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bignum.c
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bignum.c
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/* New bignum
* I am designing a new bignum data structure.
* bigcell[BIGISZE] array of 32bit integer.
* big_pt0 pointer of temporaly bignum.
* big_pt1 pointer of parmanent bignum.
* 90% of bigcell is temporaly area and rest 10% is parmanent area.
* in temporaly area rear 10% is working area for divide function.
* bigcell = [[temporaly50%,temporalyworking40%],parmanent10%]
* each bignum elementn ... element1,element0
* Car-part of the cell has the pointer of MSB.
* Cdr-part of then cell has the length
*
bigcell[int] heap[cell structure]
|(temporarly)| | |
|LSB ^ | |-------<|BIGX(car) |
| | | | | |
|MSB |<------ | |
|(working) | big_pt0 | |
| | | |
|(parmanent) | big_pt1 | |
* FFT-Multiply
* bigcell 32bit integer -> radix 10^3 complex
* bignum-x bignum-y IFFT(FFT(x)*FFT(y)) -> bigcell 32bit integer(normalize)
* complex data type uses double complex.
* It will be calculated correctly by multiplying by about 6000 digits.
* But beyond that, a complex overflow will occur. The calculation is inaccurate.
*/
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <stdlib.h>
#include <math.h>
#include "npl.h"
#define CHECKBIG0 if(big_pt0<0 || big_pt0>=BIGNUM_PARMA){error(RESOURCE_ERR,"bigcell pt0",big_pt0);}
#define CHECKBIG1 if(big_pt1<0 || big_pt1>=BIGSIZE){error(RESOURCE_ERR,"bigcell pt1",big_pt1);}
int get_length(int x)
{
return (GET_CDR(x));
}
void set_length(int x, int y)
{
SET_CDR(x, y);
}
int get_pointer(int x)
{
return (GET_CAR(x));
}
void set_pointer(int x, int y)
{
SET_CAR(x, y);
}
int makebigx(char *bignum)
{
char integer[15];
int i, j, res, sign, len;
// check sign
if (bignum[0] == '-')
sign = -1;
else
sign = 1;
// remove sign
if (bignum[0] == '-' || bignum[0] == '+') {
i = laststr(bignum);
for (j = 0; j < i; j++)
bignum[j] = bignum[j + 1];
bignum[j] = NUL;
}
// length to check long data type
len = 0;
// generate bignum data cell
res = gen_big();
i = laststr(bignum);
while (i >= 0) {
if (i > 8) {
for (j = 8; j >= 0; j--) {
integer[j] = bignum[i];
i--;
}
integer[9] = NUL;
CHECKBIG0 bigcell[big_pt0++] = atoi(integer);
len++;
} else {
integer[i + 1] = NUL;
while (i >= 0) {
integer[i] = bignum[i];
i--;
}
CHECKBIG0 bigcell[big_pt0++] = atoi(integer);
len++;
}
}
if (len == 2) {
long long int l, m;
CHECKBIG0 l = (long long int) bigcell[big_pt0 - 1] * BIGNUM_BASE;
m = (long long int) bigcell[big_pt0 - 2];
m = (l + m) * sign;
SET_TAG(res, LONGN);
SET_LONG(res, m);
return (res);
} else {
SET_TAG(res, BIGX);
set_pointer(res, big_pt0 - 1);
set_length(res, len);
set_sign(res, sign);
return (res);
}
}
int makehexbigx(char *bignum)
{
int num, i, j;
j = laststr(bignum);
i = 0;
num = makeint(0);
while (i < j) {
switch (bignum[i]) {
case '0':
num = plus(num, makeint(0));
break;
case '1':
num = plus(num, makeint(1));
break;
case '2':
num = plus(num, makeint(2));
break;
case '3':
