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// -*- mode: c++ -*-
/*
Copyright (c) 2010-2023, Intel Corporation
SPDX-License-Identifier: BSD-3-Clause
*/
#include "options_defs.h"
// Cumulative normal distribution function
static inline float
CND(float X) {
float L = abs(X);
float k = 1.0 / (1.0 + 0.2316419 * L);
float k2 = k*k;
float k3 = k2*k;
float k4 = k2*k2;
float k5 = k3*k2;
const float invSqrt2Pi = 0.39894228040f;
float w = (0.31938153f * k - 0.356563782f * k2 + 1.781477937f * k3 +
-1.821255978f * k4 + 1.330274429f * k5);
w *= invSqrt2Pi * exp(-L * L * .5f);
if (X > 0.f)
w = 1.0 - w;
return w;
}
task void
bs_task(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (uniform int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
export void
black_scholes_ispc_tasks(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int nTasks = max((uniform int)64, (uniform int)count/16384);
launch[nTasks] bs_task(Sa, Xa, Ta, ra, va, result, count);
}
export void
black_scholes_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
static inline float
binomial_put(float S, float X, float T, float r, float v) {
float V[BINOMIAL_NUM];
float dt = T / BINOMIAL_NUM;
float u = exp(v * sqrt(dt));
float d = 1. / u;
float disc = exp(r * dt);
float Pu = (disc - d) / (u - d);
for (uniform int j = 0; j < BINOMIAL_NUM; ++j) {
float upow = pow(u, (uniform float)(2*j-BINOMIAL_NUM));
V[j] = max(0., X - S * upow);
}
for (uniform int j = BINOMIAL_NUM-1; j >= 0; --j)
for (uniform int k = 0; k < j; ++k)
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc;
return V[0];
}
export void
binomial_put_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
task void
binomial_task(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (uniform int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
export void
binomial_put_ispc_tasks(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int nTasks = max((uniform int)64, (uniform int)count/16384);
launch[nTasks] binomial_task(Sa, Xa, Ta, ra, va, result, count);
}
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