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added options example

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Evghenii
2014-01-06 11:01:26 +01:00
parent c75969d7c8
commit 6878f83677
11 changed files with 1323 additions and 0 deletions
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examples_ptx/options/.gitignore vendored Normal file
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options

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examples_ptx/options/Makefile_cpu Normal file
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EXAMPLE=options
CPP_SRC=options.cpp options_serial.cpp
ISPC_SRC=options.ispc
ISPC_IA_TARGETS=avx1-i32x16
ISPC_ARM_TARGETS=neon
include ../common.mk

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examples_ptx/options/Makefile_gpu Normal file
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PROG=options
ISPC_SRC=options.ispc
CU_SRC=options.cu
CXX_SRC=options.cpp options_serial.cpp
PTXCC_REGMAX=32
LLVM_GPU=1
NVVM_GPU=1
include ../common_gpu.mk

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examples_ptx/options/options.cpp Normal file
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/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#define NOMINMAX
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <cmath>
#include <algorithm>
using std::max;
#include "options_defs.h"
#include "../timing.h"
#include "../ispc_malloc.h"
#include "options_ispc.h"
using namespace ispc;
extern void black_scholes_serial(float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count);
extern void binomial_put_serial(float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count);
static void usage() {
printf("usage: options [--count=<num options>]\n");
}
int main(int argc, char *argv[]) {
int nOptions = 128*1024;
for (int i = 1; i < argc; ++i) {
if (strncmp(argv[i], "--count=", 8) == 0) {
nOptions = atoi(argv[i] + 8);
if (nOptions <= 0) {
usage();
exit(1);
}
}
}
float *S = new float[nOptions];
float *X = new float[nOptions];
float *T = new float[nOptions];
float *r = new float[nOptions];
float *v = new float[nOptions];
float *result = new float[nOptions];
for (int i = 0; i < nOptions; ++i) {
S[i] = 100; // stock price
X[i] = 98; // option strike price
T[i] = 2; // time (years)
r[i] = .02; // risk-free interest rate
v[i] = 5; // volatility
}
double sum;
//
// Binomial options pricing model, ispc implementation
//
#ifndef _CUDA_
double binomial_ispc = 1e30;
for (int i = 0; i < 3; ++i) {
reset_and_start_timer();
binomial_put_ispc(S, X, T, r, v, result, nOptions);
double dt = get_elapsed_msec();
binomial_ispc = std::min(binomial_ispc, dt);
}
sum = 0.;
for (int i = 0; i < nOptions; ++i)
sum += result[i];
printf("[binomial ispc, 1 thread]:\t[%.3f] msec (avg %f)\n",
binomial_ispc, sum / nOptions);
#endif
//
// Binomial options pricing model, ispc implementation, tasks
//
double binomial_tasks = 1e30;
for (int i = 0; i < 3; ++i) {
reset_and_start_timer();
binomial_put_ispc_tasks(S, X, T, r, v, result, nOptions);
double dt = get_elapsed_msec();
binomial_tasks = std::min(binomial_tasks, dt);
}
sum = 0.;
for (int i = 0; i < nOptions; ++i)
sum += result[i];
