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/*
* Copyright 2015 INRIA Paris-Rocquencourt
*
* Use of this software is governed by the MIT license
*
* Written by Michael Kruse, INRIA Paris-Rocquencourt,
* Domaine de Voluceau, Rocquenqourt, B.P. 105,
* 78153 Le Chesnay Cedex France
*/
#ifndef ISL_INT_SIOIMATH_H
#define ISL_INT_SIOIMATH_H
#include <inttypes.h>
#include <limits.h>
#include <stdint.h>
#include <stdlib.h>
#include <isl_imath.h>
#include <isl/hash.h>
#define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
/* Visual Studio before VS2015 does not support the inline keyword when
* compiling in C mode because it was introduced in C99 which it does not
* officially support. Instead, it has a proprietary extension using __inline.
*/
#if defined(_MSC_VER) && (_MSC_VER < 1900)
#define inline __inline
#endif
/* The type to represent integers optimized for small values. It is either a
* pointer to an mp_int ( = mpz_t*; big representation) or an int32_t (small
* represenation) with a discriminator at the least significant bit. In big
* representation it will be always zero because of heap alignment. It is set
* to 1 for small representation and use the 32 most significant bits for the
* int32_t.
*
* Structure on 64 bit machines, with 8-byte aligment (3 bits):
*
* Big representation:
* MSB LSB
* |------------------------------------------------------------000
* | mpz_t* |
* | != NULL |
*
* Small representation:
* MSB 32 LSB
* |------------------------------|00000000000000000000000000000001
* | int32_t |
* | 2147483647 ... -2147483647 |
* ^
* |
* discriminator bit
*
* On 32 bit machines isl_sioimath type is blown up to 8 bytes, i.e.
* isl_sioimath is guaranteed to be at least 8 bytes. This is to ensure the
* int32_t can be hidden in that type without data loss. In the future we might
* optimize this to use 31 hidden bits in a 32 bit pointer. We may also use 63
* bits on 64 bit machines, but this comes with the cost of additional overflow
* checks because there is no standardized 128 bit integer we could expand to.
*
* We use native integer types and avoid union structures to avoid assumptions
* on the machine's endianness.
*
* This implementation makes the following assumptions:
* - long can represent any int32_t
* - mp_small is signed long
* - mp_usmall is unsigned long
* - adresses returned by malloc are aligned to 2-byte boundaries (leastmost
* bit is zero)
*/
#if UINT64_MAX > UINTPTR_MAX
typedef uint64_t isl_sioimath;
#else
typedef uintptr_t isl_sioimath;
#endif
/* The negation of the smallest possible number in int32_t, INT32_MIN
* (0x80000000u, -2147483648), cannot be represented in an int32_t, therefore
* every operation that may produce this value needs to special-case it.
* The operations are:
* abs(INT32_MIN)
* -INT32_MIN (negation)
* -1 * INT32_MIN (multiplication)
* INT32_MIN/-1 (any division: divexact, fdiv, cdiv, tdiv)
* To avoid checking these cases, we exclude INT32_MIN from small
* representation.
*/
#define ISL_SIOIMATH_SMALL_MIN (-INT32_MAX)
/* Largest possible number in small representation */
#define ISL_SIOIMATH_SMALL_MAX INT32_MAX
/* Used for function parameters the function modifies. */
typedef isl_sioimath *isl_sioimath_ptr;
/* Used for function parameters that are read-only. */
typedef isl_sioimath isl_sioimath_src;
/* Return whether the argument is stored in small representation.
*/
inline int isl_sioimath_is_small(isl_sioimath val)
{
return val & 0x00000001;
}
/* Return whether the argument is stored in big representation.
*/
inline int isl_sioimath_is_big(isl_sioimath val)
{
return !isl_sioimath_is_small(val);
}
/* Get the number of an isl_int in small representation. Result is undefined if
* val is not stored in that format.
*/
inline int32_t isl_sioimath_get_small(isl_sioimath val)
{
return val >> 32;
}
/* Get the number of an in isl_int in big representation. Result is undefined if
* val is not stored in that format.
*/
inline mp_int isl_sioimath_get_big(isl_sioimath val)
{
return (mp_int)(uintptr_t) val;
}
/* Return 1 if val is stored in small representation and store its value to
* small. We rely on the compiler to optimize the isl_sioimath_get_small such
* that the shift is moved into the branch that executes in case of small
* representation. If there is no such branch, then a single shift is still
* cheaper than introducing branching code.
*/
inline int isl_sioimath_decode_small(isl_sioimath val, int32_t *small)
{
*small = isl_sioimath_get_small(val);
return isl_sioimath_is_small(val);
}
/* Return 1 if val is stored in big representation and store its value to big.
*/
inline int isl_sioimath_decode_big(isl_sioimath val, mp_int *big)
{
*big = isl_sioimath_get_big(val);
return isl_sioimath_is_big(val);
}
/* Encode a small representation into an isl_int.
*/
inline isl_sioimath isl_sioimath_encode_small(int32_t val)
{
return ((isl_sioimath) val) << 32 | 0x00000001;
}
/* Encode a big representation.
