#define P 53
+#define Bias 1023
+#define Emin (-1022)
+#define Exp_1  0x3ff00000
+#define Exp_11 0x3ff00000
+#define Ebits 11
+#define Frac_mask  0xfffff
+#define Frac_mask1 0xfffff
+#define Ten_pmax 22
+#define Bletch 0x10
+#define Bndry_mask  0xfffff
+#define Bndry_mask1 0xfffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 1
+#define Tiny0 0
+#define Tiny1 1
+#define Quick_max 14
+#define Int_max 14
+#define Avoid_Underflow
+
+#define rounded_product(a,b) a *= b
+#define rounded_quotient(a,b) a /= b
+
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
+#define Big1 0xffffffff
+
+#define FFFFFFFF 0xffffffffUL
+
+#undef ULint
+
+#define Kmax 15
+
+struct
+Bigint {
+	struct Bigint *next;
+	int	k, maxwds, sign, wds;
+	unsigned int x[1];
+};
+
+typedef struct Bigint Bigint;
+
+static Bigint *freelist[Kmax+1];
+
+static Bigint *
+Balloc(int k)
+{
+	int	x;
+	Bigint * rv;
+	unsigned int	len;
+
+	ACQUIRE_DTOA_LOCK(0);
+	if (rv = freelist[k]) {
+		freelist[k] = rv->next;
+	} else {
+		x = 1 << k;
+		len = (sizeof(Bigint) + (x - 1) * sizeof(unsigned int) + sizeof(double) -1)
+		 / sizeof(double);
+		if (pmem_next - private_mem + len <= PRIVATE_mem) {
+			rv = (Bigint * )pmem_next;
+			pmem_next += len;
+		} else
+			rv = (Bigint * )malloc(len * sizeof(double));
+		rv->k = k;
+		rv->maxwds = x;
+	}
+	FREE_DTOA_LOCK(0);
+	rv->sign = rv->wds = 0;
+	return rv;
+}
+
+static void	
+Bfree(Bigint *v)
+{
+	if (v) {
+		ACQUIRE_DTOA_LOCK(0);
+		v->next = freelist[v->k];
+		freelist[v->k] = v;
+		FREE_DTOA_LOCK(0);
+	}
+}
+
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
+y->wds*sizeof(int) + 2*sizeof(int))
+
+static Bigint *
+multadd(Bigint *b, int m, int a)	/* multiply by m and add a */
+{
+	int	i, wds;
+	unsigned int carry, *x, y;
+	unsigned int xi, z;
+	Bigint * b1;
+
+	wds = b->wds;
+	x = b->x;
+	i = 0;
+	carry = a;
+	do {
+		xi = *x;
+		y = (xi & 0xffff) * m + carry;
+		z = (xi >> 16) * m + (y >> 16);
+		carry = z >> 16;
+		*x++ = (z << 16) + (y & 0xffff);
+	} while (++i < wds);
+	if (carry) {
+		if (wds >= b->maxwds) {
+			b1 = Balloc(b->k + 1);
+			Bcopy(b1, b);
+			Bfree(b);
+			b = b1;
+		}
+		b->x[wds++] = carry;
+		b->wds = wds;
+	}
+	return b;
+}
+
+static Bigint *
+s2b(const char *s, int nd0, int nd, unsigned int y9)
+{
+	Bigint * b;
+	int	i, k;
+	int x, y;
+
+	x = (nd + 8) / 9;
+	for (k = 0, y = 1; x > y; y <<= 1, k++) 
+		;
+	b = Balloc(k);
+	b->x[0] = y9;
+	b->wds = 1;
+
+	i = 9;
+	if (9 < nd0) {
+		s += 9;
+		do 
+			b = multadd(b, 10, *s++ - '0');
+		while (++i < nd0);
+		s++;
+	} else
+		s += 10;
+	for (; i < nd; i++)
+		b = multadd(b, 10, *s++ - '0');
+	return b;
+}
+
+static int	
+hi0bits(register unsigned int x)
+{
+	register int	k = 0;
+
+	if (!(x & 0xffff0000)) {
+		k = 16;
+		x <<= 16;
+	}
+	if (!(x & 0xff000000)) {
+		k += 8;
+		x <<= 8;
+	}
+	if (!(x & 0xf0000000)) {
+		k += 4;
+		x <<= 4;
+	}
+	if (!(x & 0xc0000000)) {
+		k += 2;
+		x <<= 2;
+	}
+	if (!(x & 0x80000000)) {
+		k++;
+		if (!(x & 0x40000000))
+			return 32;
+	}
+	return k;
+}
+
+static int	
+lo0bits(unsigned int *y)
+{
