/*
* Completely rewritten in CryptKit-18, 13 Jan 1997, for new IEEE-style
* curveParameters.
*/
int which_curve(giant x, curveParams *par)
/* Returns (+-1) depending on whether x is on curve
(+-)y^2 = x^3 + c x^2 + a x + b.
*/
{
giant t1;
giant t2;
giant t3;
int result;
PROF_START;
t1 = borrowGiant(par->maxDigits);
t2 = borrowGiant(par->maxDigits);
t3 = borrowGiant(par->maxDigits);
/* First, set t2:= x^3 + c x^2 + a x + b. */
gtog(x, t2); addg(par->c, t2);
mulg(x, t2); addg(par->a, t2); /* t2 := x^2 + c x + a. */
feemod(par, t2);
mulg(x, t2); addg(par->b, t2);
feemod(par, t2);
/* Next, test whether t2 is a square. */
gtog(t2, t1);
make_base(par, t3); iaddg(1, t3); gshiftright(1, t3); /* t3 = (p+1)/2. */
feepowermodg(par, t1, t3); /* t1 := t2^((p+1)/2) (mod p). */
if(gcompg(t1, t2) == 0)
result = CURVE_PLUS;
else
result = CURVE_MINUS;
returnGiant(t1);
returnGiant(t2);
returnGiant(t3);
PROF_END(whichCurveTime);
return result;
}
bh_view Expander::make_temp(bh_type type, bh_index nelem)
{
bh_view view;
view.base = make_base(type, nelem);
view.start = 0;
view.ndim = 1;
view.shape[0] = nelem;
view.stride[0] = 1;
return view;
}
/* Create a basic air critter */
static struct Critter *make_base_ac(SDL_Surface **gfx,float x,float y) {
struct Critter *c = make_base(gfx);
init_flyer(&c->flyer,AIRBORNE);
c->type = AIRCRITTER;
c->physics.x = x;
c->physics.y = y;
c->timer = 0;
c->timerfunc = ac_searchtarget;
return c;
}
int my_putnbr_adress(unsigned long int nbr, int *count)
{
char *base;
unsigned long int length;
base = make_base("0123456789abcdef");
length = 16;
if (nbr >= length)
my_putnbr_adress(nbr / length, count);
my_dischar(base[nbr % length], count);
return (0);
}
/* Create a basic water critter */
static struct Critter *make_base_wc(SDL_Surface **gfx,float x,float y) {
struct Critter *c = make_base(gfx);
init_flyer(&c->flyer,UNDERWATER);
c->flyer.speed = 0.5;
c->type = WATERCRITTER;
c->physics.x = x;
c->physics.y = y;
c->timer = 0;
c->timerfunc = ac_searchtarget;
return c;
}
/* Create a basic ground critter */
static struct Critter *make_base_gc(SDL_Surface **gfx,float x,float y) {
struct Critter *c = make_base(gfx);
c->type = GROUNDCRITTER;
init_walker(&c->walker);
c->physics.x = x;
c->physics.y = y;
c->physics.radius = 6;
c->physics.mass = 12;
c->walker.walking = rand()%2?-1:1;
c->walker.walkspeed = 1;
c->walker.slope = 5;
c->ship = 0;
c->timer = 1;
c->timerfunc = gc_dosomething;
c->die = gc_die;
return c;
}
/**
* Expand matmul at the given pc in the bhir instruction list.
*
* Returns the number of additional instructions used.
*/
int Expander::expand_matmul(bh_ir& bhir, int pc)
{
int start_pc = pc;
bh_instruction& composite = bhir.instr_list[pc];
// Lazy choice... no re-use just NOP it.
