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factor/vm/bignum.cpp

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// Copyright (C) 1989-94 Massachusetts Institute of Technology
// Portions copyright (C) 2004-2008 Slava Pestov
// This material was developed by the Scheme project at the Massachusetts
// Institute of Technology, Department of Electrical Engineering and
// Computer Science. Permission to copy and modify this software, to
// redistribute either the original software or a modified version, and
// to use this software for any purpose is granted, subject to the
// following restrictions and understandings.
// 1. Any copy made of this software must include this copyright notice
// in full.
// 2. Users of this software agree to make their best efforts (a) to
// return to the MIT Scheme project any improvements or extensions that
// they make, so that these may be included in future releases; and (b)
// to inform MIT of noteworthy uses of this software.
// 3. All materials developed as a consequence of the use of this
// software shall duly acknowledge such use, in accordance with the usual
// standards of acknowledging credit in academic research.
// 4. MIT has made no warrantee or representation that the operation of
// this software will be error-free, and MIT is under no obligation to
// provide any services, by way of maintenance, update, or otherwise.
// 5. In conjunction with products arising from the use of this material,
// there shall be no use of the name of the Massachusetts Institute of
// Technology nor of any adaptation thereof in any advertising,
// promotional, or sales literature without prior written consent from
// MIT in each case.
// Changes for Scheme 48:
// * - Converted to ANSI.
// * - Added bitwise operations.
// * - Added s48 to the beginning of all externally visible names.
// * - Cached the bignum representations of -1, 0, and 1.
// Changes for Factor:
// * - Adapt bignumint.h for Factor memory manager
// * - Add more bignum <-> C type conversions
// * - Remove unused functions
// * - Add local variable GC root recording
// * - Remove s48 prefix from function names
// * - Various fixes for Win64
// * - Port to C++
// * - Added bignum_gcd implementation
#include "master.hpp"
namespace factor {
// Exports
int factor_vm::bignum_equal_p(bignum* x, bignum* y) {
return ((BIGNUM_ZERO_P(x))
? (BIGNUM_ZERO_P(y))
: ((!(BIGNUM_ZERO_P(y))) &&
((BIGNUM_NEGATIVE_P(x)) ? (BIGNUM_NEGATIVE_P(y))
: (!(BIGNUM_NEGATIVE_P(y)))) &&
(bignum_equal_p_unsigned(x, y))));
}
enum bignum_comparison factor_vm::bignum_compare(bignum* x, bignum* y) {
return ((BIGNUM_ZERO_P(x)) ? ((BIGNUM_ZERO_P(y)) ? BIGNUM_COMPARISON_EQUAL
: (BIGNUM_NEGATIVE_P(y))
? BIGNUM_COMPARISON_GREATER
: BIGNUM_COMPARISON_LESS)
: (BIGNUM_ZERO_P(y))
? ((BIGNUM_NEGATIVE_P(x)) ? BIGNUM_COMPARISON_LESS
: BIGNUM_COMPARISON_GREATER)
: (BIGNUM_NEGATIVE_P(x))
? ((BIGNUM_NEGATIVE_P(y)) ? (bignum_compare_unsigned(y, x))
: (BIGNUM_COMPARISON_LESS))
: ((BIGNUM_NEGATIVE_P(y)) ? (BIGNUM_COMPARISON_GREATER)
: (bignum_compare_unsigned(x, y))));
}
// Allocates memory
bignum* factor_vm::bignum_add(bignum* x, bignum* y) {
return (
(BIGNUM_ZERO_P(x)) ? (y) : (BIGNUM_ZERO_P(y))
? (x)
: ((BIGNUM_NEGATIVE_P(x))
? ((BIGNUM_NEGATIVE_P(y)) ? (bignum_add_unsigned(x, y, 1))
: (bignum_subtract_unsigned(y, x)))
: ((BIGNUM_NEGATIVE_P(y)) ? (bignum_subtract_unsigned(x, y))
: (bignum_add_unsigned(x, y, 0)))));
}
// Allocates memory
bignum* factor_vm::bignum_subtract(bignum* x, bignum* y) {
return ((BIGNUM_ZERO_P(x))
? ((BIGNUM_ZERO_P(y)) ? (y) : (bignum_new_sign(
y, (!(BIGNUM_NEGATIVE_P(y))))))
: ((BIGNUM_ZERO_P(y))
? (x)
: ((BIGNUM_NEGATIVE_P(x))
? ((BIGNUM_NEGATIVE_P(y))
? (bignum_subtract_unsigned(y, x))
: (bignum_add_unsigned(x, y, 1)))
: ((BIGNUM_NEGATIVE_P(y))
? (bignum_add_unsigned(x, y, 0))
: (bignum_subtract_unsigned(x, y))))));
}
#ifdef _WIN64
bignum *factor_vm::bignum_square(bignum* x_)
{
return bignum_multiply(x_, x_);
}
#else
// Allocates memory
bignum *factor_vm::bignum_square(bignum* x_)
{
data_root<bignum> x(x_, this);
bignum_length_type length = (BIGNUM_LENGTH (x));
bignum * z = (allot_bignum_zeroed ((length + length), 0));
bignum_digit_type * scan_z = BIGNUM_START_PTR (z);
bignum_digit_type * scan_x = BIGNUM_START_PTR (x);
bignum_digit_type * end_x = scan_x + length;
for (int i = 0; i < length; ++i) {
bignum_twodigit_type carry;
bignum_twodigit_type f = BIGNUM_REF (x, i);
bignum_digit_type *pz = scan_z + (i << 1);
bignum_digit_type *px = scan_x + i + 1;
carry = *pz + f * f;
*pz++ = carry & BIGNUM_DIGIT_MASK;
carry >>= BIGNUM_DIGIT_LENGTH;
BIGNUM_ASSERT (carry <= BIGNUM_DIGIT_MASK);
f <<= 1;
while (px < end_x)
{
carry += *pz + *px++ * f;
*pz++ = carry & BIGNUM_DIGIT_MASK;
carry >>= BIGNUM_DIGIT_LENGTH;
BIGNUM_ASSERT (carry <= (BIGNUM_DIGIT_MASK << 1));
}
if (carry) {
carry += *pz;
*pz++ = carry & BIGNUM_DIGIT_MASK;
carry >>= BIGNUM_DIGIT_LENGTH;
}
if (carry)
*pz += carry & BIGNUM_DIGIT_MASK;
BIGNUM_ASSERT ((carry >> BIGNUM_DIGIT_LENGTH) == 0);
}
return (bignum_trim (z));
}
#endif
// Allocates memory
bignum* factor_vm::bignum_multiply(bignum* x, bignum* y) {
#ifndef _WIN64
if (x == y) {
return bignum_square(x);
}
#endif
bignum_length_type x_length = (BIGNUM_LENGTH(x));
bignum_length_type y_length = (BIGNUM_LENGTH(y));
int negative_p = ((BIGNUM_NEGATIVE_P(x)) ? (!(BIGNUM_NEGATIVE_P(y)))
: (BIGNUM_NEGATIVE_P(y)));
if (BIGNUM_ZERO_P(x))
return (x);
if (BIGNUM_ZERO_P(y))
return (y);
if (x_length == 1) {
bignum_digit_type digit = (BIGNUM_REF(x, 0));
if (digit == 1)
return (bignum_maybe_new_sign(y, negative_p));
if (digit < BIGNUM_RADIX_ROOT)
return (bignum_multiply_unsigned_small_factor(y, digit, negative_p));
}
if (y_length == 1) {
bignum_digit_type digit = (BIGNUM_REF(y, 0));
if (digit == 1)
return (bignum_maybe_new_sign(x, negative_p));
if (digit < BIGNUM_RADIX_ROOT)
return (bignum_multiply_unsigned_small_factor(x, digit, negative_p));
}
return (bignum_multiply_unsigned(x, y, negative_p));
}
// Allocates memory
void factor_vm::bignum_divide(bignum* numerator, bignum* denominator,
bignum** quotient, bignum** remainder) {
if (BIGNUM_ZERO_P(denominator)) {
divide_by_zero_error();
return;
}
if (BIGNUM_ZERO_P(numerator)) {
(*quotient) = numerator;
(*remainder) = numerator;
} else {
int r_negative_p = (BIGNUM_NEGATIVE_P(numerator));
int q_negative_p =
((BIGNUM_NEGATIVE_P(denominator)) ? (!r_negative_p) : r_negative_p);
switch (bignum_compare_unsigned(numerator, denominator)) {
case BIGNUM_COMPARISON_EQUAL: {
(*quotient) = (BIGNUM_ONE(q_negative_p));
(*remainder) = (BIGNUM_ZERO());
break;
}
case BIGNUM_COMPARISON_LESS: {
(*quotient) = (BIGNUM_ZERO());
(*remainder) = numerator;
break;
}
case BIGNUM_COMPARISON_GREATER: {
if ((BIGNUM_LENGTH(denominator)) == 1) {
bignum_digit_type digit = (BIGNUM_REF(denominator, 0));
if (digit == 1) {
(*quotient) = (bignum_maybe_new_sign(numerator, q_negative_p));
