mirror of
https://github.com/mruby/mruby
synced 2026-06-08 16:11:16 +00:00
Yukihiro "Matz" Matsumoto
fe4ed7e68d
implement Integer#gcd and Integer#lcm methods in mruby-numeric-ext with full support for both regular integers and bigints. key changes: - add mrb_int_gcd euclidean algorithm for regular integer gcd calculation - implement int_gcd and int_lcm methods with proper type checking and bigint fallback - add mrb_bint_gcd, mrb_bint_lcm, mrb_bint_abs functions to bigint api - register gcd and lcm methods with integer class - add comprehensive test coverage for both regular and bigint cases Co-authored-by: Claude <noreply@anthropic.com>
2911 lines
61 KiB
C
2911 lines
61 KiB
C
/**
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** @file mruby/bigint.c - Multi-precision Integer
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**
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** See Copyright Notice in mruby.h
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*/
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#include <mruby.h>
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#include <mruby/object.h>
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#include <mruby/numeric.h>
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#include <mruby/array.h>
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#include <mruby/string.h>
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#include <mruby/internal.h>
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#include <string.h>
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#include "bigint.h"
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#define DIG_SIZE (MPZ_DIG_SIZE)
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#define DIG_BASE (1ULL << DIG_SIZE)
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#define DIG_MASK (DIG_BASE - 1)
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#define HIGH(x) ((x) >> DIG_SIZE)
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#define LOW(x) ((x) & DIG_MASK)
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#define iabs(x) (((x)>0)?(x):(-x))
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#define imax(x,y) (((x)>(y))?(x):(y))
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#define imin(x,y) (((x)<(y))?(x):(y))
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#define dg(x,i) (((size_t)i < (x)->sz)?(x)->p[i]:0)
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static void
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mpz_init(mrb_state *mrb, mpz_t *s)
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{
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s->p = NULL;
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s->sn = 0;
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s->sz = 0;
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}
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/* Helper macros for safer temporary variable management */
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#define MPZ_TMP_INIT(mrb, var) \
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mpz_t var; \
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mpz_init(mrb, &var)
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#define MPZ_TMP_CLEAR(mrb, var) \
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mpz_clear(mrb, &var)
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static void
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mpz_realloc(mrb_state *mrb, mpz_t *x, size_t size)
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{
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if (x->sz < size) {
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/* Check for overflow in size calculation */
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if (size > SIZE_MAX / sizeof(mp_limb)) {
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mrb_raise(mrb, E_RUNTIME_ERROR, "bigint size too large");
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}
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size_t old_sz = x->sz;
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x->p = (mp_limb*)mrb_realloc(mrb, x->p, size * sizeof(mp_limb));
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/* Zero-initialize new limbs */
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for (size_t i = old_sz; i < size; i++) {
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x->p[i] = 0;
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}
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x->sz = size;
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}
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}
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static void
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mpz_set(mrb_state *mrb, mpz_t *y, mpz_t *x)
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{
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size_t i, k = x->sz;
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mpz_realloc(mrb, y, k);
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for (i=0;i < k; i++)
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y->p[i] = x->p[i];
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y->sz = k;
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y->sn = x->sn;
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}
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static void
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mpz_init_set(mrb_state *mrb, mpz_t *s, mpz_t *t)
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{
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mpz_init(mrb, s);
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mpz_set(mrb, s, t);
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}
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static void
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mpz_set_int(mrb_state *mrb, mpz_t *y, mrb_int v)
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{
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mrb_uint u;
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if (v == 0) {
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y->sn=0;
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u = 0;
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}
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else if (v > 0) {
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y->sn = 1;
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u = v;
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}
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else /* if (v < 0) */ {
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y->sn = -1;
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if (v == MRB_INT_MIN) u = v;
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else u = -v;
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}
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#if MRB_INT_BIT > DIG_SIZE
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if ((u & ~DIG_MASK) != 0) {
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mpz_realloc(mrb, y, 2);
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y->p[1] = (mp_limb)HIGH(u);
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y->p[0] = (mp_limb)LOW(u);
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return;
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}
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#endif
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mpz_realloc(mrb, y, 1);
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y->p[0] = (mp_limb)u;
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}
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static void
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mpz_set_uint64(mrb_state *mrb, mpz_t *y, uint64_t u)
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{
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size_t len = 0;
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for (uint64_t u0=u; u0; u0>>=DIG_SIZE,len++)
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;
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y->sn = (u != 0);
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mpz_realloc(mrb, y, len);
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for (size_t i=0; i<len; i++) {
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y->p[i] = (mp_limb)LOW(u);
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u >>= DIG_SIZE;
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}
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}
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#ifdef MRB_INT32
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static void
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mpz_set_int64(mrb_state *mrb, mpz_t *y, int64_t v)
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{
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uint64_t u;
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if (v < 0) {
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if (v == INT64_MIN) u = v;
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else u = -v;
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}
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else {
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u = v;
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}
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mpz_set_uint64(mrb, y, u);
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if (v < 0) {
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y->sn = -1;
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}
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}
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#endif
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static void
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mpz_init_set_int(mrb_state *mrb, mpz_t *y, mrb_int v)
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{
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mpz_init(mrb, y);
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mpz_set_int(mrb, y, v);
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}
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static void
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mpz_clear(mrb_state *mrb, mpz_t *s)
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{
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if (s->p) {
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mrb_free(mrb, s->p);
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s->p = NULL; /* Prevent double-free */
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}
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s->sn = 0;
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s->sz = 0;
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}
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static void
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mpz_move(mrb_state *mrb, mpz_t *y, mpz_t *x)