num = plus(num, makeint(3));
break;
case '4':
num = plus(num, makeint(4));
break;
case '5':
num = plus(num, makeint(5));
break;
case '6':
num = plus(num, makeint(6));
break;
case '7':
num = plus(num, makeint(7));
break;
case '8':
num = plus(num, makeint(8));
break;
case '9':
num = plus(num, makeint(9));
break;
case 'a':
num = plus(num, makeint(10));
break;
case 'b':
num = plus(num, makeint(11));
break;
case 'c':
num = plus(num, makeint(12));
break;
case 'd':
num = plus(num, makeint(13));
break;
case 'e':
num = plus(num, makeint(14));
break;
case 'f':
num = plus(num, makeint(15));
break;
case 'A':
num = plus(num, makeint(11));
break;
case 'B':
num = plus(num, makeint(12));
break;
case 'C':
num = plus(num, makeint(13));
break;
case 'D':
num = plus(num, makeint(14));
break;
case 'E':
num = plus(num, makeint(15));
break;
case 'F':
num = plus(num, makeint(16));
break;
}
i++;
num = mult(num, makeint(16));
}
return (num);
}
int makeoctbigx(char *bignum)
{
int num, i, j;
j = laststr(bignum);
i = 0;
num = makeint(0);
while (i < j) {
switch (bignum[i]) {
case '0':
num = plus(num, makeint(0));
break;
case '1':
num = plus(num, makeint(1));
break;
case '2':
num = plus(num, makeint(2));
break;
case '3':
num = plus(num, makeint(3));
break;
case '4':
num = plus(num, makeint(4));
break;
case '5':
num = plus(num, makeint(5));
break;
case '6':
num = plus(num, makeint(6));
break;
case '7':
num = plus(num, makeint(7));
break;
}
i++;
num = mult(num, makeint(8));
}
return (num);
}
int makebinbigx(char *bignum)
{
int num, i, j;
j = laststr(bignum);
i = 0;
num = makeint(0);
while (i < j) {
switch (bignum[i]) {
case '0':
num = plus(num, makeint(0));
break;
case '1':
num = plus(num, makeint(1));
break;
}
i++;
num = mult(num, makeint(2));
}
return (num);
}
void print_bigx(int x)
{
int y, len;
char str1[256];
if (get_sign(x) == -1)
fputc('-', GET_PORT(output_stream));
y = get_pointer(x); //get pointer of bigcell
len = get_length(x); //get length of bignum;
if (!bridge_flag)
fprintf(GET_PORT(output_stream), "%d", bigcell[y]);
else {
sprintf(str1, "%d", bigcell[y]);
strcat(bridge, str1);
}
y--;
len--;
do {
if (!bridge_flag)
fprintf(GET_PORT(output_stream), "%09d", bigcell[y]);
else {
sprintf(str1, "%09d", bigcell[y]);
strcat(bridge, str1);
}
y--;
len--;
}
while (len > 0);
}
int gen_big(void)
{
int res;
res = freshcell();
SET_CDR(res, NIL);
SET_ARITY(res, -1); //in eisl SET_PROP
return (res);
}
// set sign
void set_sign(int x, int y)
{
SET_OPT(x, y);
}
// get sign
int get_sign(int x)
{
return (GET_OPT(x));
}
int bigx_positivep(int x)
{
if (get_sign(x) == 1)
return (1);
else
return (0);
}
int bigx_negativep(int x)
{
if (get_sign(x) == -1)
return (1);
else
return (0);
}
int bigx_eqp(int x, int y)
{
int len, pointerx, pointery;
if (get_sign(x) != get_sign(y))
return (0);
else if (get_length(x) != get_length(y))
return (0);
len = get_length(x);
pointerx = get_pointer(x);
pointery = get_pointer(y);
do {
if (bigcell[pointerx] != bigcell[pointery])
return (0);
pointerx--;