(*remainder) = (BIGNUM_ZERO());
break;
} else if (digit < BIGNUM_RADIX_ROOT) {
bignum_divide_unsigned_small_denominator(numerator, digit, quotient,
remainder, q_negative_p,
r_negative_p);
break;
} else {
bignum_divide_unsigned_medium_denominator(
numerator, digit, quotient, remainder, q_negative_p,
r_negative_p);
break;
}
}
bignum_divide_unsigned_large_denominator(
numerator, denominator, quotient, remainder, q_negative_p,
r_negative_p);
break;
}
}
}
}
// Allocates memory
bignum* factor_vm::bignum_quotient(bignum* numerator, bignum* denominator) {
if (BIGNUM_ZERO_P(denominator)) {
divide_by_zero_error();
return (BIGNUM_OUT_OF_BAND);
}
if (BIGNUM_ZERO_P(numerator))
return numerator;
{
int q_negative_p =
((BIGNUM_NEGATIVE_P(denominator)) ? (!(BIGNUM_NEGATIVE_P(numerator)))
: (BIGNUM_NEGATIVE_P(numerator)));
switch (bignum_compare_unsigned(numerator, denominator)) {
case BIGNUM_COMPARISON_EQUAL:
return (BIGNUM_ONE(q_negative_p));
case BIGNUM_COMPARISON_LESS:
return (BIGNUM_ZERO());
case BIGNUM_COMPARISON_GREATER:
default: // to appease gcc -Wall
{
bignum* quotient;
if ((BIGNUM_LENGTH(denominator)) == 1) {
bignum_digit_type digit = (BIGNUM_REF(denominator, 0));
if (digit == 1)
return (bignum_maybe_new_sign(numerator, q_negative_p));
if (digit < BIGNUM_RADIX_ROOT)
bignum_divide_unsigned_small_denominator(
numerator, digit, (&quotient), ((bignum**)0), q_negative_p, 0);
else
bignum_divide_unsigned_medium_denominator(
numerator, digit, (&quotient), ((bignum**)0), q_negative_p, 0);
} else
bignum_divide_unsigned_large_denominator(
numerator, denominator, (&quotient), ((bignum**)0), q_negative_p,
0);
return (quotient);
}
}
}
}
// Allocates memory
bignum* factor_vm::bignum_remainder(bignum* numerator, bignum* denominator) {
if (BIGNUM_ZERO_P(denominator)) {
divide_by_zero_error();
return (BIGNUM_OUT_OF_BAND);
}
if (BIGNUM_ZERO_P(numerator))
return numerator;
switch (bignum_compare_unsigned(numerator, denominator)) {
case BIGNUM_COMPARISON_EQUAL:
return (BIGNUM_ZERO());
case BIGNUM_COMPARISON_LESS:
return numerator;
case BIGNUM_COMPARISON_GREATER:
default: // to appease gcc -Wall
{
bignum* remainder;
if ((BIGNUM_LENGTH(denominator)) == 1) {
bignum_digit_type digit = (BIGNUM_REF(denominator, 0));
if (digit == 1)
return (BIGNUM_ZERO());
if (digit < BIGNUM_RADIX_ROOT)
return (bignum_remainder_unsigned_small_denominator(
numerator, digit, (BIGNUM_NEGATIVE_P(numerator))));
bignum_divide_unsigned_medium_denominator(
numerator, digit, ((bignum**)0), (&remainder), 0,
(BIGNUM_NEGATIVE_P(numerator)));
} else
bignum_divide_unsigned_large_denominator(
numerator, denominator, ((bignum**)0), (&remainder), 0,
(BIGNUM_NEGATIVE_P(numerator)));
return (remainder);
}
}
}
// cell_to_bignum, fixnum_to_bignum, long_long_to_bignum, ulong_long_to_bignum
// Allocates memory
#define FOO_TO_BIGNUM(name, type, stype, utype) \
bignum* factor_vm::name##_to_bignum(type n) { \
int negative_p; \
/* Special cases win when these small constants are cached. */ \
if (n == 0) \
return (BIGNUM_ZERO()); \
if (n == 1) \
return (BIGNUM_ONE(0)); \
if (n < (type) 0 && n == (type) - 1) \
return (BIGNUM_ONE(1)); \
{ \
utype accumulator = \
((negative_p = (n < (type) 0)) ? ((type)(-(stype) n)) : n); \
if (accumulator < BIGNUM_RADIX) \
{ \
bignum* result = allot_bignum(1, negative_p); \
bignum_digit_type* scan = (BIGNUM_START_PTR(result)); \
*scan = (accumulator & BIGNUM_DIGIT_MASK); \
return (result); \
} else { \
bignum_digit_type result_digits[BIGNUM_DIGITS_FOR(type)]; \
bignum_digit_type* end_digits = result_digits; \
do { \
(*end_digits++) = (accumulator & BIGNUM_DIGIT_MASK); \
accumulator >>= BIGNUM_DIGIT_LENGTH; \
} while (accumulator != 0); \
bignum* result = \
(allot_bignum((end_digits - result_digits), negative_p)); \
bignum_digit_type* scan_digits = result_digits; \
bignum_digit_type* scan_result = (BIGNUM_START_PTR(result)); \
while (scan_digits < end_digits) \
(*scan_result++) = (*scan_digits++); \
return (result); \
} \
} \
}
FOO_TO_BIGNUM(cell, cell, fixnum, cell)
FOO_TO_BIGNUM(fixnum, fixnum, fixnum, cell)
FOO_TO_BIGNUM(long_long, int64_t, int64_t, uint64_t)
FOO_TO_BIGNUM(ulong_long, uint64_t, int64_t, uint64_t)
// cannot allocate memory
// bignum_to_cell, fixnum_to_cell, long_long_to_cell, ulong_long_to_cell
#define BIGNUM_TO_FOO(name, type, stype, utype) \
type bignum_to_##name(bignum* bn) { \
if (BIGNUM_ZERO_P(bn)) \
return (0); \
{ \
utype accumulator = 0; \
bignum_digit_type* start = (BIGNUM_START_PTR(bn)); \
bignum_digit_type* scan = (start + (BIGNUM_LENGTH(bn))); \
while (start < scan) \
accumulator = ((accumulator << BIGNUM_DIGIT_LENGTH) + (*--scan)); \
return ((BIGNUM_NEGATIVE_P(bn)) ? ((type)(-(stype) accumulator)) \
: accumulator); \
} \
}
BIGNUM_TO_FOO(cell, cell, fixnum, cell)
BIGNUM_TO_FOO(fixnum, fixnum, fixnum, cell)
BIGNUM_TO_FOO(long_long, int64_t, int64_t, uint64_t)
BIGNUM_TO_FOO(ulong_long, uint64_t, int64_t, uint64_t)
bool bignum_fits_fixnum_p(bignum* bn) {
fixnum len = BIGNUM_LENGTH(bn);
if (len == 0)
return true;
if (len > 1)
return false;
bignum_digit_type dig = BIGNUM_START_PTR(bn)[0];
return (BIGNUM_NEGATIVE_P(bn) && dig <= -fixnum_min) ||
(!BIGNUM_NEGATIVE_P(bn) && dig <= fixnum_max);
}
cell bignum_maybe_to_fixnum(bignum* bn) {
if (bignum_fits_fixnum_p(bn))
return tag_fixnum(bignum_to_fixnum(bn));
return tag<bignum>(bn);
}
// cannot allocate memory
fixnum factor_vm::bignum_to_fixnum_strict(bignum* bn) {
if (!bignum_fits_fixnum_p(bn)) {
general_error(ERROR_OUT_OF_FIXNUM_RANGE, tag<bignum>(bn), false_object);
}
fixnum fix = bignum_to_fixnum(bn);
FACTOR_ASSERT(fix <= fixnum_max && fix >= fixnum_min);
return fix;
}
#define DTB_WRITE_DIGIT(factor) \
{ \
significand *= (factor); \
digit = ((bignum_digit_type) significand); \
(*--scan) = digit; \
significand -= ((double)digit); \
}
#define inf std::numeric_limits<double>::infinity()
// Allocates memory
bignum* factor_vm::double_to_bignum(double x) {
if (x == inf || x == -inf || x != x)
return (BIGNUM_ZERO());
int exponent;
double significand = (frexp(x, (&exponent)));
if (exponent <= 0)
return (BIGNUM_ZERO());
if (exponent == 1)
return (BIGNUM_ONE(x < 0));
if (significand < 0)
significand = (-significand);
{
bignum_length_type length = (BIGNUM_BITS_TO_DIGITS(exponent));
bignum* result = (allot_bignum(length, (x < 0)));
bignum_digit_type* start = (BIGNUM_START_PTR(result));
bignum_digit_type* scan = (start + length);
bignum_digit_type digit;
int odd_bits = (exponent % BIGNUM_DIGIT_LENGTH);
if (odd_bits > 0)
DTB_WRITE_DIGIT((fixnum)1 << odd_bits);
while (start < scan) {
if (significand == 0) {
while (start < scan)
(*--scan) = 0;
break;
}
DTB_WRITE_DIGIT(BIGNUM_RADIX);
}
return (result);
}
}
#undef DTB_WRITE_DIGIT
// Comparisons
int factor_vm::bignum_equal_p_unsigned(bignum* x, bignum* y) {
bignum_length_type length = (BIGNUM_LENGTH(x));
if (length != (BIGNUM_LENGTH(y)))
return (0);
else {
bignum_digit_type* scan_x = (BIGNUM_START_PTR(x));