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{
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mpz_clear(mrb, y);
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y->sn = x->sn;
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y->sz = x->sz;
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y->p = x->p;
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x->p = NULL;
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x->sn = 0;
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x->sz = 0;
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}
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static size_t
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digits(mpz_t *x)
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{
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size_t i;
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if (x->sz == 0) return 0;
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for (i = x->sz - 1; x->p[i] == 0; i--)
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if (i == 0) break;
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return i+1;
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}
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static void
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trim(mpz_t *x)
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{
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while (x->sz && x->p[x->sz-1] == 0) {
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x->sz--;
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}
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}
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/* z = x + y, without regard for sign */
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static void
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uadd(mrb_state *mrb, mpz_t *z, mpz_t *x, mpz_t *y)
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{
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if (y->sz < x->sz) {
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mpz_t *t; /* swap x,y */
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t=x; x=y; y=t;
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}
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/* now y->sz >= x->sz */
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mpz_realloc(mrb, z, y->sz+1);
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mp_dbl_limb c = 0;
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size_t i;
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for (i=0; i<x->sz; i++) {
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c += (mp_dbl_limb)y->p[i] + (mp_dbl_limb)x->p[i];
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z->p[i] = LOW(c);
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c >>= DIG_SIZE;
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}
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for (;i<y->sz; i++) {
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c += y->p[i];
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z->p[i] = LOW(c);
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c >>= DIG_SIZE;
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}
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z->p[y->sz] = (mp_limb)c;
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}
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/* z = y - x, ignoring sign */
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/* precondition: abs(y) >= abs(x) */
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static void
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usub(mrb_state *mrb, mpz_t *z, mpz_t *y, mpz_t *x)
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{
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mpz_realloc(mrb, z, (size_t)(y->sz));
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mp_dbl_limb_signed b = 0;
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size_t i;
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for (i=0;i<x->sz;i++) {
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b += (mp_dbl_limb_signed)y->p[i];
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b -= (mp_dbl_limb_signed)x->p[i];
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z->p[i] = LOW(b);
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b = HIGH(b);
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}
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for (;i<y->sz; i++) {
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b += y->p[i];
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z->p[i] = LOW(b);
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b = HIGH(b);
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}
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z->sz = digits(z);
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}
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/* compare abs(x) and abs(y) */
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static int
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ucmp(mpz_t *y, mpz_t *x)
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{
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if (y->sz < x->sz) return -1;
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if (y->sz > x->sz) return 1;
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if (x->sz == 0) return 0;
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for (size_t i=x->sz-1;; i--) {
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mp_limb a = y->p[i];
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mp_limb b = x->p[i];
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if (a > b) return 1;
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if (a < b) return -1;
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if (i == 0) break;
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}
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return 0;
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}
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#define zero_p(x) ((x)->sn == 0)
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/* check if all digits are zero */
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static int
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uzero_p(mpz_t *x)
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{
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if (x->sz == 0) return 1;
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for (size_t i=x->sz-1;; i--) {
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if (x->p[i] != 0)
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return 0;
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if (i == 0) break;
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}
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return 1;
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}
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static void
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zero(mpz_t *x)
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{
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x->sn=0;
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if (x->p) {
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x->sz=1;
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x->p[0]=0;
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}
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else {
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x->sz=0;
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}
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}
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/* z = x + y */
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static void
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mpz_add(mrb_state *mrb, mpz_t *zz, mpz_t *x, mpz_t *y)
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{
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if (zero_p(x)) {
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mpz_set(mrb, zz, y);
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return;
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}
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if (zero_p(y)) {
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mpz_set(mrb, zz, x);
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return;
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}
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mpz_t z;
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mpz_init(mrb, &z);
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if (x->sn > 0 && y->sn > 0) {
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uadd(mrb, &z, x, y);
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z.sn = 1;
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}
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else if (x->sn < 0 && y->sn < 0) {
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uadd(mrb, &z, x, y);
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z.sn = -1;
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}
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else {
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int mg;
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/* signs differ */
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if ((mg = ucmp(x,y)) == 0) {
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zero(&z);
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}
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else if (mg > 0) { /* abs(y) < abs(x) */
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usub(mrb, &z, x, y);
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z.sn = (x->sn > 0 && y->sn < 0) ? 1 : (-1);
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}
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else { /* abs(y) > abs(x) */
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usub(mrb, &z, y, x);
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z.sn = (x->sn < 0 && y->sn > 0) ? 1 : (-1);
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}
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}
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trim(&z);
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mpz_move(mrb, zz, &z);
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}
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/* x += n */
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/* ignores sign of x */
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/* assumes n is positive and small (fits in mp_limb) */
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static void
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mpz_add_int(mrb_state *mrb, mpz_t *x, mrb_int n)
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{
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// If n is zero, no operation is needed