pointery--;
len--;
}
while (len > 0);
return (1);
}
int bigx_abs_smallerp(int x, int y)
{
int len1, len2, pointerx, pointery;
len1 = get_length(x);
len2 = get_length(y);
if (len1 < len2)
return (1);
else if (len1 > len2)
return (0);
else {
pointerx = get_pointer(x);
pointery = get_pointer(y);
do {
if (bigcell[pointerx] < bigcell[pointery])
return (1);
if (bigcell[pointerx] > bigcell[pointery])
return (0);
pointerx--;
pointery--;
len1--;
}
while (len1 > 0);
return (0);
}
}
int bigx_smallerp(int x, int y)
{
if (bigx_positivep(x) && bigx_negativep(x))
return (0);
else if (bigx_negativep(x) && bigx_positivep(y))
return (1);
else if (bigx_positivep(x) && bigx_positivep(y))
return (bigx_abs_smallerp(x, y));
else if (bigx_negativep(x) && bigx_negativep(y))
return (bigx_abs_smallerp(y, x));
else
return (0);
return (0);
}
int bigx_int_to_big(int x)
{
int res, y;
y = GET_INT(x);
CHECKBIG0 bigcell[big_pt0++] = abs(y);
res = gen_big();
SET_TAG(res, BIGX);
set_pointer(res, big_pt0 - 1);
set_length(res, 1);
if (y >= 0)
set_sign(res, 1);
else
set_sign(res, -1);
return (res);
}
int bigx_long_to_big(int x)
{
int res, i2, i1;
long long int l;
l = GET_LONG(x);
i2 = llabs(l) % BIGNUM_BASE;
i1 = llabs(l) / BIGNUM_BASE;
CHECKBIG0 bigcell[big_pt0++] = i2;
CHECKBIG0 bigcell[big_pt0++] = i1;
res = gen_big();
SET_TAG(res, BIGX);
set_pointer(res, big_pt0 - 1);
set_length(res, 2);
if (l >= 0)
set_sign(res, 1);
else
set_sign(res, -1);
return (res);
}
int bigx_simplify(int x)
{
int i1;
long long int l, l1, l2;
if (get_length(x) == 0) {
return (makeint(0));
} else if (get_length(x) == 1) {
i1 = bigcell[get_pointer(x)];
i1 = i1 * get_sign(x);
return (makeint(i1));
} else if (get_length(x) == 2) {
l1 = bigcell[get_pointer(x)];
l2 = bigcell[get_pointer(x) - 1];
l = (l1 * BIGNUM_BASE + l2) * get_sign(x);
return (makelong(l));
} else
return (x);
}
// add n-zero-cells to x
int bigx_shift(int x, int n)
{
int res, len, pointer;
len = get_length(x);
pointer = get_pointer(x) - len + 1; // LSB
res = gen_big();
SET_TAG(res, BIGX);
set_sign(res, get_sign(x));
int i;
for (i = 0; i < n; i++) {
CHECKBIG0 bigcell[big_pt0++] = 0;
}
for (i = 0; i < len; i++) {
CHECKBIG0 bigcell[big_pt0++] = bigcell[pointer + i];
}
set_pointer(res, big_pt0 - 1);
set_length(res, len + n);
return (res);
}
int bigx_to_parmanent(int x)
{
int len, pointer;
pointer = get_pointer(x);
len = get_length(x);
pointer = get_pointer(x);
big_pt1 = big_pt1 + len;
CHECKBIG1 int i;
for (i = 0; i < len; i++) {
bigcell[big_pt1 - i] = bigcell[pointer - i];
}
big_pt1++;
set_pointer(x, big_pt1 - 1);
return (x);
}
int bigx_abs(int x)
{
int res;
res = gen_big();
SET_TAG(res, BIGX);
set_sign(res, 1);
set_pointer(res, get_pointer(x));
set_length(res, get_length(x));
return (res);
}
int bigx_zerop(int x)
{
int len, pointer;
len = get_length(x);
pointer = get_pointer(x);
while (len > 0) {
if (bigcell[pointer--] != 0)
return (0);
len--;
}
return (1);
}
int bigx_plus(int arg1, int arg2)
{
int res;
res = UNDEF;
if (bigx_positivep(arg1) && bigx_positivep(arg2)) {
