def gen_FFT_M2X_finish(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block("void %s(%s *y, %s s)\n" % (funname, basetype, type))
y = parameter("y", array=True)
s = parameter("s")
f = var("f")
print
for j in range(1, M / 4):
f ^= y[2 * j + 1]
if j == M / 8:
y[2 * j] ^= y[2 * j] - f
else:
y[2 * j] ^= y[2 * j] - tan(2.0 * pi * j / M) * f
y[2 * j + 1] ^= (1.0 / cos(2.0 * pi * j / M)) * f
print
for j in range(M / 4 + 1, M / 2):
f ^= y[2 * j + 1]
if j == 3 * M / 8:
y[2 * j] ^= y[2 * j] + f
else:
y[2 * j] ^= y[2 * j] + (-tan(2.0 * pi * j / M)) * f
y[2 * j + 1] ^= (1.0 / cos(2.0 * pi * j / M)) * f
print
f ^= y[M / 2] - s
y[M / 2] ^= s
y[M / 2 + 1] ^= f
end_block()
print
def gen_core_gen_M_L(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block("void %s(int p, %s *scale, %s q, %s *dML, %s *ML)\n" % (funname, basetype, type, basetype, basetype))
scale = parameter("scale", array=True)
q = parameter("q")
dML = parameter("dML", array=True)
ML = parameter("ML", array=True, horiz_add=-1)
f = var("f")
print
begin_block("switch(p) ")
for n in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % n
for n in range(p_max, -1, -1):
print "\tcase %i:" % n
# print "\t\tf = scale[%i];" % n
f ^= scale[n] * q
for m in range((n + 1) * (n + 2) - 1, n * (n + 1) - 1, -1):
ML[m] += f * dML[m]
print "#endif /* FMM_P_MAX >= %i */" % n
end_block()
end_block()
print
def gen_core_gen_M_L(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block('void %s(int p, %s *scale, %s q, %s *dML, %s *ML)\n' %
(funname, basetype, type, basetype, basetype))
scale = parameter("scale", array=True)
q = parameter("q")
dML = parameter("dML", array=True)
ML = parameter("ML", array=True, horiz_add=-1)
f = var("f")
print
begin_block("switch(p) ")
for n in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % n
for n in range(p_max, -1, -1):
print "\tcase %i:" % n
#print "\t\tf = scale[%i];" % n
f ^= scale[n] * q
for m in range((n + 1) * (n + 2) - 1, n * (n + 1) - 1, -1):
ML[m] += f * dML[m]
print "#endif /* FMM_P_MAX >= %i */" % n
end_block()
end_block()
print
def gen_FFT_M2X_finish(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block('void %s(%s *y, %s s)\n' % (funname, basetype, type))
y = parameter("y", array=True)
s = parameter("s")
f = var("f")
print
for j in range(1, M / 4):
f ^= y[2 * j + 1]
if j == M / 8:
y[2 * j] ^= y[2 * j] - f
else:
y[2 * j] ^= y[2 * j] - tan(2.0 * pi * j / M) * f
y[2 * j + 1] ^= (1.0 / cos(2.0 * pi * j / M)) * f
print
for j in range(M / 4 + 1, M / 2):
f ^= y[2 * j + 1]
if j == 3 * M / 8:
y[2 * j] ^= y[2 * j] + f
else:
y[2 * j] ^= y[2 * j] + (-tan(2.0 * pi * j / M)) * f
y[2 * j + 1] ^= (1.0 / cos(2.0 * pi * j / M)) * f
print
f ^= y[M / 2] - s
y[M / 2] ^= s
y[M / 2 + 1] ^= f
end_block()
print
def gen_core_eval_L_M_grad_plus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
'void %s(int p, %s *scale, %s *M, %s *Y, %s *x, %s *y, %s *z)\n' %
(funname, basetype, basetype, basetype, type, type, type))
M = parameter("M", array=True, base_array=True)
Y = parameter("Y", array=True)
scale = parameter("scale", array=True)
hx = var("hx")
hy = var("hy")
hz = var("hz")
cx = var("cx")
cy = var("cy")
cz = var("cz")
f1 = var("f1")
f2 = var("f2")
print
hx ^= 0
hy ^= 0
hz ^= 0
print
begin_block("switch(p) ")
for j in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, -1, -1):
print "\tcase %i:" % j
cx ^= -sqrt(float((j + 2) * (j + 1))) * M[Re(j, 0)] * Y[Re(j + 1, 1)]
cy ^= -sqrt(float((j + 2) * (j + 1))) * M[Re(j, 0)] * Y[Im(j + 1, 1)]
cz ^= (j + 1) * M[Re(j, 0)] * Y[Re(j + 1, 0)]
for k in range(1, j + 1):
