def monte_carlo_pricer(paths, dt, interest, volatility):
n = paths.shape[0]
mm = MM(shape=n, dtype=np.double, prealloc=5)
blksz = cuda.get_current_device().MAX_THREADS_PER_BLOCK
gridsz = int(math.ceil(float(n) / blksz))
stream = cuda.stream()
prng = curand.PRNG(curand.PRNG.MRG32K3A, stream=stream)
# Allocate device side array
d_normdist = cuda.device_array(n, dtype=np.double, stream=stream)
c0 = interest - 0.5 * volatility**2
c1 = volatility * math.sqrt(dt)
d_last = cuda.to_device(paths[:, 0], to=mm.get())
for j in range(1, paths.shape[1]):
prng.normal(d_normdist, mean=0, sigma=1)
d_paths = cuda.to_device(paths[:, j], stream=stream, to=mm.get())
step(d_last, dt, c0, c1, d_normdist, out=d_paths, stream=stream)
d_paths.copy_to_host(paths[:, j], stream=stream)
mm.free(d_last)
d_last = d_paths
stream.synchronize()
def monte_carlo_pricer(paths, dt, interest, volatility):
n = paths.shape[0]
blksz = 512
gridsz = int(math.ceil(float(n) / blksz))
stream = cuda.stream()
prng = curand.PRNG(curand.PRNG.MRG32K3A, stream=stream)
qrng = curand.QRNG(curand.QRNG.SOBOL32, stream=stream)
d_normdist = cuda.device_array(n, dtype=np.double, stream=stream)
d_seed = cuda.device_array(n, dtype=np.uint32, stream=stream)
prng.normal(d_normdist, 0, 1)
qrng.generate(d_seed)
d_paths = cuda.to_device(paths, stream=stream)
c0 = interest - 0.5 * volatility**2
c1 = volatility * math.sqrt(dt)
griddim = gridsz, 1
blockdim = blksz, 1, 1
cu_monte_carlo_pricer[griddim, blockdim, stream](d_paths, dt, c0, c1,
d_normdist, d_seed)
d_paths.to_host(stream)
stream.synchronize()
def get_cuda_randoms(x, y):
rand = np.empty((x * y), np.float64)
# rand serves as a container for the randoms
# CUDA only fills 1-dimensional arrays
prng = curand.PRNG(rndtype=curand.PRNG.XORWOW)
# the argument sets the random number algorithm
prng.normal(rand, 0, 1) # filling the container
rand = rand.reshape(x, y)
# to be "fair", we reshape rand to 2 dimensions
return rand
def spca_simpler(Vd, epsilon=0.1, d=3, k=10):
p = Vd.shape[0]
numSamples = int(math.ceil((4. / epsilon)**d))
print(numSamples)
##actual algorithm
opt_x = np.zeros((p, 1))
opt_v = -np.inf
# Prepare CUDA
prng = curand.PRNG()
custr = cuda.stream()
#GENERATE ALL RANDOM SAMPLES BEFORE
# C = np.random.randn(d, numSamples).astype(float_dtype)
C = np.empty((d, numSamples), dtype=float_dtype)
prng.normal(C.ravel(), mean=0, sigma=1)
sorter = RadixSort(maxcount=Vd.shape[0],
dtype=Vd.dtype,
stream=custr,
descending=True)
for i in range(1, numSamples + 1):
#c = np.random.randn(d,1)
#c = C[:,i-1]
c = C[:, i - 1:i]
c = c / np.linalg.norm(c)
a = Vd.dot(c)
#partial argsort in numpy?
#if partial, kth largest is p-k th smallest
#but need indices more than partial
# I = np.argsort(a, axis=0)
# val = np.linalg.norm(a[I[-k:]]) #index backwards to get k largest
# I = sorter.argselect(a[:, 0], k=k, reverse=True)
I = sorter.argselect(k, a[:, 0])
val = np.linalg.norm(a[:k]) #index to get k largest
if val > opt_v:
opt_v = val
opt_x = np.zeros((p, 1), dtype=float_dtype)
opt_x[I] = a[:k] / val
return opt_x
def monte_carlo_pricer(paths, dt, interest, volatility):
n = paths.shape[0]
blksz = cuda.get_current_device().MAX_THREADS_PER_BLOCK
gridsz = int(math.ceil(float(n) / blksz))
# Instantiate cuRAND PRNG
prng = curand.PRNG(curand.PRNG.MRG32K3A)
# Allocate device side array
d_normdist = cuda.device_array(n, dtype=np.double)
c0 = interest - 0.5 * volatility**2
c1 = volatility * math.sqrt(dt)
# Simulation loop
d_last = cuda.to_device(paths[:, 0])
for j in range(1, paths.shape[1]):
prng.normal(d_normdist, mean=0, sigma=1)
d_paths = cuda.to_device(paths[:, j])
step(d_last, dt, c0, c1, d_normdist, out=d_paths)
d_paths.copy_to_host(paths[:, j])
d_last = d_paths
def __get_cuda_randoms(self): prng = curand.PRNG(rndtype=curand.PRNG.XORWOW) prng.normal(self.container,0,1)
def main(*args):
OPT_N = 4000000
iterations = 10
if len(args) >= 2:
iterations = int(args[0])
