/* bigint.c */
/*
 This file is part of the AVR-Crypto-Lib.
 Copyright (C) 2006-2015 Daniel Otte (bg@nerilex.org)

 This program is free software: you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation, either version 3 of the License, or
 (at your option) any later version.

 This program is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU General Public License for more details.

 You should have received a copy of the GNU General Public License
 along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
/**
 * \file		bigint.c
 * \author		Daniel Otte
 * \date		2010-02-22
 * 
 * \license	    GPLv3 or later
 * 
 */

#define STRING2(x) #x
#define STRING(x) STRING2(x)
#define STR_LINE STRING(__LINE__)

#include "bigint.h"
#include <string.h>
/*
 #include "cli.h"
 #include "bigint_io.h"
 */
#ifndef MAX
#define MAX(a,b) (((a)>(b))?(a):(b))
#endif

#ifndef MIN
#define MIN(a,b) (((a)<(b))?(a):(b))
#endif

#define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
#define GET_FBS(a)   ((a)->info&BIGINT_FBS_MASK)
#define SET_NEG(a)   (a)->info |= BIGINT_NEG_MASK
#define SET_POS(a)   (a)->info &= ~BIGINT_NEG_MASK
#define XCHG(a,b)    do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
#define XCHG_PTR(a,b)    do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
	                         b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
	                         a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)

#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)

/******************************************************************************/
/*
 void bigint_copy(bigint_t *dest, const bigint_t *src){
 memcpy(dest->wordv, src->wordv, src->length_W);
 dest->length_W = src->length_W;
 dest->info = src->info;
 }
 */
/******************************************************************************/

/* this should be implemented in assembly */
/*
 void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
 uint16_t t=0, i;
 if(a->length_W < b->length_W){
 XCHG_PTR(a,b);
 }
 for(i=0; i<b->length_W; ++i){
 t = a->wordv[i] + b->wordv[i] + t;
 dest->wordv[i] = (uint8_t)t;
 t>>=8;
 }
 for(; i<a->length_W; ++i){
 t = a->wordv[i] + t;
 dest->wordv[i] = (uint8_t)t;
 t>>=8;
 }
 dest->wordv[i++] = t;
 dest->length_W = i;
 bigint_adjust(dest);
 }
 */
/******************************************************************************/

/* this should be implemented in assembly */
/*
 void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, uint16_t scale){
 uint16_t i,j=0;
 uint16_t t=0;
 if(scale>dest->length_W)
 memset(dest->wordv+dest->length_W, 0, scale-dest->length_W);
 for(i=scale; i<a->length_W+scale; ++i,++j){
 t = a->wordv[j] + t;
 if(dest->length_W>i){
 t += dest->wordv[i];
 }
 dest->wordv[i] = (uint8_t)t;
 t>>=8;
 }
 while(t){
 if(dest->length_W>i){
 t = dest->wordv[i] + t;
 }
 dest->wordv[i] = (uint8_t)t;
 t>>=8;
 ++i;
 }
 if(dest->length_W < i){
 dest->length_W = i;
 }
 bigint_adjust(dest);
 }
 */
/******************************************************************************/

/* this should be implemented in assembly */
void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b)
{
    int8_t borrow = 0;
    int8_t r;
    int16_t t;
    uint16_t i, min, max;
    min = MIN(a->length_W, b->length_W);
    max = MAX(a->length_W, b->length_W);
    r = bigint_cmp_u(a, b);
    if (r == 0) {
        dest->length_W = 0;
        dest->wordv[0] = 0;
        bigint_adjust(dest);
        return;
    }
    if (b->length_W == 0) {
        dest->length_W = a->length_W;
        memcpy(dest->wordv, a->wordv, a->length_W);
        dest->info = a->info;
        SET_POS(dest);
        return;
    }
    if (a->length_W == 0) {
        dest->length_W = b->length_W;
        memcpy(dest->wordv, b->wordv, b->length_W);
        dest->info = b->info;
        SET_NEG(dest);
        return;
    }
    if (r < 0) {
        bigint_sub_u(dest, b, a);
        SET_NEG(dest);
    } else {
        for (i = 0; i < min; ++i) {
            t = a->wordv[i] - b->wordv[i] - borrow;
            if (t < 0) {
                borrow = 1;
                dest->wordv[i] = (uint8_t) t;
            } else {
                borrow = 0;
                dest->wordv[i] = (uint8_t) t;
            }
        }
        for (; i < max; ++i) {
            t = a->wordv[i] - borrow;
            if (t < 0) {
                borrow = 1;
                dest->wordv[i] = (uint8_t) t;
            } else {
                borrow = 0;
                dest->wordv[i] = (uint8_t) t;
            }