printf("[binomial ispc, tasks]:\t\t[%.3f] msec (avg %f)\n",
binomial_tasks, sum / nOptions);
//
// Binomial options, serial implementation
//
#ifndef _CUDA_
double binomial_serial = 1e30;
for (int i = 0; i < 3; ++i) {
reset_and_start_timer();
binomial_put_serial(S, X, T, r, v, result, nOptions);
double dt = get_elapsed_msec();
sum = 0.;
for (int i = 0; i < nOptions; ++i)
sum += result[i];
binomial_serial = std::min(binomial_serial, dt);
}
printf("[binomial serial]:\t\t[%.3f] msec (avg %f)\n",
binomial_serial, sum / nOptions);
printf("\t\t\t\t(%.2fx speedup from ISPC, %.2fx speedup from ISPC + tasks)\n",
binomial_serial / binomial_ispc, binomial_serial / binomial_tasks);
#endif
//
// Black-Scholes options pricing model, ispc implementation, 1 thread
//
#ifndef _CUDA_
double bs_ispc = 1e30;
for (int i = 0; i < 3; ++i) {
reset_and_start_timer();
black_scholes_ispc(S, X, T, r, v, result, nOptions);
double dt = get_elapsed_msec();
bs_ispc = std::min(bs_ispc, dt);
}
sum = 0.;
for (int i = 0; i < nOptions; ++i)
sum += result[i];
printf("[black-scholes ispc, 1 thread]:\t[%.3f] msec (avg %f)\n",
bs_ispc, sum / nOptions);
#endif
//
// Black-Scholes options pricing model, ispc implementation, tasks
//
double bs_ispc_tasks = 1e30;
for (int i = 0; i < 3; ++i) {
reset_and_start_timer();
black_scholes_ispc_tasks(S, X, T, r, v, result, nOptions);
double dt = get_elapsed_msec();
sum = 0.;
for (int i = 0; i < nOptions; ++i)
sum += result[i];
bs_ispc_tasks = std::min(bs_ispc_tasks, dt);
}
printf("[black-scholes ispc, tasks]:\t[%.3f] msec (avg %f)\n",
bs_ispc_tasks, sum / nOptions);
//
// Black-Scholes options pricing model, serial implementation
//
#ifndef _CUDA_
double bs_serial = 1e30;
for (int i = 0; i < 3; ++i) {
reset_and_start_timer();
black_scholes_serial(S, X, T, r, v, result, nOptions);
double dt = get_elapsed_msec();
sum = 0.;
for (int i = 0; i < nOptions; ++i)
sum += result[i];
bs_serial = std::min(bs_serial, dt);
}
printf("[black-scholes serial]:\t\t[%.3f] msec (avg %f)\n", bs_serial,
sum / nOptions);
printf("\t\t\t\t(%.2fx speedup from ISPC, %.2fx speedup from ISPC + tasks)\n",
bs_serial / bs_ispc, bs_serial / bs_ispc_tasks);
#endif
return 0;
}

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// -*- mode: c++ -*-
/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "options_defs.h"
#include "cuda_helpers.cuh"
__device__ static inline void __range_reduce_log(float input, float * reduced,
int * exponent) {
int int_version = __float_as_int(input); //intbits(input);
// single precision = SEEE EEEE EMMM MMMM MMMM MMMM MMMM MMMM
// exponent mask = 0111 1111 1000 0000 0000 0000 0000 0000
// 0x7 0xF 0x8 0x0 0x0 0x0 0x0 0x0
// non-exponent = 1000 0000 0111 1111 1111 1111 1111 1111
// = 0x8 0x0 0x7 0xF 0xF 0xF 0xF 0xF
//const int exponent_mask(0x7F800000)
const int nonexponent_mask = 0x807FFFFF;
// We want the reduced version to have an exponent of -1 which is -1 + 127 after biasing or 126
const int exponent_neg1 = (126l << 23);
// NOTE(boulos): We don't need to mask anything out since we know
// the sign bit has to be 0. If it's 1, we need to return infinity/nan
// anyway (log(x), x = +-0 -> infinity, x < 0 -> NaN).
