NewFloatRepresentation(F f)
: limbs{}, negative(f < 0.f), fpclass(std::fpclassify(f))
{
if (fpclass == FP_INFINITE || fpclass == FP_NAN) return;
unsigned limbIndex = Length<F>::e0;
float s = std::fabs(frexp(f, &exponent));
s *= 1<<29; // pre-scale with 2^29 to extract as many bits as possible in the first iteration
exponent -= 29; // store prescaling in exponent
limbs[limbIndex] = static_cast<limb_t>(s);
while (s) {
s -= limbs[limbIndex];
s *= 1<<29;
mult2(29);
limbIndex++;
limbs[limbIndex] = static_cast<limb_t>(s);
}
// scale to exponent=0
if (exponent < 0)
div2(-exponent);
else if (exponent > 0)
mult2(exponent);
}
int
main(void)
{
printf("%d\n", mult2(3));
int (*fmult2) (int) = mult2;
printf("%d\n", (*fmult2)(3));
}
t_vect unit(t_vect v)
{
double is;
if ((is = length(v)) > 1)
return (mult2(v, (double)(1/is)));
else
return (v);
}
int functions_test()
{
int sum(int,int);
int a,b,s;
printf("Enter two nos.");
scanf("%d%d", &a,&b);
s=sum(a,b);
printf("\nSum is = %d", s);
mult2();
return 0;
}
void test() {
complex a, b;
a.x = 2.0;
a.y = 3.0;
b.x = 4;
b.y = 5;
printf("Enter a and b where a + ib is the first complex number.\n");
printf("a = ");
scanf("%f", &a.x);
printf("b = ");
scanf("%f", &a.y);
printf("Enter c and d where c + id is the second complex number.\n");
printf("c = ");
scanf("%f", &b.x);
printf("d = ");
scanf("%f", &b.y);
printf (" The complex numbers entered are :%.1f %+.1f and %.1f %+.1fi\n", a.x,a.y,b.x,b.y);
printf ("The multiplication of complex numbers are :%.1f %+.1fi\n", mult2(a,b).x, mult2(a,b).y);
printf ("The square of complex number is :%.1f %+.1fi\n", square(a).x, square(a).y);
printf ("The addition of complex numbers are :%.1f %+.1fi\n", add2(a,b).x, add2(a,b).y);
printf ("The juliamap of complex numbers are :%.1f %+.1fi\n", juliamap(a,b).x, juliamap(a,b).y);
complex_print(a);
complex_print(b);
}
int main()
{
float a=9;
Parametro f1[2];
f1[0].amarracao = LIVRE;
f1[0].tipo = FLOAT;
f1[1].amarracao = CONSTANTE;
f1[1].tipo = FLOAT;
f1[1].valor.vFloat = 2;
mult mult2 = (mult)create(multiplicar,FLOAT,2,f1);
printf("o dobro de %.2f e: %.2f\n",a, mult2(a));
return 0;
}
/* It returns the result of the desirable function among the functions defined above (mult2, square, add2, juliamap)*/
COMPLEX get_result(char *name, COMPLEX *a, COMPLEX *b){
COMPLEX c;
if(strcmp("mult2",name)==0){
c=mult2(a,b);
}
else if(strcmp("square",name)==0){
c=square(a);
}
else if(strcmp("add2",name)==0){
c=add2(a,b);
}
else if(strcmp("juliamap",name)==0){
c=juliamap(a,b);
}
return c;
}
double light_spec(t_light *light, t_vect light_dir, t_vect norm, t_vect ray_dir, double spec)
{
double high;
t_vect v;
t_vect r;
double i;
double s;
high = dot(norm, light_dir);
v = negate(ray_dir);
r = sub(light_dir, mult2(norm, high * 2.0));
i = dot(v, r);
if (i < 0)
return (0);
s = pow(i, spec) * KS_CONST * light->i;
return (s);
}
void test(){/*this function demonstrates that all of the functions defined above,work correctly.*/
a.x=1.;
a.y=3.;
b.x=2.;
b.y=1.;
c=mult2(a,b);
assert(c.x==-1.);
assert(c.y==7.);
printf("mult2 is correct.\n");
c=square(a);
assert(c.x==-8.);
assert(c.y==6.);
printf("square is correct.\n");
