ikarus/src/ikarus-numerics.c

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/*
* Ikarus Scheme -- A compiler for R6RS Scheme.
* Copyright (C) 2006,2007,2008 Abdulaziz Ghuloum
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 3 as
* published by the Free Software Foundation.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
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#include "ikarus-data.h"
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#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <gmp.h>
#define bnfst_limb_count(x) \
(((unsigned long int)(x)) >> bignum_length_shift)
#define bnfst_negative(x) \
(((unsigned long int)(x)) & bignum_sign_mask)
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#define most_positive_fixnum \
(((unsigned long int)-1) >> (fx_shift+1))
#define most_negative_fixnum (most_positive_fixnum+1)
// #define most_positive_fixnum 0x1FFFFFFF
// #define most_negative_fixnum 0x20000000
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#define max_digits_per_limb ((wordsize==4)?10:20)
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#ifdef NDEBUG
#define verify_bignum(x,caller) (x)
#else
static ikptr
verify_bignum(ikptr x, char* caller){
if(tagof(x) != vector_tag){
fprintf(stderr, "Error in (%s) invalid primary tag 0x%016lx\n", caller, x);
exit(-1);
}
ikptr fst = ref(x, -vector_tag);
long int limb_count = ((unsigned long int) fst) >> bignum_length_shift;
if(limb_count <= 0){
fprintf(stderr,
"Error in (%s) invalid limb count in fst=0x%016lx\n",
caller, (long int)fst);
exit(-1);
}
int pos;
if((long int)fst & bignum_sign_mask){
pos = 0;
} else {
pos = 1;
}
mp_limb_t last_limb =
(mp_limb_t) ref(x, off_bignum_data + (limb_count - 1) * wordsize);
if(last_limb == 0){
fprintf(stderr,
"Error in (%s) invalid last limb = 0x%016lx", caller, last_limb);
exit(-1);
}
if(limb_count == 1){
if(pos){
if(last_limb <= most_positive_fixnum){
fprintf(stderr,
"Error in (%s) should be a positive fixnum: 0x%016lx\n",
caller, last_limb);
exit(-1);
}
} else {
if(last_limb <= most_negative_fixnum){
fprintf(stderr,
"Error in (%s) should be a negative fixnum: 0x%016lx\n",
caller, last_limb);
exit(-1);
}
}
}
/* ok */
return x;
}
#endif
#define BN(x) verify_bignum(x,"BN")
#if 0
ikptr
ikrt_isbignum(ikptr x){
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if(tagof(x) == vector_tag){
ikptr fst = ref(x, -vector_tag);
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if (bignum_tag == (bignum_mask & (int)fst)){
return true_object;
}
}
return false_object;
}
#endif
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ikptr
ikrt_positive_bn(ikptr x){
ikptr fst = ref(x, -vector_tag);
if(bnfst_negative(fst)){
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return false_object;
} else {
return true_object;
}
}
ikptr
ikrt_even_bn(ikptr x){
long int fst = (long int)ref(x, wordsize-vector_tag);
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if(fst & 1){
return false_object;
} else {
return true_object;
}
}
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ikptr
ikrt_fxfxplus(ikptr x, ikptr y, ikpcb* pcb){
long int n1 = unfix(x);
long int n2 = unfix(y);
long int r = n1 + n2;
ikptr q = fix(r);
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if(r == unfix(q)){
return q;
}
else {
ikptr bn = ik_safe_alloc(pcb, align(disp_bignum_data + wordsize));
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if(r > 0){
ref(bn, 0) = (ikptr)(bignum_tag | (1 << bignum_length_shift));
ref(bn, disp_bignum_data) = (ikptr)r;
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}
else {
ref(bn, 0) =
(ikptr)(bignum_tag |
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(1 << bignum_length_shift) |
(1 << bignum_sign_shift));
ref(bn, disp_bignum_data) = (ikptr)-r;
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}
return verify_bignum(bn+vector_tag, "fxfx+");
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}
}
ikptr
ikrt_fxbnplus(ikptr x, ikptr y, ikpcb* pcb){
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if(x == 0){ return y ; }
ikptr fst = ref(y, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
long int intx = unfix(x);
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if(intx > 0){
if(!bnfst_negative(fst)){
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/* positive fx + positive bn = even bigger positive */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(limb_count+1)*wordsize));
pcb->root0 = 0;
mp_limb_t carry =
mpn_add_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
intx);
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if(carry){
ref(r, disp_bignum_data + limb_count*wordsize) = (ikptr)1;
ref(r, 0) = (ikptr)
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(((limb_count + 1) << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn+1");
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} else {
ref(r, 0) = (ikptr)
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((limb_count << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn+2");
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}
}
else {
/* positive fx + negative bn = smaller negative bn */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+limb_count*wordsize));
pcb->root0 = 0;
mp_limb_t borrow =
mpn_sub_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
intx);
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if(borrow){
fprintf(stderr, "Error: BUG in borrow1 %ld\n", borrow);
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exit(-1);
}
long int result_size =
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(ref(r, disp_bignum_data + (limb_count-1)*wordsize))
? limb_count
: (limb_count - 1);
if(result_size == 0){
return 0;
}
if(result_size == 1){
mp_limb_t last =
(mp_limb_t) ref(r, disp_bignum_data + (result_size-1)*wordsize);
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if(last <= most_negative_fixnum){
return fix(-(long int)last);
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}
}
ref(r, 0) = (ikptr)
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((result_size << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn+3");
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}
}
else {
if(! bnfst_negative(fst)){
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/* negative fx + positive bn = smaller positive */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+limb_count*wordsize));
pcb->root0 = 0;
mp_limb_t borrow =
mpn_sub_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
- intx);
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if(borrow){
fprintf(stderr, "Error: BUG in borrow2\n");
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exit(-1);
}
long int result_size =
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(ref(r, disp_bignum_data + (limb_count-1)*wordsize) == 0)
? (limb_count - 1)
: limb_count;
if(result_size == 0){
return 0;
}
if(result_size == 1){
mp_limb_t last =
(mp_limb_t) ref(r, disp_bignum_data + (result_size-1)*wordsize);
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if(last <= most_positive_fixnum){
return fix((long int)last);
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}
}
ref(r, 0) = (ikptr)
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((result_size << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn+4");
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} else {
/* negative fx + negative bn = larger negative */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(limb_count+1)*wordsize));
pcb->root0 = 0;
mp_limb_t carry =
mpn_add_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
-intx);
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if(carry){
ref(r, disp_bignum_data + limb_count*wordsize) = (ikptr)1;
ref(r, 0) = (ikptr)
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(((limb_count + 1) << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn+5");
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} else {
ref(r, 0) = (ikptr)
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((limb_count << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn+5");
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}
}
}
}
ikptr
ikrt_bnbnplus(ikptr x, ikptr y, ikpcb* pcb){
unsigned long int xfst = (unsigned long int)ref(x, -vector_tag);
unsigned long int yfst = (unsigned long int)ref(y, -vector_tag);
long int xsign = xfst & bignum_sign_mask;
long int ysign = yfst & bignum_sign_mask;
long int xlimbs = xfst >> bignum_length_shift;
long int ylimbs = yfst >> bignum_length_shift;
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if(xsign == ysign){
long int n1,n2;
ikptr s1,s2;
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if(xlimbs > ylimbs){
n1 = xlimbs; n2 = ylimbs; s1 = x; s2 = y;
} else {
n1 = ylimbs; n2 = xlimbs; s1 = y; s2 = x;
}
pcb->root0 = &s1;
pcb->root1 = &s2;
ikptr res = ik_safe_alloc(pcb, align(disp_bignum_data + (n1+1)*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t carry =
mpn_add((mp_limb_t*)(long)(res+disp_bignum_data),
(mp_limb_t*)(long)(s1-vector_tag+disp_bignum_data),
n1,
(mp_limb_t*)(long)(s2-vector_tag+disp_bignum_data),
n2);
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if(carry){
ref(res, disp_vector_data + xlimbs*wordsize) = (ikptr)1;
ref(res, 0) = (ikptr)
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(((n1+1) << bignum_length_shift) |
xsign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn+1");
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} else {
ref(res, 0) = (ikptr)
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((n1 << bignum_length_shift) |
xsign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn+2");
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}
}
else {
ikptr s1=x, s2=y;
long int n1=xlimbs, n2=ylimbs;
long int result_sign = xsign;
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while((xlimbs == ylimbs) &&
(ref(x, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize) ==
ref(y, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize))){
xlimbs -= 1;
ylimbs -= 1;
if(xlimbs == 0){ return 0; }
}
/* |x| != |y| */