int biased_exponent = int_version >> 23; // This number is [0, 255] but it means [-127, 128]
int offset_exponent = biased_exponent + 1; // Treat the number as if it were 2^{e+1} * (1.m)/2
*exponent = offset_exponent - 127; // get the real value
// Blend the offset_exponent with the original input (do this in
// int for now, until I decide if float can have & and &not)
int blended = (int_version & nonexponent_mask) | (exponent_neg1);
*reduced = __int_as_float(blended); //floatbits(blended);
}
__device__ static inline float __Logf(const float x_full)
{
#if 1
return __logf(x_full);
#else
float reduced;
int exponent;
const int NaN_bits = 0x7fc00000;
const int Neg_Inf_bits = 0xFF800000;
const float NaN = __int_as_float(NaN_bits); //floatbits(NaN_bits);
const float neg_inf = __int_as_float(Neg_Inf_bits); //floatbits(Neg_Inf_bits);
bool use_nan = x_full < 0.f;
bool use_inf = x_full == 0.f;
bool exceptional = use_nan || use_inf;
const float one = 1.0f;
float patched = exceptional ? one : x_full;
__range_reduce_log(patched, &reduced, &exponent);
const float ln2 = 0.693147182464599609375f;
float x1 = one - reduced;
const float c1 = 0.50000095367431640625f;
const float c2 = 0.33326041698455810546875f;
const float c3 = 0.2519190013408660888671875f;
const float c4 = 0.17541764676570892333984375f;
const float c5 = 0.3424419462680816650390625f;
const float c6 = -0.599632322788238525390625f;
const float c7 = +1.98442304134368896484375f;
const float c8 = -2.4899270534515380859375f;
const float c9 = +1.7491014003753662109375f;
float result = x1 * c9 + c8;
result = x1 * result + c7;
result = x1 * result + c6;
result = x1 * result + c5;
result = x1 * result + c4;
result = x1 * result + c3;
result = x1 * result + c2;
result = x1 * result + c1;
result = x1 * result + one;
// Equation was for -(ln(red)/(1-red))
result *= -x1;
result += (float)(exponent) * ln2;
return exceptional ? (use_nan ? NaN : neg_inf) : result;
#endif
}
__device__ static inline float __Expf(const float x_full)
{
#if 1
return __expf(x_full);
#else
const float ln2_part1 = 0.6931457519f;
const float ln2_part2 = 1.4286067653e-6f;
const float one_over_ln2 = 1.44269502162933349609375f;
float scaled = x_full * one_over_ln2;
float k_real = floor(scaled);
int k = (int)k_real;
// Reduced range version of x
float x = x_full - k_real * ln2_part1;
x -= k_real * ln2_part2;
// These coefficients are for e^x in [0, ln(2)]
const float one = 1.f;
const float c2 = 0.4999999105930328369140625f;
const float c3 = 0.166668415069580078125f;
const float c4 = 4.16539050638675689697265625e-2f;
const float c5 = 8.378830738365650177001953125e-3f;
const float c6 = 1.304379315115511417388916015625e-3f;
const float c7 = 2.7555381529964506626129150390625e-4f;
float result = x * c7 + c6;
result = x * result + c5;
result = x * result + c4;
result = x * result + c3;
result = x * result + c2;
result = x * result + one;
result = x * result + one;
// Compute 2^k (should differ for float and double, but I'll avoid
// it for now and just do floats)
const int fpbias = 127;
int biased_n = k + fpbias;
bool overflow = k > fpbias;
// Minimum exponent is -126, so if k is <= -127 (k + 127 <= 0)
// we've got underflow. -127 * ln(2) -> -88.02. So the most
// negative float input that doesn't result in zero is like -88.
bool underflow = (biased_n <= 0);
const int InfBits = 0x7f800000;
biased_n <<= 23;
// Reinterpret this thing as float
float two_to_the_n = __int_as_float(biased_n); //floatbits(biased_n);
// Handle both doubles and floats (hopefully eliding the copy for float)
float elemtype_2n = two_to_the_n;
result *= elemtype_2n;
// result = overflow ? floatbits(InfBits) : result;
result = overflow ? __int_as_float(InfBits) : result;
result = underflow ? 0.0f : result;
return result;
#endif
}
// Cumulative normal distribution function
