/*
 * Copyright 1993-2007 NVIDIA Corporation.  All rights reserved.
 *
 * NOTICE TO USER:
 *
 * This source code is subject to NVIDIA ownership rights under U.S. and
 * international Copyright laws.  Users and possessors of this source code
 * are hereby granted a nonexclusive, royalty-free license to use this code
 * in individual and commercial software.
 *
 * NVIDIA MAKES NO REPRESENTATION ABOUT THE SUITABILITY OF THIS SOURCE
 * CODE FOR ANY PURPOSE.  IT IS PROVIDED "AS IS" WITHOUT EXPRESS OR
 * IMPLIED WARRANTY OF ANY KIND.  NVIDIA DISCLAIMS ALL WARRANTIES WITH
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 * MERCHANTABILITY, NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE.
 * IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY SPECIAL, INDIRECT, INCIDENTAL,
 * OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
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 * OR OTHER TORTIOUS ACTION,  ARISING OUT OF OR IN CONNECTION WITH THE USE
 * OR PERFORMANCE OF THIS SOURCE CODE.
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 * U.S. Government End Users.   This source code is a "commercial item" as
 * that term is defined at  48 C.F.R. 2.101 (OCT 1995), consisting  of
 * "commercial computer  software"  and "commercial computer software
 * documentation" as such terms are  used in 48 C.F.R. 12.212 (SEPT 1995)
 * and is provided to the U.S. Government only as a commercial end item.
 * Consistent with 48 C.F.R.12.212 and 48 C.F.R. 227.7202-1 through
 * 227.7202-4 (JUNE 1995), all U.S. Government End Users acquire the
 * source code with only those rights set forth herein.
 *
 * Any use of this source code in individual and commercial software must
 * include, in the user documentation and internal comments to the code,
 * the above Disclaimer and U.S. Government End Users Notice.
 */



///////////////////////////////////////////////////////////////////////////////
// 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 = 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 = sqrtf(T);
    d1 = (__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
////////////////////////////////////////////////////////////////////////////////
__global__ void BlackScholesGPU(
    float *d_CallResult,
    float *d_PutResult,
    float *d_StockPrice,
    float *d_OptionStrike,
    float *d_OptionYears,
    float Riskfree,
    float Volatility,
    int optN
){
    //Thread index
    const int      tid = blockDim.x * blockIdx.x + threadIdx.x;
    //Total number of threads in execution grid
    const int THREAD_N = blockDim.x * gridDim.x;

    //No matter how small is execution grid or how large OptN is,
    //exactly OptN indices will be processed with perfect memory coalescing
    for(int opt = tid; opt < optN; opt += THREAD_N)
        BlackScholesBodyGPU(
            d_CallResult[opt],
            d_PutResult[opt],
            d_StockPrice[opt],
            d_OptionStrike[opt],
            d_OptionYears[opt],
            Riskfree,
            Volatility
        );
}