mirror of
https://github.com/yuzu-emu/mbedtls.git
synced 2024-12-23 14:05:28 +00:00
Added integer divide by as separate function
Added 64bit integer divided by 32bit integer, with remainder
This commit is contained in:
Simon Butcher
parent
1f4e08c979
commit
e4ed3475b0
185
library/bignum.c
185
library/bignum.c
|
|
@ -19,13 +19,22 @@
|
|||
* with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
*/
|
||||
|
||||
/*
|
||||
* This MPI implementation is based on:
|
||||
* The following sources were referenced in the design of this Multi-precision
|
||||
* Integer library:
|
||||
*
|
||||
* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
|
||||
* http://www.stillhq.com/extracted/gnupg-api/mpi/
|
||||
* http://math.libtomcrypt.com/files/tommath.pdf
|
||||
*/
|
||||
* [1] Handbook of Applied Cryptography - 1997
|
||||
* Menezes, van Oorschot and Vanstone
|
||||
*
|
||||
* [2] Multi-Precision Math
|
||||
* Tom St Denis
|
||||
* https://github.com/libtom/libtommath/blob/develop/tommath.pdf
|
||||
*
|
||||
* [3] GNU Multi-Precision Arithmetic Library
|
||||
* https://gmplib.org/manual/index.html
|
||||
*
|
||||
*/
|
||||
|
||||
#if !defined(POLARSSL_CONFIG_FILE)
|
||||
#include "polarssl/config.h"
|
||||
|
|
@ -352,6 +361,24 @@ size_t mpi_lsb( const mpi *X )
|
|||
return( 0 );
|
||||
}
|
||||
|
||||
/*
|
||||
* Count leading zero bits in a given integer
|
||||
*/
|
||||
static size_t int_clz( const t_uint x )
|
||||
{
|
||||
size_t j;
|
||||
t_uint mask = (t_uint) 1 << (biL - 1);
|
||||
|
||||
for( j = 0; j < biL; j++ )
|
||||
{
|
||||
if( x & mask ) break;
|
||||
|
||||
mask >>= 1;
|
||||
}
|
||||
|
||||
return j;
|
||||
}
|
||||
|
||||
/*
|
||||
* Return the number of most significant bits
|
||||
*/
|
||||
|
|
@ -366,9 +393,7 @@ size_t mpi_msb( const mpi *X )
|
|||
if( X->p[i] != 0 )
|
||||
break;
|
||||
|
||||
for( j = biL; j > 0; j-- )
|
||||
if( ( ( X->p[i] >> ( j - 1 ) ) & 1 ) != 0 )
|
||||
break;
|
||||
j = biL - int_clz( X->p[i] );
|
||||
|
||||
return( ( i * biL ) + j );
|
||||
}
|
||||
|
|
@ -1192,6 +1217,98 @@ int mpi_mul_int( mpi *X, const mpi *A, t_sint b )
|
|||
return( mpi_mul_mpi( X, A, &_B ) );
|
||||
}
|
||||
|
||||
/*
|
||||
* Unsigned integer divide - 64bit dividend and 32bit divisor
|
||||
*/
|
||||
static t_uint int_div_int(t_uint u1, t_uint u0, t_uint d, t_uint *r)
|
||||
{
|
||||
#if defined(POLARSSL_HAVE_UDBL)
|
||||
t_udbl dividend, quotient;
|
||||
#endif
|
||||
|
||||
/*
|
||||
* Check for overflow
|
||||
*/
|
||||
if(( 0 == d ) || ( u1 >= d ))
|
||||
{
|
||||
if (r != NULL) *r = (~0);
|
||||
|
||||
return (~0);
|
||||
}
|
||||
|
||||
#if defined(POLARSSL_HAVE_UDBL)
|
||||
dividend = (t_udbl) u1 << biL;
|
||||
dividend |= (t_udbl) u0;
|
||||
quotient = dividend / d;
|
||||
if( quotient > ( (t_udbl) 1 << biL ) - 1 )
|
||||
quotient = ( (t_udbl) 1 << biL ) - 1;
|
||||
|
||||
if( r != NULL )
|
||||
*r = dividend - (quotient * d);
|
||||
|
||||