f1 ^= sqrt(float((j + k + 2) * (j + k + 1)))
f2 ^= sqrt(float((j - k + 2) * (j - k + 1)))
cx ^= cx - f1*(M[Re(j,k)]*Y[Re(j+1,k+1)] - M[Im(j,k)]*Y[Im(j+1,k+1)])\
-f2*(M[Im(j,k)]*Y[Im(j+1,k-1)] - M[Re(j,k)]*Y[Re(j+1,k-1)])
cy ^= cy - f1*(M[Im(j,k)]*Y[Re(j+1,k+1)] + M[Re(j,k)]*Y[Im(j+1,k+1)])\
-f2*(M[Im(j,k)]*Y[Re(j+1,k-1)] + M[Re(j,k)]*Y[Im(j+1,k-1)])
cz ^= cz - 2.0 * sqrt(float(
(j + k + 1) * (j - k + 1))) * (M[Im(j, k)] * Y[Im(j + 1, k)] -
M[Re(j, k)] * Y[Re(j + 1, k)])
hx ^= hx + scale[j] * cx
hy ^= hy + scale[j] * cy
hz ^= hz + scale[j] * cz
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
print '\t*x = hx;'
print '\t*y = hy;'
print '\t*z = hz;'
end_block()
print
def gen_FFT_X2L_finish(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block('void %s(%s *x, %s *y, %s s)\n' %
(funname, basetype, basetype, type))
x = parameter("x", array=True)
y = parameter("y", array=True)
s = parameter("s")
f0 = var("f0")
f1 = var("f1")
f2 = var("f2")
f3 = var("f3")
print
#y[0] ^= s;
#y[1] ^= 0.0;
#y[2] ^= x[0] - y[0];
#y[3] ^= x[1];
#for j in range(1, M/4):
# y[4*j] ^= x[M-2*j] + y[4*j-2];
# y[4*j+1] ^= y[4*j-1] - x[M-2*j+1];
# y[4*j+2] ^= x[2*j] - y[4*j];
# y[4*j+3] ^= x[2*j+1] - y[4*j+1];
#y[M] ^= x[M/2] + y[M-2];
#y[M+1] ^= 0.0;
f0 ^= s
f1 ^= 0.0
f2 ^= x[0] - f0
f3 ^= x[1]
y[0] ^= f0
y[1] ^= f1
y[2] ^= f2
y[3] ^= f3
for j in range(1, M / 4):
f0 ^= x[M - 2 * j] + f2
f1 ^= f3 - x[M - 2 * j + 1]
y[4 * j] ^= f0
y[4 * j + 1] ^= f1
f2 ^= x[2 * j] - f0
f3 ^= x[2 * j + 1] - f1
y[4 * j + 2] ^= f2
y[4 * j + 3] ^= f3
y[M] ^= x[M / 2] + f2
y[M + 1] ^= 0.0
end_block()
print
def gen_FFT_X2L_finish(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block("void %s(%s *x, %s *y, %s s)\n" % (funname, basetype, basetype, type))
x = parameter("x", array=True)
y = parameter("y", array=True)
s = parameter("s")
f0 = var("f0")
f1 = var("f1")
f2 = var("f2")
f3 = var("f3")
print
# y[0] ^= s;
# y[1] ^= 0.0;
# y[2] ^= x[0] - y[0];
# y[3] ^= x[1];
# for j in range(1, M/4):
# y[4*j] ^= x[M-2*j] + y[4*j-2];
# y[4*j+1] ^= y[4*j-1] - x[M-2*j+1];
# y[4*j+2] ^= x[2*j] - y[4*j];
# y[4*j+3] ^= x[2*j+1] - y[4*j+1];
# y[M] ^= x[M/2] + y[M-2];
# y[M+1] ^= 0.0;
f0 ^= s
f1 ^= 0.0
f2 ^= x[0] - f0
f3 ^= x[1]
y[0] ^= f0
y[1] ^= f1
y[2] ^= f2
y[3] ^= f3
for j in range(1, M / 4):
f0 ^= x[M - 2 * j] + f2
f1 ^= f3 - x[M - 2 * j + 1]
y[4 * j] ^= f0
y[4 * j + 1] ^= f1
f2 ^= x[2 * j] - f0
f3 ^= x[2 * j + 1] - f1
y[4 * j + 2] ^= f2
y[4 * j + 3] ^= f3
y[M] ^= x[M / 2] + f2
y[M + 1] ^= 0.0
end_block()
print
def gen_FFT_X2L_prepare(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block('void %s(%s *y, %s *h)\n' % (funname, basetype, type))
y = parameter("y", array=True)
f = var("f")
g = var("g")
s = var("s")
print
# A factor 2 is missing, to be compensated in D_w_over_M
s ^= y[0]
y[0] ^= s
y[1] ^= y[1]
for j in range(1, M / 2):
f ^= y[2 * j + 1]
g ^= y[2 * j]
s ^= s + g
if j == M / 4:
y[2 * j] ^= g + f
y[2 * j + 1] ^= 0
else:
y[2 * j] ^= g + (sin(2.0 * pi * j / M)) * f
y[2 * j + 1] ^= (cos(2.0 * pi * j / M)) * f
print '\t*h = s;'
end_block()
print
def gen_FFT_X2L_prepare(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block("void %s(%s *y, %s *h)\n" % (funname, basetype, type))
y = parameter("y", array=True)
f = var("f")
g = var("g")
s = var("s")
print
# A factor 2 is missing, to be compensated in D_w_over_M
s ^= y[0]
y[0] ^= s
y[1] ^= y[1]
for j in range(1, M / 2):
f ^= y[2 * j + 1]
g ^= y[2 * j]
s ^= s + g
if j == M / 4:
y[2 * j] ^= g + f
y[2 * j + 1] ^= 0
else:
y[2 * j] ^= g + (sin(2.0 * pi * j / M)) * f
y[2 * j + 1] ^= (cos(2.0 * pi * j / M)) * f
print "\t*h = s;"