c=add2(a,b);
assert(c.x==3.);
assert(c.y==4.);
printf("add2 is correct.\n");
c=juliamap(a,b);
assert(c.x==-6.);
assert(c.y==7.);
printf("juliamap is correct.\n");
complex_print(a);
printf("If the previous sentence is 'z=1.000000+3.000000i', the function complex_print is working correctly.\n");
}
/* Main computational kernel. The whole function will be timed,
including the call and return. */
static
void kernel_floyd_warshall(int n,
DATA_TYPE POLYBENCH_2D(path,N,N,n,n))
{
int i1, i2, j3;
#pragma scop
for(int k=0; k< _PB_N; k++){
multifor(i1=0,i2=0,j3=0; i1<k+1, i2<k+1, j3<k+1; i1++,i2++,j3++; 1,1,1; 0,1,1){
0:{
mult1(i1, path, k);
}
1:{
mult2(i2,path, n, k);
}
2:{
mult3(j3,path,n,k);
}
}
for(int i=k+1; i<n;i++){
for(int j=k+1;j<n;j++){
path[i][j] = path[i][j] < path[i][k] + path[k][j] ? path[i][j] : path[i][k] + path[k][j];
}
}
}
//source code for (k = 0; k < _PB_N; k++)
//source code {
//source code for(i = 0; i < _PB_N; i++)
//source code for (j = 0; j < _PB_N; j++)
//source code path[i][j] = path[i][j] < path[i][k] + path[k][j] ?
//source code path[i][j] : path[i][k] + path[k][j];
//source code }
#pragma endscop
}
// Point addition
void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
{
if(is_zero())
{
m_coord_x = rhs.m_coord_x;
m_coord_y = rhs.m_coord_y;
m_coord_z = rhs.m_coord_z;
return;
}
else if(rhs.is_zero())
return;
const BigInt& p = m_curve.get_p();
BigInt& rhs_z2 = ws_bn[0];
BigInt& U1 = ws_bn[1];
BigInt& S1 = ws_bn[2];
BigInt& lhs_z2 = ws_bn[3];
BigInt& U2 = ws_bn[4];
BigInt& S2 = ws_bn[5];
BigInt& H = ws_bn[6];
BigInt& r = ws_bn[7];
/*
http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
*/
curve_sqr(rhs_z2, rhs.m_coord_z);
curve_mult(U1, m_coord_x, rhs_z2);
curve_mult(S1, m_coord_y, curve_mult(rhs.m_coord_z, rhs_z2));
curve_sqr(lhs_z2, m_coord_z);
curve_mult(U2, rhs.m_coord_x, lhs_z2);
curve_mult(S2, rhs.m_coord_y, curve_mult(m_coord_z, lhs_z2));
H = U2;
H -= U1;
if(H.is_negative())
H += p;
r = S2;
r -= S1;
if(r.is_negative())
r += p;
if(H.is_zero())
{
if(r.is_zero())
{
mult2(ws_bn);
return;
}
// setting to zero:
m_coord_x = 0;
m_coord_y = 1;
m_coord_z = 0;
return;
}
curve_sqr(U2, H);
curve_mult(S2, U2, H);
U2 = curve_mult(U1, U2);
curve_sqr(m_coord_x, r);
m_coord_x -= S2;
m_coord_x -= (U2 << 1);
while(m_coord_x.is_negative())
m_coord_x += p;
U2 -= m_coord_x;
if(U2.is_negative())
U2 += p;
curve_mult(m_coord_y, r, U2);
m_coord_y -= curve_mult(S1, S2);
if(m_coord_y.is_negative())
m_coord_y += p;
curve_mult(m_coord_z, curve_mult(m_coord_z, rhs.m_coord_z), H);
}
// Square a complex number
COMPLEX square(COMPLEX *a){
return mult2(a,a);
}
// Point addition
void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
{
if(is_zero())
{
coord_x = rhs.coord_x;
coord_y = rhs.coord_y;
coord_z = rhs.coord_z;
return;
}
else if(rhs.is_zero())
return;
const BigInt& p = curve.get_p();
BigInt& rhs_z2 = ws_bn[0];
BigInt& U1 = ws_bn[1];
BigInt& S1 = ws_bn[2];
BigInt& lhs_z2 = ws_bn[3];
BigInt& U2 = ws_bn[4];
BigInt& S2 = ws_bn[5];
BigInt& H = ws_bn[6];
BigInt& r = ws_bn[7];
monty_sqr(rhs_z2, rhs.coord_z);
monty_mult(U1, coord_x, rhs_z2);
monty_mult(S1, coord_y, monty_mult(rhs.coord_z, rhs_z2));
