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The granularity test function

x f x 2 π * / 2 π * x / tanh * sqrt :

0.0178 f 0.0532

x 0.0178 ≥

0.0275 - f 0.0662

x 0.0275 - ≤

on same machine XP Home SP3 Mathcad 11 64 extended float

0.00001 f 1.26156626101009 e * 3 - ≡

2 π * 0.0178 / tanh 1

high 0.0178 1 + 15 red 15 mat :

2 π * 0.0275 - / tanh 1 -

low 0.0275 - 1 - + 15 red 15 mat :

Granularity in quick plot

x f 0.0662 2 1 sys

Invisible granularity

2 π * x / tanh

Granularity dead zone

2 π * x / tanh low high 3 1 sys

More: 1. f(x) is the Mathematica 4.0 ULP test function [ULP = Units in Last Place] 2. Maxima XY plot does not plot, insisting crashes Smath, Ah !

0.01 f 200 π * tanh sqrt 100 sqrt 2 sqrt * π sqrt * /

0.01 - f 200 π * - tanh - sqrt 100 sqrt 2 sqrt * π sqrt * /

200 π * - tanh - sqrt 100 sqrt 2 sqrt * π sqrt * / #

<= divide by zero

100 sqrt 2 sqrt * π sqrt * 25.0662827463098

73 π * - tanh - sqrt #

72 π * - tanh - sqrt 1

x π * - tanh - sqrt

114 π * tanh sqrt #

112 π * tanh sqrt 1

x 2 π * / 2 π * x / tanh * sqrt x 2 π * x / tanh * sqrt 2 sqrt π sqrt * /

x π * tanh sqrt

x q x 2 π * x / tanh * sqrt 2 sqrt π sqrt * / :

0.01 q #

x Tanh e 2 x *^1 - e 2 x *^1 + / :

112 π * Tanh sqrt 1

x Tanh 2 x * exp 1 - 2 x * exp 1 + / :

114 π * Tanh sqrt #

2114 * π * exp 1 + #

2114 * π * exp 1 - #

2112 * π * exp 1 + 4.17160578044567 10305^*

2112 * π * exp 1 - 4.17160578044567 10305^*

2113 * π * exp 1 + #

2113 * π * exp 1 - #

x f 1 x / :

x f

x fnct x0 x1 xmesh Xmesh clear U from previous U 0 : count 1 : i 1 xmesh range x i el x0 i xmesh / x1 x0 - (* + : U count el x i el fnct : count count 1 + : 31 line for x U augment 51 line :

Input string was not in correct format
wrong error message: Divide by zero V x f 5 - 5100 Xmesh :

V #

Input string was not in correct format
wrong error message: Divide by zero
Can't use 'V' ... 'V' is sick 
... now 'U' will plot. U x f 1 - 11001 Xmesh :

x not defined 1 x / x 1 - 1 int #

index was outside the 
bounds of the array 1 x 1015 -^+ / x 1 - 1 int #

index was outside the 
bounds of the array 1 x 1015 -^+ / x 1 - 1 int 6.666667 1014^* 1000 /

index was outside the 
bounds of the array 1 x 1012 -^+ / x 1 - 1 int 6.666667 108^*

index was outside the 
bounds of the array 1 x 109 -^+ / x 1 - 1 int 6.666821 105^*

index was outside the 
bounds of the array 1 x 1032 -^+ / x 1 - 1 int 6.666667 1028^*

index was outside the 
bounds of the array 1 x 10128 -^+ / x 1 - 1 int 6.666667 10124^*