end_block()
print
def gen_FFT_M2X_prepare(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block('void %s(%s *x, %s *y, %s *h)\n' %
(funname, basetype, basetype, type))
x = parameter("x", array=True)
y = parameter("y", array=True)
f0 = var("f0")
f1 = var("f1")
f2 = var("f2")
f3 = var("f3")
s = var("s")
print
#for j in range(M/4):
# y[2*j] ^= x[4*j] + x[4*j+2]
# y[2*j+1] ^= x[4*j+1] + x[4*j+3]
# y[M-2*j-2] ^= x[4*j+4] - x[4*j+2]
# y[M-2*j-1] ^= x[4*j+3] - x[4*j+5]
f0 ^= x[0]
f1 ^= x[1]
f2 ^= x[2]
f3 ^= x[3]
s ^= 0
for j in range(M / 4):
y[2 * j] ^= f0 + f2
y[2 * j + 1] ^= f1 + f3
f0 ^= x[4 * j + 4]
f1 ^= x[4 * j + 5]
y[M - 2 * j - 2] ^= f0 - f2
y[M - 2 * j - 1] ^= f3 - f1
if j < M / 4 - 1:
if (j % 2):
s ^= s + f0
else:
s ^= s - f0
f2 ^= x[4 * j + 6]
f3 ^= x[4 * j + 7]
s ^= 2 * s + f0 + x[0]
print '\t*h = s;'
end_block()
print
def gen_FFT_M2X_prepare(funname, M):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block("void %s(%s *x, %s *y, %s *h)\n" % (funname, basetype, basetype, type))
x = parameter("x", array=True)
y = parameter("y", array=True)
f0 = var("f0")
f1 = var("f1")
f2 = var("f2")
f3 = var("f3")
s = var("s")
print
# for j in range(M/4):
# y[2*j] ^= x[4*j] + x[4*j+2]
# y[2*j+1] ^= x[4*j+1] + x[4*j+3]
# y[M-2*j-2] ^= x[4*j+4] - x[4*j+2]
# y[M-2*j-1] ^= x[4*j+3] - x[4*j+5]
f0 ^= x[0]
f1 ^= x[1]
f2 ^= x[2]
f3 ^= x[3]
s ^= 0
for j in range(M / 4):
y[2 * j] ^= f0 + f2
y[2 * j + 1] ^= f1 + f3
f0 ^= x[4 * j + 4]
f1 ^= x[4 * j + 5]
y[M - 2 * j - 2] ^= f0 - f2
y[M - 2 * j - 1] ^= f3 - f1
if j < M / 4 - 1:
if j % 2:
s ^= s + f0
else:
s ^= s - f0
f2 ^= x[4 * j + 6]
f3 ^= x[4 * j + 7]
s ^= 2 * s + f0 + x[0]
print "\t*h = s;"
end_block()
print
def gen_core_eval_L_M(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block('%s %s(int p, %s *scale, %s *LM, %s *Y)\n' %
(type, funname, basetype, basetype, basetype))
LM = parameter("LM", array=True, base_array=True)
Y = parameter("Y", array=True)
scale = parameter("scale", array=True)
h = var("h")
c = var("c")
two = var("two", 2.0)
print
h ^= 0
print
begin_block("switch(p) ")
for j in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, -1, -1):
print "\tcase %i:" % j
if j == 0:
c ^= LM[Re(j, 0)] * Y[Re(j, 0)]
else:
c ^= LM[Re(j, 1)] * Y[Re(j, 1)] - LM[Im(j, 1)] * Y[Im(j, 1)]
for k in range(2, j + 1):
c += LM[Re(j, k)] * Y[Re(j, k)] - LM[Im(j, k)] * Y[Im(j, k)]
c ^= two * c + LM[Re(j, 0)] * Y[Re(j, 0)]
#h ^= c + scale*h
h += scale[j] * c
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
print '\treturn h;'
end_block()
print
def gen_core_gen_M_L_dipole_plus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
"void %s(int p, %s *scale, %s mx, %s my, %s mz, %s *Y, %s *L)\n"
% (funname, basetype, type, type, type, basetype, basetype)
)
scale = parameter("scale", array=True)
mx = parameter("mx")
my = parameter("my")
mz = parameter("mz")
Y = parameter("Y", array=True)
L = parameter("L", array=True, horiz_add=-1)
f = var("f")
print
begin_block("switch(p) ")
for j in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, -1, -1):
print "\tcase %i:" % j
# print "\t\tf = scale[%i];" % j
f ^= scale[j]
for k in range(j + 1 - 1, 2 - 1, -1):
L[Im(j, k)] += f * (
(0.5 * sqrt(float((j + k + 1) * (j + k + 2)))) * (my * Y[Re(j + 1, k + 1)] + mx * Y[Im(j + 1, k + 1)])
+ (0.5 * sqrt(float((j - k + 1) * (j - k + 2)))) * (my * Y[Re(j + 1, k - 1)] - mx * Y[Im(j + 1, k - 1)])
- (sqrt(float((j - k + 1) * (j + k + 1)))) * mz * Y[Im(j + 1, k)]
)
L[Re(j, k)] += f * (
(0.5 * sqrt(float((j + k + 1) * (j + k + 2)))) * (mx * Y[Re(j + 1, k + 1)] - my * Y[Im(j + 1, k + 1)])
