public static BigInteger Random(this System.Random generator, BigInteger limit)
{
return(new BigInteger(generator.Random(limit.Value)));
}
static void Main(string[] args)
{
// Based on https://github.com/gsvgit/Brahma.FSharp/tree/master/Source/BlackScholes
const int optionCount = 1000000;
const float riskFreeInterestRate = 0.02f;
const float volatility = 0.30f;
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;
// Helper functions
Expression <Func <float, float> > k = x => 1.0f / (1.0f + 0.2316419f * FMath.Abs(x));
Expression <Func <float, float> > cnd = x =>
1.0f - 1.0f / FMath.Sqrt(2.0f * FMath.PI)
* FMath.Exp(-(FMath.Abs(x)) * (FMath.Abs(x)) / 2.0f) * (A1 * k.Invoke(x) + A2 * k.Invoke(x) * k.Invoke(x) + A3 * FMath.Pow(k.Invoke(x), 3)
+ A4 * FMath.Pow(k.Invoke(x), 4) + A5 * FMath.Pow(k.Invoke(x), 4));
Expression <Func <float, float> > cumulativeNormalDistribution = x => (x < 0.0f) ? 1.0f - cnd.Invoke(x) : cnd.Invoke(x);
Expression <Func <float, float, float, float> > d1 =
(stockPrice, strikePrice, timeToExpirationYears) =>
FMath.Log(stockPrice / strikePrice) + (riskFreeInterestRate + volatility * volatility / 2.0f) * timeToExpirationYears
/ (volatility * FMath.Sqrt(timeToExpirationYears));
Expression <Func <float, float, float> > d2 =
(_d1, timeToExpirationYears) => _d1 - volatility * FMath.Sqrt(timeToExpirationYears);
Expression <Func <float, float, float, float, float, float> > blackScholesCallOption =
(_d1, _d2, stockPrice, strikePrice, timeToExpirationYears) =>
stockPrice *cumulativeNormalDistribution.Invoke(_d1) -
strikePrice * FMath.Exp(-(riskFreeInterestRate) * timeToExpirationYears) * cumulativeNormalDistribution.Invoke(_d2);
Expression <Func <float, float, float, float, float, float> > blackScholesPutOption =
(_d1, _d2, stockPrice, strikePrice, timeToExpirationYears) =>
strikePrice *FMath.Exp(-riskFreeInterestRate *timeToExpirationYears) *
cumulativeNormalDistribution.Invoke(-_d2) - stockPrice * cumulativeNormalDistribution.Invoke(-_d1);
// Init data
var random = new System.Random();
var data = Enumerable.Range(1, optionCount).Select(_ => new InputData
{
Stock = random.Random(5.0f, 30.0f),
Strike = random.Random(1.0f, 100.0f),
Times = random.Random(0.25f, 10.0f)
}).ToArray();
// Main code
using (GpuContext context = new GpuContext())
{
using (var _data = context.CreateGpuArray(data))
{
var query =
(from d in _data.AsGpuQueryExpr()
let _d1 = d1.Invoke(d.Stock, d.Strike, d.Times)
let _d2 = d2.Invoke(_d1, d.Times)
select new OutPutData {
Call = blackScholesCallOption.Invoke(_d1, _d2, d.Stock, d.Strike, d.Times),
Put = blackScholesPutOption.Invoke(_d1, _d2, d.Stock, d.Strike, d.Times)
}).ToArray();
var result = context.Run(query);
}
}
}
static void Main(string[] args)
{
// Based on https://github.com/gsvgit/Brahma.FSharp/tree/master/Source/BlackScholes
const int optionCount = 1000000;
const float riskFreeInterestRate = 0.02f;
const float volatility = 0.30f;
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;
// Helper functions
Expression <Func <float, float> > k = x => 1.0f / (1.0f + 0.2316419f * FMath.Abs(x));
Expression <Func <float, float> > cnd = x =>