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if (n == 0) return;
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// Assume x is positive and n is a small positive integer
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mp_dbl_limb carry = n; // Initialize carry with n
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for (size_t i = 0; i < x->sz && carry; i++) {
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carry += (mp_dbl_limb)x->p[i]; // Add current limb and carry
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x->p[i] = LOW(carry); // Store lower 32 bits in current limb
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carry = HIGH(carry); // Update carry with higher bits
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}
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if (carry != 0) {
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mpz_realloc(mrb, x, x->sz + 1);
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x->p[x->sz-1] = (mp_limb)carry;
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x->sn = 1;
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}
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trim(x);
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}
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/* z = x - y -- just use mpz_add - I'm lazy */
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static void
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mpz_sub(mrb_state *mrb, mpz_t *z, mpz_t *x, mpz_t *y)
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{
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mpz_t u;
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/* Initialize u as a view of y with negated sign - no new memory allocated */
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u.p = y->p;
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u.sz = y->sz;
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u.sn = -(y->sn);
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mpz_add(mrb, z, x, &u);
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/* No mpz_clear needed since u.p points to y->p (no separate allocation) */
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}
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/* x -= n */
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/* ignores sign of x */
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/* assumes n is positive and small (fits in mp_limb) */
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static void
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mpz_sub_int(mrb_state *mrb, mpz_t *x, mrb_int n)
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{
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// If n is zero, no operation is needed
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if (n == 0) return;
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// If x is zero, set x to n
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if (zero_p(x) || x->sz == 0) {
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mpz_set_int(mrb, x, n);
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return;
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}
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// Initialize borrow and start decrement
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mp_dbl_limb_signed borrow = (mp_limb)n;
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size_t i = 0;
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// Subtract 1 from the least significant limb and propagate if necessary
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borrow = (mp_dbl_limb_signed)x->p[i] - borrow;
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x->p[i] = LOW(borrow);
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borrow = (borrow < 0) ? 1 : 0;
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// Continue through limbs while there is a borrow
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for (i = 1; i < x->sz && borrow; i++) {
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borrow = (mp_dbl_limb_signed)x->p[i] - borrow;
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x->p[i] = LOW(borrow);
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borrow = (borrow < 0) ? 1 : 0;
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}
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// Trim any unnecessary leading zeros
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trim(x);
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}
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/* w = u * v */
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/* Simple Multiply */
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static void
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mpz_mul(mrb_state *mrb, mpz_t *ww, mpz_t *u, mpz_t *v)
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{
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if (zero_p(u) || zero_p(v)) {
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zero(ww);
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return;
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}
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mpz_t w;
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mpz_init(mrb, &w);
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mpz_realloc(mrb, &w, u->sz + v->sz);
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for (size_t j = 0; j < u->sz; j++) {
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size_t i;
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mp_dbl_limb cc = (mp_limb)0;
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mp_limb u0 = u->p[j];
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if (u0 == 0) continue;
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for (i = 0; i < v->sz; i++) {
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mp_limb v0 = v->p[i];
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if (v0 == 0) continue;
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cc += (mp_dbl_limb)w.p[i + j] + (mp_dbl_limb)u0 * (mp_dbl_limb)v0;
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w.p[i + j] = LOW(cc);
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cc = HIGH(cc);
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}
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if (cc) {
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w.p[i + j] = (mp_limb)cc;
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}
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}
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w.sn = u->sn * v->sn;
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trim(&w);
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mpz_move(mrb, ww, &w);
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}
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/* number of leading zero bits in digit */
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static int
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lzb(mp_limb x)
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{
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if (x == 0) return 0;
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#if (defined(__GNUC__) || __has_builtin(__builtin_clz))
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if (sizeof(mp_limb) == sizeof(int64_t))
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return __builtin_clzll(x);
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else if (sizeof(mp_limb) == sizeof(int32_t))
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return __builtin_clz(x);
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#endif
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int j=0;
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for (mp_limb i = ((mp_limb)1 << (DIG_SIZE-1)); i && !(x&i); j++,i>>=1)
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;
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return j;
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}
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/* c1 = a>>n */
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/* n must be < DIG_SIZE */
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static void
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urshift(mrb_state *mrb, mpz_t *c1, mpz_t *a, size_t n)
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{
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mrb_assert(n < DIG_SIZE);
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if (n == 0)
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mpz_set(mrb, c1, a);
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else if (uzero_p(a)) {
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zero(c1);
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}
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else {
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mpz_t c;
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mp_limb cc = 0;
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mp_dbl_limb rm = (((mp_dbl_limb)1<<n) - 1);
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mpz_init(mrb, &c);
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mpz_realloc(mrb, &c, a->sz);
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for (size_t i=a->sz-1;; i--) {
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c.p[i] = ((a->p[i] >> n) | cc) & DIG_MASK;
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cc = (a->p[i] & rm) << (DIG_SIZE - n);
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if (i == 0) break;
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}
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trim(&c);
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mpz_move(mrb, c1, &c);
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}
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}
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/* c1 = a<<n */
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/* n must be < DIG_SIZE */
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static void
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ulshift(mrb_state *mrb, mpz_t *c1, mpz_t *a, size_t n)
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{
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mrb_assert(n < DIG_SIZE);
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if (n == 0)
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mpz_set(mrb, c1, a);
|
|
else if (uzero_p(a)) {
|
|
zero(c1);
|
|
}
|
|
else {
|
|
mp_limb cc = 0;
|
|
mpz_t c;
|
|
mp_limb rm = (((mp_dbl_limb)1<<n) - 1) << (DIG_SIZE-n);
|
|
|
|
mpz_init(mrb, &c);
|
|
mpz_realloc(mrb, &c, a->sz+1);
|
|
|
|
size_t i;
|
|
for (i=0; i<a->sz; i++) {
|
|
c.p[i] = ((a->p[i] << n) | cc) & DIG_MASK;
|
|
cc = (a->p[i] & rm) >> (DIG_SIZE-n);
|
|
}
|
|
c.p[i] = cc;
|
|
trim(&c);
|
|
mpz_move(mrb, c1, &c);
|
|
}
|
|
}
|
|
|
|
/* Fast division by single limb */