return (t_uint) quotient;
|
||||
#else
|
||||
const t_uint radix = 1 << biH;
|
||||
t_uint d0, d1, q0, q1, rAX, r0, quotient;
|
||||
t_uint u0_msw, u0_lsw;
|
||||
int s;
|
||||
|
||||
/*
|
||||
* Algorithm D, Section 4.3.1 - The Art of Computer Programming
|
||||
* Vol. 2 - Seminumerical Algorithms, Knuth
|
||||
*/
|
||||
|
||||
/*
|
||||
* Normalize the divisor, d, and dividend, u0, u1
|
||||
*/
|
||||
s = int_clz( d );
|
||||
d = d << s;
|
||||
|
||||
u1 = u1 << s;
|
||||
u1 |= (u0 >> (32 - s)) & ( (-s) >> 31);
|
||||
u0 = u0 << s;
|
||||
|
||||
d1 = d >> biH;
|
||||
d0 = d & 0xffff;
|
||||
|
||||
u0_msw = u0 >> biH;
|
||||
u0_lsw = u0 & 0xffff;
|
||||
|
||||
/*
|
||||
* Find the first quotient and remainder
|
||||
*/
|
||||
q1 = u1 / d1;
|
||||
r0 = u1 - d1 * q1;
|
||||
|
||||
while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
|
||||
{
|
||||
q1 -= 1;
|
||||
r0 += d1;
|
||||
|
||||
if ( r0 >= radix ) break;
|
||||
}
|
||||
|
||||
rAX = (u1 * radix) + (u0_msw - q1 * d);
|
||||
q0 = rAX / d1;
|
||||
r0 = rAX - q0 * d1;
|
||||
|
||||
while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
|
||||
{
|
||||
q0 -= 1;
|
||||
r0 += d1;
|
||||
|
||||
if ( r0 >= radix ) break;
|
||||
}
|
||||
|
||||
if (r != NULL)
|
||||
*r = (rAX * radix + u0_lsw - q0 * d) >> s;
|
||||
|
||||
quotient = q1 * radix + q0;
|
||||
|
||||
return quotient;
|
||||
#endif
|
||||
}
|
||||
|
||||
/*
|
||||
* Division by mpi: A = Q * B + R (HAC 14.20)
|
||||
*/
|
||||
|
|
@ -1249,57 +1366,7 @@ int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B )
|
|||
Z.p[i - t - 1] = ~0;
|
||||
else
|
||||
{
|
||||
#if defined(POLARSSL_HAVE_UDBL)
|
||||
t_udbl r;
|
||||
|
||||
r = (t_udbl) X.p[i] << biL;
|
||||
r |= (t_udbl) X.p[i - 1];
|
||||
r /= Y.p[t];
|
||||
if( r > ( (t_udbl) 1 << biL ) - 1 )
|
||||
r = ( (t_udbl) 1 << biL ) - 1;
|
||||
|
||||
Z.p[i - t - 1] = (t_uint) r;
|
||||
#else
|
||||
/*
|
||||
* __udiv_qrnnd_c, from gmp/longlong.h
|
||||
*/
|
||||
t_uint q0, q1, r0, r1;
|
||||
t_uint d0, d1, d, m;
|
||||
|
||||
d = Y.p[t];
|
||||
d0 = ( d << biH ) >> biH;
|
||||
d1 = ( d >> biH );
|
||||
|
||||
q1 = X.p[i] / d1;
|
||||
r1 = X.p[i] - d1 * q1;
|
||||
r1 <<= biH;
|
||||
r1 |= ( X.p[i - 1] >> biH );
|
||||
|
||||
m = q1 * d0;
|
||||
if( r1 < m )
|
||||
{
|
||||
q1--, r1 += d;
|
||||
while( r1 >= d && r1 < m )
|
||||
q1--, r1 += d;
|
||||
}
|
||||
r1 -= m;
|
||||
|
||||
q0 = r1 / d1;
|
||||
r0 = r1 - d1 * q0;
|
||||
r0 <<= biH;
|
||||
r0 |= ( X.p[i - 1] << biH ) >> biH;
|
||||
|
||||
m = q0 * d0;
|
||||
if( r0 < m )
|
||||
{
|
||||
q0--, r0 += d;
|
||||
while( r0 >= d && r0 < m )
|
||||
q0--, r0 += d;
|
||||
}
|
||||
r0 -= m;
|
||||
|
||||
Z.p[i - t - 1] = ( q1 << biH ) | q0;
|
||||
#endif /* POLARSSL_HAVE_UDBL && !64-bit Apple with Clang 5.0 */
|
||||
Z.p[i - t - 1] = int_div_int( X.p[i], X.p[i - 1], Y.p[t], NULL);
|
||||
}
|
||||
|
||||
Z.p[i - t - 1]++;
|
||||
|
|
|
|||
Loading…
Reference in a new issue