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nbody.py
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nbody.py
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"""
Benchmark for n-vortex interaction
"""
import numpy as np
# from numba import float32, float64, f4, f8
# from numba import jit
from numbapro import jit, cuda, autojit, float32, float64, f4, f8
from timeit import default_timer as timer
dtype = np.float64
n = 16384
# n = 2048
blksize = 128
eps = 1.e-2
def induced_velocity3(x, xvort, gam, vel):
nx = x.shape[0]
nvort = xvort.shape[0]
for i in range(nx):
vel[i,0] = 0.
vel[i,1] = 0.
for j in range(nvort):
rsq = (x[i,0]-xvort[j,0])**2 + (x[i,1]-xvort[j,1])**2 + eps**2
vel[i,0] += gam[j] * (x[i,1]-xvort[j,1]) / rsq
vel[i,1] += -gam[j] * (x[i,0]-xvort[j,0]) / rsq
def induced_velocity_single(x, xvort, gam):
r = x - xvort
rsq = np.sum(r * r, 1) + eps**2
vel = np.transpose(np.array([r[:,1], -r[:,0]]))
vel = gam * vel / rsq[:,np.newaxis]
return vel
def induced_velocity(x, xvort, gam, vel):
vel[:] = 0.
for xv, g in zip(xvort, gam):
r = x - xv
rsq = np.sum(r * r, 1) + eps**2
vel += g * np.transpose(np.array([r[:,1], -r[:,0]])) / rsq[:, np.newaxis]
@jit('void(f8[:,:], f8[:,:], f8[:], f8[:,:])', target='cpu')
def r_squared(x1, x2, xv1, xv2):
return (x1-xv1)**2 + (x2-xv2)**2 + eps**2
@autojit(target='cpu')
def induced_velocity2(x, xvort, gam, vel):
nx = x.shape[0]
nvort = xvort.shape[0]
for i in range(nx):
vel[i,0] = 0.
vel[i,1] = 0.
for j in range(nvort):
rsq = (x[i,0]-xvort[j,0])**2 + (x[i,1]-xvort[j,1])**2 + eps**2
vel[i,0] += gam[j] * (x[i,1]-xvort[j,1]) / rsq
vel[i,1] += -gam[j] * (x[i,0]-xvort[j,0]) / rsq
@jit('void(f8[:,:], f8[:,:], f8[:], f8[:,:])', target='cpu')
def induced_velocity2_test(x, xvort, gam, vel):
# eps = 1.e-2
nx = x.shape[0]
nvort = xvort.shape[0]
for i in range(nx):
vel[i,0] = 0.
vel[i,1] = 0.
for j in range(nvort):
rsq = r_squared(x[i,0], x[i,1], xvort[j,0], xvort[j,1])
vel[i,0] += gam[j] * (x[i,1]-xvort[j,1]) / rsq
vel[i,1] += -gam[j] * (x[i,0]-xvort[j,0]) / rsq
@cuda.jit('f8[:,:], f8[:,:], f8[:], f8[:,:]')
def induced_velocity3(x, xvort, gam, vel):
# eps = float32(1.e-2)
# i, j = cuda.grid(2)
i = cuda.grid(1)
if i < x.shape[0]:
vel[i,0] = float32(0.)
vel[i,1] = float32(0.)
nvort = xvort.shape[0]
for j in range(nvort):
rsq = (x[i,0]-xvort[j,0])**2 + (x[i,1]-xvort[j,1])**2 + eps**2
vel[i,0] += gam[j] * (x[i,1]-xvort[j,1]) / rsq
vel[i,1] += -gam[j] * (x[i,0]-xvort[j,0]) / rsq
@cuda.jit('f8[:,:], f8[:,:], f8[:], f8[:,:]')
def induced_velocity4(x, xvort, gam, vel):
smem = cuda.shared.array((blksize, 3), dtype=f8)
t = cuda.threadIdx.x
i = cuda.grid(1)
# eps = 1.e-2
nvort = xvort.shape[0]
nx = x.shape[0]
if i < nx:
x0 = x[i,0]
x1 = x[i,1]
xvel = 0
yvel = 0
nvort = xvort.shape[0]
for blk in range((nvort - 1) // blksize + 1):
# load vortex positions and strengths into shared memory
j = blk * blksize + t
if j < nvort:
smem[t,0] = xvort[j,0]
smem[t,1] = xvort[j,1]
smem[t,2] = gam[j]
else:
smem[t,0] = 0
smem[t,1] = 0
smem[t,2] = 0
cuda.syncthreads()
# compute the contributions to the velocity
for k in range(blksize):
rsq = (x0-smem[k,0])**2 + (x1-smem[k,1])**2 + eps**2
xvel += smem[k,2] * (x1-smem[k,1]) / rsq
yvel += -smem[k,2] * (x0-smem[k,0]) / rsq
cuda.syncthreads()
if i < nx:
vel[i,0] = xvel
vel[i,1] = yvel
def main():
vort = np.array(np.random.rand(2*n), dtype=dtype).reshape((n,2))
gamma = np.array(np.random.rand(n), dtype=dtype)
vel = np.zeros_like(vort)
start = timer()
induced_velocity(vort, vort, gamma, vel)
numpy_time = timer() - start
print("n = %d" % n)
print("Numpy".center(40, "="))
print("Time: %f seconds" % numpy_time)
vel2 = np.zeros_like(vort)
start = timer()
induced_velocity2(vort, vort, gamma, vel2)
numba_time = timer() - start
print("Numba".center(40, "="))
print("Time: %f seconds" % numba_time)
error = np.max(np.max(np.abs(vel2 - vel)))
print("Difference: %f" % error)
print("Speedup: %f" % (numpy_time / numba_time))
stream = cuda.stream()
d_vort = cuda.to_device(vort, stream)
d_gamma = cuda.to_device(gamma, stream)
vel3 = np.zeros_like(vort)
d_vel = cuda.to_device(vel3, stream)
# blockdim = (32,32)
# griddim = (n // blockdim[0], n // blockdim[1])
griddim = (n - 1) // blksize + 1
start = timer()
induced_velocity3[griddim, blksize, stream](d_vort, d_vort, d_gamma, d_vel)
d_vel.to_host(stream)
gpu_time = timer() - start
error = np.max(np.max(np.abs(vel3 - vel)))
print("GPU".center(40, "="))
print("Time: %f seconds" % gpu_time)
print("Difference: %f" % error)
print("Speedup: %f" % (numpy_time / gpu_time))
# print(vel3)
vel4 = np.zeros_like(vort)
d_vel2 = cuda.to_device(vel4, stream)
start = timer()
induced_velocity4[griddim, blksize, stream](d_vort, d_vort, d_gamma, d_vel2)
d_vel2.to_host(stream)
gpu2_time = timer() - start
error = np.max(np.max(np.abs(vel4 - vel)))
print("GPU smem".center(40, "="))
print("Time: %f seconds" % gpu2_time)
print("Difference: %f" % error)
print("Speedup: %f" % (numpy_time / gpu2_time))
# print("Expected".center(40,'-'))
# print(vel)
# print("GPU".center(40,'-'))
# print(vel4)
# print("Difference".center(40,'-'))
# print(vel4 - vel)
if __name__ == "__main__":
main()