bignum_digit_type* scan_y = (BIGNUM_START_PTR(y));
bignum_digit_type* end_x = (scan_x + length);
while (scan_x < end_x)
if ((*scan_x++) != (*scan_y++))
return (0);
return (1);
}
}
enum bignum_comparison factor_vm::bignum_compare_unsigned(bignum* x,
bignum* y) {
bignum_length_type x_length = (BIGNUM_LENGTH(x));
bignum_length_type y_length = (BIGNUM_LENGTH(y));
if (x_length < y_length)
return BIGNUM_COMPARISON_LESS;
if (x_length > y_length)
return BIGNUM_COMPARISON_GREATER;
{
bignum_digit_type* start_x = (BIGNUM_START_PTR(x));
bignum_digit_type* scan_x = (start_x + x_length);
bignum_digit_type* scan_y = ((BIGNUM_START_PTR(y)) + y_length);
while (start_x < scan_x) {
bignum_digit_type digit_x = (*--scan_x);
bignum_digit_type digit_y = (*--scan_y);
if (digit_x < digit_y)
return BIGNUM_COMPARISON_LESS;
if (digit_x > digit_y)
return BIGNUM_COMPARISON_GREATER;
}
}
return BIGNUM_COMPARISON_EQUAL;
}
// Addition
// Allocates memory
bignum* factor_vm::bignum_add_unsigned(bignum* x_, bignum* y_, int negative_p) {
data_root<bignum> x(x_, this);
data_root<bignum> y(y_, this);
if ((BIGNUM_LENGTH(y)) > (BIGNUM_LENGTH(x))) {
swap(x, y);
}
{
bignum_length_type x_length = (BIGNUM_LENGTH(x));
bignum* r = (allot_bignum((x_length + 1), negative_p));
bignum_digit_type sum;
bignum_digit_type carry = 0;
bignum_digit_type* scan_x = (BIGNUM_START_PTR(x));
bignum_digit_type* scan_r = (BIGNUM_START_PTR(r));
{
bignum_digit_type* scan_y = (BIGNUM_START_PTR(y));
bignum_digit_type* end_y = (scan_y + (BIGNUM_LENGTH(y)));
while (scan_y < end_y) {
sum = ((*scan_x++) + (*scan_y++) + carry);
if (sum < BIGNUM_RADIX) {
(*scan_r++) = sum;
carry = 0;
} else {
(*scan_r++) = (sum - BIGNUM_RADIX);
carry = 1;
}
}
}
{
bignum_digit_type* end_x = BIGNUM_START_PTR(x) + x_length;
if (carry != 0)
while (scan_x < end_x) {
sum = ((*scan_x++) + 1);
if (sum < BIGNUM_RADIX) {
(*scan_r++) = sum;
carry = 0;
break;
} else
(*scan_r++) = (sum - BIGNUM_RADIX);
}
while (scan_x < end_x)
(*scan_r++) = (*scan_x++);
}
if (carry != 0) {
(*scan_r) = 1;
return (r);
}
return (bignum_shorten_length(r, x_length));
}
}
// Subtraction
// Allocates memory
bignum* factor_vm::bignum_subtract_unsigned(bignum* x_, bignum* y_) {
data_root<bignum> x(x_, this);
data_root<bignum> y(y_, this);
int negative_p = 0;
switch (bignum_compare_unsigned(x.untagged(), y.untagged())) {
case BIGNUM_COMPARISON_EQUAL:
return (BIGNUM_ZERO());
case BIGNUM_COMPARISON_LESS:
swap(x, y);
negative_p = 1;
break;
case BIGNUM_COMPARISON_GREATER:
negative_p = 0;
break;
}
{
bignum_length_type x_length = (BIGNUM_LENGTH(x));
bignum* r = (allot_bignum(x_length, negative_p));
bignum_digit_type difference;
bignum_digit_type borrow = 0;
bignum_digit_type* scan_x = BIGNUM_START_PTR(x);
bignum_digit_type* scan_r = BIGNUM_START_PTR(r);
{
bignum_digit_type* scan_y = BIGNUM_START_PTR(y);
bignum_digit_type* end_y = (scan_y + (BIGNUM_LENGTH(y)));
while (scan_y < end_y) {
difference = (((*scan_x++) - (*scan_y++)) - borrow);
if (difference < 0) {
(*scan_r++) = (difference + BIGNUM_RADIX);
borrow = 1;
} else {
(*scan_r++) = difference;
borrow = 0;
}
}
}
{
bignum_digit_type* end_x = BIGNUM_START_PTR(x) + x_length;
if (borrow != 0)
while (scan_x < end_x) {
difference = ((*scan_x++) - borrow);
if (difference < 0)
(*scan_r++) = (difference + BIGNUM_RADIX);
else {
(*scan_r++) = difference;
borrow = 0;
break;
}
}
BIGNUM_ASSERT(borrow == 0);
while (scan_x < end_x)
(*scan_r++) = (*scan_x++);
}
return (bignum_trim(r));
}
}
// Multiplication
// Maximum value for product_low or product_high:
// ((R * R) + (R * (R - 2)) + (R - 1))
// Maximum value for carry: ((R * (R - 1)) + (R - 1))
// where R == BIGNUM_RADIX_ROOT
// Allocates memory
bignum* factor_vm::bignum_multiply_unsigned(bignum* x_, bignum* y_,
int negative_p) {
data_root<bignum> x(x_, this);
data_root<bignum> y(y_, this);
if (BIGNUM_LENGTH(y) > BIGNUM_LENGTH(x)) {
swap(x, y);
}
{
bignum_digit_type carry;
bignum_digit_type y_digit_low;
bignum_digit_type y_digit_high;
bignum_digit_type x_digit_low;
bignum_digit_type x_digit_high;
bignum_digit_type product_low;
bignum_digit_type* scan_r;
bignum_digit_type* scan_y;
bignum_length_type x_length = BIGNUM_LENGTH(x);
bignum_length_type y_length = BIGNUM_LENGTH(y);
bignum* r = (allot_bignum_zeroed((x_length + y_length), negative_p));
bignum_digit_type* scan_x = BIGNUM_START_PTR(x);
bignum_digit_type* end_x = (scan_x + x_length);
bignum_digit_type* start_y = BIGNUM_START_PTR(y);
bignum_digit_type* end_y = (start_y + y_length);
bignum_digit_type* start_r = (BIGNUM_START_PTR(r));
#define x_digit x_digit_high
#define y_digit y_digit_high
#define product_high carry
while (scan_x < end_x) {
x_digit = (*scan_x++);
x_digit_low = (HD_LOW(x_digit));
x_digit_high = (HD_HIGH(x_digit));
carry = 0;
scan_y = start_y;
scan_r = (start_r++);
while (scan_y < end_y) {
y_digit = (*scan_y++);
y_digit_low = (HD_LOW(y_digit));
y_digit_high = (HD_HIGH(y_digit));
product_low =
((*scan_r) + (x_digit_low * y_digit_low) + (HD_LOW(carry)));
product_high =
((x_digit_high * y_digit_low) + (x_digit_low * y_digit_high) +
(HD_HIGH(product_low)) + (HD_HIGH(carry)));
(*scan_r++) = (HD_CONS((HD_LOW(product_high)), (HD_LOW(product_low))));
carry = ((x_digit_high * y_digit_high) + (HD_HIGH(product_high)));
}
(*scan_r) += carry;
}
return (bignum_trim(r));
#undef x_digit
#undef y_digit
#undef product_high
}
}
// Allocates memory
bignum* factor_vm::bignum_multiply_unsigned_small_factor(bignum* x_,
bignum_digit_type y,
int negative_p) {
data_root<bignum> x(x_, this);
bignum_length_type length_x = (BIGNUM_LENGTH(x));
bignum* p = (allot_bignum((length_x + 1), negative_p));
bignum_destructive_copy(x.untagged(), p);
(BIGNUM_REF(p, length_x)) = 0;
bignum_destructive_scale_up(p, y);
return (bignum_trim(p));
}
void factor_vm::bignum_destructive_add(bignum* bn, bignum_digit_type n) {
bignum_digit_type* scan = (BIGNUM_START_PTR(bn));
bignum_digit_type digit;
digit = ((*scan) + n);
if (digit < BIGNUM_RADIX) {
(*scan) = digit;
return;
}
(*scan++) = (digit - BIGNUM_RADIX);
while (1) {
digit = ((*scan) + 1);
if (digit < BIGNUM_RADIX) {
(*scan) = digit;
return;
}
(*scan++) = (digit - BIGNUM_RADIX);
}
}
void factor_vm::bignum_destructive_scale_up(bignum* bn,
bignum_digit_type factor) {
bignum_digit_type carry = 0;
bignum_digit_type* scan = (BIGNUM_START_PTR(bn));
bignum_digit_type two_digits;
bignum_digit_type product_low;
#define product_high carry
bignum_digit_type* end = (scan + (BIGNUM_LENGTH(bn)));
BIGNUM_ASSERT((factor > 1) && (factor < BIGNUM_RADIX_ROOT));
while (scan < end) {
two_digits = (*scan);
product_low = ((factor * (HD_LOW(two_digits))) + (HD_LOW(carry)));
product_high = ((factor * (HD_HIGH(two_digits))) + (HD_HIGH(product_low)) +
(HD_HIGH(carry)));
(*scan++) = (HD_CONS((HD_LOW(product_high)), (HD_LOW(product_low))));
carry = (HD_HIGH(product_high));
}
// A carry here would be an overflow, i.e. it would not fit.