- (0.5 * sqrt(float((j - k + 1) * (j - k + 2)))) * (mx * Y[Re(j + 1, k - 1)] + my * Y[Im(j + 1, k - 1)])
- (sqrt(float((j - k + 1) * (j + k + 1)))) * mz * Y[Re(j + 1, k)]
)
if j > 0:
L[Im(j, 1)] += f * (
(0.5 * sqrt(float((j + 1 + 1) * (j + 1 + 2)))) * (my * Y[Re(j + 1, 1 + 1)] + mx * Y[Im(j + 1, 1 + 1)])
+ (0.5 * sqrt(float((j - 1 + 1) * (j - 1 + 2)))) * my * Y[Re(j + 1, 1 - 1)]
- (sqrt(float((j - 1 + 1) * (j + 1 + 1)))) * mz * Y[Im(j + 1, 1)]
)
L[Re(j, 1)] += f * (
(0.5 * sqrt(float((j + 1 + 1) * (j + 1 + 2)))) * (mx * Y[Re(j + 1, 1 + 1)] - my * Y[Im(j + 1, 1 + 1)])
- (0.5 * sqrt(float((j - 1 + 1) * (j - 1 + 2)))) * mx * Y[Re(j + 1, 1 - 1)]
- (sqrt(float((j - 1 + 1) * (j + 1 + 1)))) * mz * Y[Re(j + 1, 1)]
)
L[Im(j, 0)] += 0
L[Re(j, 0)] += f * (
(sqrt(float(j + 1) * (j + 2))) * (mx * Y[Re(j + 1, 1)] - my * Y[Im(j + 1, 1)])
- (j + 1) * mz * Y[Re(j + 1, 0)]
)
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
end_block()
print
def gen_core_eval_L_M(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block("%s %s(int p, %s *scale, %s *LM, %s *Y)\n" % (type, funname, basetype, basetype, basetype))
LM = parameter("LM", array=True, base_array=True)
Y = parameter("Y", array=True)
scale = parameter("scale", array=True)
h = var("h")
c = var("c")
two = var("two", 2.0)
print
h ^= 0
print
begin_block("switch(p) ")
for j in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, -1, -1):
print "\tcase %i:" % j
if j == 0:
c ^= LM[Re(j, 0)] * Y[Re(j, 0)]
else:
c ^= LM[Re(j, 1)] * Y[Re(j, 1)] - LM[Im(j, 1)] * Y[Im(j, 1)]
for k in range(2, j + 1):
c += LM[Re(j, k)] * Y[Re(j, k)] - LM[Im(j, k)] * Y[Im(j, k)]
c ^= two * c + LM[Re(j, 0)] * Y[Re(j, 0)]
# h ^= c + scale*h
h += scale[j] * c
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
print "\treturn h;"
end_block()
print
def gen_core_gen_M_L_dipole_minus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
"void %s(int p, %s *scale, %s mx, %s my, %s mz, %s *Y, %s *M)\n"
% (funname, basetype, type, type, type, basetype, basetype)
)
scale = parameter("scale")
mx = parameter("mx")
my = parameter("my")
mz = parameter("mz")
Y = parameter("Y", array=True)
M = parameter("M", array=True, horiz_add=-1)
f = var("f")
print
begin_block("switch(p) ")
for j in range(1, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, 3 - 1, -1):
print "\tcase %i:" % j
##print "\t\tf = scale[%i];" % j
f ^= scale[j]
M[Im(j, j)] += f * (
(0.5 * sqrt(float(2 * j - 1) * (2 * j))) * (my * Y[Re(j - 1, j - 1)] - mx * Y[Im(j - 1, j - 1)])
)
M[Re(j, j)] += f * (
(-0.5 * sqrt(float(2 * j - 1) * (2 * j))) * (mx * Y[Re(j - 1, j - 1)] + my * Y[Im(j - 1, j - 1)])
)
if j > 1:
M[Im(j, j - 1)] += f * (
(0.5 * sqrt(float((2 * j - 2) * (2 * j - 1)))) * (my * Y[Re(j - 1, j - 2)] - mx * Y[Im(j - 1, j - 2)])
+ (sqrt(float(2 * j - 1))) * mz * Y[Im(j - 1, j - 1)]
)
M[Re(j, j - 1)] += f * (
(-0.5 * sqrt(float((2 * j - 2) * (2 * j - 1)))) * (mx * Y[Re(j - 1, j - 2)] + my * Y[Im(j - 1, j - 2)])
+ (sqrt(float(2 * j - 1))) * mz * Y[Re(j - 1, j - 1)]
)
for k in range(j - 2 + 1 - 1, 2 - 1, -1):
M[Im(j, k)] += f * (
(0.5 * sqrt(float((j - k - 1) * (j - k)))) * (my * Y[Re(j - 1, k + 1)] + mx * Y[Im(j - 1, k + 1)])
+ (0.5 * sqrt(float((j + k - 1) * (j + k)))) * (my * Y[Re(j - 1, k - 1)] - mx * Y[Im(j - 1, k - 1)])
+ (sqrt(float((j - k) * (j + k)))) * mz * Y[Im(j - 1, k)]
)
M[Re(j, k)] += f * (
(0.5 * sqrt(float((j - k - 1) * (j - k)))) * (mx * Y[Re(j - 1, k + 1)] - my * Y[Im(j - 1, k + 1)])
- (0.5 * sqrt(float((j + k - 1) * (j + k)))) * (mx * Y[Re(j - 1, k - 1)] + my * Y[Im(j - 1, k - 1)])
