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#include <stdio.h>
#include <math.h>
#include "binomialOptions_common.h"
#include "realtype.h"

///////////////////////////////////////////////////////////////////////////////
// Polynomial approximation of cumulative normal distribution function
///////////////////////////////////////////////////////////////////////////////
static real CND(real d) {
  const real A1 = (real)0.31938153;
  const real A2 = (real)-0.356563782;
  const real A3 = (real)1.781477937;
  const real A4 = (real)-1.821255978;
  const real A5 = (real)1.330274429;
  const real RSQRT2PI = (real)0.39894228040143267793994605993438;

  real K = (real)(1.0 / (1.0 + 0.2316419 * (real)fabs(d)));

  real cnd = (real)RSQRT2PI * (real)exp(-0.5 * d * d) *
             (K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5)))));

  if (d > 0) cnd = (real)1.0 - cnd;

  return cnd;
}

extern "C" void BlackScholesCall(real &callResult, TOptionData optionData) {
  real S = optionData.S;
  real X = optionData.X;
  real T = optionData.T;
  real R = optionData.R;
  real V = optionData.V;

  real sqrtT = (real)sqrt(T);
  real d1 = (real)(log(S / X) + (R + (real)0.5 * V * V) * T) / (V * sqrtT);
  real d2 = d1 - V * sqrtT;
  real CNDD1 = CND(d1);
  real CNDD2 = CND(d2);

  // Calculate Call and Put simultaneously
  real expRT = (real)exp(-R * T);
  callResult = (real)(S * CNDD1 - X * expRT * CNDD2);
}

////////////////////////////////////////////////////////////////////////////////
// Process an array of OptN options on CPU
// Note that CPU code is for correctness testing only and not for benchmarking.
////////////////////////////////////////////////////////////////////////////////
static real expiryCallValue(real S, real X, real vDt, int i) {
  real d = S * (real)exp(vDt * (real)(2 * i - NUM_STEPS)) - X;
  return (d > (real)0) ? d : (real)0;
}

extern "C" void binomialOptionsCPU(real &callResult, TOptionData optionData) {
  static real Call[NUM_STEPS + 1];

  const real S = optionData.S;
  const real X = optionData.X;
  const real T = optionData.T;
  const real R = optionData.R;
  const real V = optionData.V;

  const real dt = T / (real)NUM_STEPS;
  const real vDt = (real)V * (real)sqrt(dt);
  const real rDt = R * dt;
  // Per-step interest and discount factors
  const real If = (real)exp(rDt);
  const real Df = (real)exp(-rDt);
  // Values and pseudoprobabilities of upward and downward moves
  const real u = (real)exp(vDt);
  const real d = (real)exp(-vDt);
  const real pu = (If - d) / (u - d);
  const real pd = (real)1.0 - pu;
  const real puByDf = pu * Df;
  const real pdByDf = pd * Df;

  ///////////////////////////////////////////////////////////////////////
  // Compute values at expiration date:
  // call option value at period end is V(T) = S(T) - X
  // if S(T) is greater than X, or zero otherwise.
  // The computation is similar for put options.
  ///////////////////////////////////////////////////////////////////////
  for (int i = 0; i <= NUM_STEPS; i++) Call[i] = expiryCallValue(S, X, vDt, i);

  ////////////////////////////////////////////////////////////////////////
  // Walk backwards up binomial tree
  ////////////////////////////////////////////////////////////////////////
  for (int i = NUM_STEPS; i > 0; i--)
    for (int j = 0; j <= i - 1; j++)
      Call[j] = puByDf * Call[j + 1] + pdByDf * Call[j];

  callResult = (real)Call[0];
}