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Add support for multiprecision integer arithmetic and binary data encoding

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This commit is contained in:
Vinnie Falco
2013-09-13 10:42:56 -07:00
parent a45fc47682
commit 1dd2836f1b
9 changed files with 1281 additions and 183 deletions
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349
modules/beast_crypto/math/UnsignedInteger.cpp
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@@ -17,6 +17,327 @@
*/
//==============================================================================
//------------------------------------------------------------------------------
/* Copyright (c) 2013 the authors listed at the following URL, and/or
the authors of referenced articles or incorporated external code:
http://en.literateprograms.org/Arbitrary-precision_integer_arithmetic_(C)?action=history&offset=20100923155004
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Retrieved from: http://en.literateprograms.org/Arbitrary-precision_integer_arithmetic_(C)?oldid=16902
*/
namespace multiprecsion
{
#if 0
//------------------------------------------------------------------------------
typedef unsigned short component_t;
typedef unsigned long double_component_t;
#define MAX_COMPONENT ((component_t)(-1))
#define COMPONENT_BITS (sizeof(component_t)*CHAR_BIT)
#define LOG_2_10 3.3219280948873623478703194294894
#define MIN(x,y) ((x)<(y) ? (x) : (y))
#define MAX(x,y) ((x)>(y) ? (x) : (y))
typedef struct {
component_t* c; /* least-significant word first */
int num_components;
} integer;
integer create_integer(int components);
void free_integer(integer i);
void set_zero_integer(integer i);
void copy_integer(integer source, integer target);
void add_integer(integer left, integer right, integer result);
void subtract_integer(integer left, integer right, integer result);
void multiply_small_integer(integer left, component_t right, integer result);
void multiply_integer(integer left, integer right, integer result);
int compare_integers(integer left, integer right);
void shift_left_one_integer(integer arg);
void shift_right_one_integer(integer arg);
component_t mod_small_integer(integer left, component_t right);
void mod_integer(integer left, integer right, integer result);
void divide_small_integer(integer left, component_t right, integer result);
integer string_to_integer(char* s);
char* integer_to_string(integer x);
int is_zero_integer(integer x);
//------------------------------------------------------------------------------
integer create_integer(int components) {
integer result;
result.num_components = components;
result.c = (component_t*)malloc(sizeof(component_t)*components);
return result;
}
void free_integer(integer i) {
free(i.c);
}
void set_zero_integer(integer i) {
memset(i.c, 0, sizeof(component_t)*i.num_components);
}
int is_zero_integer(integer x) {
int i;
for(i=0; i < x.num_components; i++) {
if (x.c[i] != 0) return 0;
}
return 1;
}
void copy_integer(integer source, integer target) {
memmove(target.c, source.c,
sizeof(component_t)*MIN(source.num_components, target.num_components));
if (target.num_components > source.num_components) {
memset(target.c + source.num_components, 0,
sizeof(component_t)*(target.num_components - source.num_components));
}
}
void add_integer(integer left, integer right, integer result) {
double_component_t carry = 0;
int i;
for(i=0; i<left.num_components || i<right.num_components || carry != 0; i++) {
double_component_t partial_sum = carry;
carry = 0;
if (i < left.num_components) partial_sum += left.c[i];
if (i < right.num_components) partial_sum += right.c[i];
if (partial_sum > MAX_COMPONENT) {
partial_sum &= MAX_COMPONENT;
carry = 1;
}
result.c[i] = (component_t)partial_sum;
}
for ( ; i < result.num_components; i++) { result.c[i] = 0; }
}
void subtract_integer(integer left, integer right, integer result) {
int borrow = 0;
int i;
for(i=0; i<left.num_components; i++) {
double_component_t lhs = left.c[i];
double_component_t rhs = (i < right.num_components) ? right.c[i] : 0;
if (borrow) {
if (lhs <= rhs) {
/* leave borrow set to 1 */
lhs += (MAX_COMPONENT + 1) - 1;
} else {
borrow = 0;
lhs--;
}
}
if (lhs < rhs) {
borrow = 1;
lhs += MAX_COMPONENT + 1;
}
result.c[i] = lhs - rhs;
}
for ( ; i < result.num_components; i++) { result.c[i] = 0; }
}
void multiply_small_integer(integer left, component_t right, integer result) {
double_component_t carry = 0;
int i;
for(i=0; i<left.num_components || carry != 0; i++) {
double_component_t partial_sum = carry;
carry = 0;
if (i < left.num_components) partial_sum += left.c[i]*right;
carry = partial_sum >> COMPONENT_BITS;
result.c[i] = (component_t)(partial_sum & MAX_COMPONENT);
}
for ( ; i < result.num_components; i++) { result.c[i] = 0; }
}
void multiply_integer(integer left, integer right, integer result) {
int i, lidx, ridx;
double_component_t carry = 0;
int max_size_no_carry;
int left_max_component = left.num_components - 1;
int right_max_component = right.num_components - 1;
while(left.c[left_max_component] == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
max_size_no_carry = left_max_component + right_max_component;
for(i=0; i <= max_size_no_carry || carry != 0; i++) {
double_component_t partial_sum = carry;
carry = 0;
lidx = MIN(i, left_max_component);