        }
        SET_POS(dest);
        dest->length_W = i;
        bigint_adjust(dest);
    }
}

/******************************************************************************/

int8_t bigint_cmp_u(const bigint_t *a, const bigint_t *b)
{
    if (a->length_W > b->length_W) {
        return 1;
    }
    if (a->length_W < b->length_W) {
        return -1;
    }
    if (a->length_W == 0) {
        return 0;
    }
    uint16_t i;
    i = a->length_W - 1;
    do {
        if (a->wordv[i] != b->wordv[i]) {
            if (a->wordv[i] > b->wordv[i]) {
                return 1;
            } else {
                return -1;
            }
        }
    } while (i--);
    return 0;
}

/******************************************************************************/

void bigint_add_s(bigint_t *dest, const bigint_t *a, const bigint_t *b)
{
    uint8_t s;
    s = GET_SIGN(a) ? 2 : 0;
    s |= GET_SIGN(b) ? 1 : 0;
    switch (s) {
    case 0: /* both positive */
        bigint_add_u(dest, a, b);
        SET_POS(dest);
        break;
    case 1: /* a positive, b negative */
        bigint_sub_u(dest, a, b);
        break;
    case 2: /* a negative, b positive */
        bigint_sub_u(dest, b, a);
        break;
    case 3: /* both negative */
        bigint_add_u(dest, a, b);
        SET_NEG(dest);
        break;
    default: /* how can this happen?*/
        break;
    }
}

/******************************************************************************/

void bigint_sub_s(bigint_t *dest, const bigint_t *a, const bigint_t *b)
{
    uint8_t s;
    s = GET_SIGN(a) ? 2 : 0;
    s |= GET_SIGN(b) ? 1 : 0;
    switch (s) {
    case 0: /* both positive */
        bigint_sub_u(dest, a, b);
        break;
    case 1: /* a positive, b negative */
        bigint_add_u(dest, a, b);
        SET_POS(dest);
        break;
    case 2: /* a negative, b positive */
        bigint_add_u(dest, a, b);
        SET_NEG(dest);
        break;
    case 3: /* both negative */
        bigint_sub_u(dest, b, a);
        break;
    default: /* how can this happen?*/
        break;
    }

}

/******************************************************************************/

int8_t bigint_cmp_s(const bigint_t *a, const bigint_t *b)
{
    uint8_t s;
    if (a->length_W == 0 && b->length_W == 0) {
        return 0;
    }
    s = GET_SIGN(a) ? 2 : 0;
    s |= GET_SIGN(b) ? 1 : 0;
    switch (s) {
    case 0: /* both positive */
        return bigint_cmp_u(a, b);
        break;
    case 1: /* a positive, b negative */
        return 1;
        break;
    case 2: /* a negative, b positive */
        return -1;
        break;
    case 3: /* both negative */
        return bigint_cmp_u(b, a);
        break;
    default: /* how can this happen?*/
        break;
    }
    return 0; /* just to satisfy the compiler */
}