if(xlimbs <= ylimbs){
if(xlimbs == ylimbs){
if((ref(y, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize) >
ref(x, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize))){
s1 = y; n1 = ylimbs;
s2 = x; n2 = xlimbs;
result_sign = ysign;
}
} else {
s1 = y; n1 = ylimbs;
s2 = x; n2 = xlimbs;
result_sign = ysign;
}
}
/* |s1| > |s2| */
pcb->root0 = &s1;
pcb->root1 = &s2;
ikptr res = ik_safe_alloc(pcb, align(disp_bignum_data + n1 * wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t burrow =
mpn_sub((mp_limb_t*)(long)(res + disp_bignum_data),
(mp_limb_t*)(long)(s1 - vector_tag + disp_bignum_data),
n1,
(mp_limb_t*)(long)(s2 - vector_tag + disp_bignum_data),
n2);
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if(burrow){
fprintf(stderr, "BUG: Burrow error in bnbn+\n");
exit(-1);
}
long int len = n1;
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while(ref(res, disp_bignum_data + (len-1)*wordsize) == 0){
len--;
if(len == 0){
return 0;
}
}
if(result_sign == 0){
/* positive result */
if(len == 1){
mp_limb_t fst_limb = (mp_limb_t) ref(res, disp_bignum_data);
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if(fst_limb <= most_positive_fixnum){
return fix((long int)fst_limb);
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}
}
ref(res, 0) = (ikptr)
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((len << bignum_length_shift) |
result_sign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn+3");
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} else {
/* negative result */
if(len == 1){
mp_limb_t fst_limb = (mp_limb_t) ref(res, disp_bignum_data);
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if(fst_limb <= most_negative_fixnum){
return fix(-(long int)fst_limb);
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}
}
ref(res, 0) = (ikptr)
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((len << bignum_length_shift) |
result_sign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn+4");
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}
}
}
ikptr
ikrt_fxfxminus(ikptr x, ikptr y, ikpcb* pcb){
long int n1 = unfix(x);
long int n2 = unfix(y);
long int r = n1 - n2;
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if(r >= 0){
if(((unsigned long int)r) <= most_positive_fixnum){
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return fix(r);
} else {
ikptr bn = ik_safe_alloc(pcb, align(disp_bignum_data + wordsize));
ref(bn, 0) = (ikptr) (bignum_tag | (1 << bignum_length_shift));
ref(bn, disp_bignum_data) = (ikptr)r;
return verify_bignum(bn+vector_tag,"fxfx-1");
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}
} else {
ikptr fxr = fix(r);
if(unfix(fxr) == r){
return fxr;
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} else {
ikptr bn = ik_safe_alloc(pcb, align(disp_bignum_data + wordsize));
ref(bn, 0) = (ikptr)
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(bignum_tag |
(1 << bignum_sign_shift) |
(1 << bignum_length_shift));
ref(bn, disp_bignum_data) = (ikptr)(-r);
return verify_bignum(bn+vector_tag, "fxfx-2");
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}
}
}
ikptr
ikrt_bnnegate(ikptr x, ikpcb* pcb){
ikptr fst = ref(x, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
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if(limb_count == 1){
if(! bnfst_negative(fst)){
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/* positive bignum */
mp_limb_t limb =
(mp_limb_t) ref(x, disp_bignum_data - vector_tag);
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if(limb == (most_positive_fixnum + 1)){
return fix(-(long int)limb);
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}
}
}
pcb->root0 = &x;
ikptr bn = ik_safe_alloc(pcb, align(disp_bignum_data + limb_count * wordsize));
pcb->root0 = 0;
memcpy((char*)(long)bn+disp_bignum_data,
(char*)(long)x-vector_tag+disp_bignum_data,
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limb_count*wordsize);
ref(bn, 0) = (ikptr)
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(bignum_tag |
((1 << bignum_sign_shift) - (bignum_sign_mask & (long int)fst)) |
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(limb_count << bignum_length_shift));
return verify_bignum(bn+vector_tag, "bnneg");
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}
ikptr
ikrt_fxbnminus(ikptr x, ikptr y, ikpcb* pcb){
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if(x == 0){ return ikrt_bnnegate(y, pcb) ; }
ikptr fst = ref(y, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
long int intx = unfix(x);
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if(intx > 0){
if(bnfst_negative(fst)){
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/* positive fx - negative bn = positive bn */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(limb_count+1)*wordsize));
pcb->root0 = 0;
long int carry =
mpn_add_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
intx);
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if(carry){
ref(r, disp_bignum_data + limb_count*wordsize) = (ikptr)1;
ref(r, 0) = (ikptr)
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(((limb_count + 1) << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn-1");
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} else {
ref(r, 0) = (ikptr)
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((limb_count << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn-2");
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}
}
else {
/* positive fx - positive bn = smaller negative bn/fx */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+limb_count*wordsize));
pcb->root0 = 0;
long int borrow =
mpn_sub_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
intx);
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if(borrow){
fprintf(stderr, "Error: BUG in borrow3\n");
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exit(-1);
}
long int result_size =
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(ref(r, disp_bignum_data + (limb_count-1)*wordsize))
? limb_count
: (limb_count - 1);
if(result_size == 0){
return 0;
}
if(result_size == 1){
unsigned long int last =
(unsigned long int) ref(r, disp_bignum_data + (result_size-1)*wordsize);
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if(last <= most_negative_fixnum){
return fix(-(long int)last);
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}
}
ref(r, 0) = (ikptr)
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((result_size << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn-");
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}
}
else {
if(bnfst_negative(fst)){
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/* negative fx - negative bn = smaller positive */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+limb_count*wordsize));
pcb->root0 = 0;
long int borrow =
mpn_sub_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
- intx);
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if(borrow){
fprintf(stderr, "Error: BUG in borrow4\n");
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exit(-1);
}
long int result_size =
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(ref(r, disp_bignum_data + (limb_count-1)*wordsize) == 0)
? (limb_count - 1)
: limb_count;
if(result_size == 0){
return 0;
}
if(result_size == 1){
unsigned long int last =
(unsigned long int) ref(r, disp_bignum_data + (result_size-1)*wordsize);
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if(last <= most_positive_fixnum){
return fix((long int)last);
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}
}
ref(r, 0) = (ikptr)
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((result_size << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag,"fxbn-");
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} else {
/* negative fx - positive bn = larger negative */
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(limb_count+1)*wordsize));
pcb->root0 = 0;
long int carry =
mpn_add_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y - vector_tag + disp_bignum_data),
limb_count,
-intx);
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if(carry){
ref(r, disp_bignum_data + limb_count*wordsize) = (ikptr)1;
ref(r, 0) = (ikptr)
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(((limb_count + 1) << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn-");
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} else {
ref(r, 0) = (ikptr)
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((limb_count << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "fxbn-");
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}
}
}
}
ikptr
ikrt_bnfxminus(ikptr x, ikptr y, ikpcb* pcb){
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if(y == 0){ return x; }
ikptr fst = ref(x, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
long int inty = unfix(y);
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if(inty < 0){
if(!bnfst_negative(fst)){
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/* - negative fx + positive bn = positive bn */
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(limb_count+1)*wordsize));
pcb->root0 = 0;
long int carry =
mpn_add_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(x - vector_tag + disp_bignum_data),
limb_count,
-inty);
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if(carry){
ref(r, disp_bignum_data + limb_count*wordsize) = (ikptr)1;
ref(r, 0) = (ikptr)
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(((limb_count + 1) << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag,"bnfx-");
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} else {
ref(r, 0) = (ikptr)
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((limb_count << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag,"bnfx-");
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}
}
else {
/* - negative fx + negative bn = smaller negative bn/fx */
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+limb_count*wordsize));
pcb->root0 = 0;
long int borrow =
mpn_sub_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(x - vector_tag + disp_bignum_data),
limb_count,
-inty);