// Hopefully the callers allocate enough space that this will
// never happen.
BIGNUM_ASSERT(carry == 0);
return;
#undef product_high
}
// Division
// For help understanding this algorithm, see:
// Knuth, Donald E., "The Art of Computer Programming",
// volume 2, "Seminumerical Algorithms"
// section 4.3.1, "Multiple-Precision Arithmetic".
// Allocates memory
void factor_vm::bignum_divide_unsigned_large_denominator(
bignum* numerator_, bignum* denominator_,
bignum** quotient, bignum** remainder,
int q_negative_p, int r_negative_p) {
data_root<bignum> numerator(numerator_, this);
data_root<bignum> denominator(denominator_, this);
bignum_length_type length_n = BIGNUM_LENGTH(numerator) + 1;
bignum_length_type length_d = BIGNUM_LENGTH(denominator);
data_root<bignum> u(allot_bignum(length_n, r_negative_p), this);
int shift = 0;
BIGNUM_ASSERT(length_d > 1);
{
bignum_digit_type v1 = BIGNUM_REF(denominator.untagged(), length_d - 1);
while (v1 < (BIGNUM_RADIX / 2)) {
v1 <<= 1;
shift += 1;
}
}
if (quotient != NULL) {
bignum *q_ = allot_bignum(length_n - length_d, q_negative_p);
data_root<bignum> q(q_, this);
if (shift == 0) {
bignum_destructive_copy(numerator.untagged(), u.untagged());
(BIGNUM_REF(u.untagged(), (length_n - 1))) = 0;
bignum_divide_unsigned_normalized(u.untagged(),
denominator.untagged(),
q.untagged());
} else {
bignum* v = allot_bignum(length_d, 0);
bignum_destructive_normalization(numerator.untagged(),
u.untagged(),
shift);
bignum_destructive_normalization(denominator.untagged(), v, shift);
bignum_divide_unsigned_normalized(u.untagged(), v, q.untagged());
if (remainder != NULL)
bignum_destructive_unnormalization(u.untagged(), shift);
}
q.set_untagged(bignum_trim(q.untagged()));
*quotient = q.untagged();
} else {
if (shift == 0) {
bignum_destructive_copy(numerator.untagged(), u.untagged());
(BIGNUM_REF(u.untagged(), (length_n - 1))) = 0;
bignum_divide_unsigned_normalized(u.untagged(),
denominator.untagged(),
NULL);
} else {
bignum* v = allot_bignum(length_d, 0);
bignum_destructive_normalization(numerator.untagged(),
u.untagged(),
shift);
bignum_destructive_normalization(denominator.untagged(),
v,
shift);
bignum_divide_unsigned_normalized(u.untagged(), v, NULL);
if (remainder != NULL)
bignum_destructive_unnormalization(u.untagged(), shift);
}
}
u.set_untagged(bignum_trim(u.untagged()));
if (remainder != NULL)
*remainder = u.untagged();
}
void factor_vm::bignum_divide_unsigned_normalized(bignum* u, bignum* v,
bignum* q) {
bignum_length_type u_length = (BIGNUM_LENGTH(u));
bignum_length_type v_length = (BIGNUM_LENGTH(v));
bignum_digit_type* u_start = (BIGNUM_START_PTR(u));
bignum_digit_type* u_scan = (u_start + u_length);
bignum_digit_type* u_scan_limit = (u_start + v_length);
bignum_digit_type* u_scan_start = (u_scan - v_length);
bignum_digit_type* v_start = (BIGNUM_START_PTR(v));
bignum_digit_type* v_end = (v_start + v_length);
bignum_digit_type* q_scan = NULL;
bignum_digit_type v1 = (v_end[-1]);
bignum_digit_type v2 = (v_end[-2]);
bignum_digit_type ph; // high half of double-digit product
bignum_digit_type pl; // low half of double-digit product
bignum_digit_type guess;
bignum_digit_type gh; // high half-digit of guess
bignum_digit_type ch; // high half of double-digit comparand
bignum_digit_type v2l = (HD_LOW(v2));
bignum_digit_type v2h = (HD_HIGH(v2));
bignum_digit_type cl; // low half of double-digit comparand
#define gl ph // low half-digit of guess
#define uj pl
#define qj ph
bignum_digit_type gm; // memory loc for reference parameter
if (q != BIGNUM_OUT_OF_BAND)
q_scan = ((BIGNUM_START_PTR(q)) + (BIGNUM_LENGTH(q)));
while (u_scan_limit < u_scan) {
uj = (*--u_scan);
if (uj != v1) {
// comparand =
// (((((uj * BIGNUM_RADIX) + uj1) % v1) * BIGNUM_RADIX) + uj2);
// guess = (((uj * BIGNUM_RADIX) + uj1) / v1);
cl = (u_scan[-2]);
ch = (bignum_digit_divide(uj, (u_scan[-1]), v1, (&gm)));
guess = gm;
} else {
cl = (u_scan[-2]);
ch = ((u_scan[-1]) + v1);
guess = (BIGNUM_RADIX - 1);
}
while (1) {
// product = (guess * v2);
gl = (HD_LOW(guess));
gh = (HD_HIGH(guess));
pl = (v2l * gl);
ph = ((v2l * gh) + (v2h * gl) + (HD_HIGH(pl)));
pl = (HD_CONS((HD_LOW(ph)), (HD_LOW(pl))));
ph = ((v2h * gh) + (HD_HIGH(ph)));
// if (comparand >= product)
if ((ch > ph) || ((ch == ph) && (cl >= pl)))
break;
guess -= 1;
// comparand += (v1 << BIGNUM_DIGIT_LENGTH)
ch += v1;
// if (comparand >= (BIGNUM_RADIX * BIGNUM_RADIX))
if (ch >= BIGNUM_RADIX)
break;
}
qj = (bignum_divide_subtract(v_start, v_end, guess, (--u_scan_start)));
if (q != BIGNUM_OUT_OF_BAND)
(*--q_scan) = qj;
}
return;
#undef gl
#undef uj
#undef qj
}
bignum_digit_type factor_vm::bignum_divide_subtract(
bignum_digit_type* v_start, bignum_digit_type* v_end,
bignum_digit_type guess, bignum_digit_type* u_start) {
bignum_digit_type* v_scan = v_start;
bignum_digit_type* u_scan = u_start;
bignum_digit_type carry = 0;
if (guess == 0)
return (0);
{
bignum_digit_type gl = (HD_LOW(guess));
bignum_digit_type gh = (HD_HIGH(guess));
bignum_digit_type v;
bignum_digit_type pl;
bignum_digit_type vl;
#define vh v
#define ph carry
#define diff pl
while (v_scan < v_end) {
v = (*v_scan++);
vl = (HD_LOW(v));
vh = (HD_HIGH(v));
pl = ((vl * gl) + (HD_LOW(carry)));
ph = ((vl * gh) + (vh * gl) + (HD_HIGH(pl)) + (HD_HIGH(carry)));
diff = ((*u_scan) - (HD_CONS((HD_LOW(ph)), (HD_LOW(pl)))));
if (diff < 0) {
(*u_scan++) = (diff + BIGNUM_RADIX);
carry = ((vh * gh) + (HD_HIGH(ph)) + 1);
} else {
(*u_scan++) = diff;
carry = ((vh * gh) + (HD_HIGH(ph)));
}
}
if (carry == 0)
return (guess);
diff = ((*u_scan) - carry);
if (diff < 0)
(*u_scan) = (diff + BIGNUM_RADIX);
else {
(*u_scan) = diff;
return (guess);
}
#undef vh
#undef ph
#undef diff
}
// Subtraction generated carry, implying guess is one too large.
