dtoa.c

这是一个同样来自贝尔实验室的和UNIX有着渊源的操作系统, 其简洁的设计和实现易于我们学习和理解

/* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
/* kudos to [e-mail], gripes to [e-mail] */

/* 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) {