+ (sqrt(float((j - k) * (j + k)))) * mz * Y[Re(j - 1, k)]
)
M[Im(j, 1)] += f * (
(0.5 * sqrt(float((j - 1 - 1) * (j - 1)))) * (my * Y[Re(j - 1, 1 + 1)] + mx * Y[Im(j - 1, 1 + 1)])
+ (0.5 * sqrt(float((j + 1 - 1) * (j + 1)))) * my * Y[Re(j - 1, 1 - 1)]
+ (sqrt(float((j - 1) * (j + 1)))) * mz * Y[Im(j - 1, 1)]
)
M[Re(j, 1)] += f * (
(0.5 * sqrt(float((j - 1 - 1) * (j - 1)))) * (mx * Y[Re(j - 1, 1 + 1)] - my * Y[Im(j - 1, 1 + 1)])
- (0.5 * sqrt(float((j + 1 - 1) * (j + 1)))) * mx * Y[Re(j - 1, 1 - 1)]
+ (sqrt(float((j - 1) * (j + 1)))) * mz * Y[Re(j - 1, 1)]
)
M[Im(j, 0)] += 0
M[Re(j, 0)] += f * (
j * mz * Y[Re(j - 1, 0)] + sqrt(float((j - 1) * j)) * (mx * Y[Re(j - 1, 1)] - my * Y[Im(j - 1, 1)])
)
print "#endif /* FMM_P_MAX >= %i */" % j
print "\tcase 2:"
f ^= scale[2]
M[11] += f * (sqrt(float(3)) * (my * Y[4] - mx * Y[5]))
M[10] += f * ((-sqrt(float(3))) * (mx * Y[4] + my * Y[5]))
M[9] += f * (sqrt(float(1.5)) * my * Y[2] + sqrt(float(3)) * mz * Y[5])
M[8] += f * ((-sqrt(float(1.5))) * mx * Y[2] + sqrt(float(3)) * mz * Y[4])
M[7] += 0
M[6] += f * (2.0 * mz * Y[2] + sqrt(float(2)) * (mx * Y[4] - my * Y[5]))
print "#endif /* FMM_P_MAX >= 2 */"
print "\tcase 1:"
f ^= scale[1]
M[5] += f * sqrt(float(0.5)) * my * Y[0]
M[4] += f * (-sqrt(float(0.5))) * mx * Y[0]
M[3] += 0
M[2] += f * mz * Y[0]
print "#endif /* FMM_P_MAX >= 1 */"
print "\tcase 0:"
M[1] += 0
M[0] += 0
end_block()
end_block()
print
def gen_core_gen_M_L_dipole_minus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
'void %s(int p, %s *scale, %s mx, %s my, %s mz, %s *Y, %s *M)\n' %
(funname, basetype, type, type, type, basetype, basetype))
scale = parameter("scale")
mx = parameter("mx")
my = parameter("my")
mz = parameter("mz")
Y = parameter("Y", array=True)
M = parameter("M", array=True, horiz_add=-1)
f = var("f")
print
begin_block("switch(p) ")
for j in range(1, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, 3 - 1, -1):
print "\tcase %i:" % j
##print "\t\tf = scale[%i];" % j
f ^= scale[j]
M[Im(j,
j)] += f * ((0.5 * sqrt(float(2 * j - 1) * (2 * j))) *
(my * Y[Re(j - 1, j - 1)] - mx * Y[Im(j - 1, j - 1)]))
M[Re(j,
j)] += f * ((-0.5 * sqrt(float(2 * j - 1) * (2 * j))) *
(mx * Y[Re(j - 1, j - 1)] + my * Y[Im(j - 1, j - 1)]))
if j > 1:
M[Im(j, j - 1)] += f * (
(0.5 * sqrt(float((2 * j - 2) * (2 * j - 1)))) *
(my * Y[Re(j - 1, j - 2)] - mx * Y[Im(j - 1, j - 2)]) +
(sqrt(float(2 * j - 1))) * mz * Y[Im(j - 1, j - 1)])
M[Re(j, j - 1)] += f * (
(-0.5 * sqrt(float((2 * j - 2) * (2 * j - 1)))) *
(mx * Y[Re(j - 1, j - 2)] + my * Y[Im(j - 1, j - 2)]) +
(sqrt(float(2 * j - 1))) * mz * Y[Re(j - 1, j - 1)])
for k in range(j - 2 + 1 - 1, 2 - 1, -1):
M[Im(j, k)] += f * (
(0.5 * sqrt(float((j - k - 1) * (j - k)))) *
(my * Y[Re(j - 1, k + 1)] + mx * Y[Im(j - 1, k + 1)]) +
(0.5 * sqrt(float((j + k - 1) * (j + k)))) *
(my * Y[Re(j - 1, k - 1)] - mx * Y[Im(j - 1, k - 1)]) +
(sqrt(float((j - k) * (j + k)))) * mz * Y[Im(j - 1, k)])
M[Re(j, k)] += f * (
(0.5 * sqrt(float((j - k - 1) * (j - k)))) *
(mx * Y[Re(j - 1, k + 1)] - my * Y[Im(j - 1, k + 1)]) -
(0.5 * sqrt(float((j + k - 1) * (j + k)))) *
(mx * Y[Re(j - 1, k - 1)] + my * Y[Im(j - 1, k - 1)]) +
(sqrt(float((j - k) * (j + k)))) * mz * Y[Re(j - 1, k)])
M[Im(
j,
1)] += f * ((0.5 * sqrt(float((j - 1 - 1) * (j - 1)))) *
(my * Y[Re(j - 1, 1 + 1)] + mx * Y[Im(j - 1, 1 + 1)]) +
(0.5 * sqrt(float(
(j + 1 - 1) *
(j + 1)))) * my * Y[Re(j - 1, 1 - 1)] +
(sqrt(float(
(j - 1) * (j + 1)))) * mz * Y[Im(j - 1, 1)])
M[Re(
j,
1)] += f * ((0.5 * sqrt(float((j - 1 - 1) * (j - 1)))) *
(mx * Y[Re(j - 1, 1 + 1)] - my * Y[Im(j - 1, 1 + 1)]) -
