_fconv.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

/* Common routines for _dtoa and strtod */

#include "fconv.h"

#ifdef DEBUG
#include <stdio.h>
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif

 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
#ifdef VAX
		, 1e23, 1e24
#endif
		};


#ifdef IEEE_Arith
double _bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
double _tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
#else
#ifdef IBM
double _bigtens[] = { 1e16, 1e32, 1e64 };
double _tinytens[] = { 1e-16, 1e-32, 1e-64 };
#else
double _bigtens[] = { 1e16, 1e32 };
double _tinytens[] = { 1e-16, 1e-32 };
#endif
#endif

 static Bigint *freelist[Kmax+1];

 Bigint *
_Balloc(int k)
{
	int x;
	Bigint *rv;

	if (rv = freelist[k]) {
		freelist[k] = rv->next;
		}
	else {
		x = 1 << k;
		rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(long));
		rv->k = k;
		rv->maxwds = x;
		}
	rv->sign = rv->wds = 0;
	return rv;
	}

 void
_Bfree(Bigint *v)
{
	if (v) {
		v->next = freelist[v->k];
		freelist[v->k] = v;
		}
	}


 Bigint *
_multadd(Bigint *b, int m, int a)	/* multiply by m and add a */
{
	int i, wds;
	unsigned long *x, y;
#ifdef Pack_32
	unsigned long xi, z;
#endif
	Bigint *b1;

	wds = b->wds;
	x = b->x;
	i = 0;
	do {
#ifdef Pack_32
		xi = *x;
		y = (xi & 0xffff) * m + a;
		z = (xi >> 16) * m + (y >> 16);
		a = (int)(z >> 16);
		*x++ = (z << 16) + (y & 0xffff);
#else
		y = *x * m + a;
		a = (int)(y >> 16);
		*x++ = y & 0xffff;
#endif
		}
		while(++i < wds);
	if (a) {
		if (wds >= b->maxwds) {
			b1 = Balloc(b->k+1);
			Bcopy(b1, b);
			Bfree(b);
			b = b1;
			}
		b->x[wds++] = a;
		b->wds = wds;
		}
	return b;
	}

 int
_hi0bits(register unsigned long 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 long *y)
{
	register int k;
	register unsigned long 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;
	}

 Bigint *
_i2b(int i)
{
	Bigint *b;

	b = Balloc(1);
	b->x[0] = i;
	b->wds = 1;
	return b;
	}

 Bigint *
_mult(Bigint *a, Bigint *b)
{
	Bigint *c;
	int k, wa, wb, wc;
	unsigned long carry, y, z;
	unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
	unsigned long z2;
#endif

	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;
#ifdef Pack_32
	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;
			}
		}
#else
	for(; xb < xbe; xc0++) {
		if (y = *xb++) {
			x = xa;
			xc = xc0;
			carry = 0;
			do {
				z = *x++ * y + *xc + carry;
				carry = z >> 16;
				*xc++ = z & 0xffff;
				}
				while(x < xae);
			*xc = carry;
			}
		}
#endif
	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
	c->wds = wc;
	return c;
	}

 static Bigint *p5s;

 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 */
		p5 = p5s = i2b(625);
		p5->next = 0;
		}
	for(;;) {
		if (k & 1) {
			b1 = mult(b, p5);
			Bfree(b);
			b = b1;
			}
		if (!(k >>= 1))
			break;
		if (!(p51 = p5->next)) {
			p51 = p5->next = mult(p5,p5);
			p51->next = 0;
			}
		p5 = p51;
		}
	return b;
	}

 Bigint *
_lshift(Bigint *b, int k)
{
	int i, k1, n, n1;
	Bigint *b1;
	unsigned long *x, *x1, *xe, z;

#ifdef Pack_32
	n = k >> 5;
#else
	n = k >> 4;
#endif
	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;
#ifdef Pack_32
	if (k &= 0x1f) {
		k1 = 32 - k;
		z = 0;
		do {
			*x1++ = *x << k | z;
			z = *x++ >> k1;
			}
			while(x < xe);
		if (*x1 = z)
			++n1;
		}
#else
	if (k &= 0xf) {
		k1 = 16 - k;
		z = 0;
		do {
			*x1++ = *x << k  & 0xffff | z;
			z = *x++ >> k1;
			}
			while(x < xe);
		if (*x1 = z)
			++n1;
		}
#endif
	else do
		*x1++ = *x++;
		while(x < xe);
	b1->wds = n1 - 1;
	Bfree(b);
	return b1;
	}

 int
_cmp(Bigint *a, Bigint *b)
{
	unsigned long *xa, *xa0, *xb, *xb0;
	int i, j;

	i = a->wds;
	j = b->wds;
#ifdef DEBUG
	if (i > 1 && !a->x[i-1])
		Bug("cmp called with a->x[a->wds-1] == 0");
	if (j > 1 && !b->x[j-1])
		Bug("cmp called with b->x[b->wds-1] == 0");
#endif
	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;
	}