+	register int	k;
+	register unsigned int x = *y;
+
+	if (x & 7) {
+		if (x & 1)
+			return 0;
+		if (x & 2) {
+			*y = x >> 1;
+			return 1;
+		}
+		*y = x >> 2;
+		return 2;
+	}
+	k = 0;
+	if (!(x & 0xffff)) {
+		k = 16;
+		x >>= 16;
+	}
+	if (!(x & 0xff)) {
+		k += 8;
+		x >>= 8;
+	}
+	if (!(x & 0xf)) {
+		k += 4;
+		x >>= 4;
+	}
+	if (!(x & 0x3)) {
+		k += 2;
+		x >>= 2;
+	}
+	if (!(x & 1)) {
+		k++;
+		x >>= 1;
+		if (!x & 1)
+			return 32;
+	}
+	*y = x;
+	return k;
+}
+
+static Bigint *
+i2b(int i)
+{
+	Bigint * b;
+
+	b = Balloc(1);
+	b->x[0] = i;
+	b->wds = 1;
+	return b;
+}
+
+static Bigint *
+mult(Bigint *a, Bigint *b)
+{
+	Bigint * c;
+	int	k, wa, wb, wc;
+	unsigned int * x, *xa, *xae, *xb, *xbe, *xc, *xc0;
+	unsigned int y;
+	unsigned int carry, z;
+	unsigned int z2;
+
+	if (a->wds < b->wds) {
+		c = a;
+		a = b;
+		b = c;
+	}
+	k = a->k;
+	wa = a->wds;
+	wb = b->wds;
+	wc = wa + wb;
+	if (wc > a->maxwds)
+		k++;
+	c = Balloc(k);
+	for (x = c->x, xa = x + wc; x < xa; x++)
+		*x = 0;
+	xa = a->x;
+	xae = xa + wa;
+	xb = b->x;
+	xbe = xb + wb;
+	xc0 = c->x;
+	for (; xb < xbe; xb++, xc0++) {
+		if (y = *xb & 0xffff) {
+			x = xa;
+			xc = xc0;
+			carry = 0;
+			do {
+				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
+				carry = z >> 16;
+				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
+				carry = z2 >> 16;
+				Storeinc(xc, z2, z);
+			} while (x < xae);
+			*xc = carry;
+		}
+		if (y = *xb >> 16) {
+			x = xa;
+			xc = xc0;
+			carry = 0;
+			z2 = *xc;
+			do {
+				z = (*x & 0xffff) * y + (*xc >> 16) + carry;
+				carry = z >> 16;
+				Storeinc(xc, z, z2);
+				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
+				carry = z2 >> 16;
+			} while (x < xae);
+			*xc = z2;
+		}
+	}
+	for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) 
+		;
+	c->wds = wc;
+	return c;
+}
+
+static Bigint *p5s;
+
+static Bigint *
+pow5mult(Bigint *b, int k)
+{
+	Bigint * b1, *p5, *p51;
+	int	i;
+	static int	p05[3] = { 
+		5, 25, 125 	};
+
+	if (i = k & 3)
+		b = multadd(b, p05[i-1], 0);
+
+	if (!(k >>= 2))
+		return b;
+	if (!(p5 = p5s)) {
+		/* first time */
+		ACQUIRE_DTOA_LOCK(1);
+		if (!(p5 = p5s)) {
+			p5 = p5s = i2b(625);
+			p5->next = 0;
+		}
+		FREE_DTOA_LOCK(1);
+	}
+	for (; ; ) {
+		if (k & 1) {
+			b1 = mult(b, p5);
+			Bfree(b);
+			b = b1;
+		}
+		if (!(k >>= 1))
+			break;
+		if (!(p51 = p5->next)) {
+			ACQUIRE_DTOA_LOCK(1);
+			if (!(p51 = p5->next)) {
+				p51 = p5->next = mult(p5, p5);
+				p51->next = 0;
+			}
+			FREE_DTOA_LOCK(1);
+		}
+		p5 = p51;
+	}
+	return b;
+}
+
+static Bigint *
+lshift(Bigint *b, int k)
+{
+	int	i, k1, n, n1;
+	Bigint * b1;
+	unsigned int * x, *x1, *xe, z;
+
+	n = k >> 5;
+	k1 = b->k;
+	n1 = n + b->wds + 1;
+	for (i = b->maxwds; n1 > i; i <<= 1)
+		k1++;
+	b1 = Balloc(k1);
+	x1 = b1->x;
+	for (i = 0; i < n; i++)
+		*x1++ = 0;
+	x = b->x;
+	xe = x + b->wds;
+	if (k &= 0x1f) {
+		k1 = 32 - k;
+		z = 0;
+		do {
+			*x1++ = *x << k | z;
+			z = *x++ >> k1;
+		} while (x < xe);
+		if (*x1 = z)
+			++n1;
+	} else 
+		do
+			*x1++ = *x++;
+		while (x < xe);