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if(borrow){
fprintf(stderr, "Error: BUG in borrow5\n");
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exit(-1);
}
long int result_size =
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(ref(r, disp_bignum_data + (limb_count-1)*wordsize))
? limb_count
: (limb_count - 1);
if(result_size == 0){
return 0;
}
if(result_size == 1){
unsigned long int last =
(unsigned long int) ref(r, disp_bignum_data + (result_size-1)*wordsize);
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if(last <= most_negative_fixnum){
return fix(-(long int)last);
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}
}
ref(r, 0) = (ikptr)
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((result_size << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag,"bnfx-");
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}
}
else {
if((bignum_sign_mask & (long int)fst) == 0){
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/* - positive fx + positive bn = smaller positive */
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+limb_count*wordsize));
pcb->root0 = 0;
long int borrow =
mpn_sub_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(x - vector_tag + disp_bignum_data),
limb_count,
inty);
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if(borrow){
fprintf(stderr, "Error: BUG in borrow6\n");
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exit(-1);
}
long int result_size =
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(ref(r, disp_bignum_data + (limb_count-1)*wordsize) == 0)
? (limb_count - 1)
: limb_count;
if(result_size == 0){
return 0;
}
if(result_size == 1){
unsigned long int last =
(unsigned long int) ref(r, disp_bignum_data + (result_size-1)*wordsize);
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if(last <= most_positive_fixnum){
return fix((long int)last);
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}
}
ref(r, 0) = (ikptr)
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((result_size << bignum_length_shift) |
(0 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "bnfx-");
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} else {
/* - positive fx + negative bn = larger negative */
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(limb_count+1)*wordsize));
pcb->root0 = 0;
long int carry =
mpn_add_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(x - vector_tag + disp_bignum_data),
limb_count,
inty);
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if(carry){
ref(r, disp_bignum_data + limb_count*wordsize) = (ikptr)1;
ref(r, 0) = (ikptr)
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(((limb_count + 1) << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "bnfx-");
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} else {
ref(r, 0) = (ikptr)
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((limb_count << bignum_length_shift) |
(1 << bignum_sign_shift) |
bignum_tag);
return verify_bignum(r+vector_tag, "bnfx-");
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}
}
}
}
ikptr
ikrt_bnbnminus(ikptr x, ikptr y, ikpcb* pcb){
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if(x == y) { return 0; }
unsigned long int xfst = (unsigned long int)ref(x, -vector_tag);
unsigned long int yfst = (unsigned long int)ref(y, -vector_tag);
long int xsign = xfst & bignum_sign_mask;
long int ysign = yfst & bignum_sign_mask;
long int xlimbs = xfst >> bignum_length_shift;
long int ylimbs = yfst >> bignum_length_shift;
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if(xsign != ysign){
long int n1,n2;
ikptr s1,s2;
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if(xlimbs >= ylimbs){
n1 = xlimbs; n2 = ylimbs; s1 = x; s2 = y;
} else {
n1 = ylimbs; n2 = xlimbs; s1 = y; s2 = x;
}
pcb->root0 = &s1;
pcb->root1 = &s2;
ikptr res = ik_safe_alloc(pcb, align(disp_bignum_data + (n1+1)*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t carry =
mpn_add((mp_limb_t*)(long)(res+disp_bignum_data),
(mp_limb_t*)(long)(s1-vector_tag+disp_bignum_data),
n1,
(mp_limb_t*)(long)(s2-vector_tag+disp_bignum_data),
n2);
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if(carry){
ref(res, disp_vector_data + xlimbs*wordsize) = (ikptr)1;
ref(res, 0) = (ikptr)
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(((n1+1) << bignum_length_shift) |
xsign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn-");
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} else {
ref(res, 0) = (ikptr)
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((n1 << bignum_length_shift) |
xsign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn-");
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}
}
else {
/* same sign */
if(xlimbs == ylimbs){
while((ref(x, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize) ==
ref(y, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize))){
xlimbs -= 1;
if(xlimbs == 0){ return 0; }
}
ylimbs = xlimbs;
}
ikptr s1=x, s2=y;
long int n1=xlimbs, n2=ylimbs;
long int result_sign = xsign;
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/* |x| != |y| */
if(xlimbs <= ylimbs){
if(xlimbs == ylimbs){
if((ref(y, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize) >
ref(x, -vector_tag+disp_bignum_data+(xlimbs-1)*wordsize))){
s1 = y; n1 = ylimbs;
s2 = x; n2 = xlimbs;
result_sign = (1 << bignum_sign_shift) - ysign;
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}
} else {
s1 = y; n1 = ylimbs;
s2 = x; n2 = xlimbs;
result_sign = (1 << bignum_sign_shift) - ysign;
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}
}
/* |s1| > |s2| */
pcb->root0 = &s1;
pcb->root1 = &s2;
ikptr res = ik_safe_alloc(pcb, align(disp_bignum_data + n1 * wordsize));
bzero((void*)res+disp_bignum_data, n1*wordsize);
pcb->root0 = 0;
pcb->root1 = 0;
long int burrow =
mpn_sub((mp_limb_t*)(long)(res + disp_bignum_data),
(mp_limb_t*)(long)(s1 - vector_tag + disp_bignum_data),
n1,
(mp_limb_t*)(long)(s2 - vector_tag + disp_bignum_data),
n2);
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if(burrow){
fprintf(stderr, "BUG: Burrow error in bnbn-\n");
exit(-1);
}
long int len = n1;
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while(ref(res, disp_bignum_data + (len-1)*wordsize) == 0){
len--;
if(len == 0){
return 0;
}
}
if(result_sign == 0){
/* positive result */
if(len == 1){
unsigned long int fst_limb =
(unsigned long int) ref(res, disp_bignum_data);
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if(fst_limb <= most_positive_fixnum){
return fix((long int)fst_limb);
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}
}
ref(res, 0) = (ikptr)
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((len << bignum_length_shift) |
result_sign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn-");
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} else {
/* negative result */
if(len == 1){
unsigned long int fst_limb =
(unsigned long int) ref(res, disp_bignum_data);
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if(fst_limb <= most_negative_fixnum){
return fix(-(long int)fst_limb);
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}
}
ref(res, 0) = (ikptr)
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((len << bignum_length_shift) |
result_sign |
bignum_tag);
return verify_bignum(res+vector_tag, "bnbn-");
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}
}
}
ikptr
ikrt_fxfxmult(ikptr x, ikptr y, ikpcb* pcb){
long int n1 = unfix(x);
long int n2 = unfix(y);
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mp_limb_t lo = 0;
mp_limb_t s1 = n1;
mp_limb_t s2 = n2;
long int sign = 0;
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if(n1 < 0){
s1 = -n1;
sign = 1 - sign;
}
if(n2 < 0){
s2 = -n2;
sign = 1 - sign;
}
mp_limb_t hi = mpn_mul_1(&lo, &s1, 1, s2);
if(hi == 0){
if(sign){
if(lo <= most_negative_fixnum){
return fix(-((long int)lo));
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}
} else {
if(lo <= most_positive_fixnum){
return fix((long int)lo);
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}
}
ikptr r = ik_safe_alloc(pcb, disp_bignum_data + wordsize);
ref(r, 0) = (ikptr)
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(bignum_tag |
(sign << bignum_sign_shift) |
(1 << bignum_length_shift));
ref(r, disp_bignum_data) = (ikptr)lo;
return BN(r+vector_tag);
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} else {
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + 2*wordsize));
ref(r, 0) = (ikptr)
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(bignum_tag |
(sign << bignum_sign_shift) |
(2 << bignum_length_shift));
ref(r, disp_bignum_data) = (ikptr)lo;
ref(r, disp_bignum_data+wordsize) = (ikptr)hi;
return BN(r+vector_tag);
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}
}
ikptr
normalize_bignum(long int limbs, int sign, ikptr r){
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while(ref(r, disp_bignum_data + (limbs-1)*wordsize) == 0){
limbs--;
if(limbs == 0){ return 0;}
}
if(limbs == 1){
mp_limb_t last = (mp_limb_t) ref(r, disp_bignum_data);
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if(sign == 0){
if(last <= most_positive_fixnum){
return fix(last);
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}
} else {
if(last <= most_negative_fixnum){
return fix(-(last));
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}
}
}
ref(r, 0) = (ikptr) (bignum_tag | sign | (limbs << bignum_length_shift));
return BN(r+vector_tag);
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}
ikptr
ikrt_fxbnmult(ikptr x, ikptr y, ikpcb* pcb){
long int n2 = unfix(x);
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if(n2 == 0) { return 0; }
mp_limb_t s2 = (n2>0) ? n2 : (- n2);
ikptr fst = ref(y, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + (limb_count+1)*wordsize));
pcb->root0 = 0;
mp_limb_t hi = mpn_mul_1((mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(y-vector_tag+disp_bignum_data),
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limb_count,
s2);
ref(r, disp_bignum_data + limb_count * wordsize) = (ikptr)hi;
long int sign =
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((n2 > 0) ?