//
__device__
static inline float
CND(float X) {
float L = fabsf(X);
float k = 1.0f / (1.0f + 0.2316419f * L);
float k2 = k*k;
float k3 = k2*k;
float k4 = k2*k2;
float k5 = k3*k2;
const float invSqrt2Pi = 0.39894228040f;
float w = (0.31938153f * k - 0.356563782f * k2 + 1.781477937f * k3 +
-1.821255978f * k4 + 1.330274429f * k5);
w *= invSqrt2Pi * __Expf(-L * L * .5f);
if (X > 0.f)
w = 1.0f - w;
return w;
}
__global__
void bs_task( float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count) {
if (taskIndex >= taskCount) return;
int first = taskIndex * (count/taskCount);
int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
for (int i = programIndex + first; i < last; i += programCount)
if (i < last)
{
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (__Logf(S/X) + (r + v * v * .5f) * T) / (v * sqrtf(T));
float d2 = d1 - v * sqrtf(T);
result[i] = S * CND(d1) - X * __Expf(-r * T) * CND(d2);
}
}
extern "C"
__global__ void
black_scholes_ispc_tasks___export( float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count) {
int nTasks = 2048; //count/16384; //max((int)64, (int)count/16384);
launch(nTasks,1,1,bs_task)
(Sa, Xa, Ta, ra, va, result, count);
cudaDeviceSynchronize();
}
extern "C"
__host__ void
black_scholes_ispc_tasks( float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count) {
black_scholes_ispc_tasks___export<<<1,32>>>(Sa,Xa,Ta,ra,va,result,count);
cudaDeviceSynchronize();
}
/********/
template<int NBEG, int NEND, int STEP>
struct loop
{
__device__ static void op1(float V[], const float u, const float X, const float S)
{
const int j = NBEG;
float upow = powf(u, (float)(2*j-BINOMIAL_NUM));
V[j] = max(0.0f, X - S * upow);
loop<j+STEP,NEND,STEP>::op1(V,u,X,S);
}
__device__ static void op2(float V[], const float Pu, const float disc)
{
const int j = NBEG;
#pragma unroll
for ( int k = 0; k < j; ++k)
V[k] = ((1.0f - Pu) * V[k] + Pu * V[k+ 1]) / disc;
loop<j+STEP,NEND,STEP>::op2(V, Pu,disc);
}
};
template<int NEND, int STEP>
struct loop<NEND,NEND,STEP>
{
__device__ static void op1(float V[], const float u, const float X, const float S) {}
__device__ static void op2(float V[], const float Pu, const float disc) {}
};
__device__
static inline float
binomial_put(float S, float X, float T, float r, float v)
{
float V[BINOMIAL_NUM];
float dt = T / BINOMIAL_NUM;
float u = exp(v * sqrt(dt));
float d = 1.f / u;
float disc = exp(r * dt);
float Pu = (disc - d) / (u - d);
#if 0 /* slow */
for ( int j = 0; j < BINOMIAL_NUM; ++j) {
float upow = powf(u, (float)(2*j-BINOMIAL_NUM));
V[j] = max(0.0f, X - S * upow);
}
for ( int j = BINOMIAL_NUM-1; j >= 0; --j)
for ( int k = 0; k < j; ++k)
V[k] = ((1.0f - Pu) * V[k] + Pu * V[k+ 1]) / disc;
#else /* with loop unrolling, stores resutls in registers */
loop<0,BINOMIAL_NUM,1>::op1(V,u,X,S);
loop<BINOMIAL_NUM-1, -1, -1>::op2(V, Pu, disc);
#endif
return V[0];
}
__global__ void
binomial_task( float Sa[], float Xa[],
float Ta[], float ra[],
float va[], float result[],
int count)
{
int first = taskIndex * (count/taskCount);
int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
for (int i = programIndex + first; i < last; i += programCount)
if (i < last)
{
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
extern "C" __global__ void
binomial_put_ispc_tasks___export( float Sa[], float Xa[],
float Ta[], float ra[],
float va[], float result[],
int count) {
int nTasks = 2048; //count/16384; //max((int)64, (int)count/16384);
launch(nTasks,1,1,binomial_task)
(Sa, Xa, Ta, ra, va, result, count);
cudaDeviceSynchronize();
}
extern "C"
__host__ void
binomial_put_ispc_tasks( float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count) {
binomial_put_ispc_tasks___export<<<1,32>>>(Sa,Xa,Ta,ra,va,result,count);
cudaDeviceSynchronize();
}

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// -*- mode: c++ -*-