*/
inline isl_sioimath isl_sioimath_encode_big(mp_int val)
{
return (isl_sioimath)(uintptr_t) val;
}
/* A common situation is to call an IMath function with at least one argument
* that is currently in small representation or an integer parameter, i.e. a big
* representation of the same number is required. Promoting the original
* argument comes with multiple problems, such as modifying a read-only
* argument, the responsibility of deallocation and the execution cost. Instead,
* we make a copy by 'faking' the IMath internal structure.
*
* We reserve the maximum number of required digits on the stack to avoid heap
* allocations.
*
* mp_digit can be uint32_t or uint16_t. This code must work for little and big
* endian digits. The structure for an uint64_t argument and 32-bit mp_digits is
* sketched below.
*
* |----------------------------|
* uint64_t
*
* |-------------||-------------|
* mp_digit mp_digit
* digits[1] digits[0]
* Most sig digit Least sig digit
*/
typedef struct {
mpz_t big;
mp_digit digits[(sizeof(uintmax_t) + sizeof(mp_digit) - 1) /
sizeof(mp_digit)];
} isl_sioimath_scratchspace_t;
/* Convert a native integer to IMath's digit representation. A native integer
* might be big- or little endian, but IMath always stores the least significant
* digit in the lowest array indices. memcpy therefore is not possible.
*
* We also have to consider that long and mp_digit can be of different sizes,
* depending on the compiler (LP64, LLP64) and IMath's USE_64BIT_WORDS. This
* macro should work for all of them.
*
* "used" is set to the number of written digits. It must be minimal (IMath
* checks zeroness using the used field), but always at least one. Also note
* that the result of num>>(sizeof(num)*CHAR_BIT) is undefined.
*/
#define ISL_SIOIMATH_TO_DIGITS(num, digits, used) \
do { \
int i = 0; \
do { \
(digits)[i] = \
((num) >> (sizeof(mp_digit) * CHAR_BIT * i)); \
i += 1; \
if (i >= (sizeof(num) + sizeof(mp_digit) - 1) / \
sizeof(mp_digit)) \
break; \
if (((num) >> (sizeof(mp_digit) * CHAR_BIT * i)) == 0) \
break; \
} while (1); \
(used) = i; \
} while (0)
inline void isl_siomath_uint32_to_digits(uint32_t num, mp_digit *digits,
mp_size *used)
{
ISL_SIOIMATH_TO_DIGITS(num, digits, *used);
}
inline void isl_siomath_ulong_to_digits(unsigned long num, mp_digit *digits,
mp_size *used)
{
ISL_SIOIMATH_TO_DIGITS(num, digits, *used);
}
inline void isl_siomath_uint64_to_digits(uint64_t num, mp_digit *digits,
mp_size *used)
{
ISL_SIOIMATH_TO_DIGITS(num, digits, *used);
}
/* Get the IMath representation of an isl_int without modifying it.
* For the case it is not in big representation yet, pass some scratch space we
* can use to store the big representation in.
* In order to avoid requiring init and free on the scratch space, we directly
* modify the internal representation.
*
* The name derives from its indented use: getting the big representation of an
* input (src) argument.
*/
inline mp_int isl_sioimath_bigarg_src(isl_sioimath arg,
isl_sioimath_scratchspace_t *scratch)
{
mp_int big;
int32_t small;
uint32_t num;
if (isl_sioimath_decode_big(arg, &big))
return big;
small = isl_sioimath_get_small(arg);
scratch->big.digits = scratch->digits;
scratch->big.alloc = ARRAY_SIZE(scratch->digits);
if (small >= 0) {
scratch->big.sign = MP_ZPOS;
num = small;
} else {
scratch->big.sign = MP_NEG;
num = -small;
}
isl_siomath_uint32_to_digits(num, scratch->digits, &scratch->big.used);
return &scratch->big;
}
/* Create a temporary IMath mp_int for a signed long.
*/
inline mp_int isl_sioimath_siarg_src(signed long arg,
isl_sioimath_scratchspace_t *scratch)
{
unsigned long num;
scratch->big.digits = scratch->digits;
scratch->big.alloc = ARRAY_SIZE(scratch->digits);
if (arg >= 0) {
scratch->big.sign = MP_ZPOS;
num = arg;
} else {
scratch->big.sign = MP_NEG;
num = (arg == LONG_MIN) ? ((unsigned long) LONG_MAX) + 1 : -arg;
}
isl_siomath_ulong_to_digits(num, scratch->digits, &scratch->big.used);
return &scratch->big;
}
/* Create a temporary IMath mp_int for an int64_t.
*/
inline mp_int isl_sioimath_si64arg_src(int64_t arg,
isl_sioimath_scratchspace_t *scratch)
{
uint64_t num;
scratch->big.digits = scratch->digits;
scratch->big.alloc = ARRAY_SIZE(scratch->digits);
if (arg >= 0) {
scratch->big.sign = MP_ZPOS;
num = arg;
} else {
scratch->big.sign = MP_NEG;
num = (arg == INT64_MIN) ? ((uint64_t) INT64_MAX) + 1 : -arg;
}
isl_siomath_uint64_to_digits(num, scratch->digits, &scratch->big.used);
return &scratch->big;
}
/* Create a temporary IMath mp_int for an unsigned long.