1.0f - 1.0f / FMath.Sqrt(2.0f * FMath.PI)
* FMath.Exp(-(FMath.Abs(x)) * (FMath.Abs(x)) / 2.0f) * (A1 * k.Invoke(x) + A2 * k.Invoke(x) * k.Invoke(x) + A3 * FMath.Pow(k.Invoke(x), 3)
+ A4 * FMath.Pow(k.Invoke(x), 4) + A5 * FMath.Pow(k.Invoke(x), 5));
Expression <Func <float, float> > cumulativeNormalDistribution = x => (x < 0.0f) ? 1.0f - cnd.Invoke(x) : cnd.Invoke(x);
Expression <Func <float, float, float, float> > d1 =
(stockPrice, strikePrice, timeToExpirationYears) =>
FMath.Log(stockPrice / strikePrice) + (riskFreeInterestRate + volatility * volatility / 2.0f) * timeToExpirationYears
/ (volatility * FMath.Sqrt(timeToExpirationYears));
Expression <Func <float, float, float> > d2 =
(_d1, timeToExpirationYears) => _d1 - volatility * FMath.Sqrt(timeToExpirationYears);
Expression <Func <float, float, float, float, float, float> > blackScholesCallOption =
(_d1, _d2, stockPrice, strikePrice, timeToExpirationYears) =>
stockPrice *cumulativeNormalDistribution.Invoke(_d1) -
strikePrice * FMath.Exp(-(riskFreeInterestRate) * timeToExpirationYears) * cumulativeNormalDistribution.Invoke(_d2);
Expression <Func <float, float, float, float, float, float> > blackScholesPutOption =
(_d1, _d2, stockPrice, strikePrice, timeToExpirationYears) =>
strikePrice *FMath.Exp(-riskFreeInterestRate *timeToExpirationYears) *
cumulativeNormalDistribution.Invoke(-_d2) - stockPrice * cumulativeNormalDistribution.Invoke(-_d1);
// Init data
var random = new System.Random();
var data = Enumerable.Range(1, optionCount).Select(_ => new InputData
{
Stock = random.Random(5.0f, 30.0f),
Strike = random.Random(1.0f, 100.0f),
Times = random.Random(0.25f, 10.0f)
}).ToArray();
// Main code
Stopwatch timer = new Stopwatch();
timer.Start();
OutPutData[] results;
using (GpuContext context = new GpuContext())
{
using (var _data = context.CreateGpuArray(data))
{
var query =
(from d in _data.AsGpuQueryExpr()
let _d1 = d1.Invoke(d.Stock, d.Strike, d.Times)
let _d2 = d2.Invoke(_d1, d.Times)
select new OutPutData {
Call = blackScholesCallOption.Invoke(_d1, _d2, d.Stock, d.Strike, d.Times),
Put = blackScholesPutOption.Invoke(_d1, _d2, d.Stock, d.Strike, d.Times)
}).ToArray();
results = context.Run(query);
}
}
timer.Stop();
var elapsed = timer.ElapsedMilliseconds;
Console.WriteLine("Black Scholes computed on Gpu in {0} milliseconds", elapsed);
//String.Join<OutPutData>(", ", Enumerable.Range(1,120).
// Select(i => results.ElementAtOrDefault(i)).ToArray()));
timer.Restart();
var cpuResults = CpuBlackScholes(data);
timer.Stop();
elapsed = timer.ElapsedMilliseconds;
Console.WriteLine("Black Scholes computed on Cpu in {0} milliseconds", elapsed);
var resultsAreEqual = cpuResults.Zip(results, (a, b) => Tuple.Create(a, b)).All(pair => pair.Item1.IsEqual(pair.Item2));
Console.WriteLine("Results calculated by cpu and gpu are {0}", resultsAreEqual ? "equal" : "not equal");
Console.WriteLine("Results = {0}",
String.Join <Results>(", ", Enumerable.Range(1, 120).
Select(i => new Results()
{
Gpu = results.ElementAtOrDefault(i), Cpu = cpuResults.ElementAtOrDefault(i)
}).ToArray()));
Console.ReadLine();
}
