int get_two_normal_fixed(int seed, fixedpt *n1, fixedpt *n2)
{
fixedpt r1, r2;
fixedpt twoPI = 411775; // ??? janders -- hard-code 2PI in fixed point to avoid conversion from double
// from 2 uniform random numbers r1 and r2, we will generate two Gaussian random numbers deposited into n1 and n2
int s = seed;
r1 = get_uniform_fixed (&s);
r2 = get_uniform_fixed (&s);
int tid = omp_get_thread_num();
n1 += tid;
n2 += tid;
/*
fixedpt ln1 = fixedpt_ln( r1 );
fixedpt mul1 = fixedpt_mul(-1*FIXEDPT_TWO , ln1);
fixedpt mul2 = fixedpt_mul( twoPI , r2);
fixedpt cos1 = fixedpt_cos(mul2);
fixedpt sqrt1 = fixedpt_sqrt ( mul1);
fixedpt gaussR1 = fixedpt_mul(sqrt1, cos1);
n1 += tid;
*n1 = gaussR1;
fixedpt sin1 = fixedpt_sin(mul2);
fixedpt gaussR2 = fixedpt_mul(sqrt1, sin1);
n2 += tid;
*n2 = gaussR2;*/
*n1 = fixedpt_mul(fixedpt_sqrt ( fixedpt_mul(-1*FIXEDPT_TWO , fixedpt_ln( r1 )) ), fixedpt_cos(fixedpt_mul( twoPI , r2)));
*n2 = fixedpt_mul(fixedpt_sqrt ( fixedpt_mul(-1*FIXEDPT_TWO , fixedpt_ln( r1)) ), fixedpt_sin (fixedpt_mul( twoPI , r2)));
// if (tid==0){
// printf("seed = %d, ln1 = %d, mul1 = %d, mul2 = %d, cos1 = %d, sin1 = %d, sqrt1 = %d, gaussR1 = %d, gaussR2 = %d\n", s, ln1, mul1, mul2, cos1, sin1, sqrt1, gaussR1, gaussR2);
//}
return s;
}
void get_two_normal_fixed(int *seed, fixedpt *n1, fixedpt *n2)
{
fixedpt r1, r2;
fixedpt twoPI = 411775; // ??? janders -- hard-code 2PI in fixed point to avoid conversion from double
// from 2 uniform random numbers r1 and r2, we will generate two Gaussian random numbers deposited into n1 and n2
r1 = get_uniform_fixed (seed);
r2 = get_uniform_fixed (seed);
*n1 = fixedpt_mul(fixedpt_sqrt ( fixedpt_mul(-1*FIXEDPT_TWO , fixedpt_ln( r1 )) ), fixedpt_cos(fixedpt_mul( twoPI , r2)));
*n2 = fixedpt_mul(fixedpt_sqrt ( fixedpt_mul(-1*FIXEDPT_TWO , fixedpt_ln( r1)) ), fixedpt_sin (fixedpt_mul( twoPI , r2)));
}
fixedpt asset_path_fixed_simplified ( fixedpt s0, fixedpt mu, fixedpt sigma, fixedpt t1, int n, int *seed ){
int i;
fixedpt dt, stepnum, p;
fixedpt gaussR1 = 0, gaussR2 = 0;
// stepnum = fixedpt_rconst(n);
stepnum = n << FIXEDPT_FBITS; // ??? janders
dt = fixedpt_div(t1, stepnum);
fixedpt constA = fixedpt_mul(fixedpt_sub(mu, fixedpt_mul(sigma, sigma)), dt);
fixedpt constB = fixedpt_mul(sigma, fixedpt_sqrt ( dt ));
p = s0;
for ( i = 1; i <= n; i++ )
{
if (i & 1) // iteration is odd, generate two random Gaussian numbers (the Box-Muller transform gens 2 numbers)
get_two_normal_fixed_LUT(seed, &gaussR1, &gaussR2);
p = fixedpt_mul(p, fixedpt_exp (fixedpt_add(constA,