*/
inline mp_int isl_sioimath_uiarg_src(unsigned long arg,
isl_sioimath_scratchspace_t *scratch)
{
scratch->big.digits = scratch->digits;
scratch->big.alloc = ARRAY_SIZE(scratch->digits);
scratch->big.sign = MP_ZPOS;
isl_siomath_ulong_to_digits(arg, scratch->digits, &scratch->big.used);
return &scratch->big;
}
/* Ensure big representation. Does not preserve the current number.
* Callers may use the fact that the value _is_ preserved if the presentation
* was big before.
*/
inline mp_int isl_sioimath_reinit_big(isl_sioimath_ptr ptr)
{
if (isl_sioimath_is_small(*ptr))
*ptr = isl_sioimath_encode_big(mp_int_alloc());
return isl_sioimath_get_big(*ptr);
}
/* Set ptr to a number in small representation.
*/
inline void isl_sioimath_set_small(isl_sioimath_ptr ptr, int32_t val)
{
if (isl_sioimath_is_big(*ptr))
mp_int_free(isl_sioimath_get_big(*ptr));
*ptr = isl_sioimath_encode_small(val);
}
/* Set ptr to val, choosing small representation if possible.
*/
inline void isl_sioimath_set_int32(isl_sioimath_ptr ptr, int32_t val)
{
if (ISL_SIOIMATH_SMALL_MIN <= val && val <= ISL_SIOIMATH_SMALL_MAX) {
isl_sioimath_set_small(ptr, val);
return;
}
mp_int_init_value(isl_sioimath_reinit_big(ptr), val);
}
/* Assign an int64_t number using small representation if possible.
*/
inline void isl_sioimath_set_int64(isl_sioimath_ptr ptr, int64_t val)
{
if (ISL_SIOIMATH_SMALL_MIN <= val && val <= ISL_SIOIMATH_SMALL_MAX) {
isl_sioimath_set_small(ptr, val);
return;
}
isl_sioimath_scratchspace_t scratch;
mp_int_copy(isl_sioimath_si64arg_src(val, &scratch),
isl_sioimath_reinit_big(ptr));
}
/* Convert to big representation while preserving the current number.
*/
inline void isl_sioimath_promote(isl_sioimath_ptr dst)
{
int32_t small;
if (isl_sioimath_is_big(*dst))
return;
small = isl_sioimath_get_small(*dst);
mp_int_set_value(isl_sioimath_reinit_big(dst), small);
}
/* Convert to small representation while preserving the current number. Does
* nothing if dst doesn't fit small representation.
*/
inline void isl_sioimath_try_demote(isl_sioimath_ptr dst)
{
mp_small small;
if (isl_sioimath_is_small(*dst))
return;
if (mp_int_to_int(isl_sioimath_get_big(*dst), &small) != MP_OK)
return;
if (ISL_SIOIMATH_SMALL_MIN <= small && small <= ISL_SIOIMATH_SMALL_MAX)
isl_sioimath_set_small(dst, small);
}
/* Initialize an isl_int. The implicit value is 0 in small representation.
*/
inline void isl_sioimath_init(isl_sioimath_ptr dst)
{
*dst = isl_sioimath_encode_small(0);
}
/* Free the resources taken by an isl_int.
*/
inline void isl_sioimath_clear(isl_sioimath_ptr dst)
{
if (isl_sioimath_is_small(*dst))
return;
mp_int_free(isl_sioimath_get_big(*dst));
}
/* Copy the value of one isl_int to another.
*/
inline void isl_sioimath_set(isl_sioimath_ptr dst, isl_sioimath_src val)
{
if (isl_sioimath_is_small(val)) {
isl_sioimath_set_small(dst, isl_sioimath_get_small(val));
return;
}
mp_int_copy(isl_sioimath_get_big(val), isl_sioimath_reinit_big(dst));
}
/* Store a signed long into an isl_int.
*/
inline void isl_sioimath_set_si(isl_sioimath_ptr dst, long val)
{
if (ISL_SIOIMATH_SMALL_MIN <= val && val <= ISL_SIOIMATH_SMALL_MAX) {
isl_sioimath_set_small(dst, val);
return;
}
mp_int_set_value(isl_sioimath_reinit_big(dst), val);
}
/* Store an unsigned long into an isl_int.
*/
inline void isl_sioimath_set_ui(isl_sioimath_ptr dst, unsigned long val)
{
if (val <= ISL_SIOIMATH_SMALL_MAX) {
isl_sioimath_set_small(dst, val);
return;
}
mp_int_set_uvalue(isl_sioimath_reinit_big(dst), val);
}
/* Return whether a number can be represented by a signed long.
*/
inline int isl_sioimath_fits_slong(isl_sioimath_src val)
{
mp_small dummy;
if (isl_sioimath_is_small(val))
return 1;
return mp_int_to_int(isl_sioimath_get_big(val), &dummy) == MP_OK;
}
/* Return a number as signed long. Result is undefined if the number cannot be
* represented as long.
*/
inline long isl_sioimath_get_si(isl_sioimath_src val)
{
mp_small result;
if (isl_sioimath_is_small(val))
return isl_sioimath_get_small(val);
mp_int_to_int(isl_sioimath_get_big(val), &result);
return result;
}
/* Return whether a number can be represented as unsigned long.