(bignum_sign_mask & (long int)fst) :
((1 << bignum_sign_shift) - (bignum_sign_mask&(long int)fst)));
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return normalize_bignum(limb_count+1, sign, r);
}
ikptr
ikrt_bnbnmult(ikptr x, ikptr y, ikpcb* pcb){
long int f1 = (long int)ref(x, -vector_tag);
long int f2 = (long int)ref(y, -vector_tag);
long int n1 = bnfst_limb_count(f1);
long int n2 = bnfst_limb_count(f2);
long int nr = n1 + n2;
pcb->root0 = &x;
pcb->root1 = &y;
ikptr bn = ik_safe_alloc(pcb, align(disp_bignum_data + nr*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
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mp_limb_t r;
if(n1 >= n2){
r = mpn_mul((mp_limb_t*)(long)(bn+disp_bignum_data),
(mp_limb_t*)(long)(x-vector_tag+disp_bignum_data),
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n1,
(mp_limb_t*)(long)(y-vector_tag+disp_bignum_data),
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n2);
} else {
r = mpn_mul((mp_limb_t*)(long)(bn+disp_bignum_data),
(mp_limb_t*)(long)(y-vector_tag+disp_bignum_data),
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n2,
(mp_limb_t*)(long)(x-vector_tag+disp_bignum_data),
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n1);
}
long int sign =
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((bignum_sign_mask & f1) ?
((1 << bignum_sign_shift) - (bignum_sign_mask & f2)) :
(bignum_sign_mask & f2));
return normalize_bignum(nr, sign, bn);
}
ikptr
ikrt_bnbncomp(ikptr bn1, ikptr bn2){
ikptr f1 = ref(bn1, -vector_tag);
ikptr f2 = ref(bn2, -vector_tag);
if(bnfst_negative(f1)){
if(bnfst_negative(f2)){
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/* both negative */
long int n1 = ((mp_limb_t) f1) >> bignum_length_shift;
long int n2 = ((mp_limb_t) f2) >> bignum_length_shift;
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if(n1 < n2) {
return fix(1);
} else if(n1 > n2){
return fix(-1);
} else {
long int i;
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for(i=(n1-1); i>=0; i--){
mp_limb_t t1 =
(mp_limb_t) ref(bn1,disp_bignum_data-vector_tag+i*wordsize);
mp_limb_t t2 =
(mp_limb_t) ref(bn2,disp_bignum_data-vector_tag+i*wordsize);
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if(t1 < t2){
return fix(1);
} else if(t1 > t2){
return fix(-1);
}
}
}
return 0;
} else {
/* n1 negative, n2 positive */
return fix(-1);
}
} else {
if(bnfst_negative(f2)){
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/* n1 positive, n2 negative */
return fix(1);
} else {
/* both positive */
long int n1 = ((mp_limb_t) f1) >> bignum_length_shift;
long int n2 = ((mp_limb_t) f2) >> bignum_length_shift;
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if(n1 < n2) {
return fix(-1);
} else if(n1 > n2){
return fix(1);
} else {
long int i;
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for(i=(n1-1); i>=0; i--){
mp_limb_t t1 =
(mp_limb_t) ref(bn1,disp_bignum_data-vector_tag+i*wordsize);
mp_limb_t t2 =
(mp_limb_t) ref(bn2,disp_bignum_data-vector_tag+i*wordsize);
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if(t1 < t2){
return fix(-1);
} else if(t1 > t2){
return fix(1);
}
}
}
return 0;
}
}
}
static inline int
count_leading_ffs(int n, mp_limb_t* x){
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int idx;
for(idx=0; idx<n; idx++){
if(x[idx] != (mp_limb_t)-1){
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return idx;
}
}
return n;
}
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static void
copy_limbs(mp_limb_t* src, mp_limb_t* dst, int n1, int n2){
while(n1 < n2){
dst[n1] = src[n1];
n1++;
}
}
static void
bits_compliment(mp_limb_t* src, mp_limb_t* dst, long int n){
mp_limb_t carry = 1;
long int i;
for(i=0; i<n; i++){
mp_limb_t d = src[i];
mp_limb_t c = carry + ~ d;
dst[i] = c;
carry = (carry && ! d);
}
}
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static void
bits_compliment2(mp_limb_t* src, mp_limb_t* dst, int n1, int n2){
mp_limb_t carry = 1;
int i;
for(i=0; i<n1; i++){
mp_limb_t d = src[i];
mp_limb_t c = carry + ~ d;
dst[i] = c;
carry = (carry && ! d);
}
for(i=n1; i<n2; i++){
mp_limb_t d = 0;
mp_limb_t c = carry + ~ d;
dst[i] = c;
carry = (carry && ! d);
}
}
static int
bits_compliment_carry(mp_limb_t* src, mp_limb_t* dst, int n1, int n2, mp_limb_t carry){
int i;
for(i=n1; i<n2; i++){
mp_limb_t d = src[i];
mp_limb_t c = carry + ~ d;
dst[i] = c;
carry = (carry && ! d);
}
return carry;
}
static void
bits_compliment_with_carry(mp_limb_t* src, mp_limb_t* dst, long int n, long int carry){
long int i;
for(i=0; i<n; i++){
mp_limb_t d = src[i];
mp_limb_t c = carry + ~ d;
dst[i] = c;
carry = (carry && ! d);
}
}
static void
bits_compliment_logand(mp_limb_t* s1, mp_limb_t* s2, mp_limb_t* dst, int n){
int carry = 1;
int i;
for(i=0; i<n; i++){
mp_limb_t d = s1[i];
mp_limb_t c = carry + ~ d;
dst[i] = c & s2[i];
carry = (carry && ! d);
}
}
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static int
bits_compliment_logor(mp_limb_t* s1, mp_limb_t* s2, mp_limb_t* dst, int n){
int carry = 1;
int i;
for(i=0; i<n; i++){
mp_limb_t d = s1[i];
mp_limb_t c = carry + ~ d;
dst[i] = c | s2[i];
carry = (carry && ! d);
}
return carry;
}
static long int
bits_carry(mp_limb_t* s, int n){
/*
int carry = 1;
int i;
for(i=0; i<n; i++){
mp_limb_t d = s[i];
carry = (carry && ! d);
}
return carry;
*/
int i;
for(i=0; i<n; i++){
if (s[i] != 0){
return 0;
}
}
return 1;
}
ikptr
ikrt_bnlognot(ikptr x, ikpcb* pcb){
ikptr fst = ref(x, -vector_tag);
long int n = bnfst_limb_count(fst);
if(bnfst_negative(fst)){
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/* negative */
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + n*wordsize));
pcb->root0 = 0;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* rd = (mp_limb_t*)(long)(r+disp_bignum_data);
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int i;
for(i=0; (i<n) && (s1[i] == 0); i++) {
rd[i] = -1;
}
rd[i] = s1[i] - 1;
for(i++; i<n; i++){
rd[i] = s1[i];
}
return normalize_bignum(n, 0, r);
} else {
/* positive */
long int i;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
for(i=0; (i<n) && (s1[i] == (mp_limb_t)-1); i++) {/*nothing*/}
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if(i==n){
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + (n+1)*wordsize));
pcb->root0 = 0;
bzero((char*)(long)r+disp_bignum_data, n*wordsize);
((mp_limb_t*)(long)(r+disp_bignum_data))[n] = 1;
ref(r, 0) = (ikptr)
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(bignum_tag | (1<<bignum_sign_shift) | ((n+1) << bignum_length_shift));
return r+vector_tag;
} else {
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + n*wordsize));