(0.5 * sqrt(float(
(j + 1 - 1) *
(j + 1)))) * mx * Y[Re(j - 1, 1 - 1)] +
(sqrt(float(
(j - 1) * (j + 1)))) * mz * Y[Re(j - 1, 1)])
M[Im(j, 0)] += 0
M[Re(j, 0)] += f * (j * mz * Y[Re(j - 1, 0)] + sqrt(float(
(j - 1) * j)) * (mx * Y[Re(j - 1, 1)] - my * Y[Im(j - 1, 1)]))
print "#endif /* FMM_P_MAX >= %i */" % j
print "\tcase 2:"
f ^= scale[2]
M[11] += f * (sqrt(float(3)) * (my * Y[4] - mx * Y[5]))
M[10] += f * ((-sqrt(float(3))) * (mx * Y[4] + my * Y[5]))
M[9] += f * (sqrt(float(1.5)) * my * Y[2] + sqrt(float(3)) * mz * Y[5])
M[8] += f * ((-sqrt(float(1.5))) * mx * Y[2] + sqrt(float(3)) * mz * Y[4])
M[7] += 0
M[6] += f * (2.0 * mz * Y[2] + sqrt(float(2)) * (mx * Y[4] - my * Y[5]))
print "#endif /* FMM_P_MAX >= 2 */"
print "\tcase 1:"
f ^= scale[1]
M[5] += f * sqrt(float(0.5)) * my * Y[0]
M[4] += f * (-sqrt(float(0.5))) * mx * Y[0]
M[3] += 0
M[2] += f * mz * Y[0]
print "#endif /* FMM_P_MAX >= 1 */"
print "\tcase 0:"
M[1] += 0
M[0] += 0
end_block()
end_block()
print
def gen_core_eval_L_M_grad_plus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
"void %s(int p, %s *scale, %s *M, %s *Y, %s *x, %s *y, %s *z)\n"
% (funname, basetype, basetype, basetype, type, type, type)
)
M = parameter("M", array=True, base_array=True)
Y = parameter("Y", array=True)
scale = parameter("scale", array=True)
hx = var("hx")
hy = var("hy")
hz = var("hz")
cx = var("cx")
cy = var("cy")
cz = var("cz")
f1 = var("f1")
f2 = var("f2")
print
hx ^= 0
hy ^= 0
hz ^= 0
print
begin_block("switch(p) ")
for j in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, -1, -1):
print "\tcase %i:" % j
cx ^= -sqrt(float((j + 2) * (j + 1))) * M[Re(j, 0)] * Y[Re(j + 1, 1)]
cy ^= -sqrt(float((j + 2) * (j + 1))) * M[Re(j, 0)] * Y[Im(j + 1, 1)]
cz ^= (j + 1) * M[Re(j, 0)] * Y[Re(j + 1, 0)]
for k in range(1, j + 1):
f1 ^= sqrt(float((j + k + 2) * (j + k + 1)))
f2 ^= sqrt(float((j - k + 2) * (j - k + 1)))
cx ^= (
cx
- f1 * (M[Re(j, k)] * Y[Re(j + 1, k + 1)] - M[Im(j, k)] * Y[Im(j + 1, k + 1)])
- f2 * (M[Im(j, k)] * Y[Im(j + 1, k - 1)] - M[Re(j, k)] * Y[Re(j + 1, k - 1)])
)
cy ^= (
cy
- f1 * (M[Im(j, k)] * Y[Re(j + 1, k + 1)] + M[Re(j, k)] * Y[Im(j + 1, k + 1)])
- f2 * (M[Im(j, k)] * Y[Re(j + 1, k - 1)] + M[Re(j, k)] * Y[Im(j + 1, k - 1)])
)
cz ^= cz - 2.0 * sqrt(float((j + k + 1) * (j - k + 1))) * (
M[Im(j, k)] * Y[Im(j + 1, k)] - M[Re(j, k)] * Y[Re(j + 1, k)]
)
hx ^= hx + scale[j] * cx
hy ^= hy + scale[j] * cy
hz ^= hz + scale[j] * cz
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
print "\t*x = hx;"
print "\t*y = hy;"
print "\t*z = hz;"
end_block()
print
def gen_core_eval_L_M_grad_minus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
"void %s(int p, %s *scale, %s *L, %s *Y, %s *x, %s *y, %s *z)\n"
% (funname, basetype, basetype, basetype, type, type, type)
)
L = parameter("L", array=True, base_array=True)
Y = parameter("Y", array=True)
scale = parameter("scale", array=True)
hx = var("hx")
hy = var("hy")
hz = var("hz")
cx = var("cx")
cy = var("cy")
cz = var("cz")
f1 = var("f1")
f2 = var("f2")
print
hx ^= 0
hy ^= 0
hz ^= 0
print
begin_block("switch(p) ")
for j in range(1, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, 0, -1):
print "\tcase %i:" % j
cx ^= sqrt(float(j * (j - 1))) * L[Re(j, 0)] * Y[Re(j - 1, 1)]
cy ^= sqrt(float(j * (j - 1))) * L[Re(j, 0)] * Y[Im(j - 1, 1)]
cz ^= j * L[Re(j, 0)] * Y[Re(j - 1, 0)]
for k in range(1, j + 1):
if k <= j - 2:
f1 ^= sqrt(float((j - k) * (j - k - 1)))
f2 ^= sqrt(float((j + k) * (j + k - 1)))
cx ^= (
cx
+ f1 * (L[Re(j, k)] * Y[Re(j - 1, k + 1)] - L[Im(j, k)] * Y[Im(j - 1, k + 1)])
