The calculation of one source code multiplication

(1) Mathematical Principles:

Two number of original code multiplied , the product of the symbol is multiplied by two number of symbols of the XOR value , the value is equal to the product of the absolute value of two.

Assume [X] original =x0.x1x2. Xn ,

Y Original =y0. Y1y2. Yn,

Then there are: [X· Y] Original = (X0⊙Y0). [(x1x2. Xn)· (y1y2. Yn)]

(2) algorithm:

Suppose x=0.x1x2. Xn ,y=0.y1y2. Yn,

i.e. all positive decimal fraction X· y= X · 0.y1y2. Yn

= X• (2-1y1+2-2y2+...+2-n+1yn-1+2-nyn)

= X• (2-nyn+2-n+1yn-1+...+2-2y2+2-1y1)

= (.. ((0+ Yn X) 2-1+yn-1x) 2-1) + ...) +Y2X) 2-1) +y1x) 2--1)

Based on the above calculation procedure,

The available algorithms are as follows:

A0=0

a1=(a0+ynx) 2-1

A2=(a1+yn-1x) 2-1

...

an-1=(an-2+y2x) 2-1

an =(an-1+y1x) 2-1

Product X· Y=an

For example 1:

X =0.1101, y =-0.1011 for y * y

Calculation process:

For example 2:

X = -0.1011, y =-0.0110 for the original code (Y * y)

The calculation process is as follows:

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The calculation of one source code multiplication