+	b1->wds = n1 - 1;
+	Bfree(b);
+	return b1;
+}
+
+static int	
+cmp(Bigint *a, Bigint *b)
+{
+	unsigned int * xa, *xa0, *xb, *xb0;
+	int	i, j;
+
+	i = a->wds;
+	j = b->wds;
+	if (i -= j)
+		return i;
+	xa0 = a->x;
+	xa = xa0 + j;
+	xb0 = b->x;
+	xb = xb0 + j;
+	for (; ; ) {
+		if (*--xa != *--xb)
+			return * xa < *xb ? -1 : 1;
+		if (xa <= xa0)
+			break;
+	}
+	return 0;
+}
+
+static Bigint *
+diff(Bigint *a, Bigint *b)
+{
+	Bigint * c;
+	int	i, wa, wb;
+	unsigned int * xa, *xae, *xb, *xbe, *xc;
+	unsigned int borrow, y;
+	unsigned int z;
+
+	i = cmp(a, b);
+	if (!i) {
+		c = Balloc(0);
+		c->wds = 1;
+		c->x[0] = 0;
+		return c;
+	}
+	if (i < 0) {
+		c = a;
+		a = b;
+		b = c;
+		i = 1;
+	} else
+		i = 0;
+	c = Balloc(a->k);
+	c->sign = i;
+	wa = a->wds;
+	xa = a->x;
+	xae = xa + wa;
+	wb = b->wds;
+	xb = b->x;
+	xbe = xb + wb;
+	xc = c->x;
+	borrow = 0;
+	do {
+		y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
+		borrow = (y & 0x10000) >> 16;
+		z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
+		borrow = (z & 0x10000) >> 16;
+		Storeinc(xc, z, y);
+	} while (xb < xbe);
+	while (xa < xae) {
+		y = (*xa & 0xffff) - borrow;
+		borrow = (y & 0x10000) >> 16;
+		z = (*xa++ >> 16) - borrow;
+		borrow = (z & 0x10000) >> 16;
+		Storeinc(xc, z, y);
+	}
+	while (!*--xc)
+		wa--;
+	c->wds = wa;
+	return c;
+}
+
+static double	
+ulp(double x)
+{
+	register int L;
+	double	a;
+
+	L = (fpword0(x) & Exp_mask) - (P - 1) * Exp_msk1;
+	fpword0(a) = L;
+	fpword1(a) = 0;
+	return a;
+}
+
+static double	
+b2d(Bigint *a, int *e)
+{
+	unsigned int * xa, *xa0, w, y, z;
+	int	k;
+	double	d;
+#define d0 fpword0(d)
+#define d1 fpword1(d)
+
+	xa0 = a->x;
+	xa = xa0 + a->wds;
+	y = *--xa;
+	k = hi0bits(y);
+	*e = 32 - k;
+	if (k < Ebits) {
+		d0 = Exp_1 | y >> Ebits - k;
+		w = xa > xa0 ? *--xa : 0;
+		d1 = y << (32 - Ebits) + k | w >> Ebits - k;
+		goto ret_d;
+	}
+	z = xa > xa0 ? *--xa : 0;
+	if (k -= Ebits) {
+		d0 = Exp_1 | y << k | z >> 32 - k;
+		y = xa > xa0 ? *--xa : 0;
+		d1 = z << k | y >> 32 - k;
+	} else {
+		d0 = Exp_1 | y;
+		d1 = z;
+	}
+ret_d:
+#undef d0
+#undef d1
+	return d;
+}
+
+static Bigint *
+d2b(double d, int *e, int *bits)
+{
+	Bigint * b;
+	int	de, i, k;
+	unsigned int * x, y, z;
+#define d0 fpword0(d)
+#define d1 fpword1(d)
+
+	b = Balloc(1);
+	x = b->x;
+
+	z = d0 & Frac_mask;
+	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */
+	de = (int)(d0 >> Exp_shift);
+	z |= Exp_msk11;
+	if (y = d1) {
+		if (k = lo0bits(&y)) {
+			x[0] = y | z << 32 - k;
+			z >>= k;
+		} else
+			x[0] = y;
+		i = b->wds = (x[1] = z) ? 2 : 1;
+	} else {
+		k = lo0bits(&z);
+		x[0] = z;
+		i = b->wds = 1;
+		k += 32;
+	}
+	*e = de - Bias - (P - 1) + k;
+	*bits = P - k;
+	return b;
+}
+
+#undef d0
+#undef d1
+
+static double	
+ratio(Bigint *a, Bigint *b)
+{
+	double	da, db;
+	int	k, ka, kb;
+
+	da = b2d(a, &ka);
+	db = b2d(b, &kb);
+	k = ka - kb + 32 * (a->wds - b->wds);
+	if (k > 0)
+		fpword0(da) += k * Exp_msk1;
+	else {
+		k = -k;
+		fpword0(db) += k * Exp_msk1;
+	}
+	return da / db;
+}
+
+static const double
+tens[] = {