/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "options_defs.h"
// Cumulative normal distribution function
static inline float
CND(float X) {
float L = abs(X);
float k = 1.0 / (1.0 + 0.2316419 * L);
float k2 = k*k;
float k3 = k2*k;
float k4 = k2*k2;
float k5 = k3*k2;
const float invSqrt2Pi = 0.39894228040f;
float w = (0.31938153f * k - 0.356563782f * k2 + 1.781477937f * k3 +
-1.821255978f * k4 + 1.330274429f * k5);
w *= invSqrt2Pi * exp(-L * L * .5f);
if (X > 0.f)
w = 1.0 - w;
return w;
}
task void
bs_task(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
export void
black_scholes_ispc_tasks(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int nTasks = 2048; //count/16384; //max((int)64, (int)count/16384);
launch[nTasks] bs_task(Sa, Xa, Ta, ra, va, result, count);
}
/********/
export void
black_scholes_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
static inline float
binomial_put(float S, float X, float T, float r, float v) {
float V[BINOMIAL_NUM];
float dt = T / BINOMIAL_NUM;
float u = exp(v * sqrt(dt));
float d = 1. / u;
float disc = exp(r * dt);
float Pu = (disc - d) / (u - d);
#if 0
for (uniform int j = 0; j < BINOMIAL_NUM; ++j) {
float upow = pow(u, (float)(2*j-BINOMIAL_NUM));
V[j] = max(0., X - S * upow);
}
for (uniform int j = BINOMIAL_NUM-1; j >= 0; --j)
for (uniform int k = 0; k < j; ++k)
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc;
#else
/* loop unrolling helps NVVM to place V -> registers therefore boosting performance */
/* takes looong time to compile... */
#if BINOMIAL_NUM != 64
#error "Cannot unroll. Please use generic version above"
#endif
/* first loop */
#define OP(j) { \
float upow = pow(u, (float)(2*(j)-BINOMIAL_NUM)); \
V[j] = max(0., X - S * upow); }
#define OP10(k) \
OP(k+0); OP(k+1); OP(k+2); OP(k+3); OP(k+4) \
OP(k+5); OP(k+6); OP(k+7); OP(k+8); OP(k+9);
OP10(0)
OP10(10)
OP10(20)
OP10(30)
OP10(40)
OP10(50)
OP(60)
OP(61)
OP(62)
OP(63)
#undef OP10
#undef OP
/* second loop */
#define OP(j) {\
for (uniform int k = 0; k < (j); ++k) \
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc; }
#define OP10(k) \
OP(k+9); OP(k+8); OP(k+7); OP(k+6); OP(k+5); \
OP(k+4); OP(k+3); OP(k+2); OP(k+1); OP(k+0);
OP(63)
OP(62)
OP(61)
OP(60)
OP10(50)
OP10(40)
OP10(30)
OP10(20)
OP10(10)
OP10(0)
#undef OP10
#undef OP
#endif
return V[0];
}
export void
binomial_put_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
task void
binomial_task(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
export void
binomial_put_ispc_tasks(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int nTasks = 2048; //count/16384; //max((int)64, (int)count/16384);
launch[nTasks] binomial_task(Sa, Xa, Ta, ra, va, result, count);
}

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// -*- mode: c++ -*-
/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "options_defs.h"
// Cumulative normal distribution function
static inline float
CND(float X) {
float L = abs(X);
float k = 1.0 / (1.0 + 0.2316419 * L);
float k2 = k*k;
float k3 = k2*k;
float k4 = k2*k2;
float k5 = k3*k2;
const float invSqrt2Pi = 0.39894228040f;
float w = (0.31938153f * k - 0.356563782f * k2 + 1.781477937f * k3 +
-1.821255978f * k4 + 1.330274429f * k5);
w *= invSqrt2Pi * exp(-L * L * .5f);
if (X > 0.f)
w = 1.0 - w;
return w;
}
task void
bs_task(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
export void
black_scholes_ispc_tasks(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int nTasks = 2048; // max((int)64, (int)count/16384);
launch[nTasks] bs_task(Sa, Xa, Ta, ra, va, result, count);
}
export void
black_scholes_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
static inline float
binomial_put(float S, float X, float T, float r, float v) {
float V[BINOMIAL_NUM];
float dt = T / BINOMIAL_NUM;
float u = exp(v * sqrt(dt));