/******************************************************************************/

void bigint_shiftleft(bigint_t *a, uint16_t shift)
{
    uint16_t byteshift;
    uint16_t i;
    uint8_t bitshift;
    uint16_t t = 0;
    byteshift = (shift + 3) / 8;
    bitshift = shift & 7;
    memmove(a->wordv + byteshift, a->wordv, a->length_W);
    memset(a->wordv, 0, byteshift);
    if (bitshift != 0) {
        if (bitshift <= 4) { /* shift to the left */
            for (i = byteshift; i < a->length_W + byteshift; ++i) {
                t |= (a->wordv[i]) << bitshift;
                a->wordv[i] = (uint8_t) t;
                t >>= 8;
            }
            a->wordv[i] = (uint8_t) t;
            byteshift++;
        } else { /* shift to the right */
            for (i = a->length_W + byteshift - 1; i > byteshift - 1; --i) {
                t |= (a->wordv[i]) << (bitshift);
                a->wordv[i] = (uint8_t) (t >> 8);
                t <<= 8;
            }
            t |= (a->wordv[i]) << (bitshift);
            a->wordv[i] = (uint8_t) (t >> 8);
        }
    }
    a->length_W += byteshift;
    bigint_adjust(a);
}

/******************************************************************************/

void bigint_shiftright(bigint_t *a, uint16_t shift)
{
    uint16_t byteshift;
    uint16_t i;
    uint8_t bitshift;
    uint16_t t = 0;
    byteshift = shift / 8;
    bitshift = shift & 7;
    if (byteshift >= a->length_W) { /* we would shift out more than we have */
        bigint_set_zero(a);
        return;
    }
    if (byteshift == a->length_W - 1 && bitshift > GET_FBS(a)) {
        bigint_set_zero(a);
        return;
    }
    if (byteshift) {
        memmove(a->wordv, a->wordv + byteshift, a->length_W - byteshift);
        memset(a->wordv + a->length_W - byteshift, 0, byteshift);
    }
    if (bitshift != 0) {
        /* shift to the right */
        for (i = a->length_W - byteshift - 1; i > 0; --i) {
            t |= (a->wordv[i]) << (8 - bitshift);
            a->wordv[i] = (uint8_t) (t >> 8);
            t <<= 8;
        }
        t |= (a->wordv[0]) << (8 - bitshift);
        a->wordv[0] = (uint8_t) (t >> 8);
    }
    a->length_W -= byteshift;
    bigint_adjust(a);
}

/******************************************************************************/

void bigint_xor(bigint_t *dest, const bigint_t *a)
{
    uint16_t i;
    for (i = 0; i < a->length_W; ++i) {
        dest->wordv[i] ^= a->wordv[i];
    }
    bigint_adjust(dest);
}

