Intel® 64 and IA-32 Architectures Optimization Reference Manual

OPTIMIZING FOR SIMD INTEGER APPLICATIONS5.6.11 Complex Multiply by a ConstantComplex multiplication is an operation which requires four multiplications and twoadditions. This is exactly how the PMADDWD instruction operates. In order to usethis instruction, you need to format the data into multiple 16-bit values. The real andimaginary components should be 16-bits each. Consider Example 5-30, whichassumes that the 64-bit MMX registers are being used:• Let the input data be DR and DI, where DR is real component of the data and DIis imaginary component of the data.• Format the constant complex coefficients in memory as four 16-bit values [CR -CI CI CR]. Remember to load the values into the MMX register using MOVQ.• The real component of the complex product is PR = DR*CR - DI*CI and theimaginary component of the complex product is PI = DR*CI + DI*CR.• The output is a packed doubleword. If needed, a pack instruction can be used toconvert the result to 16-bit (thereby matching the format of the input).Example 5-30. Complex Multiply by a Constant; Input:; MM0 complex value, Dr, Di; MM1 constant complex coefficient in the form; [Cr -Ci Ci Cr]; Output:; MM0 two 32-bit dwords containing [Pr Pi];punpckldq mm0, mm0 ; makes [dr di dr di]pmaddwd mm0, mm1 ; done, the result is; [(Dr*Cr-Di*Ci)(Dr*Ci+Di*Cr)]5.6.12 Packed 32*32 MultiplyThe PMULUDQ instruction performs an unsigned multiply on the lower pair of doublewordoperands within 64-bit chunks from the two sources; the full 64-bit result fromeach multiplication is returned to the destination register.This instruction is added in both a 64-bit and 128-bit version; the latter performs 2independent operations, on the low and high halves of a 128-bit register.5.6.13 Packed 64-bit Add/SubtractThe PADDQ/PSUBQ instructions add/subtract quad-word operands within each 64-bitchunk from the two sources; the 64-bit result from each computation is written tothe destination register. Like the integer ADD/SUB instruction, PADDQ/PSUBQ canoperate on either unsigned or signed (two’s complement notation) integer operands.5-30