+	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+	1e20, 1e21, 1e22
+};
+
+static const double
+bigtens[] = { 
+	1e16, 1e32, 1e64, 1e128, 1e256 };
+
+static const double tinytens[] = { 
+	1e-16, 1e-32, 1e-64, 1e-128,
+	9007199254740992.e-256
+};
+
+/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
+/* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
+#define Scale_Bit 0x10
+#define n_bigtens 5
+
+#define NAN_WORD0 0x7ff80000
+
+#define NAN_WORD1 0
+
+static int	
+match(const char **sp, char *t)
+{
+	int	c, d;
+	const char * s = *sp;
+
+	while (d = *t++) {
+		if ((c = *++s) >= 'A' && c <= 'Z')
+			c += 'a' - 'A';
+		if (c != d)
+			return 0;
+	}
+	*sp = s + 1;
+	return 1;
+}
+
+static void	
+gethex(double *rvp, const char **sp)
+{
+	unsigned int c, x[2];
+	const char * s;
+	int	havedig, udx0, xshift;
+
+	x[0] = x[1] = 0;
+	havedig = xshift = 0;
+	udx0 = 1;
+	s = *sp;
+	while (c = *(const unsigned char * )++s) {
+		if (c >= '0' && c <= '9')
+			c -= '0';
+		else if (c >= 'a' && c <= 'f')
+			c += 10 - 'a';
+		else if (c >= 'A' && c <= 'F')
+			c += 10 - 'A';
+		else if (c <= ' ') {
+			if (udx0 && havedig) {
+				udx0 = 0;
+				xshift = 1;
+			}
+			continue;
+		} else if (/*(*/ c == ')') {
+			*sp = s + 1;
+			break;
+		} else
+			return;	/* invalid form: don't change *sp */
+		havedig = 1;
+		if (xshift) {
+			xshift = 0;
+			x[0] = x[1];
+			x[1] = 0;
+		}
+		if (udx0)
+			x[0] = (x[0] << 4) | (x[1] >> 28);
+		x[1] = (x[1] << 4) | c;
+	}
+	if ((x[0] &= 0xfffff) || x[1]) {
+		fpword0(*rvp) = Exp_mask | x[0];
+		fpword1(*rvp) = x[1];
+	}
+}
+
+static int	
+quorem(Bigint *b, Bigint *S)
+{
+	int	n;
+	unsigned int * bx, *bxe, q, *sx, *sxe;
+	unsigned int borrow, carry, y, ys;
+	unsigned int si, z, zs;
+
+	n = S->wds;
+	if (b->wds < n)
+		return 0;
+	sx = S->x;
+	sxe = sx + --n;
+	bx = b->x;
+	bxe = bx + n;
+	q = *bxe / (*sxe + 1);	/* ensure q <= true quotient */
+	if (q) {
+		borrow = 0;
+		carry = 0;
+		do {
+			si = *sx++;
+			ys = (si & 0xffff) * q + carry;
+			zs = (si >> 16) * q + (ys >> 16);
+			carry = zs >> 16;
+			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
+			borrow = (y & 0x10000) >> 16;
+			z = (*bx >> 16) - (zs & 0xffff) - borrow;
+			borrow = (z & 0x10000) >> 16;
+			Storeinc(bx, z, y);
+		} while (sx <= sxe);
+		if (!*bxe) {
+			bx = b->x;
+			while (--bxe > bx && !*bxe)
+				--n;
+			b->wds = n;
+		}
+	}
+	if (cmp(b, S) >= 0) {
+		q++;
+		borrow = 0;
+		carry = 0;
+		bx = b->x;
+		sx = S->x;
+		do {
+			si = *sx++;
+			ys = (si & 0xffff) + carry;
+			zs = (si >> 16) + (ys >> 16);
+			carry = zs >> 16;
+			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
+			borrow = (y & 0x10000) >> 16;
+			z = (*bx >> 16) - (zs & 0xffff) - borrow;
+			borrow = (z & 0x10000) >> 16;
+			Storeinc(bx, z, y);
+		} while (sx <= sxe);
+		bx = b->x;
+		bxe = bx + n;
+		if (!*bxe) {
+			while (--bxe > bx && !*bxe)
+				--n;
+			b->wds = n;
+		}
+	}
+	return q;
+}
+
+static char	*
+rv_alloc(int i)
+{
+	int	j, k, *r;
+
+	j = sizeof(unsigned int);
+	for (k = 0; 