|
|
static void
|
|
mpz_div_limb(mrb_state *mrb, mpz_t *q, mpz_t *r, mpz_t *x, mp_limb d)
|
|
{
|
|
if (zero_p(x)) {
|
|
zero(q);
|
|
zero(r);
|
|
return;
|
|
}
|
|
|
|
if (d == 0) {
|
|
mrb_raise(mrb, E_ZERODIV_ERROR, "divided by 0");
|
|
}
|
|
|
|
/* Power-of-2 divisor optimization */
|
|
if ((d & (d - 1)) == 0) {
|
|
/* d is power of 2, use bit operations */
|
|
int shift = 0;
|
|
mp_limb temp = d;
|
|
while (temp > 1) {
|
|
temp >>= 1;
|
|
shift++;
|
|
}
|
|
|
|
/* Quotient = x >> shift */
|
|
if (shift == 0) {
|
|
mpz_set(mrb, q, x);
|
|
}
|
|
else {
|
|
/* Manual right shift implementation */
|
|
size_t limb_shift = shift / DIG_SIZE;
|
|
size_t bit_shift = shift % DIG_SIZE;
|
|
|
|
if (limb_shift >= x->sz) {
|
|
zero(q);
|
|
}
|
|
else {
|
|
size_t new_size = x->sz - limb_shift;
|
|
mpz_realloc(mrb, q, new_size);
|
|
|
|
if (bit_shift == 0) {
|
|
/* Simple limb copy */
|
|
for (size_t i = 0; i < new_size; i++) {
|
|
q->p[i] = x->p[i + limb_shift];
|
|
}
|
|
}
|
|
else {
|
|
/* Bit shift within limbs */
|
|
mp_limb carry = 0;
|
|
for (size_t i = new_size; i > 0; i--) {
|
|
mp_limb current = x->p[i - 1 + limb_shift];
|
|
q->p[i - 1] = (current >> bit_shift) | carry;
|
|
carry = (current << (DIG_SIZE - bit_shift)) & DIG_MASK;
|
|
}
|
|
}
|
|
q->sz = new_size;
|
|
trim(q);
|
|
q->sn = (q->sz == 0) ? 0 : 1;
|
|
}
|
|
}
|
|
|
|
/* Remainder = x & (d - 1) */
|
|
mpz_realloc(mrb, r, 1);
|
|
r->p[0] = x->p[0] & (d - 1);
|
|
r->sz = (r->p[0] == 0) ? 0 : 1;
|
|
r->sn = (r->sz == 0) ? 0 : 1;
|
|
return;
|
|
}
|
|
|
|
/* General single-limb division */
|
|
if (x->sz == 1) {
|
|
/* Both dividend and divisor are single limb */
|
|
mpz_realloc(mrb, q, 1);
|
|
mpz_realloc(mrb, r, 1);
|
|
|
|
q->p[0] = x->p[0] / d;
|
|
r->p[0] = x->p[0] % d;
|
|
|
|
q->sz = (q->p[0] == 0) ? 0 : 1;
|
|
q->sn = (q->sz == 0) ? 0 : 1;
|
|
|
|
r->sz = (r->p[0] == 0) ? 0 : 1;
|
|
r->sn = (r->sz == 0) ? 0 : 1;
|
|
return;
|
|
}
|
|
|
|
/* Multi-limb dividend, single-limb divisor */
|
|
size_t n = x->sz;
|
|
mpz_realloc(mrb, q, n);
|
|
|
|
mp_dbl_limb remainder = 0;
|
|
|
|
/* Process from most significant limb to least significant */
|
|
for (size_t i = n; i > 0; i--) {
|
|
remainder = (remainder << DIG_SIZE) + x->p[i-1];
|
|
q->p[i-1] = (mp_limb)(remainder / d);
|
|
remainder = remainder % d;
|
|
}
|
|
|
|
/* Set remainder */
|
|
mpz_realloc(mrb, r, 1);
|
|
r->p[0] = (mp_limb)remainder;
|
|
r->sz = (remainder == 0) ? 0 : 1;
|
|
r->sn = (r->sz == 0) ? 0 : 1;
|
|
|
|
/* Trim leading zeros from quotient */
|
|
trim(q);
|
|
q->sn = (q->sz == 0) ? 0 : 1;
|
|
}
|
|
|
|
/* internal routine to compute x/y and x%y ignoring signs */
|
|
/* qq = xx/yy; rr = xx%yy */
|
|
static void
|
|
udiv(mrb_state *mrb, mpz_t *qq, mpz_t *rr, mpz_t *xx, mpz_t *yy)
|
|
{
|
|
/* simple cases */
|
|
int cmp = ucmp(xx, yy);
|
|
if (cmp == 0) {
|
|
mpz_set_int(mrb, qq, 1);
|
|
zero(rr);
|
|
return;
|
|
}
|
|
else if (cmp < 0) {
|
|
zero(qq);
|
|
mpz_set(mrb, rr, xx);
|
|
return;
|
|
}
|
|
|
|
/* Fast path for single-limb divisor */
|
|
if (yy->sz == 1) {
|
|
mpz_div_limb(mrb, qq, rr, xx, yy->p[0]);
|
|
return;
|
|
}
|
|
|
|
mpz_t q, x, y;
|
|
|
|
mrb_assert(yy->sn != 0); /* divided by zero */
|
|
mrb_assert(yy->sz > 0); /* divided by zero */
|
|
mpz_init(mrb, &q);
|
|
mpz_init(mrb, &x);
|
|
mpz_init(mrb, &y);
|
|
mpz_realloc(mrb, &x, xx->sz+1);
|
|
size_t yd = digits(yy);
|
|
size_t ns = lzb(yy->p[yd-1]);
|
|
ulshift(mrb, &x, xx, ns);
|
|
ulshift(mrb, &y, yy, ns);
|
|
size_t xd = digits(&x);
|
|
mpz_realloc(mrb, &q, xd);
|
|
mp_dbl_limb z = y.p[yd-1];
|
|
if (xd>=yd) {
|
|
for (size_t j=xd-yd;; j--) {
|
|
mp_dbl_limb_signed b=0;
|
|
mp_dbl_limb qhat;
|
|
|
|
if (j+yd == xd)
|
|
qhat = x.p[j+yd-1] / z;
|
|
else
|
|
qhat = (((mp_dbl_limb)x.p[j+yd] << DIG_SIZE) + x.p[j+yd-1]) / z;
|
|
if (qhat) {
|
|
size_t i;
|
|
|
|
for (i=0; i<yd; i++) {
|
|
mp_dbl_limb zz = qhat * y.p[i];
|
|
mp_dbl_limb_signed u = LOW(b)+x.p[i+j]-LOW(zz);
|
|
x.p[i+j] = LOW(u);
|
|
b = HIGH(b) - HIGH(zz) + HIGH(u);
|
|
}
|
|
b += x.p[i+j];
|
|
}
|
|
for (; b!=0; qhat--) {
|
|
mp_dbl_limb c = 0;
|
|
for (size_t i=0; i<yd; i++) {
|
|
c += (mp_dbl_limb)x.p[i+j] + (mp_dbl_limb)y.p[i];
|
|
x.p[i+j] = LOW(c);
|
|
c = HIGH(c);
|
|
}
|
|
b += c;
|
|
}
|
|
q.p[j] = (mp_limb)qhat;
|
|
if (j == 0) break;
|
|
}
|
|
}
|
|
x.sz = yy->sz;
|
|
urshift(mrb, rr, &x, ns);
|
|
trim(&q);
|
|
mpz_move(mrb, qq, &q);
|
|
mpz_clear(mrb, &x);
|
|
mpz_clear(mrb, &y);
|
|
}
|
|
|
|
static void
|
|
mpz_mdiv(mrb_state *mrb, mpz_t *q, mpz_t *x, mpz_t *y)
|
|
{
|
|
mpz_t r;
|
|
short sn1 = x->sn, sn2 = y->sn, qsign;
|
|
|
|
if (zero_p(x)) {
|
|
mpz_init_set_int(mrb, q, 0);
|
|
return;
|
|
}
|
|
mpz_init(mrb, &r);
|
|
udiv(mrb, q, &r, x, y);
|
|
qsign = q->sn = sn1*sn2;
|
|
if (uzero_p(q))
|
|
q->sn = 0;
|
|
/* now if r != 0 and q < 0 we need to round q towards -inf */
|
|
if (!uzero_p(&r) && qsign < 0) {
|
|
/* add 1 to magnitude */
|
|
mpz_add_int(mrb, q, 1);
|
|
/* force negative sign in case the value of q was zero before rounding */
|
|
q->sn = -1;
|
|
}
|
|
mpz_clear(mrb, &r);
|
|
}
|
|
|
|
static void
|
|
mpz_mmod(mrb_state *mrb, mpz_t *r, mpz_t *x, mpz_t *y)
|
|
{
|
|
mpz_t q;
|
|
short sn1 = x->sn, sn2 = y->sn, sn3;
|
|
|
|
mpz_init(mrb, &q);
|
|
if (sn1 == 0) {
|
|
zero(r);
|
|
return;
|
|
}
|
|
udiv(mrb, &q, r, x, y);
|
|
mpz_clear(mrb, &q);
|
|
if (uzero_p(r)) {
|
|
r->sn = 0;
|
|
return;
|
|
}
|
|
sn3 = sn1*sn2;
|
|
if (sn3 > 0)
|
|
r->sn = sn1;
|
|
else if (sn1 < 0 && sn2 > 0) {
|
|
r->sn = 1;
|
|
mpz_sub(mrb, r, y, r);
|
|
}
|
|
else {
|
|
r->sn = 1;
|
|
mpz_add(mrb, r, y, r);
|
|
}
|
|
}
|
|
|
|
static void
|
|
mpz_mdivmod(mrb_state *mrb, mpz_t *q, mpz_t *r, mpz_t *x, mpz_t *y)
|
|
{
|
|
short sn1 = x->sn, sn2 = y->sn, qsign;
|
|
|
|
if (sn1 == 0) {
|
|
zero(q);
|
|
zero(r);
|
|
return;
|
|
}
|
|
udiv(mrb, q, r, x, y);
|
|
qsign = q->sn = sn1*sn2;
|
|
if (uzero_p(r)) {
|
|
/* q != 0, since q=r=0 would mean x=0, which was tested above */
|
|
r->sn = 0;
|
|
return;
|
|
}
|
|
if (q->sn > 0)
|
|
r->sn = sn1;
|
|
else if (sn1 < 0 && sn2 > 0) {
|
|
r->sn = 1;
|
|
mpz_sub(mrb, r, y, r);
|
|
}
|
|
else {
|
|
r->sn = 1;
|
|
mpz_add(mrb, r, y, r);
|
|
}
|
|
if (uzero_p(q))
|
|
q->sn = 0;
|
|
/* now if r != 0 and q < 0 we need to round q towards -inf */
|
|
if (!uzero_p(r) && qsign < 0) {
|
|
/* add 1 to magnitude */
|
|
mpz_add_int(mrb, q, 1);
|
|
/* force negative sign in case the value of q was zero before rounding */
|
|
q->sn = -1;
|
|
}
|
|
}
|
|
|
|
/* Fast modular reduction for single-limb modulus */
|
|
static void
|
|
mpz_mod_limb(mrb_state *mrb, mpz_t *r, mpz_t *x, mp_limb m)
|
|
{
|
|
if (zero_p(x)) {
|
|
zero(r);
|
|
return;
|
|
}
|
|
|
|
if (x->sz == 1) {
|
|
/* Single limb case - simple modulo */
|
|
mp_limb result = x->p[0] % m;
|
|
mpz_set_int(mrb, r, result);
|
|
r->sn = x->sn;
|
|
return;
|
|
}
|
|
|
|
/* Multi-limb case - use repeated division */
|
|
mp_dbl_limb remainder = 0;
|
|
for (size_t i = x->sz; i > 0; i--) {
|
|
remainder = (remainder << DIG_SIZE) | x->p[i-1];
|
|
remainder %= m;
|
|
}
|
|
|
|
mpz_set_int(mrb, r, (mp_limb)remainder);
|
|
r->sn = x->sn;
|
|
if (remainder == 0)
|
|
r->sn = 0;
|
|
}
|
|
|
|
/* Forward declarations for Barrett reduction functions */
|
|
static void mpz_barrett_mu(mrb_state *mrb, mpz_t *mu, mpz_t *m);
|
|
static void mpz_barrett_reduce(mrb_state *mrb, mpz_t *r, mpz_t *x, mpz_t *m, mpz_t *mu);
|
|
|
|
static void
|
|
mpz_mod(mrb_state *mrb, mpz_t *r, mpz_t *x, mpz_t *y)
|
|
{
|
|
mpz_t q;
|
|
short sn = x->sn;
|
|
|
|
if (zero_p(x)) {
|
|
zero(r);
|
|
return;
|
|
}
|
|
|
|
/* Fast path for single-limb modulus */
|
|
if (y->sz == 1) {
|
|
mpz_mod_limb(mrb, r, x, y->p[0]);
|
|
if (y->sn < 0) r->sn = -r->sn;
|
|
return;
|
|
}
|
|
|
|
/* Barrett reduction for moderate-sized moduli */
|
|
if (y->sz >= 2 && y->sz <= 8 && x->sz >= y->sz + 2) {
|
|
mpz_t mu;
|
|
mpz_init(mrb, &mu);
|
|
mpz_barrett_mu(mrb, &mu, y);
|
|
mpz_barrett_reduce(mrb, r, x, y, &mu);
|
|
r->sn = sn;
|
|
if (uzero_p(r))
|
|
r->sn = 0;
|
|
mpz_clear(mrb, &mu);
|
|
return;
|
|
}
|
|
|
|
/* General division fallback */
|
|
mpz_init(mrb, &q);
|
|
udiv(mrb, &q, r, x, y);
|
|
r->sn = sn;
|
|
if (uzero_p(r))
|
|
r->sn = 0;
|
|
mpz_clear(mrb, &q);
|
|
}
|
|
|
|
static mrb_int
|
|
mpz_cmp(mrb_state *mrb, mpz_t *x, mpz_t *y)
|
|
{
|
|
if (x->sn < 0 && y->sn > 0)
|
|
return (-1);
|
|
if (x->sn > 0 && y->sn < 0)
|
|
return 1;
|
|
int abscmp=ucmp(x, y);
|
|
if (x->sn >=0 && y->sn >=0)
|
|
return abscmp;
|
|
return (-abscmp); // if (x->sn <=0 && y->sn <=0)
|
|
}
|
|
|
|
/* 2<=base<=36 - this overestimates the optimal value, which is OK */
|
|
static size_t
|
|
mpz_sizeinbase(mpz_t *x, mrb_int base)
|
|
{
|
|
size_t i, j;
|
|
|
|
size_t bits = digits(x) * DIG_SIZE;
|
|
mrb_assert(2 <= base && base <= 36);
|
|
|
|
if (zero_p(x) || x->sz == 0) return 0;
|
|
for (j=0,i=1; i<=(size_t)base; i*=2,j++)
|
|
;
|
|
return bits/(j-1)+1;
|
|
}
|
|
|
|
/* x = y * n (only called from mpz_init_set_str) */
|
|
/* assumes x and n are positive or zero */
|
|
/* assumes n is small (fits in mp_limb) */
|
|
static void
|
|
mpz_mul_int(mrb_state *mrb, mpz_t *x, mrb_int n)
|
|
{
|
|
if (n == 0 || zero_p(x)) {
|
|
zero(x);
|
|
return;
|
|
}
|
|
|
|
size_t x_sz = x->sz;
|
|
size_t new_sz = x_sz + 1; // Maximum possible size after multiplication
|
|
|
|
// Reallocate x if necessary
|
|
mpz_realloc(mrb, x, new_sz);
|
|
|
|
mp_dbl_limb cc = 0;
|
|
mp_limb n_limb = (mp_limb)n;
|
|
|
|
for (size_t i = 0; i < x_sz; i++) {
|
|
// Multiply each limb and add carry
|
|
cc += (mp_dbl_limb)x->p[i] * n_limb;
|
|
x->p[i] = LOW(cc);
|
|
cc = HIGH(cc);
|
|
}
|
|
|
|
if (cc) {
|
|
// If there is a remaining carry, store it
|
|
x->p[x_sz] = (mp_limb)cc;
|
|
}
|
|
else {
|
|
x->sz = x_sz;
|
|
}
|
|
|
|
x->sn = 1;
|
|
trim(x);
|
|
}
|
|
|
|
static int
|
|
mpz_init_set_str(mrb_state *mrb, mpz_t *x, const char *s, mrb_int len, mrb_int base)
|
|
{
|
|
int retval = 0;
|
|
short sn;
|
|
uint8_t k;
|
|
|
|
mpz_init(mrb, x);
|
|
if (*s == '-') {
|
|
sn = -1; s++;
|
|
}
|
|
else if (*s == '+') {
|
|
sn = 1; s++;
|
|
}
|
|
else
|
|
sn = 1;
|
|
for (mrb_int i=0; i<len; i++) {
|
|
if (s[i]=='_') continue;
|
|
if (s[i] >= '0' && s[i] <= '9')
|
|
k = (uint8_t)s[i] - (uint8_t)'0';
|
|
else if (s[i] >= 'A' && s[i] <= 'Z')
|
|
k = (uint8_t)s[i] - (uint8_t)'A'+10;
|
|
else if (s[i] >= 'a' && s[i] <= 'z')
|
|
k = (uint8_t)s[i] - (uint8_t)'a'+10;
|
|
else {
|
|
retval = (-1);
|
|
break;
|
|
}
|
|
if (k >= base) {
|
|
retval = (-1);
|
|
break;
|
|
}
|
|
mpz_mul_int(mrb, x, base);
|
|
mpz_add_int(mrb, x, k);
|
|
}
|
|
x->sn = x->sz == 0 ? 0 : sn;
|
|
return retval;
|
|
}
|
|
|
|
/* power of base no bigger than DIG_BASE */
|
|
/* power of 2 is handled differently */
|
|
static const mp_limb base_limit[34*2] = {
|
|
#ifdef MRB_NO_MPZ64BIT
|
|
59049, // 3^10
|
|
0, // 4^8 (skip)
|
|
15625, // 5^6
|
|
46656, // 6^6
|
|
16807, // 7^5
|
|
0, // 8^5 (skip)
|
|
59049, // 9^5
|
|
10000, // 10^4
|
|
14641, // 11^4
|
|
20736, // 12^4
|
|
28561, // 13^4
|
|
38416, // 14^4
|
|
50625, // 15^4
|
|
0, // 16^4 (skip)
|
|
4913, // 17^3
|
|
5832, // 18^3
|
|
