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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
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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 */

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

__device__ inline float cndGPU(float d) {
  const float A1 = 0.31938153f;
  const float A2 = -0.356563782f;
  const float A3 = 1.781477937f;
  const float A4 = -1.821255978f;
  const float A5 = 1.330274429f;
  const float RSQRT2PI = 0.39894228040143267793994605993438f;

  float K = __fdividef(1.0f, (1.0f + 0.2316419f * fabsf(d)));

  float cnd = RSQRT2PI * __expf(-0.5f * d * d) *
              (K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5)))));

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

  return cnd;
}

///////////////////////////////////////////////////////////////////////////////
// Black-Scholes formula for both call and put
///////////////////////////////////////////////////////////////////////////////
__device__ inline void BlackScholesBodyGPU(float &CallResult, float &PutResult,
                                           float S,  // Stock price
                                           float X,  // Option strike
                                           float T,  // Option years
                                           float R,  // Riskless rate
                                           float V  // Volatility rate
                                           ) {
  float sqrtT, expRT;
  float d1, d2, CNDD1, CNDD2;

  sqrtT = __fdividef(1.0F, rsqrtf(T));
  d1 = __fdividef(__logf(S / X) + (R + 0.5f * V * V) * T, V * sqrtT);
  d2 = d1 - V * sqrtT;

  CNDD1 = cndGPU(d1);
  CNDD2 = cndGPU(d2);

  // Calculate Call and Put simultaneously
  expRT = __expf(-R * T);
  CallResult = S * CNDD1 - X * expRT * CNDD2;
  PutResult = X * expRT * (1.0f - CNDD2) - S * (1.0f - CNDD1);
}

////////////////////////////////////////////////////////////////////////////////
// Process an array of optN options on GPU
////////////////////////////////////////////////////////////////////////////////
extern "C" __launch_bounds__(128) __global__
    void BlackScholesGPU(float2 *__restrict d_CallResult,
                         float2 *__restrict d_PutResult,
                         float2 *__restrict d_StockPrice,
                         float2 *__restrict d_OptionStrike,
                         float2 *__restrict d_OptionYears, float Riskfree,
                         float Volatility, int optN) {
  ////Thread index
  const int opt = blockDim.x * blockIdx.x + threadIdx.x;

  // Calculating 2 options per thread to increase ILP (instruction level
  // parallelism)
  if (opt < (optN / 2)) {
    float callResult1, callResult2;
    float putResult1, putResult2;
    BlackScholesBodyGPU(callResult1, putResult1, d_StockPrice[opt].x,
                        d_OptionStrike[opt].x, d_OptionYears[opt].x, Riskfree,
                        Volatility);
    BlackScholesBodyGPU(callResult2, putResult2, d_StockPrice[opt].y,
                        d_OptionStrike[opt].y, d_OptionYears[opt].y, Riskfree,
                        Volatility);
    d_CallResult[opt] = make_float2(callResult1, callResult2);
    d_PutResult[opt] = make_float2(putResult1, putResult2);
  }
}