// Add v back in to bring it back down.
v_scan = v_start;
u_scan = u_start;
carry = 0;
while (v_scan < v_end) {
bignum_digit_type sum = ((*v_scan++) + (*u_scan) + carry);
if (sum < BIGNUM_RADIX) {
(*u_scan++) = sum;
carry = 0;
} else {
(*u_scan++) = (sum - BIGNUM_RADIX);
carry = 1;
}
}
if (carry == 1) {
bignum_digit_type sum = ((*u_scan) + carry);
(*u_scan) = ((sum < BIGNUM_RADIX) ? sum : (sum - BIGNUM_RADIX));
}
return (guess - 1);
}
// Allocates memory
void factor_vm::bignum_divide_unsigned_medium_denominator(
bignum* numerator_, bignum_digit_type denominator, bignum** quotient,
bignum** remainder, int q_negative_p, int r_negative_p) {
data_root<bignum> numerator(numerator_, this);
bignum_length_type length_n = (BIGNUM_LENGTH(numerator));
int shift = 0;
// Because `bignum_digit_divide' requires a normalized denominator.
while (denominator < (BIGNUM_RADIX / 2)) {
denominator <<= 1;
shift += 1;
}
bignum_length_type length_q = (shift == 0) ? length_n : length_n + 1;
data_root<bignum> q(allot_bignum(length_q, q_negative_p), this);
if (shift == 0) {
bignum_destructive_copy(numerator.untagged(), q.untagged());
} else {
bignum_destructive_normalization(numerator.untagged(), q.untagged(), shift);
}
{
bignum_digit_type r = 0;
bignum_digit_type* start = (BIGNUM_START_PTR(q));
bignum_digit_type* scan = (start + length_q);
bignum_digit_type qj;
while (start < scan) {
r = (bignum_digit_divide(r, (*--scan), denominator, (&qj)));
(*scan) = qj;
}
q.set_untagged(bignum_trim(q.untagged()));
if (remainder != ((bignum**)0)) {
if (shift != 0)
r >>= shift;
(*remainder) = (bignum_digit_to_bignum(r, r_negative_p));
}
if (quotient != ((bignum**)0))
(*quotient) = q.untagged();
}
return;
}
void factor_vm::bignum_destructive_normalization(bignum* source, bignum* target,
int shift_left) {
bignum_digit_type digit;
bignum_digit_type* scan_source = (BIGNUM_START_PTR(source));
bignum_digit_type carry = 0;
bignum_digit_type* scan_target = (BIGNUM_START_PTR(target));
bignum_digit_type* end_source = (scan_source + (BIGNUM_LENGTH(source)));
bignum_digit_type* end_target = (scan_target + (BIGNUM_LENGTH(target)));
int shift_right = (BIGNUM_DIGIT_LENGTH - shift_left);
bignum_digit_type mask = (((cell)1 << shift_right) - 1);
while (scan_source < end_source) {
digit = (*scan_source++);
(*scan_target++) = (((digit & mask) << shift_left) | carry);
carry = (digit >> shift_right);
}
if (scan_target < end_target)
(*scan_target) = carry;
else
BIGNUM_ASSERT(carry == 0);
return;
}
void factor_vm::bignum_destructive_unnormalization(bignum* bn,
int shift_right) {
bignum_digit_type* start = (BIGNUM_START_PTR(bn));
bignum_digit_type* scan = (start + (BIGNUM_LENGTH(bn)));
bignum_digit_type digit;
bignum_digit_type carry = 0;
int shift_left = (BIGNUM_DIGIT_LENGTH - shift_right);
bignum_digit_type mask = (((fixnum)1 << shift_right) - 1);
while (start < scan) {
digit = (*--scan);
(*scan) = ((digit >> shift_right) | carry);
carry = ((digit & mask) << shift_left);
}
BIGNUM_ASSERT(carry == 0);
return;
}
// This is a reduced version of the division algorithm, applied to the
// case of dividing two bignum digits by one bignum digit. It is
// assumed that the numerator, denominator are normalized.
#define BDD_STEP(qn, j) \
{ \
uj = (u[j]); \
if (uj != v1) { \
uj_uj1 = (HD_CONS(uj, (u[j + 1]))); \
guess = (uj_uj1 / v1); \
comparand = (HD_CONS((uj_uj1 % v1), (u[j + 2]))); \
} else { \
guess = (BIGNUM_RADIX_ROOT - 1); \
comparand = (HD_CONS(((u[j + 1]) + v1), (u[j + 2]))); \
} \
while ((guess * v2) > comparand) { \
guess -= 1; \
comparand += (v1 << BIGNUM_HALF_DIGIT_LENGTH); \
if (comparand >= BIGNUM_RADIX) \
break; \
} \
qn = (bignum_digit_divide_subtract(v1, v2, guess, (&u[j]))); \
}
bignum_digit_type factor_vm::bignum_digit_divide(
bignum_digit_type uh, bignum_digit_type ul, bignum_digit_type v,
bignum_digit_type* q) // return value
{
bignum_digit_type guess;
bignum_digit_type comparand;
bignum_digit_type v1 = (HD_HIGH(v));
bignum_digit_type v2 = (HD_LOW(v));
bignum_digit_type uj;
bignum_digit_type uj_uj1;
bignum_digit_type q1;
bignum_digit_type q2;
bignum_digit_type u[4];
if (uh == 0) {
if (ul < v) {
(*q) = 0;
return (ul);
} else if (ul == v) {
(*q) = 1;
return (0);
}
}
(u[0]) = (HD_HIGH(uh));
(u[1]) = (HD_LOW(uh));
(u[2]) = (HD_HIGH(ul));
(u[3]) = (HD_LOW(ul));
v1 = (HD_HIGH(v));
v2 = (HD_LOW(v));
BDD_STEP(q1, 0);
BDD_STEP(q2, 1);
(*q) = (HD_CONS(q1, q2));
return (HD_CONS((u[2]), (u[3])));
}
#undef BDD_STEP
#define BDDS_MULSUB(vn, un, carry_in) \
{ \
product = ((vn * guess) + carry_in); \
diff = (un - (HD_LOW(product))); \
if (diff < 0) { \
un = (diff + BIGNUM_RADIX_ROOT); \
carry = ((HD_HIGH(product)) + 1); \
} else { \
un = diff; \
carry = (HD_HIGH(product)); \
} \
}
#define BDDS_ADD(vn, un, carry_in) \
{ \
sum = (vn + un + carry_in); \
if (sum < BIGNUM_RADIX_ROOT) { \
un = sum; \
carry = 0; \
} else { \
un = (sum - BIGNUM_RADIX_ROOT); \
carry = 1; \
} \
}
bignum_digit_type factor_vm::bignum_digit_divide_subtract(
bignum_digit_type v1, bignum_digit_type v2, bignum_digit_type guess,
bignum_digit_type* u) {
{
bignum_digit_type product;
bignum_digit_type diff;
bignum_digit_type carry;
BDDS_MULSUB(v2, (u[2]), 0);
BDDS_MULSUB(v1, (u[1]), carry);
if (carry == 0)
return (guess);
diff = ((u[0]) - carry);
if (diff < 0)
(u[0]) = (diff + BIGNUM_RADIX);
else {
(u[0]) = diff;
return (guess);
}
}
{
bignum_digit_type sum;
bignum_digit_type carry;
BDDS_ADD(v2, (u[2]), 0);
BDDS_ADD(v1, (u[1]), carry);
if (carry == 1)
(u[0]) += 1;
}
return (guess - 1);
}
#undef BDDS_MULSUB
#undef BDDS_ADD
// Allocates memory
void factor_vm::bignum_divide_unsigned_small_denominator(
bignum* numerator_, bignum_digit_type denominator, bignum** quotient,
bignum** remainder, int q_negative_p, int r_negative_p) {
data_root<bignum> numerator(numerator_, this);
bignum* q_ = bignum_new_sign(numerator.untagged(), q_negative_p);
data_root<bignum> q(q_, this);
bignum_digit_type r = bignum_destructive_scale_down(q.untagged(), denominator);
q.set_untagged(bignum_trim(q.untagged()));
if (remainder != ((bignum**)0))
(*remainder) = bignum_digit_to_bignum(r, r_negative_p);
(*quotient) = q.untagged();
return;
}
// Given (denominator > 1), it is fairly easy to show that
// (quotient_high < BIGNUM_RADIX_ROOT), after which it is easy to see
// that all digits are < BIGNUM_RADIX.