+	    sizeof(Bigint) - sizeof(unsigned int) - sizeof(int) + j <= i; 
+	    j <<= 1)
+		k++;
+	r = (int * )Balloc(k);
+	*r = k;
+	return
+	    (char *)(r + 1);
+}
+
+static char	*
+nrv_alloc(char *s, char **rve, int n)
+{
+	char	*rv, *t;
+
+	t = rv = rv_alloc(n);
+	while (*t = *s++) 
+		t++;
+	if (rve)
+		*rve = t;
+	return rv;
+}
+
+/* freedtoa(s) must be used to free values s returned by dtoa
+ * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
+ * but for consistency with earlier versions of dtoa, it is optional
+ * when MULTIPLE_THREADS is not defined.
+ */
+
+void
+freedtoa(char *s)
+{
+	Bigint * b = (Bigint * )((int *)s - 1);
+	b->maxwds = 1 << (b->k = *(int * )b);
+	Bfree(b);
+}
+
+/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
+ *
+ * Inspired by "How to Print Floating-Point Numbers Accurately" by
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *	1. Rather than iterating, we use a simple numeric overestimate
+ *	   to determine k = floor(log10(d)).  We scale relevant
+ *	   quantities using O(log2(k)) rather than O(k) multiplications.
+ *	2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
+ *	   try to generate digits strictly left to right.  Instead, we
+ *	   compute with fewer bits and propagate the carry if necessary
+ *	   when rounding the final digit up.  This is often faster.
+ *	3. Under the assumption that input will be rounded nearest,
+ *	   mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
+ *	   That is, we allow equality in stopping tests when the
+ *	   round-nearest rule will give the same floating-point value
+ *	   as would satisfaction of the stopping test with strict
+ *	   inequality.
+ *	4. We remove common factors of powers of 2 from relevant
+ *	   quantities.
+ *	5. When converting floating-point integers less than 1e16,
+ *	   we use floating-point arithmetic rather than resorting
+ *	   to multiple-precision integers.
+ *	6. When asked to produce fewer than 15 digits, we first try
+ *	   to get by with floating-point arithmetic; we resort to
+ *	   multiple-precision integer arithmetic only if we cannot
+ *	   guarantee that the floating-point calculation has given
+ *	   the correctly rounded result.  For k requested digits and
+ *	   "uniformly" distributed input, the probability is
+ *	   something like 10^(k-15) that we must resort to the int
+ *	   calculation.
+ */
+
+char	*
+dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
+{
+	/*	Arguments ndigits, decpt, sign are similar to those
+	of ecvt and fcvt; trailing zeros are suppressed from
+	the returned string.  If not null, *rve is set to point
+	to the end of the return value.  If d is +-Infinity or NaN,
+	then *decpt is set to 9999.
+
+	mode:
+		0 ==> shortest string that yields d when read in
+			and rounded to nearest.
+		1 ==> like 0, but with Steele & White stopping rule;
+			e.g. with IEEE P754 arithmetic , mode 0 gives
+			1e23 whereas mode 1 gives 9.999999999999999e22.
+		2 ==> max(1,ndigits) significant digits.  This gives a
+			return value similar to that of ecvt, except
+			that trailing zeros are suppressed.
