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/*************************************************
* Karatsuba Squaring Source File *
* (C) 1999-2008 The Botan Project *
*************************************************/
#include <botan/mp_core.h>
#include <botan/mem_ops.h>
namespace Botan {
namespace {
/*************************************************
* Simple O(N^2) Squaring *
*************************************************/
void bigint_simple_sqr(word z[], const word x[], u32bit x_size)
{
clear_mem(z, 2*x_size);
for(u32bit j = 0; j != x_size; ++j)
z[j+x_size] = bigint_mul_add_words(z + j, x, x_size, x[j]);
}
/*************************************************
* Karatsuba Squaring Operation *
*************************************************/
void karatsuba_sqr(word z[], const word x[], u32bit N, word workspace[])
{
const u32bit KARATSUBA_SQR_LOWER_SIZE = BOTAN_KARAT_SQR_THRESHOLD;
if(N == 6)
bigint_comba_sqr6(z, x);
else if(N == 8)
bigint_comba_sqr8(z, x);
else if(N < KARATSUBA_SQR_LOWER_SIZE || N % 2)
bigint_simple_sqr(z, x, N);
else
{
const u32bit N2 = N / 2;
const word* x0 = x;
const word* x1 = x + N2;
word* z0 = z;
word* z1 = z + N;
const s32bit cmp = bigint_cmp(x0, N2, x1, N2);
clear_mem(workspace, 2*N);
if(cmp)
{
if(cmp > 0)
bigint_sub3(z0, x0, N2, x1, N2);
else
bigint_sub3(z0, x1, N2, x0, N2);
karatsuba_sqr(workspace, z0, N2, workspace+N);
}
karatsuba_sqr(z0, x0, N2, workspace+N);
karatsuba_sqr(z1, x1, 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(cmp == 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 squaring *
*************************************************/
u32bit karatsuba_size(u32bit z_size, u32bit x_size, u32bit x_sw)
{
if(x_sw == x_size)
{
if(x_sw % 2)
return 0;
return x_sw;
}
for(u32bit j = x_sw; j <= x_size; ++j)
{
if(j % 2)
continue;
if(2*j > z_size)
return 0;
if(j % 4 == 2 && (j+2) <= x_size && 2*(j+2) <= z_size)
return j+2;
return j;
}
return 0;
}
/*************************************************
* Handle small operand squarings *
*************************************************/
void handle_small_sqr(word z[], u32bit z_size,
const word x[], u32bit x_size, u32bit x_sw)
{
if(x_sw == 1)
bigint_linmul3(z, x, x_sw, x[0]);
else if(x_sw <= 4 && x_size >= 4 && z_size >= 8)
bigint_comba_sqr4(z, x);
else if(x_sw <= 6 && x_size >= 6 && z_size >= 12)
bigint_comba_sqr6(z, x);
else if(x_sw <= 8 && x_size >= 8 && z_size >= 16)
bigint_comba_sqr8(z, x);
else
bigint_simple_sqr(z, x, x_sw);
}
}
/*************************************************
* Squaring Algorithm Dispatcher *
*************************************************/
void bigint_sqr(word z[], u32bit z_size, word workspace[],
const word x[], u32bit x_size, u32bit x_sw)
{
if(x_size <= 8 || x_sw <= 8)
{
handle_small_sqr(z, z_size, x, x_size, x_sw);
return;
}
const u32bit N = karatsuba_size(z_size, x_size, x_sw);
if(N)
{
clear_mem(workspace, 2*N);
karatsuba_sqr(z, x, N, workspace);
}
else
bigint_simple_sqr(z, x, x_sw);
}
}
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