6859, // 19^3
|
|
8000, // 20^3
|
|
9261, // 21^3
|
|
10648, // 22^3
|
|
12167, // 23^3
|
|
13824, // 24^3
|
|
15625, // 25^3
|
|
17576, // 26^3
|
|
19683, // 27^3
|
|
21952, // 28^3
|
|
24389, // 29^3
|
|
27000, // 30^3
|
|
29791, // 31^3
|
|
0, // 32^3 (skip)
|
|
35937, // 33^3
|
|
39304, // 34^3
|
|
42875, // 35^3
|
|
46656, // 36^3
|
|
#else
|
|
3486784401UL, // 3^20
|
|
0, // 4^16 (skip)
|
|
1220703125UL, // 5^13
|
|
2176782336UL, // 6^12
|
|
1977326743UL, // 7^11
|
|
0, // 8^10 (skip)
|
|
3486784401UL, // 9^10
|
|
1000000000UL, // 10^9
|
|
2357947691UL, // 11^9
|
|
429981696UL, // 12^8
|
|
815730721UL, // 13^8
|
|
1475789056UL, // 14^8
|
|
2562890625UL, // 15^8
|
|
0, // 16^8 (skip)
|
|
410338673UL, // 17^7
|
|
612220032UL, // 18^7
|
|
893871739UL, // 19^7
|
|
1280000000UL, // 20^7
|
|
1801088541UL, // 21^7
|
|
2494357888UL, // 22^7
|
|
3404825447UL, // 23^7
|
|
191102976UL, // 24^6
|
|
244140625UL, // 25^6
|
|
308915776UL, // 26^6
|
|
387420489UL, // 27^6
|
|
481890304UL, // 28^6
|
|
594823321UL, // 29^6
|
|
729000000UL, // 30^6
|
|
887503681UL, // 31^6
|
|
0, // 32^6 (skip)
|
|
1291467969UL, // 33^6
|
|
1544804416UL, // 34^6
|
|
1838265625UL, // 35^6
|
|
2176782336UL, // 36^6
|
|
#endif
|
|
};
|
|
|
|
static char*
|
|
mpz_get_str(mrb_state *mrb, char *s, mrb_int sz, mrb_int base, mpz_t *x)
|
|
{
|
|
mrb_assert(2 <= base && base <= 36);
|
|
if (zero_p(x)) {
|
|
*s='0';
|
|
*(s+1)='\0';
|
|
return s;
|
|
}
|
|
|
|
char *ps = s;
|
|
char *se = s+sz;
|
|
int xlen = (int)digits(x);
|
|
|
|
if ((base & (base - 1)) == 0) { // base is a power of 2
|
|
int shift = 0;
|
|
while ((1 << shift) < base) shift++;
|
|
mp_limb mask = (mp_limb)base - 1;
|
|
mp_dbl_limb value = 0;
|
|
int bits = 0;
|
|
|
|
/* Process all limbs */
|
|
for (int i = 0; i < xlen; i++) {
|
|
value |= (mp_dbl_limb)x->p[i] << bits;
|
|
bits += DIG_SIZE;
|
|
while (bits >= shift) {
|
|
mp_limb digit = value & mask;
|
|
value >>= shift;
|
|
bits -= shift;
|
|
|
|
if (digit < 10) *s++ = '0' + digit;
|
|
else *s++ = 'a' + digit - 10;
|
|
}
|
|
}
|
|
|
|
/* Handle any remaining bits */
|
|
while (bits > 0) {
|
|
mp_limb digit = value & mask;
|
|
value >>= shift;
|
|
bits -= shift;
|
|
|
|
if (digit < 10) *s++ = '0' + digit;
|
|
else *s++ = 'a' + digit - 10;
|
|
}
|
|
}
|
|
else {
|
|
/* Check for overflow in size calculation */
|
|
if (xlen > SIZE_MAX / sizeof(mp_limb)) {
|
|
mrb_raise(mrb, E_RUNTIME_ERROR, "bigint size too large for string conversion");
|
|
}
|
|
|
|
mp_limb *t = (mp_limb*)mrb_malloc(mrb, xlen * sizeof(mp_limb));
|
|
|
|
mp_limb *tend = t + xlen;
|
|
memcpy(t, x->p, xlen * sizeof(mp_limb));
|
|
mp_limb b2 = base_limit[base-3];
|
|
|
|
for (;;) {
|
|
mp_limb *d = tend;
|
|
mp_dbl_limb a = 0;
|
|
while (--d >= t) {
|
|
mp_limb d0 = *d;
|
|
a = (a<<DIG_SIZE) | d0;
|
|
*d = (mp_limb)(a / b2);
|
|
a %= b2;
|
|
}
|
|
|
|
// convert to character
|
|
for (mp_limb b=b2; b>=base; b/=base) {
|
|
char a0 = (char)(a % base);
|
|
if (a0 < 10) a0 += '0';
|
|
else a0 += 'a' - 10;
|
|
if (s == se) break;
|
|
*s++ = a0;
|
|
a /= base;
|
|
}
|
|
|
|
// check if number is zero
|
|
for (d = t; d < tend; d++) {
|
|
if (*d != 0) break;
|
|
}
|
|
if (d == tend) break;
|
|
}
|
|
mrb_free(mrb, t);
|
|
}
|
|
|
|
while (ps<s && s[-1]=='0') s--;
|
|
if (x->sn < 0) {
|
|
*s++ = '-';
|
|
}
|
|
|
|
/* reverse string */
|
|
for (char *u = ps,*v=s-1; u < v; u++,v--) {
|
|
char temp = *u;
|
|
*u = *v;
|
|
*v = temp;
|
|
}
|
|
*s = '\0'; /* null termination */
|
|
return ps;
|
|
}
|
|
|
|
static int
|
|
mpz_get_int(mpz_t *y, mrb_int *v)
|
|
{
|
|
if (zero_p(y)) {
|
|
*v = 0;
|
|
return TRUE;
|
|
}
|
|
|
|
mp_dbl_limb i = 0;
|
|
mp_limb *d = y->p + y->sz;
|
|
|
|
while (d-- > y->p) {
|
|
if (HIGH(i) != 0) {
|
|
/* will overflow */
|
|
return FALSE;
|
|
}
|
|
i = (i << DIG_SIZE) | *d;
|
|
}
|
|
if (i > MRB_INT_MAX) {
|
|
/* overflow */
|
|
return FALSE;
|
|
}
|
|
if (y->sn < 0) {
|
|
*v = -(mrb_int)i;
|
|
}
|
|
else {
|
|
*v = (mrb_int)i;
|
|
}
|
|
return TRUE;
|
|
}
|
|
|
|
static void
|
|
mpz_mul_2exp(mrb_state *mrb, mpz_t *z, mpz_t *x, mrb_int e)
|
|
{
|
|
if (e==0)
|
|
mpz_set(mrb, z, x);
|
|
else {
|
|
short sn = x->sn;
|
|
size_t digs = e / DIG_SIZE;
|
|
size_t bs = e % DIG_SIZE;
|
|
mpz_t y;
|
|
|
|
mpz_init(mrb, &y);
|
|
mpz_realloc(mrb, &y, x->sz+digs);
|
|
for (size_t i=0;i<x->sz;i++)
|
|
y.p[i+digs] = x->p[i];
|
|
if (bs) {
|
|
ulshift(mrb, z, &y, bs);
|
|
mpz_clear(mrb, &y);
|
|
}
|
|
else {
|
|
mpz_move(mrb, z, &y);
|
|
}
|
|
z->sn = sn;
|
|
}
|
|
}
|
|
|
|
static void
|
|
mpz_div_2exp(mrb_state *mrb, mpz_t *z, mpz_t *x, mrb_int e)
|
|
{
|
|
short sn = x->sn;
|
|
if (e==0)
|
|
mpz_set(mrb, z, x);
|
|
else {
|
|
size_t digs = e / DIG_SIZE;
|
|
size_t bs = e % DIG_SIZE;
|
|
mpz_t y;
|
|
|
|
mpz_init(mrb, &y);
|
|
mpz_realloc(mrb, &y, x->sz-digs);
|
|
for (size_t i=0; i < x->sz-digs; i++)
|
|
y.p[i] = x->p[i+digs];
|
|
if (bs) {
|
|
urshift(mrb, z, &y, bs);
|
|
mpz_clear(mrb, &y);
|
|
}
|
|
else {
|
|
mpz_move(mrb, z, &y);
|
|
}
|
|
if (uzero_p(z))
|
|
z->sn = 0;
|
|
else {
|
|
z->sn = sn;
|
|
}
|
|
}
|
|
}
|
|
|
|
static void
|
|
mpz_neg(mrb_state *mrb, mpz_t *x, mpz_t *y)
|
|
{
|
|
mpz_set(mrb, x, y);
|
|
x->sn = -(y->sn);
|
|
}
|
|
|
|
/* Fast modular reduction by power of 2: z = x mod 2^e */
|
|
static void
|
|
mpz_mod_2exp(mrb_state *mrb, mpz_t *z, mpz_t *x, mrb_int e)
|
|
{
|
|
if (e <= 0) {
|
|
zero(z);
|
|
return;
|
|
}
|
|
|
|
size_t eint = e / DIG_SIZE;
|
|
size_t bs = e % DIG_SIZE;
|
|
size_t sz = x->sz;
|
|
|
|
if (eint >= sz) {
|
|
/* x < 2^e, so x mod 2^e = x */
|
|
mpz_set(mrb, z, x);
|
|
return;
|
|
}
|
|
|
|
/* Need to mask off high bits */
|
|
size_t result_sz = eint + (bs > 0 ? 1 : 0);
|
|
mpz_realloc(mrb, z, result_sz);
|
|
z->sn = x->sn;
|
|
z->sz = result_sz;
|
|
|
|
/* Copy full limbs */
|
|
for (size_t i = 0; i < eint; i++) {
|
|
z->p[i] = x->p[i];
|
|
}
|
|
|
|
/* Mask partial limb if needed */
|
|
if (bs > 0) {
|
|
mp_limb mask = (1UL << bs) - 1;
|
|
z->p[eint] = x->p[eint] & mask;
|
|
}
|
|
|
|
trim(z);
|
|
}
|
|
|
|
#define make_2comp(v,c) do { v=~(v)+(c); c=((v)==0 && (c));} while (0)
|
|
|
|
static void
|
|
mpz_and(mrb_state *mrb, mpz_t *z, mpz_t *x, mpz_t *y)
|
|
{
|
|
if (zero_p(x) || zero_p(y)) {
|
|
zero(z);
|
|
return;
|
|
}
|
|
mrb_assert(x->sz > 0 || y->sz > 0);
|
|
|
|
size_t max_sz = (x->sz > y->sz) ? x->sz : y->sz;
|
|
mpz_realloc(mrb, z, max_sz);
|
|
z->sn = (x->sn == y->sn) ? x->sn : 1;
|
|
|
|
char c1 = 1, c2 = 1, c3 = 1;
|
|
for (size_t i = 0; i < max_sz; i++) {
|
|
mp_limb xv = (i < x->sz) ? x->p[i] : 0;
|
|
mp_limb yv = (i < y->sz) ? y->p[i] : 0;
|
|
|
|
if (x->sn < 0) make_2comp(xv, c1);
|
|
if (y->sn < 0) make_2comp(yv, c2);
|
|
mp_limb zv = xv & yv;
|
|
if (z->sn < 0) make_2comp(zv, c3);
|
|
z->p[i] = zv;
|
|
}
|
|
}
|
|
|
|
static void
|
|
mpz_or(mrb_state *mrb, mpz_t *z, mpz_t *x, mpz_t *y) /* not the most efficient way to do this */
|
|
{
|
|
if (zero_p(x)) {
|
|
mpz_set(mrb, z, y);
|
|
return;
|
|
}
|
|
if (zero_p(y)) {
|
|
mpz_set(mrb, z, x);
|
|
return;
|
|
}
|
|
mrb_assert(x->sz > 0 || y->sz > 0);
|
|
|
|
size_t max_sz = (x->sz > y->sz) ? x->sz : y->sz;
|
|
mpz_realloc(mrb, z, max_sz);
|
|
z->sn = (x->sn == y->sn) ? x->sn : -1;
|
|
|
|
char c1 = 1, c2 = 1, c3 = 1;
|
|
for (size_t i = 0; i < max_sz; i++) {
|
|
mp_limb xv = (i < x->sz) ? x->p[i] : 0;
|
|
mp_limb yv = (i < y->sz) ? y->p[i] : 0;
|
|
|
|
if (x->sn < 0) make_2comp(xv, c1);
|
|
if (y->sn < 0) make_2comp(yv, c2);
|
|
mp_limb zv = xv | yv;
|
|
if (z->sn < 0) make_2comp(zv, c3);
|
|
z->p[i] = zv;
|
|
}
|
|
}
|
|
|
|
static void
|
|
mpz_xor(mrb_state *mrb, mpz_t *z, mpz_t *x, mpz_t *y) /* not the most efficient way to do this */
|
|
{
|
|
if (zero_p(x)) {
|
|
mpz_set(mrb, z, y);
|
|
return;
|
|
}
|
|
if (zero_p(y)) {
|
|
mpz_set(mrb, z, x);
|
|
return;
|
|
}
|
|
mrb_assert(x->sz > 0 || y->sz > 0);
|
|
|
|
size_t max_sz = (x->sz > y->sz) ? x->sz : y->sz;
|
|
mpz_realloc(mrb, z, max_sz);
|
|
z->sn = (x->sn == y->sn) ? 1 : -1;
|
|
|
|
char c1 = 1, c2 = 1, c3 = 1;
|
|
for (size_t i = 0; i < max_sz; i++) {
|
|
mp_limb xv = (i < x->sz) ? x->p[i] : 0;
|
|
mp_limb yv = (i < y->sz) ? y->p[i] : 0;
|
|
|
|
if (x->sn < 0) make_2comp(xv, c1);
|
|
if (y->sn < 0) make_2comp(yv, c2);
|
|
mp_limb zv = xv ^ yv;
|
|
if (z->sn < 0) make_2comp(zv, c3);
|
|
z->p[i] = zv;
|
|
}
|
|
}
|
|
|
|
static void
|
|
mpz_pow(mrb_state *mrb, mpz_t *zz, mpz_t *x, mrb_int e)
|
|
{
|
|
mpz_t t;
|
|
mrb_uint mask = 1ULL<<(sizeof(mrb_int)*8-1);
|
|
|
|
if (e==0) {
|
|
mpz_set_int(mrb, zz, 1L);
|
|
return;
|
|
}
|
|
|
|
mpz_init_set(mrb, &t, x);
|
|
for (;!(mask &e); mask>>=1)
|
|
;
|
|
mask>>=1;
|
|
for (;mask!=0; mask>>=1) {
|
|
mpz_mul(mrb, &t, &t, &t);
|
|
if (e & mask)
|
|
mpz_mul(mrb, &t, &t, x);
|
|
}
|
|
mpz_move(mrb, zz, &t);
|
|
}
|
|
|
|
static void
|
|
mpz_powm(mrb_state *mrb, mpz_t *zz, mpz_t *x, mpz_t *ex, mpz_t *n)
|
|
{
|
|
if (zero_p(ex) || uzero_p(ex)) {
|
|
mpz_set_int(mrb, zz, 1);
|
|
return;
|
|
}
|
|
|
|
if (ex->sn < 0) {
|
|
return;
|
|
}
|
|
|
|
mpz_t t, b;
|
|
mpz_init_set_int(mrb, &t, 1);
|
|
mpz_init_set(mrb, &b, x);
|
|
|
|
/* Optimize with Barrett reduction for moderate-sized moduli */
|
|
mpz_t mu, temp;
|
|
int use_barrett = (n->sz >= 2 && n->sz <= 8);
|
|
mpz_init(mrb, &temp);
|
|
if (use_barrett) {
|
|
mpz_init(mrb, &mu);
|
|
mpz_barrett_mu(mrb, &mu, n);
|
|
}
|
|
|
|
size_t len = digits(ex);
|
|
for (size_t i=0; i<len; i++) {
|
|
mp_limb e = ex->p[i];
|
|
for (size_t j=0; j<sizeof(mp_limb)*8; j++) {
|
|
if ((e & 1) == 1) {
|
|
mpz_mul(mrb, &temp, &t, &b);
|
|
if (use_barrett) {
|
|
mpz_barrett_reduce(mrb, &t, &temp, n, &mu);
|
|
}
|
|
else {
|
|
mpz_mod(mrb, &t, &temp, n);
|
|
}
|
|
}
|
|
e >>= 1;
|
|
mpz_mul(mrb, &temp, &b, &b);
|
|
if (use_barrett) {
|
|
mpz_barrett_reduce(mrb, &b, &temp, n, &mu);
|
|
}
|
|
else {
|
|
mpz_mod(mrb, &b, &temp, n);
|
|
}
|
|
}
|
|
}
|
|
|
|
mpz_clear(mrb, &temp);
|
|
if (use_barrett) {
|
|
mpz_clear(mrb, &mu);
|
|
}
|
|
mpz_move(mrb, zz, &t);
|
|
mpz_clear(mrb, &b);
|
|
}
|
|
|
|
static void
|
|
mpz_powm_i(mrb_state *mrb, mpz_t *zz, mpz_t *x, mrb_int ex, mpz_t *n)
|
|
{
|
|
if (ex == 0) {
|
|
mpz_set_int(mrb, zz, 1);
|
|
return;
|
|
}
|
|
|
|
if (ex < 0) {
|
|
return;
|
|
}
|
|
|
|
mpz_t t, b;
|
|
mpz_init_set_int(mrb, &t, 1);
|
|
mpz_init_set(mrb, &b, x);
|
|
|
|
/* Optimize with Barrett reduction for moderate-sized moduli */
|
|
mpz_t mu, temp;
|
|
int use_barrett = (n->sz >= 2 && n->sz <= 8);
|
|
mpz_init(mrb, &temp);
|
|
if (use_barrett) {
|
|
mpz_init(mrb, &mu);
|
|
mpz_barrett_mu(mrb, &mu, n);
|
|
}
|
|
|
|
while (ex > 0) {
|
|
if ((ex & 1) == 1) {
|
|
mpz_mul(mrb, &temp, &t, &b);
|
|
if (use_barrett) {
|
|
mpz_barrett_reduce(mrb, &t, &temp, n, &mu);
|
|
}
|
|
else {
|
|
mpz_mod(mrb, &t, &temp, n);
|
|
}
|
|
}
|
|
ex >>= 1;
|
|
if (ex > 0) { /* Skip final squaring when ex becomes 0 */
|
|
mpz_mul(mrb, &temp, &b, &b);
|
|
if (use_barrett) {
|
|
mpz_barrett_reduce(mrb, &b, &temp, n, &mu);
|
|
}
|
|
else {
|
|
mpz_mod(mrb, &b, &temp, n);
|
|
}
|
|
}
|
|
}
|
|
|
|
mpz_clear(mrb, &temp);
|
|
if (use_barrett) {
|
|
mpz_clear(mrb, &mu);
|
|
}
|
|
mpz_move(mrb, zz, &t);
|
|
mpz_clear(mrb, &b);