/******************************************************************************/

void bigint_set_zero(bigint_t *a)
{
    a->length_W = 0;
}

/******************************************************************************/

/* using the Karatsuba-Algorithm */
/* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b)
{
    if (a->length_W == 0 || b->length_W == 0) {
        bigint_set_zero(dest);
        return;
    }
    if (dest == a || dest == b) {
        bigint_t d;
        uint8_t d_b[a->length_W + b->length_W];
        d.wordv = d_b;
        bigint_mul_u(&d, a, b);
        bigint_copy(dest, &d);
        return;
    }
    if (a->length_W == 1 || b->length_W == 1) {
        if (a->length_W != 1) {
            XCHG_PTR(a, b);
        }
        uint16_t i, t = 0;
        uint8_t x = a->wordv[0];
        for (i = 0; i < b->length_W; ++i) {
            t += b->wordv[i] * x;
            dest->wordv[i] = (uint8_t) t;
            t >>= 8;
        }
        dest->wordv[i] = (uint8_t) t;
        dest->length_W = i + 1;
        bigint_adjust(dest);
        return;
    }
    if (a->length_W <= 4 && b->length_W <= 4) {
        uint32_t p = 0, q = 0;
        uint64_t r;
        memcpy(&p, a->wordv, a->length_W);
        memcpy(&q, b->wordv, b->length_W);
        r = (uint64_t) p * (uint64_t) q;
        memcpy(dest->wordv, &r, a->length_W + b->length_W);
        dest->length_W = a->length_W + b->length_W;
        bigint_adjust(dest);
        return;
    }
    bigint_set_zero(dest);
    /* split a in xh & xl; split b in yh & yl */
    uint16_t n;
    n = (MAX(a->length_W, b->length_W) + 1) / 2;
    bigint_t xl, xh, yl, yh;
    xl.wordv = a->wordv;
    yl.wordv = b->wordv;
    if (a->length_W <= n) {
        xh.info = 0;
        xh.length_W = 0;
        xl.length_W = a->length_W;
        xl.info = 0;
    } else {
        xl.length_W = n;
        xl.info = 0;
        bigint_adjust(&xl);
        xh.wordv = a->wordv + n;
        xh.length_W = a->length_W - n;
        xh.info = 0;
    }
    if (b->length_W <= n) {
        yh.info = 0;
        yh.length_W = 0;
        yl.length_W = b->length_W;
        yl.info = b->info;
    } else {
        yl.length_W = n;
        yl.info = 0;
        bigint_adjust(&yl);
        yh.wordv = b->wordv + n;
        yh.length_W = b->length_W - n;
        yh.info = 0;
    }
    /* now we have split up a and b */
    uint8_t tmp_b[2 * n + 2], m_b[2 * (n + 1)];
    bigint_t tmp, tmp2, m;
    tmp.wordv = tmp_b;
    tmp2.wordv = tmp_b + n + 1;
    m.wordv = m_b;

    bigint_mul_u(dest, &xl, &yl); /* dest <= xl*yl     */
    bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl     */
    bigint_add_u(&tmp, &yh, &yl); /* tmp  <= yh+yl     */
    bigint_mul_u(&m, &tmp2, &tmp); /* m    <= tmp2*tmp  */
    bigint_mul_u(&tmp, &xh, &yh); /* h    <= xh*yh     */
    bigint_sub_u(&m, &m, dest); /* m    <= m-dest    */
    bigint_sub_u(&m, &m, &tmp); /* m    <= m-h       */
    bigint_add_scale_u(dest, &m, n);
    bigint_add_scale_u(dest, &tmp, 2 * n);
}

/******************************************************************************/

void bigint_mul_s(bigint_t *dest, const bigint_t *a, const bigint_t *b)
{
    uint8_t s;
    s = GET_SIGN(a) ? 2 : 0;
    s |= GET_SIGN(b) ? 1 : 0;
    switch (s) {
    case 0: /* both positive */
        bigint_mul_u(dest, a, b);
        SET_POS(dest);
        break;
    case 1: /* a positive, b negative */
        bigint_mul_u(dest, a, b);
        SET_NEG(dest);
        break;
    case 2: /* a negative, b positive */
        bigint_mul_u(dest, a, b);
        SET_NEG(dest);
        break;
    case 3: /* both negative */
        bigint_mul_u(dest, a, b);
        SET_POS(dest);
        break;
    default: /* how can this happen?*/
        break;
    }
}

/******************************************************************************/

/* square */
/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
void bigint_square(bigint_t *dest, const bigint_t *a)
{
    if (a->length_W <= 4) {
        uint64_t r = 0;
        memcpy(&r, a->wordv, a->length_W);
        r = r * r;
        memcpy(dest->wordv, &r, 2 * a->length_W);
        SET_POS(dest);
        dest->length_W = 2 * a->length_W;
        bigint_adjust(dest);
        return;
    }
    if (dest == a) {
        bigint_t d;
        uint8_t d_b[a->length_W * 2];
        d.wordv = d_b;
        bigint_square(&d, a);
        bigint_copy(dest, &d);
        return;
    }
    uint16_t n;
    n = (a->length_W + 1) / 2;
    bigint_t xh, xl, tmp; /* x-high, x-low, temp */
    uint8_t buffer[2 * n + 1];
    xl.wordv = a->wordv;
    xl.length_W = n;
    xh.wordv = a->wordv + n;
    xh.length_W = a->length_W - n;
    tmp.wordv = buffer;
    bigint_square(dest, &xl);
    bigint_square(&tmp, &xh);
    bigint_add_scale_u(dest, &tmp, 2 * n);
    bigint_mul_u(&tmp, &xl, &xh);
    bigint_shiftleft(&tmp, 1);
    bigint_add_scale_u(dest, &tmp, n);
}