res = bigx_plus1(arg1, arg2);
set_sign(res, 1);
} else if (bigx_negativep(arg1) && bigx_negativep(arg2)) {
res = bigx_plus1(arg1, arg2);
set_sign(res, -1);
} else if (bigx_positivep(arg1) && bigx_negativep(arg2)) {
if (bigx_abs_smallerp(arg1, arg2)) {
res = bigx_minus1(arg2, arg1);
set_sign(res, -1);
} else {
res = bigx_minus1(arg1, arg2);
set_sign(res, 1);
}
} else if (bigx_negativep(arg1) && bigx_positivep(arg2)) {
if (bigx_abs_smallerp(arg1, arg2)) {
res = bigx_minus1(arg2, arg1);
set_sign(res, 1);
} else {
res = bigx_minus1(arg1, arg2);
set_sign(res, -1);
}
}
if (simp_flag)
res = bigx_simplify(res);
return (res);
}
int bigx_plus1(int arg1, int arg2)
{
int len1, len2, pointerx, pointery, c, len, res;
len1 = get_length(arg1);
len2 = get_length(arg2);
pointerx = get_pointer(arg1) - len1 + 1; //LSB
pointery = get_pointer(arg2) - len2 + 1; //LSB
res = gen_big();
SET_TAG(res, BIGX);
set_sign(res, 1);
c = 0;
len = 0;
do {
int x, y, z, q;
if (len1 > 0)
x = bigcell[pointerx];
else
x = 0;
if (len2 > 0)
y = bigcell[pointery];
else
y = 0;
z = x + y + c;
c = z / BIGNUM_BASE;
q = z % BIGNUM_BASE;
CHECKBIG0 bigcell[big_pt0++] = q;
pointerx++;
pointery++;
len1--;
len2--;
len++;
}
while (len1 > 0 || len2 > 0);
if (c != 0) {
CHECKBIG0 bigcell[big_pt0++] = c;
len++;
}
set_pointer(res, big_pt0 - 1);
set_length(res, len);
return (res);
}
int bigx_minus(int arg1, int arg2)
{
int res;
res = UNDEF;
if (bigx_positivep(arg1) && bigx_positivep(arg2)) {
if (bigx_smallerp(arg1, arg2)) {
res = bigx_minus1(arg2, arg1);
set_sign(res, -1);
} else {
res = bigx_minus1(arg1, arg2);
set_sign(res, 1);
}
} else if (bigx_positivep(arg1) && bigx_negativep(arg2)) {
res = bigx_plus1(arg1, arg2);
set_sign(res, 1);
} else if (bigx_negativep(arg1) && bigx_positivep(arg2)) {
res = bigx_plus1(arg1, arg2);
set_sign(res, -1);
} else if (bigx_negativep(arg1) && bigx_negativep(arg2)) {
if (bigx_abs_smallerp(arg1, arg2)) {
res = bigx_minus1(arg2, arg1);
set_sign(res, 1);
} else {
res = bigx_minus1(arg1, arg2);
set_sign(res, -1);
}
}
if (simp_flag)
res = bigx_simplify(res);
return (res);
}
// arg1 > arg2
int bigx_minus1(int arg1, int arg2)
{
int len1, len2, pointerx, pointery, len, z, c, res;
len1 = get_length(arg1);
len2 = get_length(arg2);
pointerx = get_pointer(arg1) - len1 + 1; // LSB
pointery = get_pointer(arg2) - len2 + 1; // LSB
res = gen_big();
SET_TAG(res, BIGX);
set_sign(res, 1);
c = 0;
len = 0;
do {
int x, y;
if (len1 > 0)
x = bigcell[pointerx];
else
x = 0;
if (len2 > 0)
y = bigcell[pointery];
else
y = 0;
if ((x + c - y) < 0) {
z = (x + BIGNUM_BASE + c) - y;
c = -1;
} else {
z = (x + c) - y;
c = 0;
}
CHECKBIG0 bigcell[big_pt0++] = z;
pointerx++;
pointery++;
len1--;
len2--;
len++;
}
while (len1 > 0 || len2 > 0);
big_pt0--;
while (bigcell[big_pt0] == 0 && len > 1) {
big_pt0--;
len--;
}
big_pt0++;
set_pointer(res, big_pt0 - 1);
set_length(res, len);
return (res);
}
int bigx_mult(int arg1, int arg2)
{
int res;
if (get_length(arg1) + get_length(arg2) > 10) {
