Modification of Power Series Expansion

The serviceable orders to estimate the logarithm of a estimate using digital circuits can be separated in brace ocean collocations. On the one laborer, we feel the appear-up consideration installed algorithms and, on the other, iterative orders. The original vestibule is faster and undesigning, referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attributablewithstanding singly beneficial reposeraint frugal exactness. Reposeraint tooling it, requires vast whole of fame reposeraint increasing the truthfulness. This is ascribable to the bigness of the appear-up consideration. We singly evaluated iterative algorithms that insufficiency insignificant appear-up considerations. The dodge collocation is dilatoryer, referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attributablewithstanding suiconsideration reposeraint haughty exactness. Taylor’s course comment is unordered the most public orders to manually estimate logarithms, referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attributablewithstanding it has a sfrugal assembly and requires sfrugal operations enjoy the disruption. Hence, they are sfrugal when no embedded multipliers are serviceable. Many studies ponder mule toolations that procure advantages from twain collocations.

Our purpose required an algorithm that could be tooled on FPGAs from any vendor. It should be platarrange stubborn. Our algorithm requires close fame and no multiplier at integral to tool interpreterial and logarithm duty.

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To the best of our information there are singly brace antecedent compositions focused on the interpreterial duty [8] [9], and singly one reposeraint the logarithm duty [10] (from the harmonious authors of [9]).

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The original one [8], employs an algorithm that does referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation feat the FPGA characteristics, and consequently presents penniless enterprise. The other brace toolations [9, 10] are chaffer-out of a disingenuous composition and are intentional suiting with FPGA flexibility (using interior tailored unroving arithmetic and feating the commensurateness lineaments of the FPGA) achieving plenteous amelioadmonish consequences.

They are parameterizable toolations that, over-and-above to one f.p. reposeraintmat, too integralow smaller interpreter and mantissa bit-widths and are twain installed on input squeezeble diminution and table-driven orders to admonish the duty in the gentle squeezeble. Our ex and ln x individuals, installed on these individuals, apprehend the subjoined innovative lineaments:

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One exactness f.p. arithmetic extension. [9, 10] were intentional accordingly singly normalized estimates, referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation denormalized. Appenditional logic has been introduced to laborerle denormalized estimates at the output of ex and the input of ln x.

² Redeexpression of individuals to chaffer singly with one exactness. The lineament of bit-width config-urability of the disingenuous designs has been removed. Thus, the media insufficiencyed feel been gentle accordingly peculiar individuals, honorable reposeraint one exactness, feel been familiar.

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² Simplification of regular teemings. As suggested in [9], customary multipliers feel been removed where the teemings confused regular coe±cients, improving enterprise and reducing bigness.

² Unattested arithmetic. In [9, 10] interior unroving arithmetic with expression is explanationd. However, some operations (enjoy the ones involving squeezeble diminution and investigation of the interpreter restraint the confollowing in ex) are orderly and akin, and the expression of the confollowing can be inferred from the input expression. Reposeraint such operations expressioned arithmetic has been replaced by unsigned arithmetic with the selfcorresponding logic diminution.

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² Emendd pipelining. The expedite is enhanced by frequently introducing pipeline stages to the datapath of the interpreterial and logarithm individuals and their subunits 

The monograph [11] explains environing the toolation of effectiveness and log duty installed on a single alteration of effectiveness course comment of Taylor course. In effectiveness duty toolation, the monograph presentation at reducing the interpreter estimate to a insignificanter prize. It requires a vast whole of arrepose squeeze and hardware multipliers as polite. It becomes platarrange relying and the clock quantity may deviate from vendor to vendor. The suspension in throughput admonish is ascribable to the explanation of 18 X 18 embedded multipliers in it. The effectivenessing individual too requires aid estimate of stages which may be gentle aid.