pcb->root0 = 0;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* rd = (mp_limb_t*)(long)(r+disp_bignum_data);
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int j;
for(j=0; j<i; j++){ rd[j] = 0; }
rd[i] = s1[i] + 1;
for(j=i+1; j<n; j++){ rd[j] = s1[j]; }
ref(r, 0) = (ikptr)
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(bignum_tag | (1<<bignum_sign_shift) | (n << bignum_length_shift));
return r+vector_tag;
}
}
}
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ikptr
ikrt_fxbnlogand(ikptr x, ikptr y, ikpcb* pcb){
long int n1 = unfix(x);
ikptr fst = ref(y, -vector_tag);
if(n1 >= 0){
/* x is positive */
if(bnfst_negative(fst)){
/* y is negative */
return fix(n1 & (1+~(long int)ref(y, disp_vector_data-vector_tag)));
} else {
/* y is positive */
return fix(n1 & (long int)ref(y, disp_vector_data-vector_tag));
}
} else {
/* x is negative */
if(n1 == -1){ return y; }
if(bnfst_negative(fst)){
/* y is negative */
long int len = bnfst_limb_count(fst);
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + (len+1)*wordsize));
pcb->root0 = 0;
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
bits_compliment2(s2, s, len, len+1);
s[0] = s[0] & n1;
bits_compliment2(s, s, len+1, len+1);
return normalize_bignum(len+1, 1<<bignum_sign_shift, r);
} else {
/* y is positive */
long int len = bnfst_limb_count(fst);
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + len * wordsize));
pcb->root0 = 0;
ref(r, 0) = fst;
ref(r, disp_bignum_data) = (ikptr)
(((long int)ref(y, disp_bignum_data - vector_tag)) & n1);
int i;
for(i=1; i<len; i++){
ref(r, disp_bignum_data+i*wordsize) =
ref(y, disp_bignum_data-vector_tag+i*wordsize);
}
return BN(r+vector_tag);
}
}
}
ikptr
ikrt_bnbnlogand(ikptr x, ikptr y, ikpcb* pcb){
ikptr xfst = ref(x, -vector_tag);
ikptr yfst = ref(y, -vector_tag);
long int n1 = bnfst_limb_count(xfst);
long int n2 = bnfst_limb_count(yfst);
if(bnfst_negative(xfst)){
if(bnfst_negative(yfst)){
if(n1 >= n2){
pcb->root0 = &x;
pcb->root1 = &y;
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ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + (n1+1)*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
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bits_compliment2(s1, s, n1, n1+1);
bits_compliment_logand(s2, s, s, n2);
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bits_compliment2(s, s, n1+1, n1+1);
return normalize_bignum(n1+1, 1<<bignum_sign_shift, r);
} else {
return ikrt_bnbnlogand(y,x,pcb);
}
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} else {
return ikrt_bnbnlogand(y,x,pcb);
}
} else {
if(bnfst_negative(yfst)){
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/* x positive, y negative */
/* the result is at most n1 words long */
pcb->root0 = &x;
pcb->root1 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + n1*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
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if(n1 <= n2){
bits_compliment_logand(s2, s1, s, n1);
} else {
bits_compliment_logand(s2, s1, s, n2);
copy_limbs(s1, s, n2, n1);
}
return normalize_bignum(n1, 0, r);
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} else {
/* both positive */
int n = (n1<n2)?n1:n2;
long int i;
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for(i=n-1; i>=0; i--){
long int l1 =
(long int) ref(x, disp_bignum_data-vector_tag+i*wordsize);
long int l2 =
(long int) ref(y, disp_bignum_data-vector_tag+i*wordsize);
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unsigned long int last = l1 & l2;
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if(last){
if((i == 0) && (last < most_positive_fixnum)){
return fix(last);
}
pcb->root0 = &x;
pcb->root1 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+(i+1)*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
ref(r, 0) = (ikptr) (bignum_tag | ((i+1)<<bignum_length_shift));
ref(r, disp_bignum_data + i*wordsize) = (ikptr)last;
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int j;
for(j=0; j<i; j++){
ref(r, disp_bignum_data + j*wordsize) = (ikptr)
(((long int)ref(x, disp_bignum_data-vector_tag+j*wordsize))
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&
((long int)ref(y, disp_bignum_data-vector_tag+j*wordsize)));
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}
return r+vector_tag;
}
}
return 0;
}
}
}
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ikptr
ikrt_fxbnlogor(ikptr x, ikptr y, ikpcb* pcb){
long int n1 = unfix(x);
ikptr fst = ref(y, -vector_tag);
if(n1 < 0){
/* x is negative */
if(bnfst_negative(fst)){
/* y is negative */
return fix(n1 | (1+~(long int)ref(y, disp_vector_data-vector_tag)));
} else {
/* y is positive */
return fix(n1 | (long int)ref(y, disp_vector_data-vector_tag));
}
} else {
/* x is non negative */
if(n1 == 0){ return y; }
/* x is positive */
if(bnfst_negative(fst)){
/* y is negative */
long int len = bnfst_limb_count(fst);
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + (len+1)*wordsize));
pcb->root0 = 0;
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
bits_compliment2(s2, s, len, len+1);
s[0] = s[0] | n1;
bits_compliment2(s, s, len+1, len+1);
return normalize_bignum(len+1, 1<<bignum_sign_shift, r);
} else {
/* y is positive */
long int len = bnfst_limb_count(fst);
pcb->root0 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + len * wordsize));
pcb->root0 = 0;
ref(r, 0) = fst;
ref(r, disp_bignum_data) = (ikptr)
(((long int)ref(y, disp_bignum_data - vector_tag)) | n1);
int i;
for(i=1; i<len; i++){
ref(r, disp_bignum_data+i*wordsize) =
ref(y, disp_bignum_data-vector_tag+i*wordsize);
}
return BN(r+vector_tag);
}
}
}
ikptr
ikrt_bnbnlogor(ikptr x, ikptr y, ikpcb* pcb){
ikptr xfst = ref(x, -vector_tag);
ikptr yfst = ref(y, -vector_tag);
long int n1 = bnfst_limb_count(xfst);
long int n2 = bnfst_limb_count(yfst);
if(bnfst_negative(xfst)){
if(bnfst_negative(yfst)){
if(n1 >= n2){
pcb->root0 = &x;
pcb->root1 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + n1*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
bits_compliment2(s2, s, n2, n1);
int carry = bits_compliment_logor(s1, s, s, n1);
bits_compliment_carry(s,s,n1,n1,carry);
bits_compliment2(s, s, n1, n1);
return normalize_bignum(n1, 1<<bignum_sign_shift, r);
} else {
return ikrt_bnbnlogor(y,x,pcb);
}
} else {
return ikrt_bnbnlogor(y,x,pcb);
}
} else {
if(bnfst_negative(yfst)){
/* x positive, y negative */
/* the result is at most n2 words long */
pcb->root0 = &x;
pcb->root1 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + n2*wordsize));
pcb->root0 = 0;
pcb->root1 = 0;