/******************************************************************************/

void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale)
{
    bigint_t tmp;
    uint8_t tmp_b[b->length_W + 1];
    uint16_t i, j, byteshift = bitscale / 8;
    uint8_t borrow = 0;
    int16_t t;

    if (a->length_W < b->length_W + byteshift) {
        bigint_set_zero(a);
        return;
    }

    tmp.wordv = tmp_b;
    bigint_copy(&tmp, b);
    bigint_shiftleft(&tmp, bitscale & 7);

    for (j = 0, i = byteshift; i < tmp.length_W + byteshift; ++i, ++j) {
        t = a->wordv[i] - tmp.wordv[j] - borrow;
        a->wordv[i] = (uint8_t) t;
        if (t < 0) {
            borrow = 1;
        } else {
            borrow = 0;
        }
    }
    while (borrow) {
        if (i + 1 > a->length_W) {
            bigint_set_zero(a);
            return;
        }
        a->wordv[i] -= borrow;
        if (a->wordv[i] != 0xff) {
            borrow = 0;
        }
        ++i;
    }
    bigint_adjust(a);
}

/******************************************************************************/

void bigint_reduce(bigint_t *a, const bigint_t *r)
{
//	bigint_adjust(r);
    uint8_t rfbs = GET_FBS(r);

    if (r->length_W == 0 || a->length_W == 0) {
        return;
    }
    while (a->length_W > r->length_W) {
        bigint_sub_u_bitscale(a, r, (a->length_W - r->length_W) * 8 + GET_FBS(a)
                - rfbs - 1);
    }
    while ((GET_FBS(a) > rfbs + 1) && (a->length_W == r->length_W)) {
        bigint_sub_u_bitscale(a, r, GET_FBS(a) - rfbs - 1);
    }
    while (bigint_cmp_u(a, r) >= 0) {
        bigint_sub_u(a, a, r);
    }
    bigint_adjust(a);
}

/******************************************************************************/

/* calculate dest = a**exp % r */
/* using square&multiply */
void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp,
        const bigint_t *r)
{
    if (a->length_W == 0 || r->length_W == 0) {
        return;
    }

    bigint_t res, base;
    uint8_t base_b[MAX(a->length_W, r->length_W * 2)], res_b[r->length_W * 2];
    uint16_t i;
    uint8_t j, t;
    res.wordv = res_b;
    base.wordv = base_b;
    bigint_copy(&base, a);
    bigint_reduce(&base, r);
    res.wordv[0] = 1;
    res.length_W = 1;
    res.info = 0;
    bigint_adjust(&res);
    for (i = 0; i + 1 < exp->length_W; ++i) {
        t = exp->wordv[i];
        for (j = 0; j < 8; ++j) {
            if (t & 1) {
                bigint_mul_u(&res, &res, &base);
                bigint_reduce(&res, r);
            }
            bigint_square(&base, &base);
            bigint_reduce(&base, r);
            t >>= 1;
        }
    }
    t = exp->wordv[i];
    while (t) {
        if (t & 1) {
            bigint_mul_u(&res, &res, &base);
            bigint_reduce(&res, r);
        }
        bigint_square(&base, &base);
        bigint_reduce(&base, r);
        t >>= 1;
    }
    SET_POS(&res);
    bigint_copy(dest, &res);
}