*/
inline int isl_sioimath_fits_ulong(isl_sioimath_src val)
{
mp_usmall dummy;
if (isl_sioimath_is_small(val))
return isl_sioimath_get_small(val) >= 0;
return mp_int_to_uint(isl_sioimath_get_big(val), &dummy) == MP_OK;
}
/* Return a number as unsigned long. Result is undefined if the number cannot be
* represented as unsigned long.
*/
inline unsigned long isl_sioimath_get_ui(isl_sioimath_src val)
{
mp_usmall result;
if (isl_sioimath_is_small(val))
return isl_sioimath_get_small(val);
mp_int_to_uint(isl_sioimath_get_big(val), &result);
return result;
}
/* Return a number as floating point value.
*/
inline double isl_sioimath_get_d(isl_sioimath_src val)
{
mp_int big;
double result = 0;
int i;
if (isl_sioimath_is_small(val))
return isl_sioimath_get_small(val);
big = isl_sioimath_get_big(val);
for (i = 0; i < big->used; ++i)
result = result * (double) ((uintmax_t) MP_DIGIT_MAX + 1) +
(double) big->digits[i];
if (big->sign == MP_NEG)
result = -result;
return result;
}
/* Format a number as decimal string.
*
* The largest possible string from small representation is 12 characters
* ("-2147483647").
*/
inline char *isl_sioimath_get_str(isl_sioimath_src val)
{
char *result;
if (isl_sioimath_is_small(val)) {
result = malloc(12);
snprintf(result, 12, "%" PRIi32, isl_sioimath_get_small(val));
return result;
}
return impz_get_str(NULL, 10, isl_sioimath_get_big(val));
}
/* Return the absolute value.
*/
inline void isl_sioimath_abs(isl_sioimath_ptr dst, isl_sioimath_src arg)
{
if (isl_sioimath_is_small(arg)) {
isl_sioimath_set_small(dst, labs(isl_sioimath_get_small(arg)));
return;
}
mp_int_abs(isl_sioimath_get_big(arg), isl_sioimath_reinit_big(dst));
}
/* Return the negation of a number.
*/
inline void isl_sioimath_neg(isl_sioimath_ptr dst, isl_sioimath_src arg)
{
if (isl_sioimath_is_small(arg)) {
isl_sioimath_set_small(dst, -isl_sioimath_get_small(arg));
return;
}
mp_int_neg(isl_sioimath_get_big(arg), isl_sioimath_reinit_big(dst));
}
/* Swap two isl_ints.
*
* isl_sioimath can be copied bytewise; nothing depends on its address. It can
* also be stored in a CPU register.
*/
inline void isl_sioimath_swap(isl_sioimath_ptr lhs, isl_sioimath_ptr rhs)
{
isl_sioimath tmp = *lhs;
*lhs = *rhs;
*rhs = tmp;
}
/* Add an unsigned long to the number.
*
* On LP64 unsigned long exceeds the range of an int64_t, therefore we check in
* advance whether small representation possibly overflows.
*/
inline void isl_sioimath_add_ui(isl_sioimath_ptr dst, isl_sioimath lhs,
unsigned long rhs)
{
int32_t smalllhs;
isl_sioimath_scratchspace_t lhsscratch;
if (isl_sioimath_decode_small(lhs, &smalllhs) &&
(rhs <= (uint64_t) INT64_MAX - (uint64_t) ISL_SIOIMATH_SMALL_MAX)) {
isl_sioimath_set_int64(dst, (int64_t) smalllhs + rhs);
return;
}
impz_add_ui(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs);
isl_sioimath_try_demote(dst);
}
/* Subtract an unsigned long.
*
* On LP64 unsigned long exceeds the range of an int64_t. If
* ISL_SIOIMATH_SMALL_MIN-rhs>=INT64_MIN we can do the calculation using int64_t
* without risking an overflow.
*/
inline void isl_sioimath_sub_ui(isl_sioimath_ptr dst, isl_sioimath lhs,
unsigned long rhs)
{
int32_t smalllhs;
isl_sioimath_scratchspace_t lhsscratch;
if (isl_sioimath_decode_small(lhs, &smalllhs) &&
(rhs < (uint64_t) INT64_MIN - (uint64_t) ISL_SIOIMATH_SMALL_MIN)) {
isl_sioimath_set_int64(dst, (int64_t) smalllhs - rhs);
return;
}
impz_sub_ui(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs);
isl_sioimath_try_demote(dst);
}
/* Sum of two isl_ints.
*/
inline void isl_sioimath_add(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
int32_t smalllhs, smallrhs;
if (isl_sioimath_decode_small(lhs, &smalllhs) &&
isl_sioimath_decode_small(rhs, &smallrhs)) {
isl_sioimath_set_int64(
dst, (int64_t) smalllhs + (int64_t) smallrhs);
return;
}
mp_int_add(isl_sioimath_bigarg_src(lhs, &scratchlhs),
isl_sioimath_bigarg_src(rhs, &scratchrhs),
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
}
/* Subtract two isl_ints.
*/
inline void isl_sioimath_sub(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
int32_t smalllhs, smallrhs;
if (isl_sioimath_decode_small(lhs, &smalllhs) &&
isl_sioimath_decode_small(rhs, &smallrhs)) {
isl_sioimath_set_int64(
dst, (int64_t) smalllhs - (int64_t) smallrhs);
return;
}
mp_int_sub(isl_sioimath_bigarg_src(lhs, &scratchlhs),
isl_sioimath_bigarg_src(rhs, &scratchrhs),
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
}
/* Multiply two isl_ints.
