assembly - Do FMA (fused multiply-add) instructions always produce the same result as a mul then add instruction? -

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i have assembly (at&t syntax):

mulsd   %xmm0, %xmm1 addsd   %xmm1, %xmm2

i want replace with:

vfmadd231sd %xmm0, %xmm1, %xmm2

will transformation leave equivalent state in involved registers , flags? or result floats differ in someway? (if differ, why that?)

(about fma instructions: http://en.wikipedia.org/wiki/fma_instruction_set)

no. in fact, major part of benefit of fused multiply-add not (necessarily) produce same result separate multiply , add.

as (somewhat contrived) example, suppose have:

double = 1 + 0x1.0p-52 // 1 + 2**-52 double b = 1 - 0x1.0p-52 // 1 - 2**-52

and want compute a*b - 1. "mathematically exact" value of a*b - 1 is:

(1 + 2**-52)(1 - 2**-52) - 1 = 1 + 2**-52 - 2**52 - 2**-104 - 1 = -2**-104

but if first compute a*b using multiplication rounds 1.0, subsequent subtraction of 1.0 produces result of zero.

if use fma(a,b,-1) instead, eliminate intermediate rounding of product, allows "real" answer, -1.0p-104.

please note not different result, different flags have been set well; separate multiply , subtract sets inexact flag, whereas fused multiply-add not set flags.


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