static char rcsid[] = "$Id: H:/drh/idioms/book/RCS/ap.doc,v 1.11 1996/06/26 23:02:01 drh Exp $";#include <ctype.h>#include <limits.h>#include <stdlib.h>#include <string.h>#include "assert.h"#include "ap.h"#include "fmt.h"#include "xp.h"#include "mem.h"#define T AP_Tstruct T {	int sign;	int ndigits;	int size;	XP_T digits;};#define iszero(x) ((x)->ndigits==1 && (x)->digits[0]==0)#define maxdigits(x,y) ((x)->ndigits > (y)->ndigits ? \	(x)->ndigits : (y)->ndigits)#define isone(x) ((x)->ndigits==1 && (x)->digits[0]==1)static T normalize(T z, int n);static int cmp(T x, T y);static T mk(int size) {	T z = CALLOC(1, sizeof (*z) + size);	assert(size > 0);	z->sign = 1;	z->size = size;	z->ndigits = 1;	z->digits = (XP_T)(z + 1);	return z;}static T set(T z, long int n) {	if (n == LONG_MIN)		XP_fromint(z->size, z->digits, LONG_MAX + 1UL);	else if (n < 0)		XP_fromint(z->size, z->digits, -n);	else		XP_fromint(z->size, z->digits, n);	z->sign = n < 0 ? -1 : 1;	return normalize(z, z->size);}static T normalize(T z, int n) {	z->ndigits = XP_length(n, z->digits);	return z;}static T add(T z, T x, T y) {	int n = y->ndigits;	if (x->ndigits < n)		return add(z, y, x);	else if (x->ndigits > n) {		int carry = XP_add(n, z->digits, x->digits,			y->digits, 0);		z->digits[z->size-1] = XP_sum(x->ndigits - n,			&z->digits[n], &x->digits[n], carry);	} else		z->digits[n] = XP_add(n, z->digits, x->digits,			y->digits, 0);	return normalize(z, z->size);}static T sub(T z, T x, T y) {	int borrow, n = y->ndigits;	borrow = XP_sub(n, z->digits, x->digits,		y->digits, 0);	if (x->ndigits > n)		borrow = XP_diff(x->ndigits - n, &z->digits[n],			&x->digits[n], borrow);	assert(borrow == 0);	return normalize(z, z->size);}static T mulmod(T x, T y, T p) {	T z, xy = AP_mul(x, y);	z = AP_mod(xy, p);	AP_free(&xy);	return z;}static int cmp(T x, T y) {	if (x->ndigits != y->ndigits)		return x->ndigits - y->ndigits;	else		return XP_cmp(x->ndigits, x->digits, y->digits);}T AP_new(long int n) {	return set(mk(sizeof (long int)), n);}void AP_free(T *z) {	assert(z && *z);	FREE(*z);}T AP_neg(T x) {	T z;	assert(x);	z = mk(x->ndigits);	memcpy(z->digits, x->digits, x->ndigits);	z->ndigits = x->ndigits;	z->sign = iszero(z) ? 1 : -x->sign;	return z;}T AP_mul(T x, T y) {	T z;	assert(x);	assert(y);	z = mk(x->ndigits + y->ndigits);	XP_mul(z->digits, x->ndigits, x->digits, y->ndigits,		y->digits);	normalize(z, z->size);	z->sign = iszero(z)		|| ((x->sign^y->sign) == 0) ? 1 : -1;	return z;}T AP_add(T x, T y) {	T z;	assert(x);	assert(y);	if (((x->sign^y->sign) == 0)) {		z = add(mk(maxdigits(x,y) + 1), x, y);		z->sign = iszero(z) ? 1 : x->sign;	} else		if (cmp(x, y) > 0) {			z = sub(mk(x->ndigits), x, y);			z->sign = iszero(z) ? 1 : x->sign;		}		else {			z = sub(mk(y->ndigits), y, x);			z->sign = iszero(z) ? 