def _determinant_euclidean_asm_col_major(col0, col1, col2):
tmp0 = pyasm.Register()
det = pyasm.Register()
# Do some multiplications & subtractions in parallel with SIMD instructions:
tmp0.xyz = pyasm.mul(col0.zxy, col1.yzx) # m0.z*m1.y, m0.x*m1.z, m0.y*m1.x
tmp0.xyz = pyasm.mad(col0.yzx, col1.zxy, -tmp0.xyz) # m0.y*m1.z - m0.z*m1.y, m0.z*m1.x - m0.x*m1.z, m0.x*m1.y - m0.y*m1.x
# Now the multiplications:
tmp0.xyz = pyasm.mul(tmp0.xyz, col2.xyz)
# Sum it together to get the determinant:
det.x = pyasm.add(tmp0.x, tmp0.y)
det.x = pyasm.add(det.x, tmp0.z)
return det
def _determinant_euclidean_asm_col_major(col0, col1, col2):
tmp0 = pyasm.Register()
det = pyasm.Register()
# Do some multiplications & subtractions in parallel with SIMD instructions:
tmp0.xyz = pyasm.mul(col0.zxy, col1.yzx) # m0.z*m1.y, m0.x*m1.z, m0.y*m1.x
tmp0.xyz = pyasm.mad(
col0.yzx, col1.zxy, -tmp0.xyz
) # m0.y*m1.z - m0.z*m1.y, m0.z*m1.x - m0.x*m1.z, m0.x*m1.y - m0.y*m1.x
# Now the multiplications:
tmp0.xyz = pyasm.mul(tmp0.xyz, col2.xyz)
# Sum it together to get the determinant:
det.x = pyasm.add(tmp0.x, tmp0.y)
det.x = pyasm.add(det.x, tmp0.z)
return det
def _inverse_euclidean_asm_col_major(col0, col1, col2, det):
'''
Performs a matrix inverse in a manner as would be done in assembly.
Note that the input matrix is in column-major order, but the resulting
inverted matrix will be in ROW-major order.
'''
std_consts = pyasm.Register([0, 1, 0.0625, 0.5])
dst0 = pyasm.Register()
dst1 = pyasm.Register()
dst2 = pyasm.Register()
dst3 = pyasm.Register()
# 1st row, simplifying by assuimg the 4th column 0,0,0,1
# dst0.x = (m1.y*m2.z - m1.z*m2.y)
# dst0.y = (m1.z*m2.x - m1.x*m2.z)
# dst0.z = (m1.x*m2.y - m1.y*m2.x)
# dst0.w = 0
dst0.xyz = pyasm.mul(col1.zxy, col2.yzx)
dst0.xyz = pyasm.mad(col1.yzx, col2.zxy, -dst0.xyz)
# 2nd row
# dst1.x = (col0.z*m2.y - col0.y*m2.z)
# dst1.y = (col0.x*m2.z - col0.z*m2.x)
# dst1.z = (col0.y*m2.x - col0.x*m2.y)
# dst1.w = 0
dst1.xyz = pyasm.mul(col0.yzx, col2.zxy)
dst1.xyz = pyasm.mad(col0.zxy, col2.yzx, -dst1.xyz)
# 3nd row
# dst2.x = (col0.y*m1.z - col0.z*m1.y)
# dst2.y = (col0.z*m1.x - col0.x*m1.z)
# dst2.z = (col0.x*m1.y - col0.y*m1.x)
# dst2.w = 0
dst2.xyz = pyasm.mul(col0.zxy, col1.yzx)
dst2.xyz = pyasm.mad(col0.yzx, col1.zxy, -dst2.xyz)