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
if(n2 <= n1){
bits_compliment_logor(s2, s1, s, n2);
bits_compliment2(s, s, n2, n2);
} else {
int carry = bits_compliment_logor(s2, s1, s, n1);
bits_compliment_carry(s2, s, n1, n2, carry);
bits_compliment_carry(s, s, 0, n2, 1);
}
return normalize_bignum(n2, 1<<bignum_sign_shift, r);
} else {
/* both positive */
int n = (n1>n2)?n1:n2;
pcb->root0 = &x;
pcb->root1 = &y;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data+n*wordsize));
mp_limb_t* s = (mp_limb_t*)(long)(r+disp_bignum_data);
mp_limb_t* s1 = (mp_limb_t*)(long)(x+disp_bignum_data-vector_tag);
mp_limb_t* s2 = (mp_limb_t*)(long)(y+disp_bignum_data-vector_tag);
pcb->root0 = 0;
pcb->root1 = 0;
long int i;
if(n == n1){
for(i=0; i<n2; i++){
s[i] = s1[i] | s2[i];
}
for(i=n2; i<n1; i++){
s[i] = s1[i];
}
} else {
for(i=0; i<n1; i++){
s[i] = s1[i] | s2[i];
}
for(i=n1; i<n2; i++){
s[i] = s2[i];
}
}
return normalize_bignum(n, 0, r);
}
}
}
static void
copy_bits_shifting_right(mp_limb_t* src, mp_limb_t* dst, int n, int m){
mp_limb_t carry = src[0] >> m;
int i;
for(i=1; i<n; i++){
mp_limb_t b = src[i];
dst[i-1] = (b << (mp_bits_per_limb-m)) | carry;
carry = b >> m;
}
dst[n-1] = carry;
}
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static void
copy_bits_shifting_left(mp_limb_t* src, mp_limb_t* dst, int n, int m){
mp_limb_t carry = 0;
int i;
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for(i=0; i<n; i++){
mp_limb_t b = src[i];
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dst[i] = (b << m) | carry;
carry = b >> (mp_bits_per_limb-m);
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}
dst[n] = carry;
}
ikptr
ikrt_bignum_shift_right(ikptr x, ikptr y, ikpcb* pcb){
int limb_shift = (wordsize == 4 ? 5 : 6);
long int m = unfix(y);
ikptr fst = ref(x, -vector_tag);
long int n = bnfst_limb_count(fst);
long int whole_limb_shift = m >> limb_shift;
long int bit_shift = m & (mp_bits_per_limb-1);
long int new_limb_count = n - whole_limb_shift;
if(bnfst_negative(fst)){
if(new_limb_count <= 0){
return fix(-1);
}
if(bit_shift == 0){
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + new_limb_count * wordsize));
pcb->root0 = 0;
bits_compliment_with_carry(
(mp_limb_t*)(long)(x+off_bignum_data+whole_limb_shift*wordsize),
(mp_limb_t*)(long)(r+disp_bignum_data),
new_limb_count,
bits_carry((mp_limb_t*)(long)(x+off_bignum_data), whole_limb_shift));
bits_compliment(
(mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(r+disp_bignum_data),
new_limb_count);
return normalize_bignum(new_limb_count, 1 << bignum_sign_shift, r);
} else {
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + new_limb_count * wordsize));
pcb->root0 = 0;
bits_compliment_with_carry(
(mp_limb_t*)(long)(x+off_bignum_data+whole_limb_shift*wordsize),
(mp_limb_t*)(long)(r+disp_bignum_data),
new_limb_count,
bits_carry((mp_limb_t*)(long)(x+off_bignum_data), whole_limb_shift));
copy_bits_shifting_right(
(mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(r+disp_bignum_data),
new_limb_count,
bit_shift);
*((mp_limb_t*)(r+disp_bignum_data+(new_limb_count-1)*wordsize))
|= (-1L << (mp_bits_per_limb - bit_shift));
bits_compliment(
(mp_limb_t*)(long)(r+disp_bignum_data),
(mp_limb_t*)(long)(r+disp_bignum_data),
new_limb_count);
return normalize_bignum(new_limb_count, 1 << bignum_sign_shift, r);
fprintf(stderr, "not yet for negative bignum_shift\n");
exit(-1);
}
} else {
if(new_limb_count <= 0){
return 0;
}
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + new_limb_count * wordsize));
pcb->root0 = 0;
if(bit_shift == 0){
memcpy((char*)(long)r+disp_bignum_data,
(char*)(long)x+off_bignum_data+whole_limb_shift*wordsize,
new_limb_count * wordsize);
return normalize_bignum(new_limb_count, 0, r);
} else {
copy_bits_shifting_right(
(mp_limb_t*)(long)(x+off_bignum_data+whole_limb_shift*wordsize),
(mp_limb_t*)(long)(r+disp_bignum_data),
new_limb_count,
bit_shift);
return normalize_bignum(new_limb_count, 0, r);
}
}
}
ikptr
ikrt_fixnum_shift_left(ikptr x, ikptr y, ikpcb* pcb){
int limb_shift = (wordsize == 4 ? 5 : 6);
long int m = unfix(y);
long int n = unfix(x);
long int limb_count = (m >> limb_shift) + 2;
long int bit_shift = m & (mp_bits_per_limb-1);
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + limb_count * wordsize));
unsigned long int* s = (unsigned long int*)(long)(r+disp_bignum_data);
bzero(s, limb_count * wordsize);
if(n >= 0){
if(bit_shift){
s[limb_count-1] = n >> (mp_bits_per_limb - bit_shift);
}
s[limb_count-2] = n << bit_shift;
} else {
if(bit_shift){
s[limb_count-1] = (-n) >> (mp_bits_per_limb - bit_shift);
}
s[limb_count-2] = (-n) << bit_shift;
}
return normalize_bignum(limb_count, (n>=0)?(0):(1<<bignum_sign_shift), r);
}
ikptr
ikrt_bignum_shift_left(ikptr x, ikptr y, ikpcb* pcb){
int limb_shift = (wordsize == 4 ? 5 : 6);
long int m = unfix(y);
ikptr fst = ref(x, -vector_tag);
long int n = bnfst_limb_count(fst);
long int whole_limb_shift = m >> limb_shift;
long int bit_shift = m & (mp_bits_per_limb-1);
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if(bit_shift == 0){
long int limb_count = n + whole_limb_shift;
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + limb_count * wordsize));
pcb->root0 = 0;
unsigned int* s = (unsigned int*)(long)(r+disp_bignum_data);
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bzero(s, whole_limb_shift*wordsize);
memcpy((char*)(long)s+whole_limb_shift,
(char*)(long)x+off_bignum_data, n*wordsize);
return normalize_bignum(limb_count, bnfst_negative(fst), r);
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} else {
int limb_count = n + whole_limb_shift + 1;
pcb->root0 = &x;
ikptr r = ik_safe_alloc(pcb, align(disp_bignum_data + limb_count * wordsize));
pcb->root0 = 0;
mp_limb_t* s = (mp_limb_t*)(r+disp_bignum_data);
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bzero(s, whole_limb_shift*wordsize);
copy_bits_shifting_left(
(mp_limb_t*)(x+off_bignum_data),
(mp_limb_t*)(s+whole_limb_shift),
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n,
bit_shift);
return normalize_bignum(limb_count, bnfst_negative(fst), r);
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}
}
#if 0
From TFM:
void
mpn_tdiv_qr (
mp limb t *qp, /* quotient placed here */
mp limb t *rp, /* remainder placed here */
mp size t qxn, /* must be zero! */
const mp limb t *np, /* first number */
mp size t nn, /* its length */
const mp limb t *dp, /* second number */
mp size t dn /* its length */
)
Divide {np, nn} by {dp, dn} and put the quotient at {qp,nn-dn+1}
and the remainder at {rp, dn}. The quotient is rounded towards 0.