1 : -x->sign;		}	return z;}T AP_sub(T x, T y) {	T z;	assert(x);	assert(y);	if (!((x->sign^y->sign) == 0)) {		z = add(mk(maxdigits(x,y) + 1), x, y);		z->sign = iszero(z) ? 1 : x->sign;	} else		if (cmp(x, y) > 0) {			z = sub(mk(x->ndigits), x, y);			z->sign = iszero(z) ? 1 : x->sign;		} else {			z = sub(mk(y->ndigits), y, x);			z->sign = iszero(z) ? 1 : -x->sign;		}	return z;}T AP_div(T x, T y) {	T q, r;	assert(x);	assert(y);	assert(!iszero(y));	q = mk(x->ndigits);	r = mk(y->ndigits);	{		XP_T tmp = ALLOC(x->ndigits + y->ndigits + 2);		XP_div(x->ndigits, q->digits, x->digits,			y->ndigits, y->digits, r->digits, tmp);		FREE(tmp);	}	normalize(q, q->size);	normalize(r, r->size);	q->sign = iszero(q)		|| ((x->sign^y->sign) == 0) ? 1 : -1;	if (!((x->sign^y->sign) == 0) && !iszero(r)) {		int carry = XP_sum(q->size, q->digits,			q->digits, 1);		assert(carry == 0);		normalize(q, q->size);	}	AP_free(&r);	return q;}T AP_mod(T x, T y) {	T q, r;	assert(x);	assert(y);	assert(!iszero(y));	q = mk(x->ndigits);	r = mk(y->ndigits);	{		XP_T tmp = ALLOC(x->ndigits + y->ndigits + 2);		XP_div(x->ndigits, q->digits, x->digits,			y->ndigits, y->digits, r->digits, tmp);		FREE(tmp);	}	normalize(q, q->size);	normalize(r, r->size);	q->sign = iszero(q)		|| ((x->sign^y->sign) == 0) ? 1 : -1;	if (!((x->sign^y->sign) == 0) && !iszero(r)) {		int borrow = XP_sub(r->size, r->digits,			y->digits, r->digits, 0);		assert(borrow == 0);		normalize(r, r->size);	}	AP_free(&q);	return r;}T AP_pow(T x, T y, T p) {	T z;	assert(x);	assert(y);	assert(y->sign == 1);	assert(!p || p->sign==1 && !iszero(p) && !isone(p));	if (iszero(x))		return AP_new(0);	if (iszero(y))		return AP_new(1);	if (isone(x))		return AP_new((((y)->digits[0]&1) == 0) ? 1 : x->sign);	if (p)		if (isone(y))			z = AP_mod(x, p);		else {			T y2 = AP_rshift(y, 1), t = AP_pow(x, y2, p);			z = mulmod(t, t, p);			AP_free(&y2);			AP_free(&t);			if (!(((y)->digits[0]&1) == 0)) {				z = mulmod(y2 = AP_mod(x, p), t = z, p);				AP_free(&y2);				AP_free(&t);			}		}	else		if (isone(y))			z = AP_addi(x, 0);		else {			T y2 = AP_rshift(y, 1), t = AP_pow(x, y2, NULL);			z = AP_mul(t, t);			AP_free(&y2);			AP_free(&t);			if (!(((y)->digits[0]&1) == 0)) {				z = AP_mul(x, t = z);				AP_free(&t);			}		}	return z;}int AP_cmp(T x, T y) {	assert(x);	assert(y);	if (!((x->sign^y->sign) == 0))		return x->sign;	else if (x->sign == 1)		return cmp(x, y);	else		return cmp(y, x);}T AP_addi(T x, long int y) {	unsigned char d[sizeof (unsigned long)];	struct T t;	t.size = sizeof d;	t.digits = d;	return AP_add(x, set(&t, y));}T AP_subi(T x, long int y) {	unsigned char d[sizeof (unsigned long)];	struct T t;	t.size = sizeof d;	t.digits = d;	return AP_sub(x, set(&t, y));}T AP_muli(T x, long int y) {	unsigned char d[sizeof (unsigned long)];	struct T t;	t.size = sizeof d;	t.digits = d;	return AP_mul(x, set(&t, y));}T