fixedpt_mul(constB, i & 1 ? gaussR1 : gaussR2))));
// fixedpt_print(p);
}
return p;
}
fixedpt asset_path_fixed_simplified ( fixedpt s0, fixedpt mu, fixedpt sigma, fixedpt t1, int n, int seed ){
int i;
fixedpt dt, stepnum, p;
fixedpt gaussR1[OMP_ACCEL], gaussR2[OMP_ACCEL];
// stepnum = fixedpt_rconst(n);
stepnum = n << FIXEDPT_FBITS; // ??? janders
dt = fixedpt_div(t1, stepnum);
fixedpt constA = fixedpt_mul(fixedpt_sub(mu, fixedpt_mul(sigma, sigma)), dt);
fixedpt constB = fixedpt_mul(sigma, fixedpt_sqrt ( dt ));
int s = seed;
p = s0;
int tid;
for ( i = 1; i <= n; i++ )
{
tid = omp_get_thread_num();
if (i & 1) { // iteration is odd, generate two random Gaussian numbers (the Box-Muller transform gens 2 numbers)
s = get_two_normal_fixed(s, gaussR1, gaussR2);
}
p = fixedpt_mul(p, fixedpt_exp (fixedpt_add(constA,
fixedpt_mul(constB, i & 1 ? gaussR1[tid] : gaussR2[tid]))));
// if (tid == 0) {
// printf("i = %d, seed = %d, gaussR1 = %d, gaussR1 = %d, p = %d\n", i, s, gaussR1[tid], gaussR2[tid], p);
// }
// fixedpt_print(p);
}
return p;
}
int main() {
fixedpt A, B, C;
printf("fixedptc library version: %s\n", FIXEDPT_VCSID);
printf("Using %d-bit precision, %d.%d format\n\n", FIXEDPT_BITS, FIXEDPT_WBITS, FIXEDPT_FBITS);
printf("The most precise number: ");
fixedpt_print(1);
printf("The biggest number: ");
fixedpt_print(0x7fffff00);
printf("Here are some example numbers:\n");
printf("Random number: ");
fixedpt_print(fixedpt_rconst(143.125));
printf("PI: ");
fixedpt_print(FIXEDPT_PI);
printf("e: ");
fixedpt_print(FIXEDPT_E);
puts("");
A = fixedpt_rconst(2.5);
B = fixedpt_fromint(3);
fixedpt_print(A);
puts("+");
fixedpt_print(B);
C = fixedpt_add(A, B);
puts("=");
fixedpt_print(C);
puts("");
fixedpt_print(A);
puts("*");
fixedpt_print(B);
puts("=");
C = fixedpt_mul(A, B);
fixedpt_print(C);
puts("");
A = fixedpt_rconst(1);
B = fixedpt_rconst(4);
C = fixedpt_div(A, B);
fixedpt_print(A);
puts("/");
fixedpt_print(B);
puts("=");
fixedpt_print(C);
printf("exp(1)=");
fixedpt_print(fixedpt_exp(FIXEDPT_ONE));
puts("");
puts("sqrt(pi)=");
fixedpt_print(fixedpt_sqrt(FIXEDPT_PI));
puts("");
puts("sqrt(25)=");
fixedpt_print(fixedpt_sqrt(fixedpt_rconst(25)));
puts("");
puts("sin(pi/2)=");
fixedpt_print(fixedpt_sin(FIXEDPT_HALF_PI));
puts("");
puts("sin(3.5*pi)=");
fixedpt_print(fixedpt_sin(fixedpt_mul(fixedpt_rconst(3.5), FIXEDPT_PI)));
puts("");
puts("4^3.5=");
fixedpt_print(fixedpt_pow(fixedpt_rconst(4), fixedpt_rconst(3.5)));
puts("");
puts("4^0.5=");
fixedpt_print(fixedpt_pow(fixedpt_rconst(4), fixedpt_rconst(0.5)));
return (0);
}