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/*
* 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
* REGARD TO THIS SOURCE CODE, INCLUDING ALL IMPLIED WARRANTIES OF
* 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
* OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE
* OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE
* OR PERFORMANCE OF THIS SOURCE CODE.
*
* 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
);
}
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