 Bigint *
_diff(Bigint *a, Bigint *b)
{
	Bigint *c;
	int i, wa, wb;
	long borrow, y;	/* We need signed shifts here. */
	unsigned long *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
	long z;
#endif

	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;
#ifdef Pack_32
	do {
		y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
		borrow = z >> 16;
		Sign_Extend(borrow, z);
		Storeinc(xc, z, y);
		}
		while(xb < xbe);
	while(xa < xae) {
		y = (*xa & 0xffff) + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		z = (*xa++ >> 16) + borrow;
		borrow = z >> 16;
		Sign_Extend(borrow, z);
		Storeinc(xc, z, y);
		}
#else
	do {
		y = *xa++ - *xb++ + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		*xc++ = y & 0xffff;
		}
		while(xb < xbe);
	while(xa < xae) {
		y = *xa++ + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		*xc++ = y & 0xffff;
		}
#endif
	while(!*--xc)
		wa--;
	c->wds = wa;
	return c;
	}

 Bigint *
_d2b(double darg, int *e, int *bits)
{
	Bigint *b;
	int de, i, k;
	unsigned long *x, y, z;
	Dul d;
#ifdef VAX
	unsigned long d0, d1;
	d.d = darg;
	d0 = word0(d) >> 16 | word0(d) << 16;
	d1 = word1(d) >> 16 | word1(d) << 16;
#else
	d.d = darg;
#define d0 word0(d)
#define d1 word1(d)
#endif

#ifdef Pack_32
	b = Balloc(1);
#else
	b = Balloc(2);
#endif
	x = b->x;

	z = d0 & Frac_mask;
	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
	de = (int)(d0 >> Exp_shift);
#ifndef IBM
	z |= Exp_msk11;
#endif
#else
	if (de = (int)(d0 >> Exp_shift))
		z |= Exp_msk1;
#endif
#ifdef Pack_32
	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 {
#ifdef DEBUG
		if (!z)
			Bug("Zero passed to d2b");
#endif
		k = lo0bits(&z);
		x[0] = z;
		i = b->wds = 1;
		k += 32;
		}
#else
	if (y = d1) {
		if (k = lo0bits(&y))
			if (k >= 16) {
				x[0] = y | z << 32 - k & 0xffff;
				x[1] = z >> k - 16 & 0xffff;
				x[2] = z >> k;
				i = 2;
				}
			else {
				x[0] = y & 0xffff;
				x[1] = y >> 16 | z << 16 - k & 0xffff;
				x[2] = z >> k & 0xffff;
				x[3] = z >> k+16;
				i = 3;
				}
		else {
			x[0] = y & 0xffff;
			x[1] = y >> 16;
			x[2] = z & 0xffff;
			x[3] = z >> 16;
			i = 3;
			}
		}
	else {
#ifdef DEBUG
		if (!z)
			Bug("Zero passed to d2b");
#endif
		k = lo0bits(&z);
		if (k >= 16) {
			x[0] = z;
			i = 0;
			}
		else {
			x[0] = z & 0xffff;
			x[1] = z >> 16;
			i = 1;
			}
		k += 32;
		}
	while(!x[i])
		--i;
	b->wds = i + 1;
#endif
#ifndef Sudden_Underflow
	if (de) {
#endif
#ifdef IBM
		*e = (de - Bias - (P-1) << 2) + k;
		*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
#else
		*e = de - Bias - (P-1) + k;
		*bits = P - k;
#endif
#ifndef Sudden_Underflow
		}
	else {
		*e = de - Bias - (P-1) + 1 + k;
#ifdef Pack_32
		*bits = 32*i - hi0bits(x[i-1]);
#else
		*bits = (i+2)*16 - hi0bits(x[i]);
#endif
		}
#endif
	return b;
	}
#undef d0
#undef d1