composite.opcode = BH_NONE;
// Grab operands
bh_view out = composite.operand[0];
bh_view a = composite.operand[1];
bh_view b = composite.operand[2];
// Grab the shape
int n = a.shape[0];
int m = a.shape[1];
int k = b.shape[1];
// Construct intermediary operands
// Needs broadcast
bh_view a_3d = a;
// Needs transposition + broadcast
bh_view b_3d = b;
a_3d.ndim = 3;
b_3d.ndim = 3;
// Set the shape
a_3d.shape[0] = b_3d.shape[0] = n;
a_3d.shape[1] = b_3d.shape[1] = k;
a_3d.shape[2] = b_3d.shape[2] = m;
// Construct broadcast
a_3d.stride[0] = a.stride[0];
a_3d.stride[1] = 0;
a_3d.stride[2] = a.stride[1];
// Construct transpose + broadcast
b_3d.stride[0] = 0;
b_3d.stride[1] = b.stride[1];
b_3d.stride[2] = b.stride[0];
// Construct temp for mul-result
bh_view c_3d = b_3d;
// Count number of elements
bh_intp nelements = 1;
// Set contiguous stride
for(bh_intp dim=c_3d.ndim-1; dim >= 0; --dim) {
c_3d.stride[dim] = nelements;
nelements *= c_3d.shape[dim];
}
c_3d.start = 0;
c_3d.base = make_base(b_3d.base->type, nelements);
// Expand sequence
inject(bhir, ++pc, BH_MULTIPLY, c_3d, a_3d, b_3d);
inject(bhir, ++pc, BH_ADD_REDUCE, out, c_3d, (int64_t)2, BH_INT64);
inject(bhir, ++pc, BH_FREE, c_3d);
verbose_print("[Matmul] Expanding BH_MATMUL");
return pc - start_pc;
}
bh_view Expander::make_temp(bh_view& meta, bh_type type, bh_index nelem)
{
bh_view view = meta;
view.base = make_base(type, nelem);
return view;
}
static Uri make_base(const std::string& document)
{
return make_base(Uri{ document });
}
/*
* Completely rewritten in CryptKit-18, 13 Jan 1997, for new IEEE-style
* curveParameters.
*/
void elliptic_add(giant x1, giant x2, giant x3, curveParams *par, int s) {
/* Addition algorithm for x3 = x1 + x2 on the curve, with sign ambiguity s.
From theory, we know that if {x1,1} and {x2,1} are on a curve, then
their elliptic sum (x1,1} + {x2,1} = {x3,1} must have x3 as one of two
values:
x3 = U/2 + s*Sqrt[U^2/4 - V]
where sign s = +-1, and U,V are functions of x1,x2. Tho present function
is called a maximum of twice, to settle which of +- is s. When a call
is made, it is guaranteed already that x1, x2 both lie on the same curve
(+- curve); i.e., which curve (+-) is not connected at all with sign s of
the x3 relation.
*/
giant cur_n;
giant t1;
giant t2;
giant t3;
giant t4;
giant t5;
PROF_START;
cur_n = borrowGiant(par->maxDigits);
t1 = borrowGiant(par->maxDigits);
t2 = borrowGiant(par->maxDigits);
t3 = borrowGiant(par->maxDigits);
t4 = borrowGiant(par->maxDigits);
t5 = borrowGiant(par->maxDigits);
if(gcompg(x1, x2)==0) {
int_to_giant(1, t1);
numer_double(x1, t1, x3, par);
denom_double(x1, t1, t2, par);
binvg_cp(par, t2);
mulg(t2, x3); feemod(par, x3);
goto out;
}
numer_plus(x1, x2, t1, par);
int_to_giant(1, t3);
numer_times(x1, t3, x2, t3, t2, par);
int_to_giant(1, t4); int_to_giant(1, t5);
denom_times(x1, t4, x2, t5, t3, par);
binvg_cp(par, t3);
mulg(t3, t1); feemod(par, t1); /* t1 := U/2. */
mulg(t3, t2); feemod(par, t2); /* t2 := V. */
/* Now x3 will be t1 +- Sqrt[t1^2 - t2]. */
gtog(t1, t4); gsquare(t4); feemod(par, t4);
subg(t2, t4);
make_base(par, cur_n); iaddg(1, cur_n); gshiftright(2, cur_n);
/* cur_n := (p+1)/4. */
feepowermodg(par, t4, cur_n); /* t4 := t2^((p+1)/4) (mod p). */
gtog(t1, x3);
if(s != SIGN_PLUS) negg(t4);
addg(t4, x3);
feemod(par, x3);
out:
returnGiant(cur_n);
returnGiant(t1);
returnGiant(t2);
returnGiant(t3);
returnGiant(t4);
returnGiant(t5);
PROF_END(ellAddTime);
}