return (bigx_ntt_mult(arg1, arg2));
}
res = UNDEF;
if (bigx_positivep(arg1) && bigx_positivep(arg2)) {
res = bigx_mult1(arg1, arg2);
set_sign(res, 1);
} else if (bigx_positivep(arg1) && bigx_negativep(arg2)) {
res = bigx_mult1(arg1, arg2);
set_sign(res, -1);
} else if (bigx_negativep(arg1) && bigx_positivep(arg2)) {
res = bigx_mult1(arg1, arg2);
set_sign(res, -1);
} else if (bigx_negativep(arg1) && bigx_negativep(arg2)) {
res = bigx_mult1(arg1, arg2);
set_sign(res, 1);
}
if (simp_flag) {
res = bigx_simplify(res);
}
return (res);
}
int bigx_mult1(int arg1, int arg2)
{
int res, len1, len2, pointerx, pointery, len;
long long int x, y, z, l1, l2, c;
res = gen_big();
SET_TAG(res, BIGX);
len1 = get_length(arg1);
len2 = get_length(arg2);
len = len1 + len2;
set_sign(res, 1);
// clear area of calculate
int i, j;
for (i = 0; i <= len; i++) {
CHECKBIG0 bigcell[i + big_pt0] = 0;
}
pointery = get_pointer(arg2) - len2 + 1; //LSB
for (j = 0; j < len2; j++) {
pointerx = get_pointer(arg1) - len1 + 1; //LSB
for (i = 0; i < len1; i++) {
x = (long long int) bigcell[pointerx + i];
y = (long long int) bigcell[pointery + j];
z = x * y;
l2 = z % BIGNUM_BASE;
l1 = z / BIGNUM_BASE;
l2 = l2 + (long long int) bigcell[big_pt0 + j + i];
if (l2 >= BIGNUM_BASE) {
c = l2 / BIGNUM_BASE;
l2 = l2 % BIGNUM_BASE;
} else {
c = 0;
}
l1 = l1 + c + (long long int) bigcell[big_pt0 + j + i + 1];
CHECKBIG0 bigcell[big_pt0 + j + i] = (int) l2;
bigcell[big_pt0 + j + i + 1] = (int) l1;
}
}
big_pt0 = big_pt0 + len;
while (bigcell[big_pt0] == 0 && len > 1) {
big_pt0--;
len--;
}
big_pt0++;
set_pointer(res, big_pt0 - 1);
set_length(res, len + 1);
return (res);
}
int bigx_div(int arg1, int arg2)
{
int res, x, y;
res = UNDEF;
// if devidend is smaller than divisor,return 0
if (bigx_abs_smallerp(arg1, arg2))
return (makeint(0));
if (bigx_positivep(arg1) && bigx_positivep(arg2)) {
res = bigx_div1(arg1, arg2);
} else if (bigx_positivep(arg1) && bigx_negativep(arg2)) {
y = bigx_abs(arg2);
res = bigx_div1(arg1, y);
set_sign(res, -1);
} else if (bigx_negativep(arg1) && bigx_positivep(arg2)) {
x = bigx_abs(arg1);
res = bigx_div1(x, arg2);
set_sign(res, -1);
} else if (bigx_negativep(arg1) && bigx_negativep(arg2)) {
x = bigx_abs(arg1);
y = bigx_abs(arg2);
res = bigx_div1(x, y);
set_sign(res, 1);
}
if (simp_flag)
res = bigx_simplify(res);
return (res);
}
int bigx_div1(int arg1, int arg2)
{
int shift, save0, save1, d,
res, len, q, dividend, subtract, pointerx, pointery, msb1, msb2;
long long int lmsb1;
// arg1 < arg2 -> 0
if (smallerp(arg1, arg2))
return (makeint(0));
simp_flag = 0;
pointery = get_pointer(arg2); //MSB pointer
// Knuth The art of computer programing D-algorithm
if (bigcell[pointery] < BIGNUM_BASE / 2) {
d = BIGNUM_BASE / (1 + bigcell[pointery]);
arg1 = bigx_mult1(arg1, bigx_int_to_big(makeint(d)));
arg2 = bigx_mult1(arg2, bigx_int_to_big(makeint(d)));
}
res = gen_big();
SET_TAG(res, BIGX);
set_sign(res, 1);
len = 0;
big_pt0 = big_pt0 + get_length(arg1); // prepare area of answer.