+		3 ==> through ndigits past the decimal point.  This
+			gives a return value similar to that from fcvt,
+			except that trailing zeros are suppressed, and
+			ndigits can be negative.
+		4-9 should give the same return values as 2-3, i.e.,
+			4 <= mode <= 9 ==> same return as mode
+			2 + (mode & 1).  These modes are mainly for
+			debugging; often they run slower but sometimes
+			faster than modes 2-3.
+		4,5,8,9 ==> left-to-right digit generation.
+		6-9 ==> don't try fast floating-point estimate
+			(if applicable).
+
+		Values of mode other than 0-9 are treated as mode 0.
+
+		Sufficient space is allocated to the return value
+		to hold the suppressed trailing zeros.
+	*/
+
+	int	bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
+	j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+	spec_case, try_quick;
+	int L;
+	Bigint * b, *b1, *delta, *mlo=nil, *mhi, *S;
+	double	d2, ds, eps;
+	char	*s, *s0;
+
+	if (fpword0(d) & Sign_bit) {
+		/* set sign for everything, including 0's and NaNs */
+		*sign = 1;
+		fpword0(d) &= ~Sign_bit;	/* clear sign bit */
+	} else
+		*sign = 0;
+
+	if ((fpword0(d) & Exp_mask) == Exp_mask) {
+		/* Infinity or NaN */
+		*decpt = 9999;
+		if (!fpword1(d) && !(fpword0(d) & 0xfffff))
+			return nrv_alloc("Infinity", rve, 8);
+		return nrv_alloc("NaN", rve, 3);
+	}
+	if (!d) {
+		*decpt = 1;
+		return nrv_alloc("0", rve, 1);
+	}
+
+	b = d2b(d, &be, &bbits);
+	i = (int)(fpword0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
+	d2 = d;
+	fpword0(d2) &= Frac_mask1;
+	fpword0(d2) |= Exp_11;
+
+	/* log(x)	~=~ log(1.5) + (x-1.5)/1.5
+		 * log10(x)	 =  log(x) / log(10)
+		 *		~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
+		 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
+		 *
+		 * This suggests computing an approximation k to log10(d) by
+		 *
+		 * k = (i - Bias)*0.301029995663981
+		 *	+ ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
+		 *
+		 * We want k to be too large rather than too small.
+		 * The error in the first-order Taylor series approximation
+		 * is in our favor, so we just round up the constant enough
+		 * to compensate for any error in the multiplication of
+		 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
+		 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
+		 * adding 1e-13 to the constant term more than suffices.
+		 * Hence we adjust the constant term to 0.1760912590558.
+		 * (We could get a more accurate k by invoking log10,
+		 *  but this is probably not worthwhile.)
+		 */
+
+	i -= Bias;
+	ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
+	k = (int)ds;
+	if (ds < 0. && ds != k)
+		k--;	/* want k = floor(ds) */
+	k_check = 1;
+	if (k >= 0 && k <= Ten_pmax) {
+		if (d < tens[k])
+			k--;
+		k_check = 0;
+	}
+	j = bbits - i - 1;
+	if (j >= 0) {
+		b2 = 0;
+		s2 = j;
+	} else {
+		b2 = -j;
+		s2 = 0;
+	}
+	if (k >= 0) {
+		b5 = 0;
+		s5 = k;
+		s2 += k;
+	} else {
+		b2 -= k;
+		b5 = -k;
+		s5 = 0;
+	}
+	if (mode < 0 || mode > 9)
+		mode = 0;
+	try_quick = 1;
+	if (mode > 5) {
+		mode -= 4;
+		try_quick = 0;
+	}
+	leftright = 1;
+	switch (mode) {
+	case 0:
+	case 1:
+		ilim = ilim1 = -1;
+		i = 18;
+		ndigits = 0;
+		break;
+	case 2:
+		leftright = 0;
+		/* no break */
+	case 4:
+		if (ndigits <= 0)
+			ndigits = 1;