+ f2 * (L[Im(j, k)] * Y[Im(j - 1, k - 1)] - L[Re(j, k)] * Y[Re(j - 1, k - 1)])
)
cy ^= (
cy
+ f1 * (L[Im(j, k)] * Y[Re(j - 1, k + 1)] + L[Re(j, k)] * Y[Im(j - 1, k + 1)])
+ f2 * (L[Im(j, k)] * Y[Re(j - 1, k - 1)] + L[Re(j, k)] * Y[Im(j - 1, k - 1)])
)
else:
cx ^= cx - sqrt(float((j + k) * (j + k - 1))) * (
L[Re(j, k)] * Y[Re(j - 1, k - 1)] - L[Im(j, k)] * Y[Im(j - 1, k - 1)]
)
cy ^= cy + sqrt(float((j + k) * (j + k - 1))) * (
L[Im(j, k)] * Y[Re(j - 1, k - 1)] + L[Re(j, k)] * Y[Im(j - 1, k - 1)]
)
cz ^= cz + 2.0 * sqrt(float((j + k) * (j - k))) * (
L[Re(j, k)] * Y[Re(j - 1, k)] - L[Im(j, k)] * Y[Im(j - 1, k)]
)
hx ^= hx + scale[j] * cx
hy ^= hy + scale[j] * cy
hz ^= hz + scale[j] * cz
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
print "\t*x = hx;"
print "\t*y = hy;"
print "\t*z = hz;"
end_block()
print
def gen_core_gen_M_L_dipole_plus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
'void %s(int p, %s *scale, %s mx, %s my, %s mz, %s *Y, %s *L)\n' %
(funname, basetype, type, type, type, basetype, basetype))
scale = parameter("scale", array=True)
mx = parameter("mx")
my = parameter("my")
mz = parameter("mz")
Y = parameter("Y", array=True)
L = parameter("L", array=True, horiz_add=-1)
f = var("f")
print
begin_block("switch(p) ")
for j in range(0, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, -1, -1):
print "\tcase %i:" % j
#print "\t\tf = scale[%i];" % j
f ^= scale[j]
for k in range(j + 1 - 1, 2 - 1, -1):
L[Im(j, k)] += f * (
(0.5 * sqrt(float((j + k + 1) * (j + k + 2)))) *
(my * Y[Re(j + 1, k + 1)] + mx * Y[Im(j + 1, k + 1)]) +
(0.5 * sqrt(float((j - k + 1) * (j - k + 2)))) *
(my * Y[Re(j + 1, k - 1)] - mx * Y[Im(j + 1, k - 1)]) -
(sqrt(float(
(j - k + 1) * (j + k + 1)))) * mz * Y[Im(j + 1, k)])
L[Re(j, k)] += f * (
(0.5 * sqrt(float((j + k + 1) * (j + k + 2)))) *
(mx * Y[Re(j + 1, k + 1)] - my * Y[Im(j + 1, k + 1)]) -
(0.5 * sqrt(float((j - k + 1) * (j - k + 2)))) *
(mx * Y[Re(j + 1, k - 1)] + my * Y[Im(j + 1, k - 1)]) -
(sqrt(float(
(j - k + 1) * (j + k + 1)))) * mz * Y[Re(j + 1, k)])
if j > 0:
L[Im(j, 1)] += f * (
(0.5 * sqrt(float((j + 1 + 1) * (j + 1 + 2)))) *
(my * Y[Re(j + 1, 1 + 1)] + mx * Y[Im(j + 1, 1 + 1)]) +
(0.5 * sqrt(float(
(j - 1 + 1) * (j - 1 + 2)))) * my * Y[Re(j + 1, 1 - 1)] -
(sqrt(float(
(j - 1 + 1) * (j + 1 + 1)))) * mz * Y[Im(j + 1, 1)])
L[Re(j, 1)] += f * (
(0.5 * sqrt(float((j + 1 + 1) * (j + 1 + 2)))) *
(mx * Y[Re(j + 1, 1 + 1)] - my * Y[Im(j + 1, 1 + 1)]) -
(0.5 * sqrt(float(
(j - 1 + 1) * (j - 1 + 2)))) * mx * Y[Re(j + 1, 1 - 1)] -
(sqrt(float(
(j - 1 + 1) * (j + 1 + 1)))) * mz * Y[Re(j + 1, 1)])
L[Im(j, 0)] += 0
L[Re(j, 0)] += f * ((sqrt(float(j + 1) * (j + 2))) *
(mx * Y[Re(j + 1, 1)] - my * Y[Im(j + 1, 1)]) -
(j + 1) * mz * Y[Re(j + 1, 0)])
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
end_block()
print
def gen_spherical_harmonics(funname, p):
Fact = [0.0 for i in range(2 * p + 1)]
Fact[0] = 1.0
for n in range(1, len(Fact)):
Fact[n] = n * Fact[n - 1]
B = [0.0 for i in range((p * (p + 1)) / 2 + p + 1)]
for n in range(p + 1):
for m in range(n + 1):
B[J(n, m)] = math.sqrt(Fact[n - abs(m)] / Fact[n + abs(m)])
R = [0.0] + [1.0 / i for i in range(1, p + 1)]
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
'void %s_p%i(int p, %s *Y, %s sin_phi, %s cos_phi, %s cos_theta)\n' %
(funname, p, basetype, type, type, type))
Y = parameter("Y", array=True)
sin_phi = parameter("sin_phi")
cos_phi = parameter("cos_phi")
cos_theta = parameter("cos_theta")
pmm = var("pmm")
pm1 = var("pm1")
pm2 = var("pm2")
pml = var("pml")
c = var("c")
s = var("s")
h = var("h")
alpha = var("alpha")
