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 *    notice, this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *  * Neither the name of NVIDIA CORPORATION nor the names of its
 *    contributors may be used to endorse or promote products derived
 *    from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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 */

#include <math.h>

///////////////////////////////////////////////////////////////////////////////
// Polynomial approximation of cumulative normal distribution function
///////////////////////////////////////////////////////////////////////////////

static double CND(double d) {
  const double A1 = 0.31938153;
  const double A2 = -0.356563782;
  const double A3 = 1.781477937;
  const double A4 = -1.821255978;
  const double A5 = 1.330274429;
  const double RSQRT2PI = 0.39894228040143267793994605993438;

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

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

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

  return cnd;
}

///////////////////////////////////////////////////////////////////////////////
// Black-Scholes formula for both call and put
///////////////////////////////////////////////////////////////////////////////
static void BlackScholesBodyCPU(float &callResult, float &putResult,
                                float Sf,  // Stock price
                                float Xf,  // Option strike
                                float Tf,  // Option years
                                float Rf,  // Riskless rate
                                float Vf  // Volatility rate
                                ) {
  double S = Sf, X = Xf, T = Tf, R = Rf, V = Vf;
  double sqrtT = sqrt(T);
  double d1 = (log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT);
  double d2 = d1 - V * sqrtT;
  double CNDD1 = CND(d1);
  double CNDD2 = CND(d2);

  // Calculate Call and Put simultaneously
  double expRT = exp(-R * T);

  callResult = (float)(S * CNDD1 - X * expRT * CNDD2);
  putResult = (float)(X * expRT * (1.0 - CNDD2) - S * (1.0 - CNDD1));
}

////////////////////////////////////////////////////////////////////////////////
// Process an array of optN options
////////////////////////////////////////////////////////////////////////////////

extern "C" void BlackScholesCPU(float *h_CallResult, float *h_PutResult,
                                float *h_StockPrice, float *h_OptionStrike,
                                float *h_OptionYears, float Riskfree,
                                float Volatility, int optN) {
  for (int opt = 0; opt < optN; opt++)
    BlackScholesBodyCPU(h_CallResult[opt], h_PutResult[opt], h_StockPrice[opt],
                        h_OptionStrike[opt], h_OptionYears[opt], Riskfree,
                        Volatility);
}