No overlap is permitted between arguments. nn must be greater than
or equal to dn. The most significant limb of dp must be non-zero.
The qxn operand must be zero.
#endif
ikptr
ikrt_bnbndivrem(ikptr x, ikptr y, ikpcb* pcb){
ikptr xfst = ref(x, -vector_tag);
ikptr yfst = ref(y, -vector_tag);
mp_size_t xn = bnfst_limb_count(xfst);
mp_size_t yn = bnfst_limb_count(yfst);
if(xn < yn){
/* quotient is zero, remainder is x */
pcb->root0 = &x;
pcb->root1 = &y;
ikptr rv = ik_safe_alloc(pcb, pair_size);
pcb->root0 = 0;
pcb->root1 = 0;
ref(rv, disp_car) = 0;
ref(rv, disp_cdr) = x;
return rv+pair_tag;
}
mp_size_t qn = xn - yn + 1;
mp_size_t rn = yn;
/*
ikptr q = ik_unsafe_alloc(pcb, align(disp_bignum_data + qn*wordsize));
ikptr r = ik_unsafe_alloc(pcb, align(disp_bignum_data + rn*wordsize));
*/
pcb->root0 = &x;
pcb->root1 = &y;
ikptr q = ik_safe_alloc(pcb,
align(disp_bignum_data + qn*wordsize) +
align(disp_bignum_data + rn*wordsize));
ikptr r = q + align(disp_bignum_data + qn*wordsize);
pcb->root0 = 0;
pcb->root1 = 0;
mpn_tdiv_qr (
(mp_limb_t*)(long)(q+disp_bignum_data),
(mp_limb_t*)(long)(r+disp_bignum_data),
0,
(mp_limb_t*)(long)(x+off_bignum_data),
xn,
(mp_limb_t*)(long)(y+off_bignum_data),
yn);
if(bnfst_negative(xfst)){
/* x is negative => remainder is negative */
r = normalize_bignum(rn, 1 << bignum_sign_shift, r);
} else {
r = normalize_bignum(rn, 0, r);
}
if(bnfst_negative(yfst)){
/* y is negative => quotient is opposite of x */
long int sign = bignum_sign_mask - bnfst_negative(xfst);
q = normalize_bignum(qn, sign, q);
} else {
/* y is positive => quotient is same as x */
long int sign = bnfst_negative(xfst);
q = normalize_bignum(qn, sign, q);
}
pcb->root0 = &q;
pcb->root1 = &r;
ikptr rv = ik_safe_alloc(pcb, pair_size);
pcb->root0 = 0;
pcb->root1 = 0;
ref(rv, disp_car) = q;
ref(rv, disp_cdr) = r;
return rv+pair_tag;
}
#if 0
[Function]
mp_limb_t
mpn_divrem_1 (
mp limb t *r1p,
mp size t qxn,
mp limb t *s2p,
mp size t s2n,
mp limb t s3limb
)
Divide {s2p, s2n} by s3limb, and write the quotient at r1p. Return the remainder.
The integer quotient is written to {r1p+qxn, s2n} and in addition qxn fraction limbs are
developed and written to {r1p, qxn}. Either or both s2n and qxn can be zero. For most
usages, qxn will be zero.
#endif
ikptr
ikrt_bnfxdivrem(ikptr x, ikptr y, ikpcb* pcb){
long int yint = unfix(y);
ikptr fst = ref(x, -vector_tag);
mp_size_t s2n = bnfst_limb_count(fst);
pcb->root0 = &x;
ikptr quot = ik_safe_alloc(pcb, align(s2n*wordsize + disp_bignum_data));
pcb->root0 = 0;
mp_limb_t* s2p = (mp_limb_t*)(long)(x+off_bignum_data);
mp_limb_t rv = mpn_divrem_1(
(mp_limb_t*)(long)(quot+disp_bignum_data),
0,
s2p,
s2n,
labs(yint));
ikptr rem;
if(yint < 0){
/* y is negative => quotient is opposite of x */
long int sign = bignum_sign_mask - bnfst_negative(fst);
quot = normalize_bignum(s2n, sign, quot);
} else {
/* y is positive => quotient is same as x */
long int sign = bnfst_negative(fst);
quot = normalize_bignum(s2n, sign, quot);
}
/* the remainder is always less than |y|, so it will
always be a fixnum. (if y == most_negative_fixnum,
then |remainder| will be at most most_positive_fixnum). */
if(bnfst_negative(fst)){
/* x is negative => remainder is negative */
rem = (ikptr) -(rv << fx_shift);
} else {
rem = fix(rv);
}
pcb->root0 = &quot;
pcb->root1 = &rem;
ikptr p = ik_safe_alloc(pcb, pair_size);
pcb->root0 = 0;
pcb->root1 = 0;
ref(p, disp_car) = quot;
ref(p, disp_cdr) = rem;
return p+pair_tag;
}
ikptr
ikrt_bnfx_modulo(ikptr x, ikptr y /*, ikpcb* pcb */){
int yint = unfix(y);
mp_limb_t* s2p = (mp_limb_t*)(long)(x+off_bignum_data);
ikptr fst = ref(x, -vector_tag);
mp_size_t s2n = bnfst_limb_count(fst);
if(yint < 0){
if(bnfst_negative(fst)){
/* x negative, y negative */
mp_limb_t m = mpn_mod_1(s2p, s2n, -yint);
return fix(-m);
} else {
/* x positive, y negative */
mp_limb_t m = mpn_mod_1(s2p, s2n, -yint);
return fix(yint+m);
}
} else {
if(bnfst_negative(fst)){
/* x negative, y positive */
mp_limb_t m = mpn_mod_1(s2p, s2n, yint);
return fix(yint-m);
} else {
/* x positive, y positive */
mp_limb_t m = mpn_mod_1(s2p, s2n, yint);
return fix(m);
}
}
}
static int
limb_length(unsigned long int n){
int i=0;
while(n != 0){
n = n >> 1;
i++;
}
return i;
}
ikptr
ikrt_bignum_length(ikptr x){
ikptr fst = ref(x, -vector_tag);
mp_limb_t* sp = (mp_limb_t*)(long)(x+off_bignum_data);
mp_size_t sn = bnfst_limb_count(fst);
mp_limb_t last = sp[sn-1];
int n0 = limb_length(last);
if(((unsigned long int) fst) & bignum_sign_mask){
/* negative */
if (last == (mp_limb_t)(1L<<(n0-1))){
/* single bit set in last limb */
int i;
for(i=0; i<(sn-1); i++){
if(sp[i] != 0){
/* another bit set */
return fix((sn-1)*mp_bits_per_limb + n0);
}
}
/* number is - #b100000000000000000000000000 */
/* fxnot(n) = #b011111111111111111111111111 */
/* so, subtract 1. */
return fix((sn-1)*mp_bits_per_limb + n0 - 1);
} else {
return fix((sn-1)*mp_bits_per_limb + n0);
}
} else {
return fix((sn-1)*mp_bits_per_limb + n0);
}
}
ikptr
ikrt_bignum_to_bytevector(ikptr x, ikpcb* pcb){
2006-11-23 19:48:14 -05:00
/* FIXME: avoid calling malloc, instead, use the heap pointer itself
* as a buffer to hold the temporary data after ensuring that it has enough
* space */
ikptr fst = ref(x, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
2006-11-23 19:48:14 -05:00
if(limb_count <= 0){
fprintf(stderr, "BUG: nbtostring: invalid length %ld\n", limb_count);
2006-11-23 19:48:14 -05:00
exit(-1);
}
long int sign_bit = bignum_sign_mask & (long int) fst;