/******************************************************************************/
/* gcd <-- gcd(x,y) a*x+b*y=gcd */
void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x,
        const bigint_t *y)
{
    bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
    volatile uint16_t i = 0;
    if (x->length_W == 0 || y->length_W == 0) {
        return;
    }
    while (x->wordv[i] == 0 && y->wordv[i] == 0) {
        ++i;
    }
    uint8_t g_b[i + 2], x_b[x->length_W - i], y_b[y->length_W - i];
    uint8_t u_b[x->length_W - i], v_b[y->length_W - i];
    uint8_t a_b[y->length_W + 2], c_b[y->length_W + 2];
    uint8_t b_b[x->length_W + 2], d_b[x->length_W + 2];

    g.wordv = g_b;
    x_.wordv = x_b;
    y_.wordv = y_b;
    memset(g_b, 0, i);
    g_b[i] = 1;
    g.length_W = i + 1;
    g.info = 0;
    x_.info = y_.info = 0;
    x_.length_W = x->length_W - i;
    y_.length_W = y->length_W - i;
    memcpy(x_.wordv, x->wordv + i, x_.length_W);
    memcpy(y_.wordv, y->wordv + i, y_.length_W);
    for (i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0;
            ++i) {
    }

    bigint_adjust(&x_);
    bigint_adjust(&y_);

    if (i) {
        bigint_shiftleft(&g, i);
        bigint_shiftright(&x_, i);
        bigint_shiftright(&y_, i);
    }
    u.wordv = u_b;
    v.wordv = v_b;
    a_.wordv = a_b;
    b_.wordv = b_b;
    c_.wordv = c_b;
    d_.wordv = d_b;

    bigint_copy(&u, &x_);
    bigint_copy(&v, &y_);
    a_.wordv[0] = 1;
    a_.length_W = 1;
    a_.info = 0;
    d_.wordv[0] = 1;
    d_.length_W = 1;
    d_.info = 0;
    bigint_set_zero(&b_);
    bigint_set_zero(&c_);
    do {
        while ((u.wordv[0] & 1) == 0) {
            bigint_shiftright(&u, 1);
            if ((a_.wordv[0] & 1) || (b_.wordv[0] & 1)) {
                bigint_add_s(&a_, &a_, &y_);
                bigint_sub_s(&b_, &b_, &x_);
            }
            bigint_shiftright(&a_, 1);
            bigint_shiftright(&b_, 1);
        }
        while ((v.wordv[0] & 1) == 0) {
            bigint_shiftright(&v, 1);
            if ((c_.wordv[0] & 1) || (d_.wordv[0] & 1)) {
                bigint_add_s(&c_, &c_, &y_);
                bigint_sub_s(&d_, &d_, &x_);
            }
            bigint_shiftright(&c_, 1);
            bigint_shiftright(&d_, 1);

        }
        if (bigint_cmp_u(&u, &v) >= 0) {
            bigint_sub_u(&u, &u, &v);
            bigint_sub_s(&a_, &a_, &c_);
            bigint_sub_s(&b_, &b_, &d_);
        } else {
            bigint_sub_u(&v, &v, &u);
            bigint_sub_s(&c_, &c_, &a_);
            bigint_sub_s(&d_, &d_, &b_);
        }
    } while (u.length_W);
    if (gcd) {
        bigint_mul_s(gcd, &v, &g);
    }
    if (a) {
        bigint_copy(a, &c_);
    }
    if (b) {
        bigint_copy(b, &d_);
    }
}

/******************************************************************************/

void bigint_inverse(bigint_t *dest, const bigint_t *a, const bigint_t *m)
{
    bigint_gcdext(NULL, dest, NULL, a, m);
    while (dest->info & BIGINT_NEG_MASK) {
        bigint_add_s(dest, dest, m);
    }
}

/******************************************************************************/

void bigint_changeendianess(bigint_t *a)
{
    uint8_t t, *p, *q;
    p = a->wordv;
    q = p + a->length_W - 1;
    while (p < q) {
        t = *p;
        *p = *q;
        *q = t;
        ++p;
        --q;
    }
}

/******************************************************************************/