|
|
}
|
|
|
|
static void
|
|
mpz_abs(mrb_state *mrb, mpz_t *x, mpz_t *y)
|
|
{
|
|
mpz_init_set(mrb, x, y);
|
|
if (zero_p(y))
|
|
x->sn = 0;
|
|
else
|
|
x->sn = 1;
|
|
}
|
|
|
|
/* Fast GCD for single limbs using binary algorithm */
|
|
static mp_limb
|
|
limb_gcd(mp_limb a, mp_limb b)
|
|
{
|
|
if (a == 0) return b;
|
|
if (b == 0) return a;
|
|
|
|
/* Find power of 2 dividing both a and b */
|
|
int shift = 0;
|
|
while (((a | b) & 1) == 0) {
|
|
a >>= 1;
|
|
b >>= 1;
|
|
shift++;
|
|
}
|
|
|
|
/* Make a odd */
|
|
while ((a & 1) == 0) {
|
|
a >>= 1;
|
|
}
|
|
|
|
/* From here on, a is always odd */
|
|
do {
|
|
/* Make b odd */
|
|
while ((b & 1) == 0) {
|
|
b >>= 1;
|
|
}
|
|
|
|
/* Now both a and b are odd. Ensure a >= b */
|
|
if (a < b) {
|
|
mp_limb temp = a;
|
|
a = b;
|
|
b = temp;
|
|
}
|
|
|
|
/* Replace b with (b - a) */
|
|
b = b - a;
|
|
|
|
} while (b != 0);
|
|
|
|
/* Restore common factors of 2 */
|
|
return a << shift;
|
|
}
|
|
|
|
/* Count trailing zero bits in a multi-precision integer */
|
|
static size_t
|
|
mpz_trailing_zeros(mpz_t *x)
|
|
{
|
|
if (zero_p(x) || x->sz == 0) return 0;
|
|
|
|
size_t zeros = 0;
|
|
|
|
/* Count complete zero limbs */
|
|
size_t i = 0;
|
|
while (i < x->sz && x->p[i] == 0) {
|
|
zeros += DIG_SIZE;
|
|
i++;
|
|
}
|
|
|
|
/* Count trailing zeros in first non-zero limb */
|
|
if (i < x->sz) {
|
|
mp_limb limb = x->p[i];
|
|
#if (defined(__GNUC__) || __has_builtin(__builtin_ctzll))
|
|
if (sizeof(mp_limb) == sizeof(unsigned long long)) {
|
|
zeros += __builtin_ctzll(limb);
|
|
}
|
|
else if (sizeof(mp_limb) == sizeof(unsigned long)) {
|
|
zeros += __builtin_ctzl(limb);
|
|
}
|
|
else {
|
|
zeros += __builtin_ctz(limb);
|
|
}
|
|
#else
|
|
/* Fallback bit counting */
|
|
while ((limb & 1) == 0) {
|
|
limb >>= 1;
|
|
zeros++;
|
|
}
|
|
#endif
|
|
}
|
|
|
|
return zeros;
|
|
}
|
|
|
|
/* Check if a number is a power of 2 */
|
|
static int
|
|
mpz_power_of_2_p(mpz_t *x)
|
|
{
|
|
if (zero_p(x) || x->sz == 0) return 0;
|
|
|
|
/* Count non-zero limbs */
|
|
size_t non_zero_limbs = 0;
|
|
size_t non_zero_index = 0;
|
|
|
|
for (size_t i = 0; i < x->sz; i++) {
|
|
if (x->p[i] != 0) {
|
|
non_zero_limbs++;
|
|
non_zero_index = i;
|
|
if (non_zero_limbs > 1) return 0; /* More than one non-zero limb */
|
|
}
|
|
}
|
|
|
|
if (non_zero_limbs == 0) return 0; /* All zero */
|
|
if (non_zero_limbs > 1) return 0; /* Multiple non-zero limbs */
|
|
|
|
/* Check if the single non-zero limb is a power of 2 */
|
|
mp_limb limb = x->p[non_zero_index];
|
|
return (limb != 0) && ((limb & (limb - 1)) == 0);
|
|
}
|
|
|
|
/* Binary GCD algorithm (Stein's algorithm) - faster than Euclidean GCD */
|
|
static void
|
|
mpz_gcd(mrb_state *mrb, mpz_t *gg, mpz_t *aa, mpz_t *bb)
|
|
{
|
|
mpz_t a, b;
|
|
|
|
/* Handle special cases */
|
|
if (zero_p(aa)) {
|
|
mpz_abs(mrb, gg, bb);
|
|
return;
|
|
}
|
|
if (zero_p(bb)) {
|
|
mpz_abs(mrb, gg, aa);
|
|
return;
|
|
}
|
|
|
|
/* Fast path for single-limb numbers */
|
|
if (aa->sz <= 1 && bb->sz <= 1) {
|
|
mp_limb a_limb = (aa->sz == 0) ? 0 : aa->p[0];
|
|
mp_limb b_limb = (bb->sz == 0) ? 0 : bb->p[0];
|
|
mp_limb result = limb_gcd(a_limb, b_limb);
|
|
|
|
mpz_init(mrb, gg);
|
|
if (result == 0) {
|
|
gg->sn = 0;
|
|
gg->sz = 0;
|
|
}
|
|
else {
|
|
mpz_realloc(mrb, gg, 1);
|
|
gg->p[0] = result;
|
|
gg->sn = 1;
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* Fast path for powers of 2 */
|
|
if (mpz_power_of_2_p(aa)) {
|
|
size_t a_zeros = mpz_trailing_zeros(aa);
|
|
size_t b_zeros = mpz_trailing_zeros(bb);
|
|
size_t min_zeros = (a_zeros < b_zeros) ? a_zeros : b_zeros;
|
|
|
|
mpz_init_set_int(mrb, gg, 1);
|
|
mpz_mul_2exp(mrb, gg, gg, min_zeros);
|
|
return;
|
|
}
|
|
if (mpz_power_of_2_p(bb)) {
|
|
size_t a_zeros = mpz_trailing_zeros(aa);
|
|
size_t b_zeros = mpz_trailing_zeros(bb);
|
|
size_t min_zeros = (a_zeros < b_zeros) ? a_zeros : b_zeros;
|
|
|
|
mpz_init_set_int(mrb, gg, 1);
|
|
mpz_mul_2exp(mrb, gg, gg, min_zeros);
|
|
return;
|
|
}
|
|
|
|
mpz_abs(mrb, &a, aa);
|
|
mpz_abs(mrb, &b, bb);
|
|
|
|
/* Find power of 2 that divides both a and b */
|
|
size_t a_zeros = mpz_trailing_zeros(&a);
|
|
size_t b_zeros = mpz_trailing_zeros(&b);
|
|
size_t shift = (a_zeros < b_zeros) ? a_zeros : b_zeros;
|
|
|
|
/* Remove common factors of 2 */
|
|
if (shift > 0) {
|
|
mpz_div_2exp(mrb, &a, &a, shift);
|
|
mpz_div_2exp(mrb, &b, &b, shift);
|
|
}
|
|
|
|
/* Remove remaining factors of 2 from a */
|
|
if (a_zeros > shift) {
|
|
mpz_div_2exp(mrb, &a, &a, a_zeros - shift);
|
|
}
|
|
|
|
/* Remove remaining factors of 2 from b */
|
|
if (b_zeros > shift) {
|
|
mpz_div_2exp(mrb, &b, &b, b_zeros - shift);
|
|
}
|
|
|
|
/* Use Lehmer's algorithm for large multi-limb numbers (> 3 limbs) */
|
|
if (a.sz > 3 && b.sz > 3) {
|
|
/* Extract the two most significant limbs for approximation */
|
|
mp_limb a_high = a.p[a.sz - 1];
|
|
mp_limb a_low = a.p[a.sz - 2];
|
|
mp_limb b_high = b.p[b.sz - 1];
|
|
mp_limb b_low = b.p[b.sz - 2];
|
|
|
|
/* Perform Lehmer reduction on double-precision approximations */
|
|
mp_limb u0 = 1, u1 = 0, v0 = 0, v1 = 1;
|
|
|
|
while (b_high > 0) {
|
|
/* Calculate quotient using double-precision approximation */
|
|
mp_limb q;
|
|
if (a_high == b_high) {
|
|
q = (a_low >= b_low) ? 1 : 0;
|
|
}
|
|
else {
|
|
/* Approximate quotient from most significant limbs */
|
|
q = a_high / (b_high + 1);
|
|
}
|
|
|
|
if (q == 0) break;
|
|
|
|
/* Check if applying this quotient would cause overflow */
|
|
mp_limb max_limb = (mp_limb)(-1);
|
|
if (u1 > 0 && q > max_limb / u1) break;
|
|
if (v1 > 0 && q > max_limb / v1) break;
|
|
|
|
/* Update transformation matrix */
|
|
mp_limb t;
|
|
t = u0 - q * u1; u0 = u1; u1 = t;
|
|
t = v0 - q * v1; v0 = v1; v1 = t;
|
|
t = a_high - q * b_high; a_high = b_high; b_high = t;
|
|
|
|
/* Stop if coefficients get too large */
|
|
if (u1 == 0 && v1 == 0) break;
|
|
}
|
|
|
|
/* Apply the transformation if it's non-trivial */
|
|
if (u1 != 0 || v1 != 0) {
|
|
mpz_t temp_a, temp_b, u0_a, v0_b, u1_a, v1_b;
|
|
mpz_init(mrb, &temp_a);
|
|
mpz_init(mrb, &temp_b);
|
|
mpz_init_set(mrb, &u0_a, &a);
|
|
mpz_init_set(mrb, &v0_b, &b);
|
|
mpz_init_set(mrb, &u1_a, &a);
|
|
mpz_init_set(mrb, &v1_b, &b);
|
|
|
|
/* Compute u0*a, v0*b, u1*a, v1*b */
|
|
mpz_mul_int(mrb, &u0_a, u0);
|
|
mpz_mul_int(mrb, &v0_b, v0);
|
|
mpz_mul_int(mrb, &u1_a, u1);
|
|
mpz_mul_int(mrb, &v1_b, v1);
|
|
|
|
/* temp_a = u0*a + v0*b */
|
|
mpz_add(mrb, &temp_a, &u0_a, &v0_b);
|
|
|
|
/* temp_b = u1*a + v1*b */
|
|
mpz_add(mrb, &temp_b, &u1_a, &v1_b);
|
|
|
|
/* Update a and b */
|
|
mpz_set(mrb, &a, &temp_a);
|
|
mpz_set(mrb, &b, &temp_b);
|
|
|
|
mpz_clear(mrb, &temp_a);
|
|
mpz_clear(mrb, &temp_b);
|
|
mpz_clear(mrb, &u0_a);
|
|
mpz_clear(mrb, &v0_b);
|
|
mpz_clear(mrb, &u1_a);
|
|
mpz_clear(mrb, &v1_b);
|
|
|
|
/* Ensure a >= b after transformation */
|
|
if (mpz_cmp(mrb, &a, &b) < 0) {
|
|
mpz_t temp_holder = a;
|
|
a = b;
|
|
b = temp_holder;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* From here on, a is always odd */
|
|
do {
|
|
/* Make b odd efficiently */
|
|
if ((b.p[0] & 1) == 0) {
|
|
size_t b_trailing = mpz_trailing_zeros(&b);
|
|
if (b_trailing > 0) {
|
|
mpz_div_2exp(mrb, &b, &b, b_trailing);
|
|
}
|
|
}
|
|
|
|
/* Now both a and b are odd. Ensure a >= b */
|
|
if (mpz_cmp(mrb, &a, &b) < 0) {
|
|
/* In-place swap without temporary variable */
|
|
mpz_t temp_holder = a;
|
|
a = b;
|
|
b = temp_holder;
|
|
}
|
|
|
|
/* Replace a with (a - b) */
|
|
mpz_sub(mrb, &a, &a, &b);
|
|
|
|
/* Remove factors of 2 from the result if it's even */
|
|
if (a.sz > 0 && (a.p[0] & 1) == 0) {
|
|
size_t a_trailing = mpz_trailing_zeros(&a);
|
|
if (a_trailing > 0) {
|
|
mpz_div_2exp(mrb, &a, &a, a_trailing);
|
|
}
|
|
}
|
|
|
|
} while (!zero_p(&a));
|
|
|
|
/* Restore common factors of 2 */
|
|
mpz_mul_2exp(mrb, &b, &b, shift);
|
|
|
|
trim(&b);
|
|
mpz_move(mrb, gg, &b);
|
|
mpz_clear(mrb, &a);
|
|
}
|
|
|
|
static size_t
|
|
mpz_bits(const mpz_t *x)
|
|
{
|
|
if (x->sz == 0 || x->sn == 0) return 0;
|
|
|
|
size_t limb_bits = sizeof(mp_limb) * 8;
|
|
|
|
// Get the most significant limb
|
|
size_t i = x->sz - 1;
|
|
mp_limb high = x->p[i];
|
|
|
|
// Number of bits = total full limbs + significant bits in top limb
|
|
return i * limb_bits + (limb_bits - lzb(high));
|
|
}
|
|
|
|
/* Compute Barrett parameter μ = floor(2^(2k) / m) where k ≈ log₂(m) */
|
|
static void
|
|
mpz_barrett_mu(mrb_state *mrb, mpz_t *mu, mpz_t *m)
|
|
{
|
|
size_t k = mpz_bits(m);
|
|
mpz_t temp;
|
|
|
|
mpz_init_set_int(mrb, &temp, 1);
|
|
mpz_mul_2exp(mrb, &temp, &temp, 2 * k); /* temp = 2^(2k) */
|
|
mpz_mdiv(mrb, mu, &temp, m); /* mu = floor(2^(2k) / m) */
|
|
mpz_clear(mrb, &temp);
|
|
}
|
|
|
|
/* Barrett reduction: r = x mod m using precomputed μ */
|
|
static void
|
|
mpz_barrett_reduce(mrb_state *mrb, mpz_t *r, mpz_t *x, mpz_t *m, mpz_t *mu)
|
|
{
|
|
size_t k = mpz_bits(m);
|
|
|
|
/* If x < m, then x mod m = x */
|
|
if (mpz_cmp(mrb, x, m) < 0) {
|
|
mpz_set(mrb, r, x);
|
|
return;
|
|
}
|
|
|
|
mpz_t q1, q2, q3, r1, r2;
|
|
mpz_init(mrb, &q1);
|
|
mpz_init(mrb, &q2);
|
|
mpz_init(mrb, &q3);
|
|
mpz_init(mrb, &r1);
|
|
mpz_init(mrb, &r2);
|
|
|
|
/* Step 1: q1 = floor(x / 2^(k-1)) */
|
|
if (k > 1) {
|
|
mpz_div_2exp(mrb, &q1, x, k - 1);
|
|
}
|
|
else {
|
|
mpz_set(mrb, &q1, x);
|
|
}
|
|
|
|
/* Step 2: q2 = q1 * μ */
|
|
mpz_mul(mrb, &q2, &q1, mu);
|
|
|
|
/* Step 3: q3 = floor(q2 / 2^(k+1)) */
|
|
mpz_div_2exp(mrb, &q3, &q2, k + 1);
|
|
|
|
/* Step 4: r1 = x mod 2^(k+1) */
|
|
mpz_mod_2exp(mrb, &r1, x, k + 1);
|
|
|
|
/* Step 5: r2 = (q3 * m) mod 2^(k+1) */
|
|
mpz_mul(mrb, &r2, &q3, m);
|
|
mpz_mod_2exp(mrb, &r2, &r2, k + 1);
|
|
|
|
/* Step 6: r = r1 - r2 */
|
|
if (mpz_cmp(mrb, &r1, &r2) >= 0) {
|
|
mpz_sub(mrb, r, &r1, &r2);
|
|
}
|
|
else {
|
|
/* r1 < r2, so add 2^(k+1) to r1 */
|
|
mpz_t power;
|
|
mpz_init_set_int(mrb, &power, 1);
|
|
mpz_mul_2exp(mrb, &power, &power, k + 1);
|
|
mpz_add(mrb, &r1, &r1, &power);
|
|
mpz_sub(mrb, r, &r1, &r2);
|
|
mpz_clear(mrb, &power);
|
|
}
|
|
|
|
/* Step 7: Final correction - ensure 0 ≤ r < m */
|
|
while (mpz_cmp(mrb, r, m) >= 0) {
|
|
mpz_sub(mrb, r, r, m);
|
|
}
|
|
|
|
mpz_clear(mrb, &q1);
|
|
mpz_clear(mrb, &q2);
|
|
mpz_clear(mrb, &q3);
|
|
mpz_clear(mrb, &r1);
|
|
mpz_clear(mrb, &r2);
|
|
}
|
|
|
|
static void
|
|
mpz_sqrt(mrb_state *mrb, mpz_t *z, mpz_t *x)
|
|
{
|
|
mrb_assert(x->sn >= 0);
|
|
|
|
if (x->sz == 0) {
|
|
// sqrt(0) = 0
|
|
z->sn = 0;
|
|
z->sz = 0;
|
|
return;
|
|
}
|
|
|
|
// Estimate initial value: 1 << (bit_length(x) / 2)
|
|
size_t xbits = mpz_bits(x);
|
|
size_t sbit = (xbits + 1) / 2;
|
|
mpz_t s, t;
|
|
mpz_init_set_int(mrb, &s, 1);
|
|
mpz_mul_2exp(mrb, &s, &s, sbit);
|
|
|
|
mpz_init(mrb, &t);
|
|
|
|
// Iteratively refine s using Newton-Raphson method:
|
|
// s = (s + x / s) / 2
|
|
for (;;) {
|
|
mpz_mdiv(mrb, &t, x, &s); // t = x / s
|
|
mpz_add(mrb, &t, &t, &s); // t = s + x/s
|
|
mpz_div_2exp(mrb, &t, &t, 1); // t = (s + x/s) / 2
|
|
|
|
if (mpz_cmp(mrb, &t, &s) >= 0) {
|
|
// Converged: t >= s
|
|
break;
|
|
}
|
|
|
|