bignum_digit_type factor_vm::bignum_destructive_scale_down(
bignum* bn, bignum_digit_type denominator) {
bignum_digit_type numerator;
bignum_digit_type remainder = 0;
bignum_digit_type two_digits;
#define quotient_high remainder
bignum_digit_type* start = (BIGNUM_START_PTR(bn));
bignum_digit_type* scan = (start + (BIGNUM_LENGTH(bn)));
BIGNUM_ASSERT((denominator > 1) && (denominator < BIGNUM_RADIX_ROOT));
while (start < scan) {
two_digits = (*--scan);
numerator = (HD_CONS(remainder, (HD_HIGH(two_digits))));
quotient_high = (numerator / denominator);
numerator = (HD_CONS((numerator % denominator), (HD_LOW(two_digits))));
(*scan) = (HD_CONS(quotient_high, (numerator / denominator)));
remainder = (numerator % denominator);
}
return (remainder);
#undef quotient_high
}
// Allocates memory
bignum* factor_vm::bignum_remainder_unsigned_small_denominator(
bignum* n, bignum_digit_type d, int negative_p) {
bignum_digit_type two_digits;
bignum_digit_type* start = (BIGNUM_START_PTR(n));
bignum_digit_type* scan = (start + (BIGNUM_LENGTH(n)));
bignum_digit_type r = 0;
BIGNUM_ASSERT((d > 1) && (d < BIGNUM_RADIX_ROOT));
while (start < scan) {
two_digits = (*--scan);
r = ((HD_CONS(((HD_CONS(r, (HD_HIGH(two_digits)))) % d),
(HD_LOW(two_digits)))) %
d);
}
return (bignum_digit_to_bignum(r, negative_p));
}
// Allocates memory
bignum* factor_vm::bignum_digit_to_bignum(bignum_digit_type digit,
int negative_p) {
if (digit == 0)
return (BIGNUM_ZERO());
else {
bignum* result = (allot_bignum(1, negative_p));
(BIGNUM_REF(result, 0)) = digit;
return (result);
}
}
// Allocates memory
bignum* factor_vm::allot_bignum(bignum_length_type length, int negative_p) {
BIGNUM_ASSERT((length >= 0) || (length < BIGNUM_RADIX));
bignum* result = allot_uninitialized_array<bignum>(length + 1);
BIGNUM_SET_NEGATIVE_P(result, negative_p);
return (result);
}
// Allocates memory
bignum* factor_vm::allot_bignum_zeroed(bignum_length_type length,
int negative_p) {
bignum* result = allot_bignum(length, negative_p);
bignum_digit_type* scan = (BIGNUM_START_PTR(result));
bignum_digit_type* end = (scan + length);
while (scan < end)
(*scan++) = 0;
return (result);
}
// Allocates memory
bignum* factor_vm::bignum_shorten_length(bignum* bn,
bignum_length_type length) {
bignum_length_type current_length = (BIGNUM_LENGTH(bn));
BIGNUM_ASSERT((length >= 0) || (length <= current_length));
if (length < current_length) {
bn = reallot_array(bn, length + 1);
BIGNUM_SET_NEGATIVE_P(bn, (length != 0) && (BIGNUM_NEGATIVE_P(bn)));
}
return (bn);
}
// Allocates memory
bignum* factor_vm::bignum_trim(bignum* bn) {
bignum_digit_type* start = (BIGNUM_START_PTR(bn));
bignum_digit_type* end = (start + (BIGNUM_LENGTH(bn)));
bignum_digit_type* scan = end;
while ((start <= scan) && ((*--scan) == 0))
;
scan += 1;
if (scan < end) {
bignum_length_type length = (scan - start);
bn = reallot_array(bn, length + 1);
BIGNUM_SET_NEGATIVE_P(bn, (length != 0) && (BIGNUM_NEGATIVE_P(bn)));
}
return (bn);
}
// Copying
// Allocates memory
bignum* factor_vm::bignum_new_sign(bignum* x_, int negative_p) {
data_root<bignum> x(x_, this);
bignum* result = allot_bignum(BIGNUM_LENGTH(x), negative_p);
bignum_destructive_copy(x.untagged(), result);
return result;
}
// Allocates memory
bignum* factor_vm::bignum_maybe_new_sign(bignum* x_, int negative_p) {
if ((BIGNUM_NEGATIVE_P(x_)) ? negative_p : (!negative_p))
return x_;
else {
return bignum_new_sign(x_, negative_p);
}
}
void factor_vm::bignum_destructive_copy(bignum* source, bignum* target) {
bignum_digit_type* scan_source = (BIGNUM_START_PTR(source));
bignum_digit_type* end_source = (scan_source + (BIGNUM_LENGTH(source)));
bignum_digit_type* scan_target = (BIGNUM_START_PTR(target));
while (scan_source < end_source)
(*scan_target++) = (*scan_source++);
return;
}
// * Added bitwise operations (and oddp).
// Allocates memory
bignum* factor_vm::bignum_bitwise_not(bignum* x_) {
int carry = 1;
bignum_length_type size = BIGNUM_LENGTH(x_);
int is_negative = BIGNUM_NEGATIVE_P(x_);
data_root<bignum> x(x_, this);
data_root<bignum> y(allot_bignum(size, is_negative ? 0 : 1), this);
bignum_digit_type* scan_x = BIGNUM_START_PTR(x);
bignum_digit_type* end_x = scan_x + size;
bignum_digit_type* scan_y = BIGNUM_START_PTR(y);
if (is_negative) {
while (scan_x < end_x) {
if (*scan_x == 0) {
*scan_y++ = BIGNUM_RADIX - 1;
scan_x++;
} else {
*scan_y++ = *scan_x++ - 1;
carry = 0;
break;
}
}
} else {
while (scan_x < end_x) {
if (*scan_x == (BIGNUM_RADIX - 1)) {
*scan_y++ = 0;
scan_x++;
} else {
*scan_y++ = *scan_x++ + 1;
carry = 0;
break;
}
}
}
while (scan_x < end_x) {
*scan_y++ = *scan_x++;
}
if (carry) {
bignum* ret = allot_bignum(size + 1, BIGNUM_NEGATIVE_P(y));
bignum_destructive_copy(y.untagged(), ret);
bignum_digit_type* ret_start = BIGNUM_START_PTR(ret);
*(ret_start + size) = 1;
return ret;
} else {
return bignum_trim(y.untagged());
}
}
// Allocates memory
bignum* factor_vm::bignum_arithmetic_shift(bignum* arg1, fixnum n) {
if (BIGNUM_NEGATIVE_P(arg1) && n < 0)
return bignum_bitwise_not(
bignum_magnitude_ash(bignum_bitwise_not(arg1), n));
else
return bignum_magnitude_ash(arg1, n);
}
#define AND_OP 0
#define IOR_OP 1
#define XOR_OP 2
// Allocates memory
bignum* factor_vm::bignum_bitwise_and(bignum* arg1, bignum* arg2) {
return ((BIGNUM_NEGATIVE_P(arg1)) ? (BIGNUM_NEGATIVE_P(arg2))
? bignum_negneg_bitwise_op(AND_OP, arg1, arg2)
: bignum_posneg_bitwise_op(AND_OP, arg2, arg1)
: (BIGNUM_NEGATIVE_P(arg2))
? bignum_posneg_bitwise_op(AND_OP, arg1, arg2)
: bignum_pospos_bitwise_op(AND_OP, arg1, arg2));
}
// Allocates memory
bignum* factor_vm::bignum_bitwise_ior(bignum* arg1, bignum* arg2) {
return ((BIGNUM_NEGATIVE_P(arg1)) ? (BIGNUM_NEGATIVE_P(arg2))
? bignum_negneg_bitwise_op(IOR_OP, arg1, arg2)
: bignum_posneg_bitwise_op(IOR_OP, arg2, arg1)
: (BIGNUM_NEGATIVE_P(arg2))
? bignum_posneg_bitwise_op(IOR_OP, arg1, arg2)
: bignum_pospos_bitwise_op(IOR_OP, arg1, arg2));
}
// Allocates memory
bignum* factor_vm::bignum_bitwise_xor(bignum* arg1, bignum* arg2) {
return ((BIGNUM_NEGATIVE_P(arg1)) ? (BIGNUM_NEGATIVE_P(arg2))
? bignum_negneg_bitwise_op(XOR_OP, arg1, arg2)
: bignum_posneg_bitwise_op(XOR_OP, arg2, arg1)
: (BIGNUM_NEGATIVE_P(arg2))
? bignum_posneg_bitwise_op(XOR_OP, arg1, arg2)
: bignum_pospos_bitwise_op(XOR_OP, arg1, arg2));
}
// Allocates memory
// ash for the magnitude
// assume arg1 is a big number, n is a long
bignum* factor_vm::bignum_magnitude_ash(bignum* arg1_, fixnum n) {
data_root<bignum> arg1(arg1_, this);
