ln ln_exp_int(ln i,int b,res_type restype)
{
ln j=NULL,k=NULL;
assert(b>=0);
if(b==0)
{
if(restype==newln)
return str2ln(NULL,"1");
else
return ln_setval(i,1);
}
else if(b==1)
{
if(restype==newln)
return copy_lns(NULL,i);
else
return i;
}
else if(b==2)
{
if(restype==newln)
return ln_square(i,newln);
else
return ln_square(i,firstln);
}
else
{
j=copy_lns(NULL,i);
if(b%2==0)
k=init_ln(1);
else
{
k=copy_lns(NULL,i);
b--;
}
while(1)
{
ln_square(j,firstln);
b/=2;
if(b==1)
break;
if(b%2!=0)
{
ln_multiply(k,j,firstln);
b--;
}
}
ln_multiply(k,j,firstln);
ln_free(j);
if(restype==newln)
return k;
else
{
copy_lns(&i,k);
ln_free(k);
return i;
}
}
}
ln ln_square(ln a,res_type restype)
{
ln b;
cell i,j,k,l;
int res;
if(a->lsd==a->msd)
{
if(restype==newln)
return ln_multiply(a,a,newln);
else
return ln_multiply(a,a,firstln);
}
b=ln_creat(ln_nodenum(a)*2);
b->sign=1;
b->power=a->power*2;
i=a->lsd;
j=b->lsd;
do
{
k=i;
l=j;
if(i->num !=0)
{
do
{
if(i==k)
res=i->num*k->num+l->num;
else
res=(i->num*k->num*2)+l->num;
if(res>=UNIT)
{
l->num=res%UNIT;
l->hcell->num+=res/UNIT;
}
else
l->num=res;
k=k->hcell;
l=l->hcell;
}
while(k != a->msd->hcell);
}
i=i->hcell;
j=j->hcell->hcell;
}
while(i != a->msd->hcell);
b->msd=j->lcell;
if(restype==newln)
return b;
else
{
copy_lns(&a,b);
ln_free(b);
return a;
}
}
/*
* 作用:把ln a乘以int b
* 副作用:调用ln_stripleadingzero()消除a前置0并且用ln_stripendingzero()调整a的指数
* 副作用:调用ln_stripleadingzero()消除结果的前置0
* 参数:
* a:待相乘的ln
* b:待相乘的int
* restype:结果存放方式
* 返回值:
* 成功:返回相加结果
* 失败:NULL
*/
ln ln_multiply_int(ln a,int b,res_type restype)
{
ln c,d;
//验证参数
if(ln_checknull(a)!=0)
{
fprintf(stderr,"[%s %d] %s error,reason: ln_checknull fail\n",__FILE__,__LINE__,__FUNCTION__);
return NULL;
}
//去除前置0
ln_stripleadingzero(a);
//简单地去掉后置0
ln_stripendingzero(a);
//把int转换为ln
c=ln_init(b);
if(c==NULL)
{
fprintf(stderr,"[%s %d] %s error,reason: ln_init fail\n",__FILE__,__LINE__,__FUNCTION__);
return NULL;
}
//相乘
d=ln_multiply(a,c,restype);
if(d==NULL)
{
fprintf(stderr,"[%s %d] %s error,reason: ln_multiply fail\n",__FILE__,__LINE__,__FUNCTION__);
return NULL;
}
ln_free(&c);
return d;
}
int main(int argc, const char *argv[])
{
int n;
for (n=1; n<0xffffffff; n++)
{
char s[16];
char d[16];
sprintf(s, "%d", n);
ln_multiply(s, "2", d, 16);
char ret = digitals_equal(s, d);
if (ret == 0)
continue;
ln_multiply(s, "3", d, 16);
ret = digitals_equal(s, d);
if (ret == 0)
continue;
ln_multiply(s, "4", d, 16);
ret = digitals_equal(s, d);
if (ret == 0)
continue;
ln_multiply(s, "5", d, 16);
ret = digitals_equal(s, d);
if (ret == 0)
continue;
ln_multiply(s, "6", d, 16);
ret = digitals_equal(s, d);
if (ret == 0)
continue;
printf("%s\n", s);
break;
}
return 0;
}
//add the two numbers
char* add_nums(const char* num1,const char* base1,const char* num2,const char* base2)
{
const char* base_str[2];
const char* num_str[2];
char *p,*q;
int base_gcd;
int i,test_res;
int base[2];
ln numerator[3],denominator[3];
vector digits;
//test bases
base_str[0]=base1;
base_str[1]=base2;
for(i=0;i<2;i++)
{
base[i]=test_base(base_str[i]);
if(base[i]==-1)
{
printf("Error: invalid base [%s]!\n",base_str[i]);
return NULL;
}
else if(base[i]==-2)
{
printf("Error: base [%s] is out of range "MACRO2STR(MIN_BASE)"-"MACRO2STR(MAX_BASE)"!\n",base_str[i]);
return NULL;
}
}
//test numbers
num_str[0]=num1;
num_str[1]=num2;
for(i=0;i<2;i++)
{
test_res=test_num(num_str[i],base[i]);
if(test_res==0)
{
printf("Error: invalid number [%s],the number should match the regular expression [0-9]+(.[0-9]+)? !\n",num_str[i]);
return NULL;
}
else if(test_res==2)