+		ilim = ilim1 = i = ndigits;
+		break;
+	case 3:
+		leftright = 0;
+		/* no break */
+	case 5:
+		i = ndigits + k + 1;
+		ilim = i;
+		ilim1 = i - 1;
+		if (i <= 0)
+			i = 1;
+	}
+	s = s0 = rv_alloc(i);
+
+	if (ilim >= 0 && ilim <= Quick_max && try_quick) {
+
+		/* Try to get by with floating-point arithmetic. */
+
+		i = 0;
+		d2 = d;
+		k0 = k;
+		ilim0 = ilim;
+		ieps = 2; /* conservative */
+		if (k > 0) {
+			ds = tens[k&0xf];
+			j = k >> 4;
+			if (j & Bletch) {
+				/* prevent overflows */
+				j &= Bletch - 1;
+				d /= bigtens[n_bigtens-1];
+				ieps++;
+			}
+			for (; j; j >>= 1, i++)
+				if (j & 1) {
+					ieps++;
+					ds *= bigtens[i];
+				}
+			d /= ds;
+		} else if (j1 = -k) {
+			d *= tens[j1 & 0xf];
+			for (j = j1 >> 4; j; j >>= 1, i++)
+				if (j & 1) {
+					ieps++;
+					d *= bigtens[i];
+				}
+		}
+		if (k_check && d < 1. && ilim > 0) {
+			if (ilim1 <= 0)
+				goto fast_failed;
+			ilim = ilim1;
+			k--;
+			d *= 10.;
+			ieps++;
+		}
+		eps = ieps * d + 7.;
+		fpword0(eps) -= (P - 1) * Exp_msk1;
+		if (ilim == 0) {
+			S = mhi = 0;
+			d -= 5.;
+			if (d > eps)
+				goto one_digit;
+			if (d < -eps)
+				goto no_digits;
+			goto fast_failed;
+		}
+		/* Generate ilim digits, then fix them up. */
+		eps *= tens[ilim-1];
+		for (i = 1; ; i++, d *= 10.) {
+			L = d;
+			d -= L;
+			*s++ = '0' + (int)L;
+			if (i == ilim) {
+				if (d > 0.5 + eps)
+					goto bump_up;
+				else if (d < 0.5 - eps) {
+					while (*--s == '0')
+						;
+					s++;
+					goto ret1;
+				}
+				break;
+			}
+		}
+fast_failed:
+		s = s0;
+		d = d2;
+		k = k0;
+		ilim = ilim0;
+	}
+
+	/* Do we have a "small" integer? */
+
+	if (be >= 0 && k <= Int_max) {
+		/* Yes. */
+		ds = tens[k];
+		if (ndigits < 0 && ilim <= 0) {
+			S = mhi = 0;
+			if (ilim < 0 || d <= 5 * ds)
+				goto no_digits;
+			goto one_digit;
+		}
+		for (i = 1; ; i++) {
+			L = d / ds;
+			d -= L * ds;
+			*s++ = '0' + (int)L;
+			if (i == ilim) {
+				d += d;
+				if (d > ds || d == ds && L & 1) {
+bump_up:
+					while (*--s == '9')
+						if (s == s0) {
+							k++;
+							*s = '0';
+							break;
+						}
+					++ * s++;
+				}
+				break;
+			}
+			if (!(d *= 10.))
+				break;
+		}
+		goto ret1;
+	}
+
+	m2 = b2;
+	m5 = b5;
+	mhi = mlo = 0;
+	if (leftright) {
+		if (mode < 2) {
+			i = 
+			    1 + P - bbits;
+		} else {
+			j = ilim - 1;
+			if (m5 >= j)
+				m5 -= j;
+			else {
+				s5 += j -= m5;
+				b5 += j;
+				m5 = 0;
+			}
+			if ((i = ilim) < 0) {
+				m2 -= i;
+				i = 0;
+			}
+		}
+		b2 += i;
+		s2 += i;
+		mhi = i2b(1);
+	}
+	if (m2 > 0 && s2 > 0) {
+		i = m2 < s2 ? m2 : s2;
+		b2 -= i;
+		m2 -= i;
+		s2 -= i;
+	}
+	if (b5 > 0) {
+		if (leftright) {
+			if (m5 > 0) {
+				mhi = pow5mult(mhi, m5);
+				b1 = mult(mhi, b);
+				Bfree(b);
+				b = b1;
+			}
+			if (j = b5 - m5)
+				b = pow5mult(b, j);
+		} else
+			b = pow5mult(b, b5);
+	}
+	S = i2b(1);
+	if (s5 > 0)
+		S = pow5mult(S, s5);
+
+	/* Check for special case that d is a normalized power of 2. */
+
+	spec_case = 0;
+	if (mode < 2) {
+		if (!fpword1(d) && !(fpword0(d) & Bndry_mask)
+		    ) {
+			/* The special case */
+			b2 += Log2P;
+			s2 += Log2P;
+			spec_case = 1;
+		}
+	}
+
+	/* Arrange for convenient computation of quotients:
+	 * shift left if necessary so divisor has 4 leading 0 bits.