ridx = i - lidx;
while(lidx >= 0 && ridx <= right_max_component) {
partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
carry += partial_sum >> COMPONENT_BITS;
partial_sum &= MAX_COMPONENT;
lidx--; ridx++;
}
result.c[i] = partial_sum;
}
for ( ; i < result.num_components; i++) { result.c[i] = 0; }
}
int compare_integers(integer left, integer right) {
int i = MAX(left.num_components - 1, right.num_components - 1);
for ( ; i >= 0; i--) {
component_t left_comp =
(i < left.num_components) ? left.c[i] : 0;
component_t right_comp =
(i < right.num_components) ? right.c[i] : 0;
if (left_comp < right_comp)
return -1;
else if (left_comp > right_comp)
return 1;
}
return 0;
}
void shift_left_one_integer(integer arg) {
int i;
arg.c[arg.num_components - 1] <<= 1;
for (i = arg.num_components - 2; i >= 0; i--) {
arg.c[i + 1] |= arg.c[i] >> (COMPONENT_BITS - 1);
arg.c[i] <<= 1;
}
}
void shift_right_one_integer(integer arg) {
int i;
arg.c[0] >>= 1;
for (i = 1; i < arg.num_components; i++) {
arg.c[i - 1] |= (arg.c[i] & 1) << (COMPONENT_BITS - 1);
arg.c[i] >>= 1;
}
}
component_t mod_small_integer(integer left, component_t right) {
double_component_t mod_two_power = 1;
double_component_t result = 0;
int i, bit;
for(i=0; i<left.num_components; i++) {
for(bit=0; bit<COMPONENT_BITS; bit++) {
if ((left.c[i] & (1 << bit)) != 0) {
result += mod_two_power;
if (result >= right) {
result -= right;
}
}
mod_two_power <<= 1;
if (mod_two_power >= right) {
mod_two_power -= right;
}
}
}
return (component_t)result;
}
void mod_integer(integer left, integer right, integer result) {
integer mod_two_power = create_integer(right.num_components + 1);
int i, bit;
set_zero_integer(result);
set_zero_integer(mod_two_power);
mod_two_power.c[0] = 1;
for(i=0; i<left.num_components; i++) {
for(bit=0; bit<COMPONENT_BITS; bit++) {
if ((left.c[i] & (1 << bit)) != 0) {
add_integer(result, mod_two_power, result);
if (compare_integers(result, right) >= 0) {
subtract_integer(result, right, result);
}
}
shift_left_one_integer(mod_two_power);
if (compare_integers(mod_two_power, right) >= 0) {
subtract_integer(mod_two_power, right, mod_two_power);
}
}
}
free_integer(mod_two_power);
}
void divide_small_integer(integer left, component_t right, integer result) {
double_component_t dividend = 0;
int i;
for (i = left.num_components - 1; i >= 0; i--) {
dividend |= left.c[i];
result.c[i] = dividend/right;
dividend = (dividend % right) << COMPONENT_BITS;
}
}
integer string_to_integer(char* s) {
integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
set_zero_integer(result);
integer digit = create_integer(1);
int i;
for (i = 0; s[i] != '\0'; i++) {
multiply_small_integer(result, 10, result);
digit.c[0] = s[i] - '0';
add_integer(result, digit, result);
}
free_integer(digit);
return result;
}
char* integer_to_string(integer x) {
int i, result_len;
char* result =
(char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
integer ten = create_integer(1);
ten.c[0] = 10;
if (is_zero_integer(x)) {
strcpy(result, "0");
} else {
for (i = 0; !is_zero_integer(x); i++) {
result[i] = (char)mod_small_integer(x, 10) + '0';
divide_small_integer(x, 10, x);
}
result[i] = '\0';
}
result_len = strlen(result);
for(i=0; i < result_len/2; i++) {
char temp = result[i];
result[i] = result[result_len - i - 1];
result[result_len - i - 1] = temp;
}
free_integer(ten);
return result;
}
#endif
}
//------------------------------------------------------------------------------
class UnsignedIntegerTests : public UnitTest
{
public:
@@ -27,21 +348,21 @@ public:
template <unsigned int Bytes>
void runTest ()
{
typedef UnsignedInteger <Bytes> UInt;
String s;
s << "Bytes=" << String(Bytes);
beginTestCase (s);
UnsignedInteger <Bytes> zero;
UInt zero;
zero.fill (0);
expect (zero.isZero (), "should be zero");
expect (! zero.isNotZero (), "sould not be non-zero");
UnsignedInteger <Bytes> one;
one.clear ();
one [Bytes - 1] = 1;
expect (one == UnsignedInteger <Bytes>::createFromInteger (1U), "should be equal");
UInt one (UInt::createFromInteger (1U));
expect (one == UInt::createFromInteger (1U), "should be equal");
expect (! one.isZero (), "should not be zero");
expect (one.isNotZero (), "sould be non-zero");
@@ -54,23 +375,13 @@ public:
expect (zero == zero, "should be equal");
expect (zero != one, "should not be equal");
expect ((zero | zero) == zero, "should be zero");
expect ((zero | one) != zero, "should not be zero");
expect ((one | one) != zero, "should not be zero");
expect (zero == UInt::createFromInteger (0U), "should be zero");
expect (one == UInt::createFromInteger (1U), "should be one");
expect (one != UInt::createFromInteger (2U), "should not be two");
expect ((one & zero) == zero, "should be zero");
expect ((one & one) == one, "should be one");
expect ((zero & zero) == zero, "should be zero");
expect (zero == UnsignedInteger <Bytes>::createFromInteger (0U), "should be zero");
expect (one == UnsignedInteger <Bytes>::createFromInteger (1U), "should be one");
expect (one != UnsignedInteger <Bytes>::createFromInteger (2U), "should not be two");
UnsignedInteger <Bytes> largest = UnsignedInteger <Bytes>::createFilled (0xff);
UInt largest = UInt::createFilled (0xff);
expect (largest > zero && largest > one, "should be greater");
expect (~largest == zero, "should be zero");
expect (~one < largest, "should be less");
}
void runTest()