*/
inline void isl_sioimath_mul(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
int32_t smalllhs, smallrhs;
if (isl_sioimath_decode_small(lhs, &smalllhs) &&
isl_sioimath_decode_small(rhs, &smallrhs)) {
isl_sioimath_set_int64(
dst, (int64_t) smalllhs * (int64_t) smallrhs);
return;
}
mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs),
isl_sioimath_bigarg_src(rhs, &scratchrhs),
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
}
/* Shift lhs by rhs bits to the left and store the result in dst. Effectively,
* this operation computes 'lhs * 2^rhs'.
*/
inline void isl_sioimath_mul_2exp(isl_sioimath_ptr dst, isl_sioimath lhs,
unsigned long rhs)
{
isl_sioimath_scratchspace_t scratchlhs;
int32_t smalllhs;
if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs <= 32ul)) {
isl_sioimath_set_int64(dst, ((int64_t) smalllhs) << rhs);
return;
}
mp_int_mul_pow2(isl_sioimath_bigarg_src(lhs, &scratchlhs), rhs,
isl_sioimath_reinit_big(dst));
}
/* Multiply an isl_int and a signed long.
*/
inline void isl_sioimath_mul_si(isl_sioimath_ptr dst, isl_sioimath lhs,
signed long rhs)
{
isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
int32_t smalllhs;
if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs > LONG_MIN) &&
(labs(rhs) <= UINT32_MAX)) {
isl_sioimath_set_int64(dst, (int64_t) smalllhs * (int64_t) rhs);
return;
}
mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs),
isl_sioimath_siarg_src(rhs, &scratchrhs),
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
}
/* Multiply an isl_int and an unsigned long.
*/
inline void isl_sioimath_mul_ui(isl_sioimath_ptr dst, isl_sioimath lhs,
unsigned long rhs)
{
isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
int32_t smalllhs;
if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs <= UINT32_MAX)) {
isl_sioimath_set_int64(dst, (int64_t) smalllhs * (int64_t) rhs);
return;
}
mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs),
isl_sioimath_uiarg_src(rhs, &scratchrhs),
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
}
/* Compute the power of an isl_int to an unsigned long.
* Always let IMath do it; the result is unlikely to be small except in some
* special cases.
* Note: 0^0 == 1
*/
inline void isl_sioimath_pow_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
unsigned long rhs)
{
isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
int32_t smalllhs;
switch (rhs) {
case 0:
isl_sioimath_set_small(dst, 1);
return;
case 1:
isl_sioimath_set(dst, lhs);
return;
case 2:
isl_sioimath_mul(dst, lhs, lhs);
return;
}
if (isl_sioimath_decode_small(lhs, &smalllhs)) {
switch (smalllhs) {
case 0:
isl_sioimath_set_small(dst, 0);
return;
case 1:
isl_sioimath_set_small(dst, 1);
return;
case 2:
isl_sioimath_set_small(dst, 1);
isl_sioimath_mul_2exp(dst, *dst, rhs);
return;
default:
if ((MP_SMALL_MIN <= rhs) && (rhs <= MP_SMALL_MAX)) {
mp_int_expt_value(smalllhs, rhs,
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
return;
}
}
}
mp_int_expt_full(isl_sioimath_bigarg_src(lhs, &scratchlhs),
isl_sioimath_uiarg_src(rhs, &scratchrhs),
isl_sioimath_reinit_big(dst));
isl_sioimath_try_demote(dst);
}
/* Fused multiply-add.
*/
inline void isl_sioimath_addmul(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath tmp;
isl_sioimath_init(&tmp);
isl_sioimath_mul(&tmp, lhs, rhs);
isl_sioimath_add(dst, *dst, tmp);
isl_sioimath_clear(&tmp);
}
/* Fused multiply-add with an unsigned long.
*/
inline void isl_sioimath_addmul_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
unsigned long rhs)
{
isl_sioimath tmp;
isl_sioimath_init(&tmp);
isl_sioimath_mul_ui(&tmp, lhs, rhs);
isl_sioimath_add(dst, *dst, tmp);
isl_sioimath_clear(&tmp);
}
/* Fused multiply-subtract.
*/
inline void isl_sioimath_submul(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath tmp;
isl_sioimath_init(&tmp);
isl_sioimath_mul(&tmp, lhs, rhs);
isl_sioimath_sub(dst, *dst, tmp);
isl_sioimath_clear(&tmp);
}
/* Fused multiply-add with an unsigned long.
*/
inline void isl_sioimath_submul_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
unsigned long rhs)
{
isl_sioimath tmp;
isl_sioimath_init(&tmp);
isl_sioimath_mul_ui(&tmp, lhs, rhs);
isl_sioimath_sub(dst, *dst, tmp);
isl_sioimath_clear(&tmp);
}
void isl_sioimath_gcd(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs);
void isl_sioimath_lcm(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs);
/* Divide lhs by rhs, rounding to zero (Truncate).