mpz_set(mrb, &s, &t);
|
|
}
|
|
|
|
mpz_move(mrb, z, &s);
|
|
mpz_clear(mrb, &t);
|
|
}
|
|
|
|
/* Barrett reduction for efficient modular arithmetic with repeated operations */
|
|
|
|
/* --- mruby functions --- */
|
|
/* initialize mpz_t from RBigint (not need to clear) */
|
|
static void
|
|
bint_as_mpz(struct RBigint *b, mpz_t *x)
|
|
{
|
|
x->p = RBIGINT_ARY(b);
|
|
x->sz = RBIGINT_SIZE(b);
|
|
x->sn = RBIGINT_SIGN(b);
|
|
}
|
|
|
|
static struct RBigint*
|
|
bint_new(mrb_state *mrb, mpz_t *x)
|
|
{
|
|
struct RBigint *b = MRB_OBJ_ALLOC(mrb, MRB_TT_BIGINT, mrb->integer_class);
|
|
if (x->sz <= RBIGINT_EMBED_SIZE_MAX) {
|
|
RBIGINT_SET_EMBED_SIZE(b, x->sz);
|
|
RBIGINT_SET_EMBED_SIGN(b, x->sn);
|
|
if (x->p) memcpy(RBIGINT_EMBED_ARY(b), x->p, x->sz*sizeof(mp_limb));
|
|
mpz_clear(mrb, x);
|
|
}
|
|
else {
|
|
RBIGINT_SET_HEAP(b);
|
|
b->as.heap = *x;
|
|
}
|
|
return b;
|
|
}
|
|
|
|
static struct RBigint*
|
|
bint_new_int(mrb_state *mrb, mrb_int n)
|
|
{
|
|
mpz_t x;
|
|
|
|
mpz_init_set_int(mrb, &x, n);
|
|
return bint_new(mrb, &x);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_new_int(mrb_state *mrb, mrb_int x)
|
|
{
|
|
struct RBigint *b = bint_new_int(mrb, x);
|
|
return mrb_obj_value(b);
|
|
}
|
|
|
|
#ifdef MRB_INT32
|
|
mrb_value
|
|
mrb_bint_new_int64(mrb_state *mrb, int64_t n)
|
|
{
|
|
mpz_t x;
|
|
mpz_set_int64(mrb, &x, n);
|
|
struct RBigint *b = bint_new(mrb, &x);
|
|
return mrb_obj_value(b);
|
|
}
|
|
#endif
|
|
|
|
mrb_value
|
|
mrb_bint_new_uint64(mrb_state *mrb, uint64_t x)
|
|
{
|
|
mpz_t z;
|
|
mpz_init(mrb, &z);
|
|
mpz_set_uint64(mrb, &z, x);
|
|
struct RBigint *b = bint_new(mrb ,&z);
|
|
return mrb_obj_value(b);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_new_str(mrb_state *mrb, const char *x, mrb_int len, mrb_int base)
|
|
{
|
|
mpz_t z;
|
|
|
|
int sn = 1;
|
|
if (base < 0) {
|
|
base = -base;
|
|
sn = -1;
|
|
}
|
|
mrb_assert(2 <= base && base <= 36);
|
|
mpz_init_set_str(mrb, &z, x, len, base);
|
|
if (sn < 0) {
|
|
z.sn = sn;
|
|
}
|
|
struct RBigint *b = bint_new(mrb, &z);
|
|
return mrb_obj_value(b);
|
|
}
|
|
|
|
static mrb_value
|
|
bint_norm(mrb_state *mrb, struct RBigint *b)
|
|
{
|
|
mrb_int i;
|
|
mpz_t a;
|
|
|
|
bint_as_mpz(b, &a);
|
|
if (mpz_get_int(&a, &i)) {
|
|
return mrb_int_value(mrb, i);
|
|
}
|
|
return mrb_obj_value(b);
|
|
}
|
|
|
|
void
|
|
mrb_gc_free_bint(mrb_state *mrb, struct RBasic *x)
|
|
{
|
|
struct RBigint *b = (struct RBigint*)x;
|
|
if (!RBIGINT_EMBED_P(b)) {
|
|
mpz_clear(mrb, &b->as.heap);
|
|
}
|
|
}
|
|
|
|
#ifndef MRB_NO_FLOAT
|
|
mrb_value
|
|
mrb_bint_new_float(mrb_state *mrb, mrb_float x)
|
|
{
|
|
/* x should not be NaN nor Infinity */
|
|
mrb_assert(x == x && x != x * 0.5);
|
|
|
|
if (FIXABLE_FLOAT(x)) {
|
|
return mrb_int_value(mrb, (mrb_int)x);
|
|
}
|
|
|
|
int sn;
|
|
if (x < 0.0) {
|
|
x = -x;
|
|
sn = -1;
|
|
}
|
|
else {
|
|
sn = 1;
|
|
}
|
|
if (x < 1.0) {
|
|
return mrb_fixnum_value(0);
|
|
}
|
|
|
|
mpz_t r;
|
|
mpz_init(mrb, &r);
|
|
r.sn = sn;
|
|
|
|
mrb_float b = (double)DIG_BASE;
|
|
mrb_float bi = 1.0 / b;
|
|
size_t rn;
|
|
|
|
for (rn = 1; x >= b; rn++)
|
|
x *= bi;
|
|
|
|
mpz_realloc(mrb, &r, rn);
|
|
mp_limb *rp = r.p;
|
|
for (size_t i=rn-1;;i--) {
|
|
mp_limb f = LOW((mp_limb)x);
|
|
x -= f;
|
|
mrb_assert(x < 1.0);
|
|
rp[i] = f;
|
|
if (i == 0) break;
|
|
}
|
|
return bint_norm(mrb, bint_new(mrb, &r));
|
|
}
|
|
|
|
mrb_float
|
|
mrb_bint_as_float(mrb_state *mrb, mrb_value self)
|
|
{
|
|
mpz_t m;
|
|
bint_as_mpz(RBIGINT(self), &m);
|
|
|
|
mp_limb *d = m.p + m.sz;
|
|
mrb_float val = 0;
|
|
|
|
while (d-- > m.p) {
|
|
val = val * DIG_BASE + *d;
|
|
}
|
|
|
|
if (m.sn < 0) {
|
|
val = -val;
|
|
}
|
|
return val;
|
|
}
|
|
#endif
|
|
|
|
mrb_value
|
|
mrb_as_bint(mrb_state *mrb, mrb_value x)
|
|
{
|
|
if (mrb_bigint_p(x)) return x;
|
|
return mrb_bint_new_int(mrb, mrb_as_int(mrb, x));
|
|
}
|
|
|
|
mrb_int
|
|
mrb_bint_as_int(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t m;
|
|
mrb_int i;
|
|
|
|
bint_as_mpz(RBIGINT(x), &m);
|
|
if (!mpz_get_int(&m, &i)) {
|
|
mrb_raise(mrb, E_RANGE_ERROR, "integer out of range");
|
|
}
|
|
return i;
|
|
}
|
|
|
|
#ifdef MRB_INT32
|
|
int64_t
|
|
mrb_bint_as_int64(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t m;
|
|
bint_as_mpz(RBIGINT(x), &m);
|
|
|
|
uint64_t u = 0;
|
|
size_t len = digits(&m);
|
|
|
|
if (len*sizeof(mp_limb) > sizeof(uint64_t)) {
|
|
out_of_range:
|
|
mrb_raise(mrb, E_RANGE_ERROR, "integer out of range");
|
|
}
|
|
for (size_t i=len-1; ; i--) {
|
|
u <<= DIG_SIZE;
|
|
u |= m.p[i];
|
|
if (i==0) break;
|
|
}
|
|
if (u > INT64_MAX) goto out_of_range;
|
|
if (m.sn < 0) return -(int64_t)u;
|
|
return (int64_t)u;
|
|
}
|
|
#endif
|
|
|
|
uint64_t
|
|
mrb_bint_as_uint64(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t m;
|
|
bint_as_mpz(RBIGINT(x), &m);
|
|
|
|
uint64_t u = 0;
|
|
size_t len = digits(&m);
|
|
|
|
if (m.sn < 0 || len*sizeof(mp_limb) > sizeof(uint64_t)) {
|
|
mrb_raise(mrb, E_RANGE_ERROR, "integer out of range");
|
|
}
|
|
for (size_t i=len-1; ; i--) {
|
|
u <<= DIG_SIZE;
|
|
u |= m.p[i];
|
|
if (i==0) break;
|
|
}
|
|
return u;
|
|
}
|
|
|
|
static mrb_bool
|
|
int_fit_limb_p(mrb_int i)
|
|
{
|
|
#if DIG_SIZE == 32
|
|
# ifdef MRB_INT64
|
|
// if mp_limb is int32_t
|
|
return (i > INT32_MIN && i <= INT32_MAX);
|
|
# else
|
|
// if mp_limb is also int32_t, it always fits
|
|
return TRUE;
|
|
# endif
|
|
#else /* if DIG_SIZE == 16 */
|
|
// if mp_limb is int16_t
|
|
return (i > INT16_MIN && i <= INT16_MAX);
|
|
#endif
|
|
}
|
|
|
|
/* unnormalize version of mrb_bint_add */
|
|
mrb_value
|
|
mrb_bint_add_n(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b, z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (mrb_integer_p(y)) {
|
|
mrb_int n = mrb_integer(y);
|
|
if (int_fit_limb_p(n)) {
|
|
mpz_init_set(mrb, &z, &a);
|
|
if ((n > 0) ^ (z.sn > 0)) {
|
|
mpz_sub_int(mrb, &z, n<0 ? -n : n);
|
|
}
|
|
else {
|
|
mpz_add_int(mrb, &z, n<0 ? -n : n);
|
|
}
|
|
struct RBigint *v = bint_new(mrb, &z);
|
|
return mrb_obj_value(v);
|
|
}
|
|
}
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
mpz_init(mrb, &z);
|
|
mpz_add(mrb, &z, &a, &b);
|
|
struct RBigint *v = bint_new(mrb, &z);
|
|
return mrb_obj_value(v);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_add(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
#ifndef MRB_NO_FLOAT
|
|
if (mrb_float_p(y)) {
|
|
mrb_float v1 = mrb_bint_as_float(mrb, x);
|
|
mrb_float v2 = mrb_float(y);
|
|
return mrb_float_value(mrb,v1+v2);
|
|
}
|
|
#endif
|
|
x = mrb_bint_add_n(mrb, x, y);
|
|
return bint_norm(mrb, RBIGINT(x));
|
|
}
|
|
|
|
/* unnormalize version of mrb_bint_sub */
|
|
mrb_value
|
|
mrb_bint_sub_n(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b, z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (mrb_integer_p(y)) {
|
|
mrb_int n = mrb_integer(y);
|
|
if (int_fit_limb_p(n)) {
|
|
mpz_init_set(mrb, &z, &a);
|
|
if ((n > 0) ^ (z.sn > 0)) {
|
|
mpz_add_int(mrb, &z, n<0 ? -n : n);
|
|
}
|
|
else {
|
|
mpz_sub_int(mrb, &z, n<0 ? -n : n);
|
|
}
|
|
struct RBigint *v = bint_new(mrb, &z);
|
|
return mrb_obj_value(v);
|
|
}
|
|
}
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
mpz_init(mrb, &z);
|
|
mpz_sub(mrb, &z, &a, &b);
|
|
struct RBigint *v = bint_new(mrb, &z);
|
|
return mrb_obj_value(v);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_sub(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
#ifndef MRB_NO_FLOAT
|
|
if (mrb_float_p(y)) {
|
|
mrb_float v1 = mrb_bint_as_float(mrb, x);
|
|
mrb_float v2 = mrb_float(y);
|
|
return mrb_float_value(mrb,v1-v2);
|
|
}
|
|
#endif
|
|
x = mrb_bint_sub_n(mrb, x, y);
|
|
return bint_norm(mrb, RBIGINT(x));
|
|
}
|
|
|
|
static struct RBigint*
|
|
bint_mul(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b, z;
|
|
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
mpz_init(mrb, &z);
|
|
mpz_mul(mrb, &z, &a, &b);
|
|
return bint_new(mrb, &z);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_mul(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
if (mrb_integer_p(y)) {
|
|
if (mrb_integer(y) == 0) return mrb_fixnum_value(0);
|
|
if (mrb_integer(y) == 1) return bint_norm(mrb, RBIGINT(x));
|
|
}
|
|
#ifndef MRB_NO_FLOAT
|
|
if (mrb_float_p(y)) {
|
|
mrb_float v1 = mrb_bint_as_float(mrb, x);
|
|
mrb_float v2 = mrb_float(y);
|
|
return mrb_float_value(mrb,v1*v2);
|
|
}
|
|
#endif
|
|
return bint_norm(mrb, bint_mul(mrb, x, y));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_mul_n(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
struct RBigint *b = bint_mul(mrb, x, y);
|
|
return mrb_obj_value(b);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_div(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
if (mrb_integer_p(y)) {
|
|
if (mrb_integer(y) == 0) mrb_int_zerodiv(mrb);
|
|
if (mrb_integer(y) == 1) return bint_norm(mrb, RBIGINT(x));
|
|
}
|
|
#ifndef MRB_NO_FLOAT
|
|
if (mrb_float_p(y)) {
|
|
mrb_float v1 = mrb_bint_as_float(mrb, x);
|
|
mrb_float v2 = mrb_float(y);
|
|
return mrb_float_value(mrb,v1*v2);
|
|
}
|
|
#endif
|
|
mpz_t a, b, z;
|
|
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&b) || uzero_p(&b)) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &z);
|
|
mpz_mdiv(mrb, &z, &a, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_add_ii(mrb_state *mrb, mrb_int x, mrb_int y)
|
|
{
|
|
mpz_t a, b, z;
|
|
|
|
mpz_init_set_int(mrb, &a, x);
|
|
mpz_init_set_int(mrb, &b, y);
|
|
mpz_init(mrb, &z);
|
|
mpz_add(mrb, &z, &a, &b);
|
|
mpz_clear(mrb, &a);
|
|
mpz_clear(mrb, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_sub_ii(mrb_state *mrb, mrb_int x, mrb_int y)
|
|
{
|
|
mpz_t a, b, z;
|
|
|
|
mpz_init_set_int(mrb, &a, x);
|
|
mpz_init_set_int(mrb, &b, y);
|
|
mpz_init(mrb, &z);
|
|
mpz_sub(mrb, &z, &a, &b);
|
|
mpz_clear(mrb, &a);
|
|
mpz_clear(mrb, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_mul_ii(mrb_state *mrb, mrb_int x, mrb_int y)
|
|
{
|
|
mpz_t a, b, z;
|
|
|
|
mpz_init_set_int(mrb, &a, x);
|
|
mpz_init_set_int(mrb, &b, y);
|
|
mpz_init(mrb, &z);
|
|
mpz_mul(mrb, &z, &a, &b);
|
|
mpz_clear(mrb, &a);
|
|
mpz_clear(mrb, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_mod(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
#ifndef MRB_NO_FLOAT
|
|
if (mrb_float_p(y)) {
|
|
mrb_float v1 = mrb_bint_as_float(mrb, x);
|
|
mrb_float v2 = mrb_float(y);
|
|
return mrb_float_value(mrb, fmod(v1, v2));
|
|
}
|
|
#endif
|
|
if (mrb_integer_p(y) && mrb_integer(y) == 0) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
mpz_t a, b, z;
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&b) || uzero_p(&b)) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &z);
|
|
mpz_mmod(mrb, &z, &a, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_rem(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
/* called from mrbgems/mruby-numeric-ext/src/numeric_ext.c */
|
|
/* y should not be float */
|
|
if (mrb_integer_p(y) && mrb_integer(y) == 0) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
mpz_t a, b, z;
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&b) || uzero_p(&b)) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &z);