AP_divi(T x, long int y) {	unsigned char d[sizeof (unsigned long)];	struct T t;	t.size = sizeof d;	t.digits = d;	return AP_div(x, set(&t, y));}int AP_cmpi(T x, long int y) {	unsigned char d[sizeof (unsigned long)];	struct T t;	t.size = sizeof d;	t.digits = d;	return AP_cmp(x, set(&t, y));}long int AP_modi(T x, long int y) {	long int rem;	T r;	unsigned char d[sizeof (unsigned long)];	struct T t;	t.size = sizeof d;	t.digits = d;	r = AP_mod(x, set(&t, y));	rem = XP_toint(r->ndigits, r->digits);	AP_free(&r);	return rem;}T AP_lshift(T x, int s) {	T z;	assert(x);	assert(s >= 0);	z = mk(x->ndigits + ((s+7)&~7)/8);	XP_lshift(z->size, z->digits, x->ndigits,		x->digits, s, 0);	z->sign = x->sign;	return normalize(z, z->size);}T AP_rshift(T x, int s) {	assert(x);	assert(s >= 0);	if (s >= 8*x->ndigits)		return AP_new(0);	else {		T z = mk(x->ndigits - s/8);		XP_rshift(z->size, z->digits, x->ndigits,			x->digits, s, 0);		normalize(z, z->size);		z->sign = iszero(z) ? 1 : x->sign;		return z;	}}long int AP_toint(T x) {	unsigned long u;	assert(x);	u = XP_toint(x->ndigits, x->digits)%(LONG_MAX + 1UL);	if (x->sign == -1)		return -(long)u;	else		return  (long)u;}T AP_fromstr(const char *str, int base, char **end) {	T z;	const char *p = str;	char *endp, sign = '\0';	int carry;	assert(p);	assert(base >= 2 && base <= 36);	while (*p && isspace(*p))		p++;	if (*p == '-' || *p == '+')		sign = *p++;	{		const char *start;		int k, n = 0;		for ( ; *p == '0' && p[1] == '0'; p++)			;		start = p;		for ( ; (  '0' <= *p && *p <= '9' && *p < '0' + base			|| 'a' <= *p && *p <= 'z' && *p < 'a' + base - 10			|| 'A' <= *p && *p <= 'Z' && *p < 'A' + base - 10); p++)			n++;		for (k = 1; (1<<k) < base; k++)			;		z = mk(((k*n + 7)&~7)/8);		p = start;	}	carry = XP_fromstr(z->size, z->digits, p,		base, &endp);	assert(carry == 0);	normalize(z, z->size);	if (endp == p) {		endp = (char *)str;		z = AP_new(0);	} else		z->sign = iszero(z) || sign != '-' ? 1 : -1;	if (end)		*end = (char *)endp;	return z;}char *AP_tostr(char *str, int size, int base, T x) {	XP_T q;	assert(x);	assert(base >= 2 && base <= 36);	assert(str == NULL || size > 1);	if (str == NULL) {		{			int k;			for (k = 5; (1<<k) > base; k--)				;			size = (8*x->ndigits)/k + 1 + 1;			if (x->sign == 1)				size++;		}		str = ALLOC(size);	}	q = ALLOC(x->ndigits);	memcpy(q, x->digits, x->ndigits);	if (x->sign == -1) {		str[0] = '-';		XP_tostr(str + 1, size - 1, base, x->ndigits, q);	} else		XP_tostr(str, size, base, x->ndigits, q);	FREE(q);	return str;}void AP_fmt(int code, va_list *app,	int put(int c, void *cl), void *cl,	unsigned char flags[], int width, int precision) {	T x;	char *buf;	assert(app && flags);	x = va_arg(*app, T);	assert(x);	buf = AP_tostr(NULL, 0, 10, x);	Fmt_putd(buf, strlen(buf), put, cl, flags,		width, precision);	FREE(buf);}