*/
inline void isl_sioimath_tdiv_q(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, rhssmall;
if (isl_sioimath_decode_small(lhs, &lhssmall) &&
isl_sioimath_decode_small(rhs, &rhssmall)) {
isl_sioimath_set_small(dst, lhssmall / rhssmall);
return;
}
mp_int_div(isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_bigarg_src(rhs, &rhsscratch),
isl_sioimath_reinit_big(dst), NULL);
isl_sioimath_try_demote(dst);
return;
}
/* Divide lhs by an unsigned long rhs, rounding to zero (Truncate).
*/
inline void isl_sioimath_tdiv_q_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
unsigned long rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall;
if (isl_sioimath_is_small(lhs) && (rhs <= (unsigned long) INT32_MAX)) {
lhssmall = isl_sioimath_get_small(lhs);
isl_sioimath_set_small(dst, lhssmall / (int32_t) rhs);
return;
}
if (rhs <= MP_SMALL_MAX) {
mp_int_div_value(isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs,
isl_sioimath_reinit_big(dst), NULL);
isl_sioimath_try_demote(dst);
return;
}
mp_int_div(isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_uiarg_src(rhs, &rhsscratch),
isl_sioimath_reinit_big(dst), NULL);
isl_sioimath_try_demote(dst);
}
/* Divide lhs by rhs, rounding to positive infinity (Ceil).
*/
inline void isl_sioimath_cdiv_q(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
int32_t lhssmall, rhssmall;
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t q;
if (isl_sioimath_decode_small(lhs, &lhssmall) &&
isl_sioimath_decode_small(rhs, &rhssmall)) {
if ((lhssmall >= 0) && (rhssmall >= 0))
q = ((int64_t) lhssmall + (int64_t) rhssmall - 1) /
rhssmall;
else if ((lhssmall < 0) && (rhssmall < 0))
q = ((int64_t) lhssmall + (int64_t) rhssmall + 1) /
rhssmall;
else
q = lhssmall / rhssmall;
isl_sioimath_set_small(dst, q);
return;
}
impz_cdiv_q(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_bigarg_src(rhs, &rhsscratch));
isl_sioimath_try_demote(dst);
}
/* Compute the division of lhs by a rhs of type unsigned long, rounding towards
* positive infinity (Ceil).
*/
inline void isl_sioimath_cdiv_q_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
unsigned long rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, q;
if (isl_sioimath_decode_small(lhs, &lhssmall) && (rhs <= INT32_MAX)) {
if (lhssmall >= 0)
q = ((int64_t) lhssmall + ((int64_t) rhs - 1)) /
(int64_t) rhs;
else
q = lhssmall / (int32_t) rhs;
isl_sioimath_set_small(dst, q);
return;
}
impz_cdiv_q(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_uiarg_src(rhs, &rhsscratch));
isl_sioimath_try_demote(dst);
}
/* Divide lhs by rhs, rounding to negative infinity (Floor).
*/
inline void isl_sioimath_fdiv_q(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, rhssmall;
int32_t q;
if (isl_sioimath_decode_small(lhs, &lhssmall) &&
isl_sioimath_decode_small(rhs, &rhssmall)) {
if ((lhssmall < 0) && (rhssmall >= 0))
q = ((int64_t) lhssmall - ((int64_t) rhssmall - 1)) /
rhssmall;
else if ((lhssmall >= 0) && (rhssmall < 0))
q = ((int64_t) lhssmall - ((int64_t) rhssmall + 1)) /
rhssmall;
else
q = lhssmall / rhssmall;
isl_sioimath_set_small(dst, q);
return;
}
impz_fdiv_q(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_bigarg_src(rhs, &rhsscratch));
isl_sioimath_try_demote(dst);
}
/* Compute the division of lhs by a rhs of type unsigned long, rounding towards
* negative infinity (Floor).
*/
inline void isl_sioimath_fdiv_q_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
unsigned long rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, q;
if (isl_sioimath_decode_small(lhs, &lhssmall) && (rhs <= INT32_MAX)) {
if (lhssmall >= 0)
q = (uint32_t) lhssmall / rhs;
else
q = ((int64_t) lhssmall - ((int64_t) rhs - 1)) /
(int64_t) rhs;
isl_sioimath_set_small(dst, q);
return;
}
impz_fdiv_q(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_uiarg_src(rhs, &rhsscratch));
isl_sioimath_try_demote(dst);
}
/* Get the remainder of: lhs divided by rhs rounded towards negative infinite
* (Floor).
