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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
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 *    contributors may be used to endorse or promote products derived
 *    from this software without specific prior written permission.
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
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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);
}
