Справочник Пользователя для AMD 250

25112

Rev. 3.06

September 2005

Use vectorizing SSE, SSE2 and 3DNow! instructions to perform complex number calculations.

This optimization applies to:

•

32-bit software

•

64-bit software

Complex numbers have a “real” part and an “imaginary” part (where the imaginary part is denoted by 
the letter i). For example, the complex number z1 might have a real part equal to 4 and an imaginary 
part equal to 3, written as 4 + 3i. Multiplying and adding complex numbers is an integral part of 
digital signal processing. Complex number addition is illustrated here using two complex numbers, z1 
(4 + 3i) and z2 (5 + 2i):

z1 + z2 = (4 + 3i) + (5 + 2i) = [4+5] + [3+2]i = 9 + 5i

or:

sum.real = z1.real + z2.real

sum.imag = z1.imag + z2.imag

Complex number addition is illustrated here using the same two complex numbers:

z1 + z2 = (4 + 3i)(5 + 2i) = [4 

× 5 - 3 × 2] + [3 × 5 + 4 × 2]i = 14 + 23i

or:

product.real = z1.real * z2.real - z1.imag * z2.imag

product.imag = z1.real * z2.imag + z1.imag * z2.real

Complex numbers are stored as streams of two-element vectors, the two elements being the real and 
imaginary parts of the complex numbers. Addition of complex numbers can be achieved using 
vectorizing SSE or 3DNow!instructions, such as PFADD, ADDPS, and ADDPD. Multiplication of 
complex numbers is more involved.

From the formulas for multiplication, the real and imaginary parts of one of the numbers needs to be 
interchanged, and, additionally, the products must be positively or negatively accumulated depending 
upon whether we are computing the imaginary or real portion of the product.