*/
inline void isl_sioimath_fdiv_r(isl_sioimath_ptr dst, isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int64_t lhssmall, rhssmall;
int32_t r;
if (isl_sioimath_is_small(lhs) && isl_sioimath_is_small(rhs)) {
lhssmall = isl_sioimath_get_small(lhs);
rhssmall = isl_sioimath_get_small(rhs);
r = (rhssmall + lhssmall % rhssmall) % rhssmall;
isl_sioimath_set_small(dst, r);
return;
}
impz_fdiv_r(isl_sioimath_reinit_big(dst),
isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_bigarg_src(rhs, &rhsscratch));
isl_sioimath_try_demote(dst);
}
void isl_sioimath_read(isl_sioimath_ptr dst, const char *str);
/* Return:
* +1 for a positive number
* -1 for a negative number
* 0 if the number is zero
*/
inline int isl_sioimath_sgn(isl_sioimath_src arg)
{
int32_t small;
if (isl_sioimath_decode_small(arg, &small))
return (small > 0) - (small < 0);
return mp_int_compare_zero(isl_sioimath_get_big(arg));
}
/* Return:
* +1 if lhs > rhs
* -1 if lhs < rhs
* 0 if lhs = rhs
*/
inline int isl_sioimath_cmp(isl_sioimath_src lhs, isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, rhssmall;
if (isl_sioimath_decode_small(lhs, &lhssmall) &&
isl_sioimath_decode_small(rhs, &rhssmall))
return (lhssmall > rhssmall) - (lhssmall < rhssmall);
if (isl_sioimath_decode_small(rhs, &rhssmall))
return mp_int_compare_value(
isl_sioimath_bigarg_src(lhs, &lhsscratch), rhssmall);
if (isl_sioimath_decode_small(lhs, &lhssmall))
return -mp_int_compare_value(
isl_sioimath_bigarg_src(rhs, &rhsscratch), lhssmall);
return mp_int_compare(
isl_sioimath_get_big(lhs), isl_sioimath_get_big(rhs));
}
/* As isl_sioimath_cmp, but with signed long rhs.
*/
inline int isl_sioimath_cmp_si(isl_sioimath_src lhs, signed long rhs)
{
int32_t lhssmall;
if (isl_sioimath_decode_small(lhs, &lhssmall))
return (lhssmall > rhs) - (lhssmall < rhs);
return mp_int_compare_value(isl_sioimath_get_big(lhs), rhs);
}
/* Return:
* +1 if |lhs| > |rhs|
* -1 if |lhs| < |rhs|
* 0 if |lhs| = |rhs|
*/
inline int isl_sioimath_abs_cmp(isl_sioimath_src lhs, isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, rhssmall;
if (isl_sioimath_decode_small(lhs, &lhssmall) &&
isl_sioimath_decode_small(rhs, &rhssmall)) {
lhssmall = labs(lhssmall);
rhssmall = labs(rhssmall);
return (lhssmall > rhssmall) - (lhssmall < rhssmall);
}
return mp_int_compare_unsigned(
isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_bigarg_src(rhs, &rhsscratch));
}
/* Return whether lhs is divisible by rhs.
* In particular, can rhs be multiplied by some integer to result in lhs?
* If rhs is zero, then this means lhs has to be zero too.
*/
inline int isl_sioimath_is_divisible_by(isl_sioimath_src lhs,
isl_sioimath_src rhs)
{
isl_sioimath_scratchspace_t lhsscratch, rhsscratch;
int32_t lhssmall, rhssmall;
mpz_t rem;
int cmp;
if (isl_sioimath_sgn(rhs) == 0)
return isl_sioimath_sgn(lhs) == 0;
if (isl_sioimath_decode_small(lhs, &lhssmall) &&
isl_sioimath_decode_small(rhs, &rhssmall))
return lhssmall % rhssmall == 0;
if (isl_sioimath_decode_small(rhs, &rhssmall))
return mp_int_divisible_value(
isl_sioimath_bigarg_src(lhs, &lhsscratch), rhssmall);
mp_int_init(&rem);
mp_int_div(isl_sioimath_bigarg_src(lhs, &lhsscratch),
isl_sioimath_bigarg_src(rhs, &rhsscratch), NULL, &rem);
cmp = mp_int_compare_zero(&rem);
mp_int_clear(&rem);
return cmp == 0;
}
/* Return a hash code of an isl_sioimath.
* The hash code for a number in small and big representation must be identical
* on the same machine because small representation if not obligatory if fits.
*/
inline uint32_t isl_sioimath_hash(isl_sioimath_src arg, uint32_t hash)
{
int32_t small;
int i;
uint32_t num;
mp_digit digits[(sizeof(uint32_t) + sizeof(mp_digit) - 1) /
sizeof(mp_digit)];
mp_size used;
const unsigned char *digitdata = (const unsigned char *) &digits;
if (isl_sioimath_decode_small(arg, &small)) {
if (small < 0)
isl_hash_byte(hash, 0xFF);
num = labs(small);
isl_siomath_uint32_to_digits(num, digits, &used);
for (i = 0; i < used * sizeof(mp_digit); i += 1)
isl_hash_byte(hash, digitdata[i]);
return hash;
}
return isl_imath_hash(isl_sioimath_get_big(arg), hash);
}
/* Return the number of digits in a number of the given base or more, i.e. the
* string length without sign and null terminator.
*
* Current implementation for small representation returns the maximal number
* of binary digits in that representation, which can be much larger than the
* smallest possible solution.