long int nbsize = limb_count * sizeof(mp_limb_t);
long int strsize = limb_count * max_digits_per_limb;
long int mem_req = nbsize + strsize + 1;
2006-11-23 19:48:14 -05:00
unsigned char* mem = malloc(mem_req);
if(! mem){
fprintf(stderr, "Error allocating space for bignum\n");
exit(-1);
}
memcpy((char*)(long)mem,
(char*)(long)x - vector_tag + disp_bignum_data,
nbsize);
2006-11-23 19:48:14 -05:00
mp_size_t bytes =
mpn_get_str(mem+nbsize, /* output string */
10, /* base */
(mp_limb_t*) mem, /* limb */
limb_count /* number of limbs */
);
unsigned char* string_start = mem + nbsize;
while(*string_start == 0){
string_start++;
bytes--;
}
ikptr bv = ik_safe_alloc(pcb, align(bytes + disp_bytevector_data + (sign_bit?1:0)));
ref(bv, 0) = fix(bytes + (sign_bit?1:0));
char* dest = (char*)(long)(bv + disp_bytevector_data);
2006-11-23 19:48:14 -05:00
if(sign_bit){
*dest = '-';
dest++;
}
{
long int i = 0;
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while(i < bytes){
dest[i] = string_start[i] + '0';
i++;
}
dest[bytes] = 0;
}
free(mem);
return bv + bytevector_tag;
2006-11-23 19:48:14 -05:00
}
ikptr
ikrt_fxrandom(ikptr x){
int mask = 1;
int n = unfix(x);
{
while(mask < n){
mask = (mask << 1) | 1;
}
}
while(1){
long r = random() & mask;
if(r < n){
return fix(r);
}
}
}
static int
limb_size(mp_limb_t x){
int i = 0;
while(x){
i++;
x = x>>1;
}
return i;
}
static int
all_zeros(mp_limb_t* start, mp_limb_t* end){
while(start <= end){
if(*end) return 0;
end--;
}
return 1;
}
#define PRECISION 53
static ikptr
ikrt_bignum_to_flonum64(ikptr bn, ikptr more_bits, ikptr fl){
ikptr fst = ref(bn, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
mp_limb_t* sp = (mp_limb_t*)(long)(bn+off_bignum_data);
double pos_result;
if(limb_count == 1){
pos_result = sp[0];
} else {
mp_limb_t hi = sp[limb_count-1];
int bc = limb_size(hi);
if(bc < 64){
mp_limb_t mi = sp[limb_count-2];
hi = (hi << (64-bc)) | (mi >> bc);
}
/* now hi has 64 full bits */
mp_limb_t mask = ((1L<<(64-PRECISION)) - 1);
if((hi & mask) == ((mask+1)>>1)){
/* exactly at break point */
if(((sp[limb_count-2] << (64-bc)) == 0) &&
all_zeros(sp, sp+limb_count-3) &&
(more_bits == 0)){
if(hi & (1L<<(64-PRECISION))){
/* odd number, round to even */
hi = hi | mask;
}
} else {
/* round up */
hi = hi | mask;
}
} else if ((hi & mask) > ((mask+1)>>1)){
/* also round up */
hi = hi | mask;
} else {
/* keep it to round down */
}
pos_result = hi;
int bignum_bits = bc + (mp_bits_per_limb * (limb_count-1));
int exponent = bignum_bits - mp_bits_per_limb;
while(exponent){
pos_result *= 2.0;
exponent -= 1;
}
}
if(bnfst_negative(fst)){
flonum_data(fl) = - pos_result;
} else {
flonum_data(fl) = pos_result;
}
return fl;
}
ikptr
ikrt_bignum_to_flonum(ikptr bn, ikptr more_bits, ikptr fl){
if(mp_bits_per_limb == 64){
return ikrt_bignum_to_flonum64(bn, more_bits, fl);
}
ikptr fst = ref(bn, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
mp_limb_t* sp = (mp_limb_t*)(long)(bn+off_bignum_data);
double pos_result;
if(limb_count == 1){
pos_result = sp[0];
} else if (limb_count == 2){
mp_limb_t lo = sp[0];
mp_limb_t hi = sp[1];
pos_result = hi;
pos_result = pos_result * 4294967296.0;
pos_result = pos_result + lo;
} else {
mp_limb_t hi = sp[limb_count-1];
mp_limb_t mi = sp[limb_count-2];
int bc = limb_size(hi);
if(bc < 32){
mp_limb_t lo = sp[limb_count-3];
hi = (hi << (32-bc)) | (mi >> bc);
mi = (mi << (32-bc)) | (lo >> bc);
}
/* now hi has 32 full bits, and mi has 32 full bits */
mp_limb_t mask = ((1<<(64-PRECISION)) - 1);
if((mi & mask) == ((mask+1)>>1)){
/* exactly at break point */
if(((sp[limb_count-3] << (32-bc)) == 0) &&
all_zeros(sp, sp+limb_count-4) &&
(more_bits == 0)){
if(mi & (1<<(64-PRECISION))){
/* odd number, round to even */
mi = mi | mask;
}
} else {
/* round up */
mi = mi | mask;
}
} else if ((mi & mask) > ((mask+1)>>1)){
/* also round up */
mi = mi | mask;
} else {
/* keep it to round down */
}
pos_result = hi;
pos_result = pos_result * 4294967296.0;
pos_result = pos_result + mi;
int bignum_bits = bc + (mp_bits_per_limb * (limb_count-1));
int exponent = bignum_bits - (2 * mp_bits_per_limb);
while(exponent){
pos_result *= 2.0;
exponent -= 1;
}
}
if(bnfst_negative(fst)){
flonum_data(fl) = - pos_result;
} else {
flonum_data(fl) = pos_result;
}
return fl;
}
2008-07-19 17:41:06 -04:00
ikptr
ikrt_exact_fixnum_sqrt(ikptr fx /*, ikpcb* pcb*/){
mp_limb_t x = unfix(fx);
mp_limb_t s;
mp_limb_t r;
mpn_sqrtrem(&s, &r, &x, 1);
return fix(s);
}
ikptr
ikrt_exact_bignum_sqrt(ikptr bn, ikpcb* pcb){
ikptr fst = ref(bn, -vector_tag);
long int limb_count = bnfst_limb_count(fst);
long int result_limb_count = (limb_count + 1)/2;
pcb->root0 = &bn;
ikptr s = ik_safe_alloc(pcb,
align(disp_bignum_data+result_limb_count*wordsize))
+ vector_tag;
ref(s, -vector_tag) =
(ikptr) (bignum_tag | (result_limb_count << bignum_length_shift));
pcb->root1 = &s;
ikptr r = ik_safe_alloc(pcb,
align(disp_bignum_data+limb_count*wordsize))
+ vector_tag;
ref(r, -vector_tag) =
(ikptr) (bignum_tag | (limb_count << bignum_length_shift));
pcb->root0 = &r;
ikptr pair = ik_safe_alloc(pcb, pair_size) + pair_tag;
pcb->root0 = 0;
pcb->root1 = 0;
mp_size_t r_actual_limbs = mpn_sqrtrem(
(mp_limb_t*) (s+off_bignum_data),
(mp_limb_t*) (r+off_bignum_data),
(mp_limb_t*) (bn+off_bignum_data),
limb_count);
ref(pair, off_car) = normalize_bignum(result_limb_count, 0, s-vector_tag);
if(r_actual_limbs == 0) {
/* perfect square */
ref(pair, off_cdr) = 0;
} else {
ref(pair, off_cdr) = normalize_bignum(r_actual_limbs, 0, r-vector_tag);
}
return pair;
}