monty_sqr(lhs_z2, coord_z);
monty_mult(U2, rhs.coord_x, lhs_z2);
monty_mult(S2, rhs.coord_y, monty_mult(coord_z, lhs_z2));
H = U2;
H -= U1;
if(H.is_negative())
H += p;
r = S2;
r -= S1;
if(r.is_negative())
r += p;
if(H.is_zero())
{
if(r.is_zero())
{
mult2(ws_bn);
return;
}
*this = PointGFp(curve); // setting myself to zero
return;
}
monty_sqr(U2, H);
monty_mult(S2, U2, H);
U2 = monty_mult(U1, U2);
monty_sqr(coord_x, r);
coord_x -= S2;
coord_x -= (U2 << 1);
while(coord_x.is_negative())
coord_x += p;
U2 -= coord_x;
if(U2.is_negative())
U2 += p;
monty_mult(coord_y, r, U2);
coord_y -= monty_mult(S1, S2);
if(coord_y.is_negative())
coord_y += p;
monty_mult(coord_z, monty_mult(coord_z, rhs.coord_z), H);
}
void test()
{
/* From now on, we will be using . right after an integer in order to be in full agreement with the definition of
* my x_realpart and y_imagpart since they were defined as long double */
COMPLEX compl1;
compl1.x_realpart = 1.;
compl1.y_imagpart = 2.;
COMPLEX compl2;
compl2.x_realpart = 3.;
compl2.y_imagpart = 4.;
/* let's test */
/* let's compute the multipliction*/
COMPLEX expected1;
expected1.x_realpart = -5.; /* this is the real part of the complex number obtained by computing 1+2i and 3+4i*/
expected1.y_imagpart = 10.; /* this is the imaginary part of the complex number obtained by computing 1+2i and 3+4i */
COMPLEX result1;
COMPLEX *cptr11, *cptr12;
cptr11 = &compl1;
cptr12 = &compl2;
result1 = mult2(cptr11,cptr12);
/*complex_print(result1)*/; /* print the result of the multiplication of two complex numbers*/
assert (expected1.x_realpart == result1.x_realpart);
assert (expected1.y_imagpart == result1.y_imagpart);
/* let's compute the square of the first complex given above */
COMPLEX expected2;
expected2.x_realpart = -3.; /* this is the real part of the complex number obtained by squaring 1+2i*/
expected2.y_imagpart = 4.; /* this is the imaginary part of the complex number obtained by squaring 1+2i*/
COMPLEX result2;
COMPLEX *cptr2;
cptr2 = &compl1;
result2 = square(cptr2);
/*complex_print(result2)*/; /* print the result of the square of compl1*/
assert (expected2.x_realpart == result2.x_realpart);
assert (expected2.y_imagpart == result2.y_imagpart);
/* let's compute the addition of two complex numbers */
COMPLEX expected3;
expected3.x_realpart = 4.; /* this is the real part of the complex number obtained by adding 1+2i and 3+4i*/
expected3.y_imagpart = 6.; /* this ia the imag part of the complex number obtained by adding 1+2i and 3+4i*/
COMPLEX result3;
COMPLEX *cptr31, *cptr32;
cptr31 = &compl1;
cptr32 = &compl2;
result3 = add2(cptr31,cptr32);
/*complex_print(result3)*/; /* print the result of the addition of compl1 and compl2*/
assert (expected3.x_realpart == result3.x_realpart);
assert (expected3.y_imagpart == result3.y_imagpart);
/* let's compute the juliamap where z= compl1 is the first variable and c= compl2 is the second variable*/
COMPLEX expected4;
expected4.x_realpart = 0.; /* this is the real part of the complex number obtained by adding the square of compl1 to compl2*/
expected4.y_imagpart = 8.; /* this is the imag part of the complex number obtained by adding the square of compl1 to compl2*/