*/
inline size_t isl_sioimath_sizeinbase(isl_sioimath_src arg, int base)
{
int32_t small;
if (isl_sioimath_decode_small(arg, &small))
return sizeof(int32_t) * CHAR_BIT - 1;
return impz_sizeinbase(isl_sioimath_get_big(arg), base);
}
void isl_sioimath_print(FILE *out, isl_sioimath_src i, int width);
void isl_sioimath_dump(isl_sioimath_src arg);
typedef isl_sioimath isl_int[1];
#define isl_int_init(i) isl_sioimath_init((i))
#define isl_int_clear(i) isl_sioimath_clear((i))
#define isl_int_set(r, i) isl_sioimath_set((r), *(i))
#define isl_int_set_si(r, i) isl_sioimath_set_si((r), i)
#define isl_int_set_ui(r, i) isl_sioimath_set_ui((r), i)
#define isl_int_fits_slong(r) isl_sioimath_fits_slong(*(r))
#define isl_int_get_si(r) isl_sioimath_get_si(*(r))
#define isl_int_fits_ulong(r) isl_sioimath_fits_ulong(*(r))
#define isl_int_get_ui(r) isl_sioimath_get_ui(*(r))
#define isl_int_get_d(r) isl_sioimath_get_d(*(r))
#define isl_int_get_str(r) isl_sioimath_get_str(*(r))
#define isl_int_abs(r, i) isl_sioimath_abs((r), *(i))
#define isl_int_neg(r, i) isl_sioimath_neg((r), *(i))
#define isl_int_swap(i, j) isl_sioimath_swap((i), (j))
#define isl_int_swap_or_set(i, j) isl_sioimath_swap((i), (j))
#define isl_int_add_ui(r, i, j) isl_sioimath_add_ui((r), *(i), j)
#define isl_int_sub_ui(r, i, j) isl_sioimath_sub_ui((r), *(i), j)
#define isl_int_add(r, i, j) isl_sioimath_add((r), *(i), *(j))
#define isl_int_sub(r, i, j) isl_sioimath_sub((r), *(i), *(j))
#define isl_int_mul(r, i, j) isl_sioimath_mul((r), *(i), *(j))
#define isl_int_mul_2exp(r, i, j) isl_sioimath_mul_2exp((r), *(i), j)
#define isl_int_mul_si(r, i, j) isl_sioimath_mul_si((r), *(i), j)
#define isl_int_mul_ui(r, i, j) isl_sioimath_mul_ui((r), *(i), j)
#define isl_int_pow_ui(r, i, j) isl_sioimath_pow_ui((r), *(i), j)
#define isl_int_addmul(r, i, j) isl_sioimath_addmul((r), *(i), *(j))
#define isl_int_addmul_ui(r, i, j) isl_sioimath_addmul_ui((r), *(i), j)
#define isl_int_submul(r, i, j) isl_sioimath_submul((r), *(i), *(j))
#define isl_int_submul_ui(r, i, j) isl_sioimath_submul_ui((r), *(i), j)
#define isl_int_gcd(r, i, j) isl_sioimath_gcd((r), *(i), *(j))
#define isl_int_lcm(r, i, j) isl_sioimath_lcm((r), *(i), *(j))
#define isl_int_divexact(r, i, j) isl_sioimath_tdiv_q((r), *(i), *(j))
#define isl_int_divexact_ui(r, i, j) isl_sioimath_tdiv_q_ui((r), *(i), j)
#define isl_int_tdiv_q(r, i, j) isl_sioimath_tdiv_q((r), *(i), *(j))
#define isl_int_cdiv_q(r, i, j) isl_sioimath_cdiv_q((r), *(i), *(j))
#define isl_int_cdiv_q_ui(r, i, j) isl_sioimath_cdiv_q_ui((r), *(i), j)
#define isl_int_fdiv_q(r, i, j) isl_sioimath_fdiv_q((r), *(i), *(j))
#define isl_int_fdiv_r(r, i, j) isl_sioimath_fdiv_r((r), *(i), *(j))
#define isl_int_fdiv_q_ui(r, i, j) isl_sioimath_fdiv_q_ui((r), *(i), j)
#define isl_int_read(r, s) isl_sioimath_read((r), s)
#define isl_int_sgn(i) isl_sioimath_sgn(*(i))
#define isl_int_cmp(i, j) isl_sioimath_cmp(*(i), *(j))
#define isl_int_cmp_si(i, si) isl_sioimath_cmp_si(*(i), si)
#define isl_int_eq(i, j) (isl_sioimath_cmp(*(i), *(j)) == 0)
#define isl_int_ne(i, j) (isl_sioimath_cmp(*(i), *(j)) != 0)
#define isl_int_lt(i, j) (isl_sioimath_cmp(*(i), *(j)) < 0)
#define isl_int_le(i, j) (isl_sioimath_cmp(*(i), *(j)) <= 0)
#define isl_int_gt(i, j) (isl_sioimath_cmp(*(i), *(j)) > 0)
#define isl_int_ge(i, j) (isl_sioimath_cmp(*(i), *(j)) >= 0)
#define isl_int_abs_cmp(i, j) isl_sioimath_abs_cmp(*(i), *(j))
#define isl_int_abs_eq(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) == 0)
#define isl_int_abs_ne(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) != 0)
#define isl_int_abs_lt(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) < 0)
#define isl_int_abs_gt(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) > 0)
#define isl_int_abs_ge(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) >= 0)
#define isl_int_is_divisible_by(i, j) isl_sioimath_is_divisible_by(*(i), *(j))
#define isl_int_hash(v, h) isl_sioimath_hash(*(v), h)
#define isl_int_free_str(s) free(s)
#define isl_int_print(out, i, width) isl_sioimath_print(out, *(i), width)
#endif /* ISL_INT_SIOIMATH_H */
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