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Faster multiplication using karatsuba algorithm #22

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64 changes: 45 additions & 19 deletions bn.c
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Original file line number Diff line number Diff line change
Expand Up @@ -248,29 +248,55 @@ void bignum_mul(struct bn* a, struct bn* b, struct bn* c)
require(b, "b is null");
require(c, "c is null");

struct bn row;
struct bn tmp;
int i, j;

bignum_init(c);

for (i = 0; i < BN_ARRAY_SIZE; ++i)
{
bignum_init(&row);
if (bignum_is_zero(a)) {return;}
if (bignum_is_zero(b)) {return;}

for (j = 0; j < BN_ARRAY_SIZE; ++j)
{
if (i + j < BN_ARRAY_SIZE)
{
bignum_init(&tmp);
DTYPE_TMP intermediate = ((DTYPE_TMP)a->array[i] * (DTYPE_TMP)b->array[j]);
bignum_from_int(&tmp, intermediate);
_lshift_word(&tmp, i + j);
bignum_add(&tmp, &row, &row);
}
}
bignum_add(c, &row, c);
struct bn tmp;
struct bn max_val;
bignum_from_int(&max_val, MAX_VAL);

struct bn a1;
DTYPE_TMP a0;
struct bn b1;
DTYPE_TMP b0;
struct bn z0;
struct bn z1;
struct bn z2;

bignum_rshift(a, &a1, WORD_SIZE*8);
bignum_rshift(b, &b1, WORD_SIZE*8);
a0 = (DTYPE_TMP)(a->array[0]);
b0 = (DTYPE_TMP)(b->array[0]);
DTYPE_TMP z0_small = a0*b0;

bignum_init(&z0);
z0.array[0] = z0_small & MAX_VAL;
z0.array[1] = (z0_small & (MAX_VAL << (WORD_SIZE*8))) >> (WORD_SIZE*8);
if (bignum_is_zero(&a1) && bignum_is_zero(&b1)) {
bignum_assign(c, &z0);
return;
}
bignum_mul(&a1, &b1, &z2);
struct bn a0_big;
struct bn b0_big;
bignum_from_int(&a0_big, a0);
bignum_from_int(&b0_big, b0);

struct bn tmpa;
struct bn tmpb;
struct bn tmpz1;
bignum_add(&a1, &a0_big, &tmpa);
bignum_add(&b1, &b0_big, &tmpb);
bignum_mul(&tmpa, &tmpb, &tmpz1);
bignum_sub(&tmpz1, &z2, &tmpa);
bignum_sub(&tmpa, &z0, &z1);

bignum_lshift(&z2, &tmp, WORD_SIZE*8);
bignum_add(&tmp, &z1, c);
bignum_lshift(c, &tmp, WORD_SIZE*8);
bignum_add(&tmp, &z0, c);
}


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