COMPLEX result4;
COMPLEX *cptr41, *cptr42;
cptr41 = &compl1;
cptr42 = &compl2;
result4 = juliamap(cptr41,cptr42);
/*complex_print(result4)*/; /* print the result of the juliamap*/
assert (expected4.x_realpart == result4.x_realpart);
assert (expected4.y_imagpart == result4.y_imagpart);
/* let's compute the complex_return function with compl1 as the argument*/
COMPLEX expected5;
expected5.x_realpart = 1.;
expected5.y_imagpart = 2.;
COMPLEX *cptr5;
cptr5 = &expected5;
complex_print(cptr5);
printf(" if the previous sentence is z = 1.000000+2.000000i, then the complex return is working as expected \n" );
}
struct complex square(struct complex a){/*we define a function square that takes a complex structure and returns the square of that structure*/
z=mult2(a,a);
return z;
}
// Projection functions
inline void projectedOnto2(vec2 * r, vec2 a, vec2 b) {
mult2( r, a, dot2(a, b) );
invScale2( r, length2(a) * length2(b) );
}
inline void reflect2(vec2 * r, vec2 n) {
vec2 i = *r;
mult2( r, n, dot2( n, i ) * ((scalar)2) );
subFrom2( r, i );
}
inline void projectOnto2(vec2 a, vec2 * r) {
scalar l = length2(a) * length2(*r);
mult2( r, a, dot2(a, *r) );
invScale2( r, l );
}
// Point addition
void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
{
if(is_zero())
{
m_coord_x = rhs.m_coord_x;
m_coord_y = rhs.m_coord_y;
m_coord_z = rhs.m_coord_z;
return;
}
else if(rhs.is_zero())
return;
const BigInt& p = m_curve.get_p();
const size_t cap_size = 2*m_curve.get_p_words() + 2;
for(size_t i = 0; i != ws_bn.size(); ++i)
ws_bn[i].ensure_capacity(cap_size);
BigInt& rhs_z2 = ws_bn[0];
BigInt& U1 = ws_bn[1];
BigInt& S1 = ws_bn[2];
BigInt& lhs_z2 = ws_bn[3];
BigInt& U2 = ws_bn[4];
BigInt& S2 = ws_bn[5];
BigInt& H = ws_bn[6];
BigInt& r = ws_bn[7];
BigInt& tmp = ws_bn[9];
secure_vector<word>& monty_ws = ws_bn[8].get_word_vector();
/*
https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
*/
m_curve.sqr(rhs_z2, rhs.m_coord_z, monty_ws);
m_curve.mul(U1, m_coord_x, rhs_z2, monty_ws);
m_curve.mul(tmp, rhs.m_coord_z, rhs_z2, monty_ws); // z^3
m_curve.mul(S1, m_coord_y, tmp, monty_ws);
m_curve.sqr(lhs_z2, m_coord_z, monty_ws);
m_curve.mul(U2, rhs.m_coord_x, lhs_z2, monty_ws);
m_curve.mul(tmp, m_coord_z, lhs_z2, monty_ws);
m_curve.mul(S2, rhs.m_coord_y, tmp, monty_ws);
H = U2;
H -= U1;
if(H.is_negative())
H += p;
r = S2;
r -= S1;
if(r.is_negative())
r += p;
if(H.is_zero())
{
if(r.is_zero())
{
mult2(ws_bn);
return;
}
// setting to zero:
m_coord_x = 0;
m_coord_y = 1;
m_coord_z = 0;
return;
}
m_curve.sqr(U2, H, monty_ws);
m_curve.mul(S2, U2, H, monty_ws);
m_curve.mul(tmp, U1, U2, monty_ws);
U2 = tmp;
m_curve.sqr(m_coord_x, r, monty_ws);
m_coord_x -= S2;
m_coord_x -= (U2 << 1);
while(m_coord_x.is_negative())
m_coord_x += p;
U2 -= m_coord_x;
if(U2.is_negative())
U2 += p;
m_curve.mul(m_coord_y, r, U2, monty_ws);
m_curve.mul(tmp, S1, S2, monty_ws);
m_coord_y -= tmp;
if(m_coord_y.is_negative())
m_coord_y += p;
m_curve.mul(tmp, m_coord_z, rhs.m_coord_z, monty_ws);
m_curve.mul(m_coord_z, tmp, H, monty_ws);
}
void multstore(long x, long y, long* dest){
long t = mult2(x, y);
*dest = t;
}