|
|
mpz_mod(mrb, &z, &a, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_divmod(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
/* called from src/numeric.c */
|
|
/* y should not be float */
|
|
if (mrb_integer_p(y) && mrb_integer(y) == 0) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
y = mrb_as_bint(mrb, y);
|
|
mpz_t a, b, c, d;
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&b) || uzero_p(&b)) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &c);
|
|
mpz_init(mrb, &d);
|
|
mpz_mdivmod(mrb, &c, &d, &a, &b);
|
|
return mrb_assoc_new(mrb, bint_norm(mrb, bint_new(mrb, &c)), bint_norm(mrb, bint_new(mrb, &d)));
|
|
}
|
|
|
|
mrb_int
|
|
mrb_bint_cmp(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
#ifndef MRB_NO_FLOAT
|
|
if (mrb_float_p(y)) {
|
|
mrb_float v1 = mrb_bint_as_float(mrb, x);
|
|
mrb_float v2 = mrb_float(y);
|
|
if (v1 == v2) return 0;
|
|
if (v1 > v2) return 1;
|
|
return -1;
|
|
}
|
|
#endif
|
|
mpz_t a;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (!mrb_bigint_p(y)) {
|
|
if (!mrb_integer_p(y)) return -2; /* type mismatch */
|
|
|
|
mrb_int i1, i2 = mrb_integer(y);
|
|
if (mpz_get_int(&a, &i1)) {
|
|
if (i1 == i2) return 0;
|
|
if (i1 > i2) return 1;
|
|
return -1;
|
|
}
|
|
if (a.sn > 0) return 1;
|
|
return -1;
|
|
}
|
|
mpz_t b;
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
return mpz_cmp(mrb, &a, &b);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_pow(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
switch (mrb_type(y)) {
|
|
case MRB_TT_INTEGER:
|
|
break;
|
|
case MRB_TT_BIGINT:
|
|
mrb_raise(mrb, E_TYPE_ERROR, "too big power");
|
|
default:
|
|
mrb_raisef(mrb, E_TYPE_ERROR, "%Y cannot be convert to integer", y);
|
|
}
|
|
|
|
mpz_t z;
|
|
mpz_init(mrb, &z);
|
|
mpz_pow(mrb, &z, &a, mrb_integer(y));
|
|
|
|
struct RBigint *b = bint_new(mrb, &z);
|
|
return mrb_obj_value(b);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_powm(mrb_state *mrb, mrb_value x, mrb_value exp, mrb_value mod)
|
|
{
|
|
mpz_t a, b, c, z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (mrb_integer_p(mod)) {
|
|
mrb_int m = mrb_integer(mod);
|
|
if (m == 0) mrb_int_zerodiv(mrb);
|
|
mpz_init_set_int(mrb, &c, m);
|
|
}
|
|
else {
|
|
mod = mrb_as_bint(mrb, mod);
|
|
bint_as_mpz(RBIGINT(mod), &c);
|
|
if (zero_p(&c) || uzero_p(&c)) {
|
|
mrb_int_zerodiv(mrb);
|
|
}
|
|
}
|
|
mpz_init(mrb, &z);
|
|
if (mrb_bigint_p(exp)) {
|
|
bint_as_mpz(RBIGINT(exp), &b);
|
|
if (b.sn < 0) goto raise;
|
|
mpz_powm(mrb, &z, &a, &b, &c);
|
|
}
|
|
else {
|
|
mrb_int e = mrb_integer(exp);
|
|
if (e < 0) goto raise;
|
|
mpz_powm_i(mrb, &z, &a, e, &c);
|
|
}
|
|
if (mrb_integer_p(mod)) mpz_clear(mrb, &c);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
|
|
raise:
|
|
if (mrb_integer_p(mod)) mpz_clear(mrb, &c);
|
|
mrb_raise(mrb, E_ARGUMENT_ERROR, "int.pow(n,m): n must be positive");
|
|
/* not reached */
|
|
return mrb_nil_value();
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_to_s(mrb_state *mrb, mrb_value x, mrb_int base)
|
|
{
|
|
mpz_t a;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (zero_p(&a) || uzero_p(&a)) {
|
|
return mrb_str_new_lit(mrb, "0");
|
|
}
|
|
size_t len = mpz_sizeinbase(&a, (int)base);
|
|
if (sizeof(size_t) >= sizeof(mrb_int) && MRB_INT_MAX-2 < len) {
|
|
mrb_raise(mrb, E_ARGUMENT_ERROR, "too long string from Integer");
|
|
}
|
|
mrb_value str = mrb_str_new(mrb, NULL, len+2);
|
|
mpz_get_str(mrb, RSTRING_PTR(str), len, base, &a);
|
|
RSTR_SET_LEN(RSTRING(str), strlen(RSTRING_PTR(str)));
|
|
return str;
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_and(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b, c;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (mrb_integer_p(y)) {
|
|
mrb_int z = mrb_integer(y);
|
|
if (z == 0) return mrb_fixnum_value(0);
|
|
if (z > 0 && (mp_dbl_limb)z < DIG_BASE) {
|
|
z &= a.p[0];
|
|
return mrb_int_value(mrb, z);
|
|
}
|
|
if (z == -1) return x;
|
|
}
|
|
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&a) || zero_p(&b)) return mrb_fixnum_value(0);
|
|
mpz_init(mrb, &c);
|
|
mpz_and(mrb, &c, &a, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &c));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_or(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b, c;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (mrb_integer_p(y)) {
|
|
mrb_int z = mrb_integer(y);
|
|
if (z == 0) return x;
|
|
if (z == -1) return y;
|
|
}
|
|
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&a)) return y;
|
|
if (zero_p(&b)) return x;
|
|
mpz_init(mrb, &c);
|
|
mpz_or(mrb, &c, &b, &a);
|
|
return bint_norm(mrb, bint_new(mrb, &c));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_xor(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b, c;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (mrb_integer_p(y) && a.sn > 0) {
|
|
mrb_int z = mrb_integer(y);
|
|
if (z == 0) return x;
|
|
if (0 < z && (mp_dbl_limb)z < DIG_BASE) {
|
|
mpz_init_set(mrb, &c, &a);
|
|
c.p[0] ^= z;
|
|
return bint_norm(mrb, bint_new(mrb, &c));
|
|
}
|
|
}
|
|
y = mrb_as_bint(mrb, y);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
if (zero_p(&a)) return y;
|
|
if (zero_p(&b)) return x;
|
|
mpz_init(mrb, &c);
|
|
mpz_xor(mrb, &c, &a, &b);
|
|
return bint_norm(mrb, bint_new(mrb, &c));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_neg(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t a, b;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &b);
|
|
mpz_neg(mrb, &b, &a);
|
|
struct RBigint *b2 = bint_new(mrb, &b);
|
|
/* no normalization */
|
|
return mrb_obj_value(b2);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_rev(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t a, b;
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &b);
|
|
mpz_neg(mrb, &b, &a);
|
|
mpz_sub_int(mrb, &b, 1);
|
|
return bint_norm(mrb, bint_new(mrb, &b));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_lshift(mrb_state *mrb, mrb_value x, mrb_int width)
|
|
{
|
|
mpz_t a, z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &z);
|
|
if (width < 0) {
|
|
mpz_div_2exp(mrb, &z, &a, -width);
|
|
}
|
|
else {
|
|
mpz_mul_2exp(mrb, &z, &a, width);
|
|
}
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_rshift(mrb_state *mrb, mrb_value x, mrb_int width)
|
|
{
|
|
mpz_t a, z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &z);
|
|
if (width < 0) {
|
|
mpz_mul_2exp(mrb, &z, &a, -width);
|
|
}
|
|
else {
|
|
mpz_div_2exp(mrb, &z, &a, width);
|
|
}
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
void
|
|
mrb_bint_copy(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t a, b;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
mpz_init_set(mrb, &a, &b);
|
|
}
|
|
|
|
size_t
|
|
mrb_bint_memsize(mrb_value x)
|
|
{
|
|
mpz_t z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &z);
|
|
return z.sz * sizeof(mp_limb);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_sqrt(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t a;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
if (a.sn < 0) {
|
|
mrb_raise(mrb, E_ARGUMENT_ERROR, "square root of negative number");
|
|
}
|
|
|
|
mpz_t z;
|
|
mpz_init(mrb, &z);
|
|
mpz_sqrt(mrb, &z, &a);
|
|
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_int
|
|
mrb_bint_sign(mrb_state *mrb, mrb_value bint)
|
|
{
|
|
return RBIGINT_SIGN(RBIGINT(bint));
|
|
}
|
|
|
|
mrb_int
|
|
mrb_bint_size(mrb_state *mrb, mrb_value bint)
|
|
{
|
|
mpz_t z;
|
|
bint_as_mpz(RBIGINT(bint), &z);
|
|
return z.sz * sizeof(mp_limb);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_from_bytes(mrb_state *mrb, const uint8_t *bytes, mrb_int len)
|
|
{
|
|
mpz_t z;
|
|
mpz_init(mrb, &z);
|
|
size_t limb_len = (len + sizeof(mp_limb) - 1) / sizeof(mp_limb);
|
|
mpz_realloc(mrb, &z, limb_len);
|
|
memcpy(z.p, bytes, len);
|
|
z.sn = (len > 0) ? 1 : 0;
|
|
z.sz = limb_len;
|
|
trim(&z);
|
|
return bint_norm(mrb, bint_new(mrb, &z));
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_hash(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &z);
|
|
uint32_t hash = mrb_byte_hash((uint8_t*)z.p, z.sz*sizeof(mp_limb));
|
|
hash = mrb_byte_hash_step((uint8_t*)&z.sn, sizeof(z.sn), hash);
|
|
return mrb_int_value(mrb, hash);
|
|
}
|
|
|
|
/* to be used only from mruby-sprintf */
|
|
mrb_value
|
|
mrb_bint_2comp(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t a, z;
|
|
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_init(mrb, &z);
|
|
mrb_assert(a.sn < 0);
|
|
size_t size = a.sz;
|
|
mpz_realloc(mrb, &z, size);
|
|
mp_limb *ds = a.p;
|
|
mp_limb *dd = z.p;
|
|
char carry = 1;
|
|
for (size_t i=0; i<size; i++) {
|
|
mp_limb xv = ds[i];
|
|
make_2comp(xv, carry);
|
|
dd[i] = xv;
|
|
}
|
|
z.sn = 1;
|
|
|
|
struct RBigint *b2 = bint_new(mrb, &z);
|
|
return mrb_obj_value(b2);
|
|
}
|
|
|
|
#ifdef MRB_USE_RATIONAL
|
|
void
|
|
mrb_bint_reduce(mrb_state *mrb, mrb_value *xp, mrb_value *yp)
|
|
{
|
|
mpz_t r, x, y, a, b;
|
|
mpz_init(mrb, &r);
|
|
mpz_init(mrb, &a); mpz_init(mrb, &b);
|
|
|
|
bint_as_mpz(RBIGINT(*xp), &x);
|
|
bint_as_mpz(RBIGINT(*yp), &y);
|
|
|
|
mpz_gcd(mrb, &r, &x, &y);
|
|
|
|
mpz_mdiv(mrb, &a, &x, &r);
|
|
mpz_mdiv(mrb, &b, &y, &r);
|
|
|
|
mpz_clear(mrb, &r);
|
|
|
|
struct RBigint *b1 = bint_new(mrb, &a);
|
|
struct RBigint *b2 = bint_new(mrb, &b);
|
|
*xp = mrb_obj_value(b1);
|
|
*yp = mrb_obj_value(b2);
|
|
}
|
|
#endif
|
|
|
|
mrb_value
|
|
mrb_bint_gcd(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t r, a, b;
|
|
|
|
mpz_init(mrb, &r);
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
bint_as_mpz(RBIGINT(y), &b);
|
|
|
|
mpz_gcd(mrb, &r, &a, &b);
|
|
|
|
struct RBigint *result = bint_new(mrb, &r);
|
|
mpz_clear(mrb, &r);
|
|
return bint_norm(mrb, result);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_lcm(mrb_state *mrb, mrb_value x, mrb_value y)
|
|
{
|
|
mpz_t gcd_val, x_mpz, y_mpz, abs_x, abs_y, product, result_mpz;
|
|
mrb_value zero = mrb_bint_new_int(mrb, 0);
|
|
|
|
if (mrb_bint_cmp(mrb, x, zero) == 0 || mrb_bint_cmp(mrb, y, zero) == 0) {
|
|
return zero;
|
|
}
|
|
|
|
mpz_init(mrb, &gcd_val);
|
|
mpz_init(mrb, &abs_x);
|
|
mpz_init(mrb, &abs_y);
|
|
mpz_init(mrb, &product);
|
|
mpz_init(mrb, &result_mpz);
|
|
|
|
bint_as_mpz(RBIGINT(x), &x_mpz);
|
|
bint_as_mpz(RBIGINT(y), &y_mpz);
|
|
|
|
mpz_abs(mrb, &abs_x, &x_mpz);
|
|
mpz_abs(mrb, &abs_y, &y_mpz);
|
|
|
|
mpz_gcd(mrb, &gcd_val, &abs_x, &abs_y);
|
|
mpz_mul(mrb, &product, &abs_x, &abs_y);
|
|
mpz_mdiv(mrb, &result_mpz, &product, &gcd_val);
|
|
|
|
mpz_clear(mrb, &gcd_val);
|
|
mpz_clear(mrb, &abs_x);
|
|
mpz_clear(mrb, &abs_y);
|
|
mpz_clear(mrb, &product);
|
|
|
|
struct RBigint *result = bint_new(mrb, &result_mpz);
|
|
mpz_clear(mrb, &result_mpz);
|
|
return mrb_obj_value(result);
|
|
}
|
|
|
|
mrb_value
|
|
mrb_bint_abs(mrb_state *mrb, mrb_value x)
|
|
{
|
|
mpz_t a, result_mpz;
|
|
|
|
mpz_init(mrb, &result_mpz);
|
|
bint_as_mpz(RBIGINT(x), &a);
|
|
mpz_abs(mrb, &result_mpz, &a);
|
|
|
|
struct RBigint *result = bint_new(mrb, &result_mpz);
|
|
mpz_clear(mrb, &result_mpz);
|
|
return mrb_obj_value(result);
|
|
}
|