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/*************************************************
* Karatsuba Multiplication Source File *
* (C) 1999-2007 Jack Lloyd *
*************************************************/
#include <botan/mp_core.h>
#include <botan/mem_ops.h>
namespace Botan {
namespace {
/*************************************************
* Simple O(N^2) Multiplication *
*************************************************/
void bigint_simple_mul(word z[], const word x[], u32bit x_size,
const word y[], u32bit y_size)
{
clear_mem(z, x_size + y_size);
for(u32bit j = 0; j != x_size; ++j)
z[j+y_size] = bigint_mul_add_words(z + j, y, y_size, x[j]);
}
/*************************************************
* Karatsuba Multiplication Operation *
*************************************************/
void karatsuba_mul(word z[], const word x[], const word y[], u32bit N,
word workspace[])
{
const u32bit KARATSUBA_MUL_LOWER_SIZE = BOTAN_KARAT_MUL_THRESHOLD;
if(N == 6)
bigint_comba_mul6(z, x, y);
else if(N == 8)
bigint_comba_mul8(z, x, y);
else if(N < KARATSUBA_MUL_LOWER_SIZE || N % 2)
bigint_simple_mul(z, x, N, y, N);
else
{
const u32bit N2 = N / 2;
const word* x0 = x;
const word* x1 = x + N2;
const word* y0 = y;
const word* y1 = y + N2;
word* z0 = z;
word* z1 = z + N;
const s32bit cmp0 = bigint_cmp(x0, N2, x1, N2);
const s32bit cmp1 = bigint_cmp(y1, N2, y0, N2);
clear_mem(workspace, 2*N);
if(cmp0 && cmp1)
{
if(cmp0 > 0)
bigint_sub3(z0, x0, N2, x1, N2);
else
bigint_sub3(z0, x1, N2, x0, N2);
if(cmp1 > 0)
bigint_sub3(z1, y1, N2, y0, N2);
else
bigint_sub3(z1, y0, N2, y1, N2);
karatsuba_mul(workspace, z0, z1, N2, workspace+N);
}
karatsuba_mul(z0, x0, y0, N2, workspace+N);
karatsuba_mul(z1, x1, y1, N2, workspace+N);
word carry = bigint_add3_nc(workspace+N, z0, N, z1, N);
carry += bigint_add2_nc(z + N2, N, workspace + N, N);
bigint_add2_nc(z + N + N2, N2, &carry, 1);
if((cmp0 == cmp1) || (cmp0 == 0) || (cmp1 == 0))
bigint_add2(z + N2, 2*N-N2, workspace, N);
else
bigint_sub2(z + N2, 2*N-N2, workspace, N);
}
}
/*************************************************
* Pick a good size for the Karatsuba multiply *
*************************************************/
u32bit karatsuba_size(u32bit z_size,
u32bit x_size, u32bit x_sw,
u32bit y_size, u32bit y_sw)
{
if(x_sw > x_size || x_sw > y_size || y_sw > x_size || y_sw > y_size)
return 0;
if(((x_size == x_sw) && (x_size % 2)) ||
((y_size == y_sw) && (y_size % 2)))
return 0;
const u32bit start = (x_sw > y_sw) ? x_sw : y_sw;
const u32bit end = (x_size < y_size) ? x_size : y_size;
if(start == end)
{
if(start % 2)
return 0;
return start;
}
for(u32bit j = start; j <= end; ++j)
{
if(j % 2)
continue;
if(2*j > z_size)
return 0;
if(x_sw <= j && j <= x_size && y_sw <= j && j <= y_size)
{
if(j % 4 == 2 &&
(j+2) <= x_size && (j+2) <= y_size && 2*(j+2) <= z_size)
return j+2;
return j;
}
}
return 0;
}
/*************************************************
* Handle small operand multiplies *
*************************************************/
void handle_small_mul(word z[], u32bit z_size,
const word x[], u32bit x_size, u32bit x_sw,
const word y[], u32bit y_size, u32bit y_sw)
{
if(x_sw == 1) bigint_linmul3(z, y, y_sw, x[0]);
else if(y_sw == 1) bigint_linmul3(z, x, x_sw, y[0]);
else if(x_sw <= 4 && x_size >= 4 &&
y_sw <= 4 && y_size >= 4 && z_size >= 8)
bigint_comba_mul4(z, x, y);
else if(x_sw <= 6 && x_size >= 6 &&
y_sw <= 6 && y_size >= 6 && z_size >= 12)
bigint_comba_mul6(z, x, y);
else if(x_sw <= 8 && x_size >= 8 &&
y_sw <= 8 && y_size >= 8 && z_size >= 16)
bigint_comba_mul8(z, x, y);
else
bigint_simple_mul(z, x, x_sw, y, y_sw);
}
}
/*************************************************
* Multiplication Algorithm Dispatcher *
*************************************************/
void bigint_mul(word z[], u32bit z_size, word workspace[],
const word x[], u32bit x_size, u32bit x_sw,
const word y[], u32bit y_size, u32bit y_sw)
{
if(x_size <= 8 || y_size <= 8)
{
handle_small_mul(z, z_size, x, x_size, x_sw, y, y_size, y_sw);
return;
}
const u32bit N = karatsuba_size(z_size, x_size, x_sw, y_size, y_sw);
if(N)
{
clear_mem(workspace, 2*N);
karatsuba_mul(z, x, y, N, workspace);
}
else
bigint_simple_mul(z, x, x_sw, y, y_sw);
}
}
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