beta = var("beta")
sqrt_1_minus_cos_theta_2 = var("sqrt_1_minus_cos_theta_2",
sqrt(1.0 - cos_theta * cos_theta))
print
pmm ^= 1.0
## m==0: #############################
Y[0] ^= B[0] * pmm
Y[1] ^= 0.0
pm2 ^= pmm
pml ^= pmm * cos_theta
Y[2] ^= pml
Y[3] ^= 0.0
k = 1
for l in range(2, p + 1):
pm1 ^= pml
pml ^= R[l] * ((2 * l - 1) * cos_theta * pm1 - (l - 1) * pm2)
pm2 ^= pm1
k += l
Y[2 * k] ^= pml
Y[2 * k + 1] ^= 0.0
## m==1: #############################
m = 1
pmm *= -sqrt_1_minus_cos_theta_2
s ^= sin_phi
c ^= cos_phi
alpha ^= 1 - c
beta ^= s
h ^= B[2] * pmm
Y[4] ^= c * h
Y[5] ^= s * h
pm2 ^= pmm
pml ^= 3 * pmm * cos_theta
h ^= B[4] * pml
Y[8] ^= c * h
Y[9] ^= s * h
#k = (m+1)*(m+2)/2 + m
k = 4
for l in range(3, p + 1):
pm1 ^= pml
pml ^= R[l - 1] * ((2 * l - 1) * cos_theta * pm1 - l * pm2)
pm2 ^= pm1
k += l
h ^= B[k] * pml
Y[2 * k] ^= c * h
Y[2 * k + 1] ^= s * h
## 2 <= m <= p-1: #############################
kk = 1
for m in range(2, p):
pmm *= (1 - 2 * m) * sqrt_1_minus_cos_theta_2
h ^= (alpha * c + beta * s)
s ^= s - alpha * s + beta * c # to simplify transformation to fma, fms, fnms
c -= h
kk += m
k = kk + m
h ^= B[k] * pmm
Y[2 * k] ^= c * h
Y[2 * k + 1] ^= s * h
pm2 ^= pmm
pml ^= (2 * m + 1) * pmm * cos_theta
k += m + 1
h ^= B[k] * pml
Y[2 * k] ^= c * h
Y[2 * k + 1] ^= s * h
for l in range(m + 2, p + 1):
pm1 ^= pml
pml ^= R[l - m] * ((2 * l - 1) * cos_theta * pm1 -
(l + m - 1) * pm2)
pm2 ^= pm1
k += l
h ^= B[k] * pml
Y[2 * k] ^= c * h
Y[2 * k + 1] ^= s * h
## m==p: #############################
m = p
pmm *= (1 - 2 * m) * sqrt_1_minus_cos_theta_2
h ^= (alpha * c + beta * s)
s ^= s - alpha * s + beta * c # to simplify transformation to fma, fms, fnms
c -= h
kk += m
k = kk + m
h ^= B[k] * pmm
Y[2 * k] ^= c * h
Y[2 * k + 1] ^= s * h
end_block()
def gen_core_eval_L_M_grad_minus(funname, p_max):
type = Op.templates["type"]
basetype = Op.templates["basetype"]
begin_block(
'void %s(int p, %s *scale, %s *L, %s *Y, %s *x, %s *y, %s *z)\n' %
(funname, basetype, basetype, basetype, type, type, type))
L = parameter("L", array=True, base_array=True)
Y = parameter("Y", array=True)
scale = parameter("scale", array=True)
hx = var("hx")
hy = var("hy")
hz = var("hz")
cx = var("cx")
cy = var("cy")
cz = var("cz")
f1 = var("f1")
f2 = var("f2")
print
hx ^= 0
hy ^= 0
hz ^= 0
print
begin_block("switch(p) ")
for j in range(1, p_max + 1):
print "#if FMM_P_MAX >= %i" % j
for j in range(p_max, 0, -1):
print "\tcase %i:" % j
cx ^= sqrt(float(j * (j - 1))) * L[Re(j, 0)] * Y[Re(j - 1, 1)]
cy ^= sqrt(float(j * (j - 1))) * L[Re(j, 0)] * Y[Im(j - 1, 1)]
cz ^= j * L[Re(j, 0)] * Y[Re(j - 1, 0)]
for k in range(1, j + 1):
if k <= j - 2:
f1 ^= sqrt(float((j - k) * (j - k - 1)))
f2 ^= sqrt(float((j + k) * (j + k - 1)))
cx ^= cx + f1*(L[Re(j,k)]*Y[Re(j-1,k+1)] - L[Im(j,k)]*Y[Im(j-1,k+1)])\
+ f2*(L[Im(j,k)]*Y[Im(j-1,k-1)] - L[Re(j,k)]*Y[Re(j-1,k-1)])
cy ^= cy + f1*(L[Im(j,k)]*Y[Re(j-1,k+1)] + L[Re(j,k)]*Y[Im(j-1,k+1)])\
+ f2*(L[Im(j,k)]*Y[Re(j-1,k-1)] + L[Re(j,k)]*Y[Im(j-1,k-1)])
else:
cx ^= cx - sqrt(float(
(j + k) *
(j + k - 1))) * (L[Re(j, k)] * Y[Re(j - 1, k - 1)] -
L[Im(j, k)] * Y[Im(j - 1, k - 1)])
cy ^= cy + sqrt(float(
(j + k) *
(j + k - 1))) * (L[Im(j, k)] * Y[Re(j - 1, k - 1)] +
L[Re(j, k)] * Y[Im(j - 1, k - 1)])
cz ^= cz + 2.0 * sqrt(float(
(j + k) * (j - k))) * (L[Re(j, k)] * Y[Re(j - 1, k)] -
L[Im(j, k)] * Y[Im(j - 1, k)])
hx ^= hx + scale[j] * cx
hy ^= hy + scale[j] * cy
hz ^= hz + scale[j] * cz
print "#endif /* FMM_P_MAX >= %i */" % j
end_block()
print '\t*x = hx;'
print '\t*y = hy;'
print '\t*z = hz;'
end_block()
print
