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I've got a function, integratedadvthirdaltb, that I'm trying to use in plotting some graphs:

thirdaltb[KP_, Ps_, C_, M_] :=

NSolve[Sqrt[2*M]*b +

InverseCDF[NormalDistribution[0, 1], Ps]*

Sqrt[4*(InverseCDF[NormalDistribution[0, 1], Ps]^2) +

4*Sqrt[2*M]*b + (2.785398163397448309616)*M] ==

KP*C - 2*(InverseCDF[NormalDistribution[0, 1], Ps]^2), b,

WorkingPrecision -> 20]

directadv[b_] := -Log2[1 - CDF[NormalDistribution[0, 1], b]]

integratedadvthirdaltb[KP_, Ps_, C_, M_] :=

directadv[b /. thirdaltb[KP, Ps, C, M]]

So far so good. However, the first graph I've tried to plot is giving me a lot of "The precision of the argument function ({6.6073 +4\ Sqrt[2]\ \

b+1.83842\ Sqrt[58.0856 +16\Sqrt[2]\b]}\\n) is less than \

WorkingPrecision" errors (in fact, that's not the only argument function that apparently has less than WorkingPrecision.) Having WorkingPrecision->20 in the definition of the thirdaltb function, I'm at a loss as to why I'm getting these errors.

That said, the first graph does get plotted. Here's the instruction to do so

LogLinearPlot[{integratedadvthirdaltb[x, 0.967, 2^(-5.35614381),

2^(4)]}, {x, 2^(9), 2^(13)}, AxesLabel -> {KPs, advantage},

PlotLabel ->

Style["HEYSFIRST6622NONLINEAR - theoretical advantage with Ps = \

0.97"], PlotRange -> {0, 12}, PlotStyle -> {Blue},

Ticks -> {{{2^(9), Superscript[2, Log2[2^(9)]]}, {2^(10),

Superscript[2, Log2[2^(10)]]}, {2^(11),

Superscript[2, Log2[2^(11)]]}, {2^(12),

Superscript[2, Log2[2^(12)]]}, {2^(13),

Superscript[2, Log2[2^(13)]]}}, Automatic},

WorkingPrecision -> 20]

The next graph I've tried to plot, however, is completely blank. Only the axes and heading/labels appear on screen. And I'm getting a lot more "The precision of the argument function ... is less than Working Precision" messages than I was for its predecessor:

LogLinearPlot[{integratedadvthirdaltb[x, 0.967, 2^(-8), 1]}, {x,

2^(9), 2^(13)}, AxesLabel -> {KPs, advantage},

PlotLabel ->

Style["CRYPRACTHREEFOURROUNDSTWELVEBITS - theoretical advantage \

with Ps = 0.97"], PlotRange -> {0, 12}, PlotStyle -> {Red},

Ticks -> {{{2^(9), Superscript[2, Log2[2^(9)]]}, {2^(10),

Superscript[2, Log2[2^(10)]]}, {2^(11),

Superscript[2, Log2[2^(11)]]}, {2^(12),

Superscript[2, Log2[2^(12)]]}, {2^(13),

Superscript[2, Log2[2^(13)]]}}, Automatic},

WorkingPrecision -> 20]

Does any one have any idea as to where I'm going wrong and what I should do to fix it?

Thanks!

James McLaughlin.

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# The precision of the argument function error message, graph not plotted

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