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https://github.com/yuzu-emu/mbedtls.git
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Added integer divide by as separate function
Added 64bit integer divided by 32bit integer, with remainder
This commit is contained in:
Simon Butcher
parent
0d1cf0fec1
commit
15f0bbef2d
195
library/bignum.c
195
library/bignum.c
@ -19,13 +19,22 @@
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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/*
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* This MPI implementation is based on:
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* The following sources were referenced in the design of this Multi-precision
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* Integer library:
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*
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* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
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* http://www.stillhq.com/extracted/gnupg-api/mpi/
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* http://math.libtomcrypt.com/files/tommath.pdf
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*/
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* [1] Handbook of Applied Cryptography - 1997
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* Menezes, van Oorschot and Vanstone
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*
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* [2] Multi-Precision Math
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* Tom St Denis
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* https://github.com/libtom/libtommath/blob/develop/tommath.pdf
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*
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* [3] GNU Multi-Precision Arithmetic Library
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* https://gmplib.org/manual/index.html
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*
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*/
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#include "polarssl/config.h"
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@ -228,6 +237,24 @@ size_t mpi_lsb( const mpi *X )
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return( 0 );
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}
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/*
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* Count leading zero bits in a given integer
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*/
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static size_t int_clz( const t_uint x )
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{
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size_t j;
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t_uint mask = (t_uint) 1 << (biL - 1);
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for( j = 0; j < biL; j++ )
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{
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if( x & mask ) break;
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mask >>= 1;
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}
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return j;
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}
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/*
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* Return the number of most significant bits
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*/
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@ -239,9 +266,7 @@ size_t mpi_msb( const mpi *X )
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if( X->p[i] != 0 )
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break;
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for( j = biL; j > 0; j-- )
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if( ( ( X->p[i] >> ( j - 1 ) ) & 1 ) != 0 )
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break;
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j = biL - int_clz( X->p[i] );
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return( ( i * biL ) + j );
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}
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@ -1065,6 +1090,98 @@ int mpi_mul_int( mpi *X, const mpi *A, t_sint b )
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return( mpi_mul_mpi( X, A, &_B ) );
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}
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/*
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* Unsigned integer divide - 64bit dividend and 32bit divisor
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*/
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static t_uint int_div_int(t_uint u1, t_uint u0, t_uint d, t_uint *r)
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{
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#if defined(POLARSSL_HAVE_UDBL)
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t_udbl dividend, quotient;
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#endif
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/*
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* Check for overflow
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*/
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if(( 0 == d ) || ( u1 >= d ))
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{
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if (r != NULL) *r = (~0);
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return (~0);
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}
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#if defined(POLARSSL_HAVE_UDBL)
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dividend = (t_udbl) u1 << biL;
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dividend |= (t_udbl) u0;
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quotient = dividend / d;
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if( quotient > ( (t_udbl) 1 << biL ) - 1 )
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quotient = ( (t_udbl) 1 << biL ) - 1;
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if( r != NULL )
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*r = dividend - (quotient * d);
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return (t_uint) quotient;
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#else
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const t_uint radix = 1 << biH;
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t_uint d0, d1, q0, q1, rAX, r0, quotient;
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t_uint u0_msw, u0_lsw;
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int s;
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/*
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* Algorithm D, Section 4.3.1 - The Art of Computer Programming
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* Vol. 2 - Seminumerical Algorithms, Knuth
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*/
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/*
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* Normalize the divisor, d, and dividend, u0, u1
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*/
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s = int_clz( d );
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d = d << s;
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u1 = u1 << s;
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u1 |= (u0 >> (32 - s)) & ( (-s) >> 31);
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u0 = u0 << s;
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d1 = d >> biH;
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d0 = d & 0xffff;
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u0_msw = u0 >> biH;
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u0_lsw = u0 & 0xffff;
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/*
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* Find the first quotient and remainder
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*/
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q1 = u1 / d1;
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r0 = u1 - d1 * q1;
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while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
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{
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q1 -= 1;
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r0 += d1;
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if ( r0 >= radix ) break;
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}
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rAX = (u1 * radix) + (u0_msw - q1 * d);
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q0 = rAX / d1;
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r0 = rAX - q0 * d1;
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while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
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{
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q0 -= 1;
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r0 += d1;
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if ( r0 >= radix ) break;
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}
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if (r != NULL)
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*r = (rAX * radix + u0_lsw - q0 * d) >> s;
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quotient = q1 * radix + q0;
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return quotient;
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#endif
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}
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/*
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* Division by mpi: A = Q * B + R (HAC 14.20)
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*/
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@ -1122,67 +1239,7 @@ int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B )
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Z.p[i - t - 1] = ~0;
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else
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{
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/*
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* The version of Clang shipped by Apple with Mavericks around
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* 2014-03 can't handle 128-bit division properly. Disable
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* 128-bits division for this version. Let's be optimistic and
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* assume it'll be fixed in the next minor version (next
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* patchlevel is probably a bit too optimistic).
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*/
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#if defined(POLARSSL_HAVE_UDBL) && \
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! ( defined(__x86_64__) && defined(__APPLE__) && \
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defined(__clang_major__) && __clang_major__ == 5 && \
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defined(__clang_minor__) && __clang_minor__ == 0 )
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t_udbl r;
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r = (t_udbl) X.p[i] << biL;
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r |= (t_udbl) X.p[i - 1];
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r /= Y.p[t];
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if( r > ((t_udbl) 1 << biL) - 1)
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r = ((t_udbl) 1 << biL) - 1;
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Z.p[i - t - 1] = (t_uint) r;
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#else
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/*
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* __udiv_qrnnd_c, from gmp/longlong.h
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*/
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t_uint q0, q1, r0, r1;
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t_uint d0, d1, d, m;
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d = Y.p[t];
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d0 = ( d << biH ) >> biH;
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d1 = ( d >> biH );
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q1 = X.p[i] / d1;
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r1 = X.p[i] - d1 * q1;
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r1 <<= biH;
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r1 |= ( X.p[i - 1] >> biH );
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m = q1 * d0;
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if( r1 < m )
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{
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q1--, r1 += d;
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while( r1 >= d && r1 < m )
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q1--, r1 += d;
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}
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r1 -= m;
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q0 = r1 / d1;
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r0 = r1 - d1 * q0;
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r0 <<= biH;
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r0 |= ( X.p[i - 1] << biH ) >> biH;
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m = q0 * d0;
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if( r0 < m )
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{
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q0--, r0 += d;
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while( r0 >= d && r0 < m )
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q0--, r0 += d;
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}
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r0 -= m;
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Z.p[i - t - 1] = ( q1 << biH ) | q0;
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#endif
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Z.p[i - t - 1] = int_div_int( X.p[i], X.p[i - 1], Y.p[t], NULL);
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}
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Z.p[i - t - 1]++;
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