float d = 1. / u;
float disc = exp(r * dt);
float Pu = (disc - d) / (u - d);
for (uniform int j = 0; j < BINOMIAL_NUM; ++j) {
float upow = pow(u, (float)(2*j-BINOMIAL_NUM));
V[j] = max(0., X - S * upow);
}
for (uniform int j = BINOMIAL_NUM-1; j >= 0; --j)
for (uniform int k = 0; k < j; ++k)
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc;
return V[0];
}
export void
binomial_put_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
task void
binomial_task(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
export void
binomial_put_ispc_tasks(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int nTasks = 2048; //max((int)64, (int)count/16384);
launch[nTasks] binomial_task(Sa, Xa, Ta, ra, va, result, count);
}

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<?xml version="1.0" encoding="utf-8"?>
<Project DefaultTargets="Build" ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
<ItemGroup Label="ProjectConfigurations">
<ProjectConfiguration Include="Debug|Win32">
<Configuration>Debug</Configuration>
<Platform>Win32</Platform>
</ProjectConfiguration>
<ProjectConfiguration Include="Debug|x64">
<Configuration>Debug</Configuration>
<Platform>x64</Platform>
</ProjectConfiguration>
<ProjectConfiguration Include="Release|Win32">
<Configuration>Release</Configuration>
<Platform>Win32</Platform>
</ProjectConfiguration>
<ProjectConfiguration Include="Release|x64">
<Configuration>Release</Configuration>
<Platform>x64</Platform>
</ProjectConfiguration>
</ItemGroup>
<PropertyGroup Label="Globals">
<ProjectGuid>{8C7B5D29-1E76-44E6-BBB8-09830E5DEEAE}</ProjectGuid>
<Keyword>Win32Proj</Keyword>
<RootNamespace>options</RootNamespace>
<ISPC_file>options</ISPC_file>
<default_targets>sse2,sse4-x2,avx1-x2</default_targets>
</PropertyGroup>
<Import Project="..\common.props" />
<ItemGroup>
<ClCompile Include="options.cpp" />
<ClCompile Include="options_serial.cpp" />
<ClCompile Include="../tasksys.cpp" />
<ClInclude Include="options_defs.h" />
</ItemGroup>
</Project>

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// -*- mode: c++ -*-
/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "options_defs.h"
// Cumulative normal distribution function
static inline float
CND(float X) {
float L = abs(X);
float k = 1.0 / (1.0 + 0.2316419 * L);
float k2 = k*k;
float k3 = k2*k;
float k4 = k2*k2;
float k5 = k3*k2;
const float invSqrt2Pi = 0.39894228040f;
float w = (0.31938153f * k - 0.356563782f * k2 + 1.781477937f * k3 +
-1.821255978f * k4 + 1.330274429f * k5);
w *= invSqrt2Pi * exp(-L * L * .5f);
if (X > 0.f)
w = 1.0 - w;
return w;
}
task void
bs_task(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
export void
black_scholes_ispc_tasks(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
uniform int nTasks = 2048; //count/16384; //max((int)64, (int)count/16384);
launch[nTasks] bs_task(Sa, Xa, Ta, ra, va, result, count);
}
/********/
export void
black_scholes_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
float d1 = (log(S/X) + (r + v * v * .5f) * T) / (v * sqrt(T));
float d2 = d1 - v * sqrt(T);
result[i] = S * CND(d1) - X * exp(-r * T) * CND(d2);
}
}
static inline float
binomial_put(float S, float X, float T, float r, float v) {
float V[BINOMIAL_NUM];
float dt = T / BINOMIAL_NUM;
float u = exp(v * sqrt(dt));
float d = 1. / u;
float disc = exp(r * dt);
float Pu = (disc - d) / (u - d);
#if 0
for (uniform int j = 0; j < BINOMIAL_NUM; ++j) {
float upow = pow(u, (float)(2*j-BINOMIAL_NUM));
V[j] = max(0., X - S * upow);
}
for (uniform int j = BINOMIAL_NUM-1; j >= 0; --j)
for (uniform int k = 0; k < j; ++k)
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc;
#else
/* loop unrolling helps NVVM to place V -> registers therefore boosting performance */
/* takes looong time to compile... */
#if BINOMIAL_NUM != 64