bignum* result = NULL;
bignum_digit_type* scan1;
bignum_digit_type* scanr;
bignum_digit_type* end;
fixnum digit_offset, bit_offset;
if (BIGNUM_ZERO_P(arg1))
return arg1.untagged();
if (n > 0) {
digit_offset = n / BIGNUM_DIGIT_LENGTH;
bit_offset = n % BIGNUM_DIGIT_LENGTH;
result = allot_bignum_zeroed(BIGNUM_LENGTH(arg1) + digit_offset + 1,
BIGNUM_NEGATIVE_P(arg1));
scanr = BIGNUM_START_PTR(result) + digit_offset;
scan1 = BIGNUM_START_PTR(arg1);
end = scan1 + BIGNUM_LENGTH(arg1);
while (scan1 < end) {
*scanr = *scanr | (*scan1 & BIGNUM_DIGIT_MASK) << bit_offset;
*scanr = *scanr & BIGNUM_DIGIT_MASK;
scanr++;
*scanr = *scan1++ >> (BIGNUM_DIGIT_LENGTH - bit_offset);
*scanr = *scanr & BIGNUM_DIGIT_MASK;
}
} else if (n < 0 && (-n >= (BIGNUM_LENGTH(arg1) * (bignum_length_type)
BIGNUM_DIGIT_LENGTH))) {
result = BIGNUM_ZERO();
} else if (n < 0) {
digit_offset = -n / BIGNUM_DIGIT_LENGTH;
bit_offset = -n % BIGNUM_DIGIT_LENGTH;
result = allot_bignum_zeroed(BIGNUM_LENGTH(arg1) - digit_offset,
BIGNUM_NEGATIVE_P(arg1));
scanr = BIGNUM_START_PTR(result);
scan1 = BIGNUM_START_PTR(arg1) + digit_offset;
end = scanr + BIGNUM_LENGTH(result) - 1;
while (scanr < end) {
*scanr = (*scan1++ & BIGNUM_DIGIT_MASK) >> bit_offset;
*scanr = (*scanr | *scan1 << (BIGNUM_DIGIT_LENGTH - bit_offset)) &
BIGNUM_DIGIT_MASK;
scanr++;
}
*scanr = (*scan1++ & BIGNUM_DIGIT_MASK) >> bit_offset;
} else if (n == 0) {
result = arg1.untagged();
}
return bignum_trim(result);
}
// Allocates memory
bignum* factor_vm::bignum_pospos_bitwise_op(int op, bignum* arg1_,
bignum* arg2_) {
data_root<bignum> arg1(arg1_, this);
data_root<bignum> arg2(arg2_, this);
bignum_length_type max_length;
bignum_digit_type* scan1, *end1, digit1;
bignum_digit_type* scan2, *end2, digit2;
bignum_digit_type* scanr, *endr;
max_length =
(BIGNUM_LENGTH(arg1) > BIGNUM_LENGTH(arg2)) ? BIGNUM_LENGTH(arg1)
: BIGNUM_LENGTH(arg2);
bignum* result = allot_bignum(max_length, 0);
scanr = BIGNUM_START_PTR(result);
scan1 = BIGNUM_START_PTR(arg1);
scan2 = BIGNUM_START_PTR(arg2);
endr = scanr + max_length;
end1 = scan1 + BIGNUM_LENGTH(arg1);
end2 = scan2 + BIGNUM_LENGTH(arg2);
while (scanr < endr) {
digit1 = (scan1 < end1) ? *scan1++ : 0;
digit2 = (scan2 < end2) ? *scan2++ : 0;
*scanr++ =
(op == AND_OP) ? digit1 & digit2 : (op == IOR_OP) ? digit1 | digit2
: digit1 ^ digit2;
}
return bignum_trim(result);
}
// Allocates memory
bignum* factor_vm::bignum_posneg_bitwise_op(int op, bignum* arg1_,
bignum* arg2_) {
data_root<bignum> arg1(arg1_, this);
data_root<bignum> arg2(arg2_, this);
bignum_length_type max_length;
bignum_digit_type* scan1, *end1, digit1;
bignum_digit_type* scan2, *end2, digit2, carry2;
bignum_digit_type* scanr, *endr;
char neg_p = op == IOR_OP || op == XOR_OP;
max_length =
(BIGNUM_LENGTH(arg1) > BIGNUM_LENGTH(arg2) + 1) ? BIGNUM_LENGTH(arg1)
: BIGNUM_LENGTH(arg2) + 1;
bignum* result = allot_bignum(max_length, neg_p);
scanr = BIGNUM_START_PTR(result);
scan1 = BIGNUM_START_PTR(arg1);
scan2 = BIGNUM_START_PTR(arg2);
endr = scanr + max_length;
end1 = scan1 + BIGNUM_LENGTH(arg1);
end2 = scan2 + BIGNUM_LENGTH(arg2);
carry2 = 1;
while (scanr < endr) {
digit1 = (scan1 < end1) ? *scan1++ : 0;
digit2 = (~((scan2 < end2) ? *scan2++ : 0) & BIGNUM_DIGIT_MASK) + carry2;
if (digit2 < BIGNUM_RADIX)
carry2 = 0;
else {
digit2 = (digit2 - BIGNUM_RADIX);
carry2 = 1;
}
*scanr++ =
(op == AND_OP) ? digit1 & digit2 : (op == IOR_OP) ? digit1 | digit2
: digit1 ^ digit2;
}
if (neg_p)
bignum_negate_magnitude(result);
return bignum_trim(result);
}
// Allocates memory
bignum* factor_vm::bignum_negneg_bitwise_op(int op, bignum* arg1_,
bignum* arg2_) {
data_root<bignum> arg1(arg1_, this);
data_root<bignum> arg2(arg2_, this);
bignum_length_type max_length;
bignum_digit_type* scan1, *end1, digit1, carry1;
bignum_digit_type* scan2, *end2, digit2, carry2;
bignum_digit_type* scanr, *endr;
char neg_p = op == AND_OP || op == IOR_OP;
max_length =
(BIGNUM_LENGTH(arg1) > BIGNUM_LENGTH(arg2)) ? BIGNUM_LENGTH(arg1) + 1
: BIGNUM_LENGTH(arg2) + 1;
bignum* result = allot_bignum(max_length, neg_p);
scanr = BIGNUM_START_PTR(result);
scan1 = BIGNUM_START_PTR(arg1);
scan2 = BIGNUM_START_PTR(arg2);
endr = scanr + max_length;
end1 = scan1 + BIGNUM_LENGTH(arg1);
end2 = scan2 + BIGNUM_LENGTH(arg2);
carry1 = 1;
carry2 = 1;
while (scanr < endr) {
digit1 = (~((scan1 < end1) ? *scan1++ : 0) & BIGNUM_DIGIT_MASK) + carry1;
digit2 = (~((scan2 < end2) ? *scan2++ : 0) & BIGNUM_DIGIT_MASK) + carry2;
if (digit1 < BIGNUM_RADIX)
carry1 = 0;
else {
digit1 = (digit1 - BIGNUM_RADIX);
carry1 = 1;
}
if (digit2 < BIGNUM_RADIX)
carry2 = 0;
else {
digit2 = (digit2 - BIGNUM_RADIX);
carry2 = 1;
}
*scanr++ =
(op == AND_OP) ? digit1 & digit2 : (op == IOR_OP) ? digit1 | digit2
: digit1 ^ digit2;
}
if (neg_p)
bignum_negate_magnitude(result);
return bignum_trim(result);
}
void factor_vm::bignum_negate_magnitude(bignum* arg) {
bignum_digit_type* scan;
bignum_digit_type* end;
bignum_digit_type digit;
bignum_digit_type carry;
scan = BIGNUM_START_PTR(arg);
end = scan + BIGNUM_LENGTH(arg);
carry = 1;
while (scan < end) {
digit = (~ * scan & BIGNUM_DIGIT_MASK) + carry;
if (digit < BIGNUM_RADIX)
carry = 0;
else {
digit = (digit - BIGNUM_RADIX);
carry = 1;
}
*scan++ = digit;
}
}
// Allocates memory
bignum* factor_vm::bignum_integer_length(bignum* x_) {
data_root<bignum> x(x_, this);
bignum_length_type index = ((BIGNUM_LENGTH(x)) - 1);
bignum_digit_type digit = (BIGNUM_REF(x, index));
bignum_digit_type carry = 0;
bignum* result;
while (digit > 1) {
carry += 1;
digit >>= 1;
}
if (index < BIGNUM_RADIX_ROOT) {
result = allot_bignum(1, 0);
(BIGNUM_REF(result, 0)) = (index * BIGNUM_DIGIT_LENGTH) + carry;
} else {
result = allot_bignum(2, 0);
(BIGNUM_REF(result, 0)) = index;
(BIGNUM_REF(result, 1)) = 0;
bignum_destructive_scale_up(result, BIGNUM_DIGIT_LENGTH);
bignum_destructive_add(result, carry);
}
return (bignum_trim(result));
}
// Allocates memory
int factor_vm::bignum_logbitp(int shift, bignum* arg) {
return ((BIGNUM_NEGATIVE_P(arg))
? !bignum_unsigned_logbitp(shift, bignum_bitwise_not(arg))
: bignum_unsigned_logbitp(shift, arg));
}
int factor_vm::bignum_unsigned_logbitp(int shift, bignum* bn) {
bignum_length_type len = (BIGNUM_LENGTH(bn));
int index = shift / BIGNUM_DIGIT_LENGTH;
if (index >= len)
return 0;
bignum_digit_type digit = (BIGNUM_REF(bn, index));
int p = shift % BIGNUM_DIGIT_LENGTH;
bignum_digit_type mask = ((fixnum)1) << p;
return (digit & mask) ? 1 : 0;
}
#ifdef _WIN64
// Allocates memory.