blockdim = 1024, 1
griddim = int(math.ceil(float(OPT_N) / blockdim[0])), 1
# Use cuRand to generate random numbers directyl on the gpu
# to avoid memory transfers.
prng = curand.PRNG(rndtype=curand.PRNG.XORWOW)
time0 = time.time()
# malloc
d_stockPrice = cuda.device_array(shape=(OPT_N), dtype=np.float32)
d_optionStrike = cuda.device_array(shape=(OPT_N), dtype=np.float32)
d_optionYears = cuda.device_array(shape=(OPT_N), dtype=np.float32)
# Base distribution
prng.uniform(d_stockPrice)
prng.uniform(d_optionStrike)
prng.uniform(d_optionYears)
stream = cuda.stream()
cfg_distribute = c_distribute[griddim, blockdim, stream]
cfg_distribute(d_stockPrice, 5.0, 30.0)
cfg_distribute(d_optionStrike, 1.0, 100.0)
cfg_distribute(d_optionYears, 0.25, 10.)
stream.synchronize()
callResultNumbapro = np.zeros(OPT_N)
putResultNumbapro = -np.ones(OPT_N)
d_callResult = cuda.to_device(callResultNumbapro, stream)
d_putResult = cuda.to_device(putResultNumbapro, stream)
time1 = time.time()
# Preconfigure the kernel as it's called multiple times in a loop.
cfg_black_scholes_cuda = black_scholes_cuda[griddim, blockdim, stream]
for i in range(iterations):
cfg_black_scholes_cuda(d_callResult, d_putResult, d_stockPrice,
d_optionStrike, d_optionYears, RISKFREE,
VOLATILITY)
d_callResult.to_host(stream)
d_putResult.to_host(stream)
stream.synchronize()
time2 = time.time()
dt = (time1 - time0) * 10 + (time2 - time1)
print("numbapro.cuda time: %f msec" % ((1000 * dt) / iterations))
def get_cuda_randoms(x, y):
rand = np.empty((x * y), np.float64)
prng = curand.PRNG(rndtype=curand.PRNG.XORWOW)
prng.normal(rand, 0, 1) # filling the container
rand = rand.reshape((x, y))
return rand
def spca_full(Vd, epsilon=0.1, d=3, k=10):
p = Vd.shape[0]
initNumSamples = int(math.ceil((4. / epsilon)**d))
print(initNumSamples)
maxSize = 6400
##actual algorithm
opt_x = np.zeros((p, 1), dtype=float_dtype)
opt_v = -np.inf
# Send Vd to GPU
dVd = cuda.to_device(Vd)
remaining = initNumSamples
custr = cuda.stream()
# sorter = RadixSort(maxcount=Vd.shape[0], dtype=Vd.dtype, stream=custr,
# descending=True)
prng = curand.PRNG(stream=custr)
while remaining:
numSamples = min(remaining, maxSize)
remaining -= numSamples
# Prepare storage for vector A
# print(Vd.dtype)
# print('dA', (Vd.shape[0], numSamples))
# print('dI', (k, numSamples))
dA = cuda.device_array(shape=(Vd.shape[0], numSamples),
order='F',
dtype=Vd.dtype)
dI = cuda.device_array(shape=(Vd.shape[0], numSamples),
dtype=np.uint32,
order='F')
daInorm = cuda.device_array(shape=numSamples, dtype=Vd.dtype)
dC = cuda.device_array(shape=(d, numSamples),
order='F',
dtype=Vd.dtype)
#GENERATE ALL RANDOM SAMPLES BEFORE
# Also do normalization on the device
prng.normal(dC.reshape(dC.size), mean=0, sigma=1)
norm_random_nums[calc_ncta1d(dC.shape[1], 512), 512, custr](dC, d)
#C = dC.copy_to_host()
# Replaces: a = Vd.dot(c)
# XXX: Vd.shape[0] must be within compute capability requirement
# Note: this kernel can be easily scaled due to the use of num of samples
# as the ncta
batch_matmul[numSamples, 512, custr](dVd, dC, dA)
# Replaces: I = np.argsort(a, axis=0)
# Note: the k-selection is dominanting the time
nn = Vd.shape[0]