In the designed order, we are going to classify failure and emend the throughput admonish by dodgeing the embedded multipliers and arrepose RAMs. In this monograph, we are referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation wholly dodge appear up considerations, referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attributablewithstanding any prize of logarithm or interpreterial can be admonishd, by adjusting the appear up consideration prizes to the desired estimate

[8] C. C. Doss and R. L. Riley, FPGA-Installed toolation of a muscular IEEE-754 ex-ponential individual,” in IEEE Field-Programmable Custom Computing Machines, 2004, pp. 229{238.

[9] J. Detrey and F. de Dinechin, A parameterized °oating-point interpreterial duty reposeraint FPGAs,” in IEEE International Conference Field-Programmable Technology, 2005, pp.27{34.

[10] ||, A parameterized °oating-point logarithm operator reposeraint FPGAs,” in Signals, Systems and Estimaters, 2005. Conference Record of the Thirty-Ninth Asilomar Conference, 2005, pp. 1186{1190.

[11] Pedro Echeverra, Marisa Lopez-Vallejo,”An FPGA Toolation of the Effectivenessing Duty with One Exactness Floating-Point Arithmetic

“An FPGA Toolation of the Effectivenessing Duty with One Exactness Floating-Point Arithmetic”

PROPOSED METHOD

The designed order dodges teeming and disruption operations, and is thus suiconsideration reposeraint toolation in software on orderors that noncommunication such instructions (or where the instructions are dilatory) or in hardware on a programmable logic expedient or dedicated piece. This order is suiconsideration when removeers are serviceable in capacious. It is an extension to the toolation of sine and cosine explained in CORDIC. The designed algorithm evaluates the effectiveness dutys reposeraint twain absolute and privative prizes. There are some regulars by which it is referable attribuconsultation attributable-difficult to increase. Reposeraint specimen, increaseing by 2n, where n is a absolute or a privative integer, can be achieved by merely mutation a estimate by n places. The remove obtain be to the left (division) if n is absolute, to the straight (multiplication) if n is privative. It is almost as referable attribuconsultation attributable-difficult to increase by estimates of the reposeraintm ±2n±1. These merely implicate an append (or) deduct a remove.

Implementation of EXP:    

Restraint tooling y = exp(x). The algorithm is going to geneadmonish a following of prizes reposeraint x and y, and we are going to execute assured that reposeraint each pair

K

Exp(k)

5.5452

256

2.7726

16

1.3863

4

0.6931

2

0.4055

3/2

0.2231

5/4

0.1178

9/8

0.0606

17/16

0.0308

33/32

0.0155

65/64

0.0078

129/128

y=exp(4)·

y′=exp(4)·exp(-(xk))

=exp(4)·exp(-x)·exp(k)

=y·exp(k).

In other utterance, if we deductkfromx, we feel to increaseyby exp(k). Integral we feel to do now is execute assured that exp(k) is a particular estimate, so we can increase by it largely, and the repose is undesigning. Referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attributablee thatkitself does referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation feel to be particular, as we are singly deducting that, referable attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation attribuconsultation increaseing by it. Here are some particular prizes of exp(k) and the selfcorresponding (referable attribuconsultation attribuconsultation necessarily particular) prizes ofk.

The ffrugal of algorithm is as follows reposeraint absolute effectivenesss of x:

Here in each harping, we deduct the input from the nearepose prize of exp(k) as listed in the consideration. If the discord is privative, we increase the output by the selfcorresponding exp(k). The order continues withaid entities in our consideration of k, finally we acquire the consequence. In the harmonious habit the ffrugal chart is mentioned reposeraint nagative effectivenesss of x.

K

Exp(k)

5.5452

256

2.7726

16

1.3863

4

0.6931

2

0.2877

3/4

0.1335

7/8

0.0645

15/16

0.0317

31/32

0.0157

63/64

0.0078

127/128

0.0039

255/256

The ffrugal of algorithm is as follows reposeraint privative effectivenesss of x:

Here in each harping, we deduct the input from the nearepose prize of exp(k) as listed in the consideration. If the discord is absolute, we part the output by the selfcorresponding exp(k). The order continues withaid entities in our consideration of k, finally we acquire the consequence.

Implementation of LOG :

Restraint tooling Y=log (x), the progress is harmonious to the toolation of interpreterial duty

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