#error "Cannot unroll. Please use generic version above"
#endif
/* first loop */
#define OP(j) { \
float upow = pow(u, (float)(2*(j)-BINOMIAL_NUM)); \
V[j] = max(0., X - S * upow); }
#define OP10(k) \
OP(k+0); OP(k+1); OP(k+2); OP(k+3); OP(k+4) \
OP(k+5); OP(k+6); OP(k+7); OP(k+8); OP(k+9);
OP10(0)
OP10(10)
OP10(20)
OP10(30)
OP10(40)
OP10(50)
OP(60)
OP(61)
OP(62)
OP(63)
#undef OP10
#undef OP
/* second loop */
#define OP(j) {\
for (uniform int k = 0; k < (j); ++k) \
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc; }
#define OP10(k) \
OP(k+9); OP(k+8); OP(k+7); OP(k+6); OP(k+5); \
OP(k+4); OP(k+3); OP(k+2); OP(k+1); OP(k+0);
OP(63)
OP(62)
OP(61)
OP(60)
OP10(50)
OP10(40)
OP10(30)
OP10(20)
OP10(10)
OP10(0)
#undef OP10
#undef OP
#endif
return V[0];
}
export void
binomial_put_ispc(uniform float Sa[], uniform float Xa[], uniform float Ta[],
uniform float ra[], uniform float va[],
uniform float result[], uniform int count) {
foreach (i = 0 ... count) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
task void
binomial_task(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int first = taskIndex * (count/taskCount);
uniform int last = min(count, (int)((taskIndex+1) * (count/taskCount)));
foreach (i = first ... last) {
float S = Sa[i], X = Xa[i], T = Ta[i], r = ra[i], v = va[i];
result[i] = binomial_put(S, X, T, r, v);
}
}
export void
binomial_put_ispc_tasks(uniform float Sa[], uniform float Xa[],
uniform float Ta[], uniform float ra[],
uniform float va[], uniform float result[],
uniform int count) {
uniform int nTasks = 2048; //count/16384; //max((int)64, (int)count/16384);
launch[nTasks] binomial_task(Sa, Xa, Ta, ra, va, result, count);
}

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/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef OPTIONS_DEFS_H
#define OPTIONS_DEFS_H 1
#define BINOMIAL_NUM 64
#endif // OPTIONS_DEFS_H

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/*
Copyright (c) 2010-2011, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
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 Intel 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 AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifdef _MSC_VER
#define _CRT_SECURE_NO_WARNINGS
#define NOMINMAX
#pragma warning (disable: 4244)
#pragma warning (disable: 4305)
#endif
#include "options_defs.h"
#include <math.h>
#include <algorithm>
// Cumulative normal distribution function
static inline float
CND(float X) {
float L = fabsf(X);
float k = 1.f / (1.f + 0.2316419f * L);
float k2 = k*k;
float k3 = k2*k;
float k4 = k2*k2;
float k5 = k3*k2;
const float invSqrt2Pi = 0.39894228040f;
float w = (0.31938153f * k - 0.356563782f * k2 + 1.781477937f * k3 +
-1.821255978f * k4 + 1.330274429f * k5);
w *= invSqrt2Pi * expf(-L * L * .5f);
if (X > 0.f)
w = 1.f - w;
return w;
}
void
black_scholes_serial(float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count) {
for (int i = 0; i < count; ++i) {
float S = Sa[i], X = Xa[i];
float T = Ta[i], r = ra[i];
float v = va[i];
float d1 = (logf(S/X) + (r + v * v * .5f) * T) / (v * sqrtf(T));
float d2 = d1 - v * sqrtf(T);
result[i] = S * CND(d1) - X * expf(-r * T) * CND(d2);
}
}
void
binomial_put_serial(float Sa[], float Xa[], float Ta[],
float ra[], float va[],
float result[], int count) {
float V[BINOMIAL_NUM];
for (int i = 0; i < count; ++i) {
float S = Sa[i], X = Xa[i];
float T = Ta[i], r = ra[i];
float v = va[i];
float dt = T / BINOMIAL_NUM;
float u = expf(v * sqrtf(dt));
float d = 1.f / u;
float disc = expf(r * dt);
float Pu = (disc - d) / (u - d);
for (int j = 0; j < BINOMIAL_NUM; ++j) {
float upow = powf(u, (float)(2*j-BINOMIAL_NUM));
V[j] = std::max(0.f, X - S * upow);
}
for (int j = BINOMIAL_NUM-1; j >= 0; --j)
for (int k = 0; k < j; ++k)
V[k] = ((1 - Pu) * V[k] + Pu * V[k + 1]) / disc;
result[i] = V[0];
}
}