segments = (np.arange(numSamples - 1, dtype=np.int32) + 1) * nn
blksz = 32
init_indices[(divup(dI.shape[0], blksz), divup(dI.shape[1], blksz)),
(blksz, blksz), custr](dI)
segmented_sort(dA, dI, segments, stream=custr)
# async_dA = dA.bind(custr)
# async_dI = dI.bind(custr)
# selnext = sorter.batch_argselect(dtype=dA.dtype,
# count=dA.shape[0],
# k=k,
# reverse=True)
# for i in range(numSamples):
# dIi = selnext(async_dA[:, i])
# async_dI[:, i].copy_to_device(dIi, stream=custr)
# for i in range(numSamples):
# # radix_argselect(async_dA[:, i], k=k, stream=custr,
# # storeidx=async_dI[:, i])
# dIi = sorter.argselect(k, async_dA[:, i])
# async_dI[:, i].copy_to_device(dIi, stream=custr)
# Replaces: val = np.linalg.norm(a[I[-k:]])
# batch_scatter_norm[calc_ncta1d(numSamples, 512), 512, custr](dA, dI,
# daInorm)
dA = dA.bind(custr)[-k:]
dI = dI.bind(custr)[-k:]
batch_norm[calc_ncta1d(numSamples, 512), 512, custr](dA, daInorm, k)
aInorm = daInorm.copy_to_host(stream=custr)
custr.synchronize()
for i in xrange(numSamples):
val = aInorm[i]
if val > opt_v:
opt_v = val
opt_x.fill(0)
# Only copy what we need
Ik = dI[:, i].copy_to_host()
aIk = dA[:, i].copy_to_host().reshape(k, 1)
opt_x[Ik] = (aIk / val)
# Free allocations
del dA, dI, daInorm, dC
return opt_x
def monte_carlo_pricer(paths, dt, interest, volatility):
n = paths.shape[0]
num_streams = 2
part_width = int(math.ceil(float(n) / num_streams))
partitions = [(0, part_width)]
for i in range(1, num_streams):
begin, end = partitions[i - 1]
begin, end = end, min(end + (end - begin), n)
partitions.append((begin, end))
partlens = [end - begin for begin, end in partitions]
mm = MM(shape=part_width, dtype=np.double, prealloc=10 * num_streams)
device = cuda.get_current_device()
blksz = device.MAX_THREADS_PER_BLOCK
gridszlist = [
int(math.ceil(float(partlen) / blksz)) for partlen in partlens
]
strmlist = [cuda.stream() for _ in range(num_streams)]
prnglist = [
curand.PRNG(curand.PRNG.MRG32K3A, stream=strm) for strm in strmlist
]
# Allocate device side array
d_normlist = [
cuda.device_array(partlen, dtype=np.double, stream=strm)
for partlen, strm in zip(partlens, strmlist)
]
c0 = interest - 0.5 * volatility**2
c1 = volatility * math.sqrt(dt)
# Configure the kernel
# Similar to CUDA-C: cu_monte_carlo_pricer<<<gridsz, blksz, 0, stream>>>
steplist = [
cu_step[gridsz, blksz, strm]
for gridsz, strm in zip(gridszlist, strmlist)
]
d_lastlist = [
cuda.to_device(paths[s:e, 0], to=mm.get(stream=strm))
for (s, e), strm in zip(partitions, strmlist)
]
for j in xrange(1, paths.shape[1]):
for prng, d_norm in zip(prnglist, d_normlist):
prng.normal(d_norm, mean=0, sigma=1)
d_pathslist = [
cuda.to_device(paths[s:e, j], stream=strm, to=mm.get(stream=strm))
for (s, e), strm in zip(partitions, strmlist)
]
for step, args in zip(steplist, zip(d_lastlist, d_pathslist,
d_normlist)):
d_last, d_paths, d_norm = args
step(d_last, d_paths, dt, c0, c1, d_norm)
for d_paths, strm, (s, e) in zip(d_pathslist, strmlist, partitions):
d_paths.copy_to_host(paths[s:e, j], stream=strm)
mm.free(d_last, stream=strm)
d_lastlist = d_pathslist
for strm in strmlist:
strm.synchronize()