# 4th row
# dst3.x = - col0.w*dst0.x - col1.w*dst1.x - col2.w*dst2.x
# dst3.y = - col0.w*dst0.y - col1.w*dst1.y - col2.w*dst2.y
# dst3.z = - col0.w*dst0.z - col1.w*dst1.z - col2.w*dst2.z
# dst3.w = col0.x*dst0.x + col1.x*dst1.x + col2.x*dst2.x (always 1?)
dst3.xyzw = pyasm.mul(col0.wwwx, dst0.xyzx)
dst3.xyzw = pyasm.mad(col1.wwwx, dst1.xyzx, dst3.xyzw)
dst3.xyzw = pyasm.mad(col2.wwwx, dst2.xyzx, dst3.xyzw)
dst3.xyz = pyasm.mov(-dst3)
# Multiply against 1/determinant (and zero out 4th column):
inv_det = pyasm.rcp(det.x)
inv_det.y = pyasm.mov(std_consts.x)
dst0 = pyasm.mul(dst0, inv_det.xxxy)
dst1 = pyasm.mul(dst1, inv_det.xxxy)
dst2 = pyasm.mul(dst2, inv_det.xxxy)
dst3 = pyasm.mul(dst3, inv_det.xxxx)
# Note that this matrix has been transposed and is now in ROW major order!
return (dst0, dst1, dst2, dst3)
def _inverse_euclidean_asm_col_major(col0, col1, col2, det):
'''
Performs a matrix inverse in a manner as would be done in assembly.
Note that the input matrix is in column-major order, but the resulting
inverted matrix will be in ROW-major order.
'''
std_consts = pyasm.Register([0, 1, 0.0625, 0.5])
dst0 = pyasm.Register()
dst1 = pyasm.Register()
dst2 = pyasm.Register()
dst3 = pyasm.Register()
inv_det = pyasm.Register()
# 1st row, simplifying by assuimg the 4th column 0,0,0,1
# dst0.x = (m1.y*m2.z - m1.z*m2.y)
# dst0.y = (m1.z*m2.x - m1.x*m2.z)
# dst0.z = (m1.x*m2.y - m1.y*m2.x)
# dst0.w = 0
dst0.xyz = pyasm.mul(col1.zxy, col2.yzx)
dst0.xyz = pyasm.mad(col1.yzx, col2.zxy, -dst0.xyz)
# 2nd row
# dst1.x = (col0.z*m2.y - col0.y*m2.z)
# dst1.y = (col0.x*m2.z - col0.z*m2.x)
# dst1.z = (col0.y*m2.x - col0.x*m2.y)
# dst1.w = 0
dst1.xyz = pyasm.mul(col0.yzx, col2.zxy)
dst1.xyz = pyasm.mad(col0.zxy, col2.yzx, -dst1.xyz)
# 3nd row
# dst2.x = (col0.y*m1.z - col0.z*m1.y)
# dst2.y = (col0.z*m1.x - col0.x*m1.z)
# dst2.z = (col0.x*m1.y - col0.y*m1.x)
# dst2.w = 0
dst2.xyz = pyasm.mul(col0.zxy, col1.yzx)
dst2.xyz = pyasm.mad(col0.yzx, col1.zxy, -dst2.xyz)
# 4th row
# dst3.x = - col0.w*dst0.x - col1.w*dst1.x - col2.w*dst2.x
# dst3.y = - col0.w*dst0.y - col1.w*dst1.y - col2.w*dst2.y
# dst3.z = - col0.w*dst0.z - col1.w*dst1.z - col2.w*dst2.z
# dst3.w = col0.x*dst0.x + col1.x*dst1.x + col2.x*dst2.x (always 1?)
dst3.xyzw = pyasm.mul(col0.wwwx, dst0.xyzx)
dst3.xyzw = pyasm.mad(col1.wwwx, dst1.xyzx, dst3.xyzw)
dst3.xyzw = pyasm.mad(col2.wwwx, dst2.xyzx, dst3.xyzw)
dst3.xyz = pyasm.mov(-dst3)
# Multiply against 1/determinant (and zero out 4th column):
inv_det.x = pyasm.rcp(det.x)
inv_det.y = pyasm.mov(std_consts.x)
dst0 = pyasm.mul(dst0, inv_det.xxxy)
dst1 = pyasm.mul(dst1, inv_det.xxxy)
dst2 = pyasm.mul(dst2, inv_det.xxxy)
dst3 = pyasm.mul(dst3, inv_det.xxxx)
# Note that this matrix has been transposed and is now in ROW major order!
return (dst0, dst1, dst2, dst3)