+	 *
+	 * Perhaps we should just compute leading 28 bits of S once
+	 * and for all and pass them and a shift to quorem, so it
+	 * can do shifts and ors to compute the numerator for q.
+	 */
+	if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
+		i = 32 - i;
+	if (i > 4) {
+		i -= 4;
+		b2 += i;
+		m2 += i;
+		s2 += i;
+	} else if (i < 4) {
+		i += 28;
+		b2 += i;
+		m2 += i;
+		s2 += i;
+	}
+	if (b2 > 0)
+		b = lshift(b, b2);
+	if (s2 > 0)
+		S = lshift(S, s2);
+	if (k_check) {
+		if (cmp(b, S) < 0) {
+			k--;
+			b = multadd(b, 10, 0);	/* we botched the k estimate */
+			if (leftright)
+				mhi = multadd(mhi, 10, 0);
+			ilim = ilim1;
+		}
+	}
+	if (ilim <= 0 && mode > 2) {
+		if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0) {
+			/* no digits, fcvt style */
+no_digits:
+			k = -1 - ndigits;
+			goto ret;
+		}
+one_digit:
+		*s++ = '1';
+		k++;
+		goto ret;
+	}
+	if (leftright) {
+		if (m2 > 0)
+			mhi = lshift(mhi, m2);
+
+		/* Compute mlo -- check for special case
+		 * that d is a normalized power of 2.
+		 */
+
+		mlo = mhi;
+		if (spec_case) {
+			mhi = Balloc(mhi->k);
+			Bcopy(mhi, mlo);
+			mhi = lshift(mhi, Log2P);
+		}
+
+		for (i = 1; ; i++) {
+			dig = quorem(b, S) + '0';
+			/* Do we yet have the shortest decimal string
+			 * that will round to d?
+			 */
+			j = cmp(b, mlo);
+			delta = diff(S, mhi);
+			j1 = delta->sign ? 1 : cmp(b, delta);
+			Bfree(delta);
+			if (j1 == 0 && !mode && !(fpword1(d) & 1)) {
+				if (dig == '9')
+					goto round_9_up;
+				if (j > 0)
+					dig++;
+				*s++ = dig;
+				goto ret;
+			}
+			if (j < 0 || j == 0 && !mode
+			     && !(fpword1(d) & 1)
+			    ) {
+				if (j1 > 0) {
+					b = lshift(b, 1);
+					j1 = cmp(b, S);
+					if ((j1 > 0 || j1 == 0 && dig & 1)
+					     && dig++ == '9')
+						goto round_9_up;
+				}
+				*s++ = dig;
+				goto ret;
+			}
+			if (j1 > 0) {
+				if (dig == '9') { /* possible if i == 1 */
+round_9_up:
+					*s++ = '9';
+					goto roundoff;
+				}
+				*s++ = dig + 1;
+				goto ret;
+			}
+			*s++ = dig;
+			if (i == ilim)
+				break;
+			b = multadd(b, 10, 0);
+			if (mlo == mhi)
+				mlo = mhi = multadd(mhi, 10, 0);
+			else {
+				mlo = multadd(mlo, 10, 0);
+				mhi = multadd(mhi, 10, 0);
+			}
+		}
+	} else
+		for (i = 1; ; i++) {
+			*s++ = dig = quorem(b, S) + '0';
+			if (i >= ilim)
+				break;
+			b = multadd(b, 10, 0);
+		}
+
+	/* Round off last digit */
+
+	b = lshift(b, 1);
+	j = cmp(b, S);
+	if (j > 0 || j == 0 && dig & 1) {
+roundoff:
+		while (*--s == '9')
+			if (s == s0) {
+				k++;
+				*s++ = '1';
+				goto ret;
+			}
+		++ * s++;
+	} else {
+		while (*--s == '0')
+			;
+		s++;
+	}
+ret:
+	Bfree(S);
+	if (mhi) {
+		if (mlo && mlo != mhi)
+			Bfree(mlo);
+		Bfree(mhi);
+	}
+ret1:
+	Bfree(b);
+	*s = 0;
+	*decpt = k + 1;
+	if (rve)
+		*rve = s;
+	return s0;
+}
+