set_pointer(res, big_pt0);
pointery = get_pointer(arg2); //MSB pointer
msb2 = bigcell[pointery]; // value of MSB
dividend = arg1;
save1 = BIGNUM_WORK;
do {
save0 = big_pt0;
big_pt0 = save1;
shift = get_length(dividend) - get_length(arg2);
pointerx = get_pointer(dividend); // MSB
msb1 = bigcell[pointerx];
if (msb1 > msb2) {
q = msb1 / msb2;
} else {
lmsb1 =
(long long int) bigcell[pointerx] * BIGNUM_BASE +
(long long int) bigcell[pointerx - 1];
q = (int) (lmsb1 / (long long int) msb2);
shift--;
// exception if q >= 10^10 , q = q/BIGNUMBASE. q must be smaller than BIGNUM_BASE
if (q >= BIGNUM_BASE) {
q = q / BIGNUM_BASE;
shift++;
}
}
subtract =
bigx_shift(bigx_mult1(arg2, bigx_int_to_big(makeint(q))),
shift);
dividend = bigx_minus(dividend, subtract);
// e.g. (div 100000000000000000000000000 25000000000000000000000002) = 3 (not 4)
while (negativep(dividend)) {
dividend = plus(dividend, bigx_shift(arg2, shift));
q--;
}
save1 = big_pt0;
big_pt0 = save0;
CHECKBIG0 bigcell[big_pt0 - len] = q;
len++;
}
while (!bigx_zerop(dividend) && !smallerp(dividend, arg2));
// when divident is smaller than divisior and shift > 0 insert zero
//e.q. div(3000000000000000000,30000000000)
while (shift > 0) {
CHECKBIG0 bigcell[big_pt0 - len] = 0;
shift--;
len++;
}
simp_flag = 1;
big_pt0++;
set_pointer(res, big_pt0 - 1);
set_length(res, len);
return (res);
}
int bigx_remainder(int arg1, int arg2)
{
int shift,
res, len, q, dividend, subtract,
pointerx, pointery, save0, pointer, msb1, msb2;
long long int lmsb1;
// arg1 > arg2 -> 0
if (smallerp(arg1, arg2))
return (makeint(0));
res = gen_big();
SET_TAG(res, BIGX);
set_sign(res, 1);
big_pt0 = big_pt0 + get_length(arg1); // prepare area of answer.
set_pointer(res, big_pt0);
pointery = get_pointer(arg2); //MSB pointer
msb2 = bigcell[pointery]; // value of MSB
dividend = arg1;
save0 = big_pt0;
big_pt0 = BIGNUM_WORK; // change to working area
do {
shift = get_length(dividend) - get_length(arg2);
pointerx = get_pointer(dividend); // MSB
msb1 = bigcell[pointerx];
if (msb1 > msb2) {
q = msb1 / msb2;
} else {
lmsb1 =
(long long int) bigcell[pointerx] * BIGNUM_BASE +
(long long int) bigcell[pointerx - 1];
q = (int) (lmsb1 / (long long int) msb2);
shift--;
}
subtract =
bigx_shift(bigx_mult1(arg2, bigx_int_to_big(makeint(q))),
shift);
dividend = bigx_minus(dividend, subtract);
// e.g. (div 100000000000000000000000000 25000000000000000000000002) = 3 (not 4)
while (negativep(dividend)) {
dividend = plus(dividend, bigx_shift(arg2, shift));
q--;
}
}
while (!smallerp(dividend, arg2));
big_pt0 = save0; //restore pointer
// copy dividend to big_pt0 temporarly area
len = get_length(dividend);
pointer = get_pointer(dividend) - len + 1; //LSB
int i;
for (i = 0; i < len; i++) {
CHECKBIG0 bigcell[big_pt0++] = bigcell[pointer++];
}
set_pointer(res, big_pt0 - 1);
set_length(res, len);
return (res);
}