{
printf("Error: invalid number [%s] in base %d !\n",num_str[i],base[i]);
return NULL;
}
}
//convert the two numbers into fraction form
for(i=0;i<2;i++)
{
denominator[i]=get_denominator(num_str[i],base[i]);
numerator[i]=get_numerator(num_str[i],base[i]);
}
for(i=0;i<2;i++)
{
p=ln2str(numerator[i]);
q=ln2str(denominator[i]);
printf("operand in fraction:%s/%s\n",p,q);
fflush(stdout);
free(p);
free(q);
}
//compute the fraction
denominator[2]=ln_multiply(denominator[0],denominator[1],newln);
numerator[0]=ln_multiply(numerator[0],denominator[1],firstln);
numerator[1]=ln_multiply(numerator[1],denominator[0],firstln);
numerator[2]=ln_add(numerator[0],numerator[1],newln);
//free unused numbers
for(i=0;i<2;i++)
{
ln_free(&(numerator[i]));
ln_free(&(denominator[i]));
}
p=ln2str(numerator[2]);
q=ln2str(denominator[2]);
printf("result in fraction:%s/%s\n",p,q);
//simplifying the result fraction
base_gcd=gcd(base[0],base[1]);
if(base_gcd !=1)
{
while(ln_divideable_num(numerator[2],base_gcd)==1 && ln_divideable_num(denominator[2],base_gcd)==1)
{
ln_divide_int(numerator[2],base_gcd,0,trunc_res,firstln);
ln_divide_int(denominator[2],base_gcd,0,trunc_res,firstln);
}
}
p=ln2str(numerator[2]);
q=ln2str(denominator[2]);
printf("result in fraction:%s/%s\n",p,q);
fflush(stdout);
if(strcmp(q,"1")==0)
{
free(q);
q=(char*)malloc(strlen(p)+4);
if(!q)
{
ln_free(&(numerator[2]));
ln_free(&(denominator[2]));
printf("Error: coverting fraction to decimal number failed at line %d",__LINE__);
return NULL;
}
sprintf(q,"%s 10",p);
free(p);
return q;
}
free(p);
free(q);
digits=get_decimal_digit(numerator[2],denominator[2]);
if(!digits)
{
ln_free(&(numerator[2]));
ln_free(&(denominator[2]));
printf("Error: coverting fraction to decimal number failed at line %d",__LINE__);
return NULL;
}
p=get_decimalstr(digits,denominator[2]);
if(!p)
{
ln_free(&(numerator[2]));
ln_free(&(denominator[2]));
free_digit(digits);
printf("Error: coverting fraction to decimal number failed at line %d",__LINE__);
return NULL;
}
return p;
}
/*
* get the decimal digits
*/
vector get_decimal_digit(const ln numerator,const ln denominator)
{
ln a,b,c;
ln i,j,k,l,temp;
int power;
vector digits;
digits=vect_create_pointer();
if(!digits)
return NULL;
a=ln_copy(NULL,numerator);
b=ln_copy(NULL,denominator);
//get the digits
if(ln_cmp(a,b)<0)
{
vect_pushelm(digits,a);
ln_free(&b);
return digits;
}
//find out the maxpower
power=1;
c=ln_exp_int(b,power,newln);
while(ln_cmp(c,a)<=0)
{
ln_free(c);
power++;
c=ln_exp_int(b,power,newln);
}
ln_free(c);
power--;
while(ln_cmp(a,b)>=0)
{
c=ln_exp_int(b,power,newln);
//binary search
i=ln_setval(NULL,0); //i=0
j=ln_add_num(b,-1,newln); //j=numerator-1
while(1)
{
k=ln_add(i,j,newln); //k=(i+j)/2
k=ln_divide_num(k,2,0,trunc,firstln);
temp=ln_multiply(k,c,newln);
if(ln_cmp(temp,a)>0) //k*c>a
{
ln_free(j);
j=ln_add_num(k,-1,newln); //j=k-1
ln_free(k);
ln_free(temp);
}
else if(ln_cmp(temp,a)==0) //k*c=a
{
ln_free(i);
ln_free(j);
ln_free(c);
break;
}
else //k*c<a
{
l=ln_add_num(k,1,newln);
ln_free(temp);
temp=ln_multiply(l,c,newln);
if(ln_cmp(temp,a)==0) //(k+1)*c=a
{
ln_copy(&k,l);
ln_free(i);
ln_free(j);
ln_free(c);
ln_free(l);
break;
}
else if(ln_cmp(temp,a)>0) //(k+1)*c>a
{
ln_free(temp);
temp=ln_multiply(k,c,newln);
ln_free(i);
ln_free(j);
ln_free(l);
ln_free(c);
break;
}
else //(k+1) <a
{
ln_free(i);
i=ln_add_num(k,2,newln); //i=k+2
ln_free(k);
ln_free(temp);
}
}
}
vect_pushelm(digits,k);
minus_lns(a,temp,firstln);
ln_free(temp);
power--;
}
vect_pushelm(digits,a);
ln_free(b);
return digits;
}