bignum* factor_vm::bignum_gcd(bignum* a_, bignum* b_) {
data_root<bignum> a(a_, this);
data_root<bignum> b(b_, this);
// Copies of a and b with that are both positive.
data_root<bignum> ac(bignum_maybe_new_sign(a.untagged(), 0), this);
data_root<bignum> bc(bignum_maybe_new_sign(b.untagged(), 0), this);
if (bignum_compare(ac.untagged(), bc.untagged()) == BIGNUM_COMPARISON_LESS) {
swap(ac, bc);
}
while (BIGNUM_LENGTH(bc) != 0) {
data_root<bignum> d(bignum_remainder(ac.untagged(), bc.untagged()), this);
if (d.untagged() == BIGNUM_OUT_OF_BAND) {
return d.untagged();
}
ac = bc;
bc = d;
}
return ac.untagged();
}
#else
// Allocates memory
bignum* factor_vm::bignum_gcd(bignum* a_, bignum* b_) {
data_root<bignum> a(a_, this);
data_root<bignum> b(b_, this);
bignum_twodigit_type x, y, q, s, t, A, B, C, D;
int nbits, k;
bignum_length_type size_a, size_b, size_c;
bignum_digit_type* scan_a, *scan_b, *scan_c, *scan_d;
bignum_digit_type* a_end, *b_end, *c_end;
// clone the bignums so we can modify them in-place
size_a = BIGNUM_LENGTH(a);
data_root<bignum> c(allot_bignum(size_a, 0), this);
// c = allot_bignum(size_a, 0);
scan_a = BIGNUM_START_PTR(a);
a_end = scan_a + size_a;
scan_c = BIGNUM_START_PTR(c);
while (scan_a < a_end)
(*scan_c++) = (*scan_a++);
a = c;
size_b = BIGNUM_LENGTH(b);
data_root<bignum> d(allot_bignum(size_b, 0), this);
scan_b = BIGNUM_START_PTR(b);
b_end = scan_b + size_b;
scan_d = BIGNUM_START_PTR(d);
while (scan_b < b_end)
(*scan_d++) = (*scan_b++);
b = d;
// Initial reduction: make sure that 0 <= b <= a.
if (bignum_compare(a.untagged(), b.untagged()) == BIGNUM_COMPARISON_LESS) {
swap(a, b);
std::swap(size_a, size_b);
}
while (size_a > 1) {
nbits = log2(BIGNUM_REF(a, size_a - 1));
x = ((BIGNUM_REF(a, size_a - 1) << (BIGNUM_DIGIT_LENGTH - nbits)) |
(BIGNUM_REF(a, size_a - 2) >> nbits));
y = ((size_b >= size_a - 1 ? BIGNUM_REF(b, size_a - 2) >> nbits : 0) |
(size_b >= size_a
? BIGNUM_REF(b, size_a - 1) << (BIGNUM_DIGIT_LENGTH - nbits)
: 0));
// inner loop of Lehmer's algorithm;
A = 1;
B = 0;
C = 0;
D = 1;
for (k = 0;; k++) {
if (y - C == 0)
break;
q = (x + (A - 1)) / (y - C);
s = B + (q * D);
t = x - (q * y);
if (s > t)
break;
x = y;
y = t;
t = A + (q * C);
A = D;
B = C;
C = s;
D = t;
}
if (k == 0) {
// no progress; do a Euclidean step
if (size_b == 0) {
return bignum_trim(a.untagged());
}
data_root<bignum> e(bignum_trim(a.untagged()), this);
data_root<bignum> f(bignum_trim(b.untagged()), this);
c.set_untagged(bignum_remainder(e.untagged(), f.untagged()));
if (c.untagged() == BIGNUM_OUT_OF_BAND) {
return c.untagged();
}
// copy 'b' to 'a'
scan_a = BIGNUM_START_PTR(a);
scan_b = BIGNUM_START_PTR(b);
a_end = scan_a + size_a;
b_end = scan_b + size_b;
while (scan_b < b_end)
*(scan_a++) = *(scan_b++);
while (scan_a < a_end)
*(scan_a++) = 0;
size_a = size_b;
// copy 'c' to 'b'
scan_b = BIGNUM_START_PTR(b);
scan_c = BIGNUM_START_PTR(c);
size_c = BIGNUM_LENGTH(c);
c_end = scan_c + size_c;
while (scan_c < c_end)
*(scan_b++) = *(scan_c++);
while (scan_b < b_end)
*(scan_b++) = 0;
size_b = size_c;
continue;
}
// a, b = A*b - B*a, D*a - C*b if k is odd
// a, b = A*a - B*b, D*b - C*a if k is even
scan_a = BIGNUM_START_PTR(a);
scan_b = BIGNUM_START_PTR(b);
scan_c = scan_a;
scan_d = scan_b;
a_end = scan_a + size_a;
b_end = scan_b + size_b;
s = 0;
t = 0;
if (k & 1) {
while (scan_b < b_end) {
s += (A * *scan_b) - (B * *scan_a);
t += (D * *scan_a++) - (C * *scan_b++);
*scan_c++ = (bignum_digit_type)(s & BIGNUM_DIGIT_MASK);
*scan_d++ = (bignum_digit_type)(t & BIGNUM_DIGIT_MASK);
s >>= BIGNUM_DIGIT_LENGTH;
t >>= BIGNUM_DIGIT_LENGTH;
}
while (scan_a < a_end) {
s -= (B * *scan_a);
t += (D * *scan_a++);
*scan_c++ = (bignum_digit_type)(s & BIGNUM_DIGIT_MASK);
//*scan_d++ = (bignum_digit_type) (t & BIGNUM_DIGIT_MASK);
s >>= BIGNUM_DIGIT_LENGTH;
t >>= BIGNUM_DIGIT_LENGTH;
}
} else {
while (scan_b < b_end) {
s += (A * *scan_a) - (B * *scan_b);
t += (D * *scan_b++) - (C * *scan_a++);
*scan_c++ = (bignum_digit_type)(s & BIGNUM_DIGIT_MASK);
*scan_d++ = (bignum_digit_type)(t & BIGNUM_DIGIT_MASK);
s >>= BIGNUM_DIGIT_LENGTH;
t >>= BIGNUM_DIGIT_LENGTH;
}
while (scan_a < a_end) {
s += (A * *scan_a);
t -= (C * *scan_a++);
*scan_c++ = (bignum_digit_type)(s & BIGNUM_DIGIT_MASK);
//*scan_d++ = (bignum_digit_type) (t & BIGNUM_DIGIT_MASK);
s >>= BIGNUM_DIGIT_LENGTH;
t >>= BIGNUM_DIGIT_LENGTH;
}
}
BIGNUM_ASSERT(s == 0);
BIGNUM_ASSERT(t == 0);
// update size_a and size_b to remove any zeros at end
while (size_a > 0 && *(--scan_a) == 0)
size_a--;
while (size_b > 0 && *(--scan_b) == 0)
size_b--;
BIGNUM_ASSERT(size_a >= size_b);
}
// a fits into a fixnum, so b must too
fixnum xx = bignum_to_fixnum(a.untagged());
fixnum yy = bignum_to_fixnum(b.untagged());
fixnum tt;
// usual Euclidean algorithm for longs
while (yy != 0) {
tt = yy;
yy = xx % yy;
xx = tt;
}
return fixnum_to_bignum(xx);
}
#endif
}
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