243f1f68-97e2-4ad1-88d8-074821e4154f 14 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

The Smath granularity

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 - ≤

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

Insisible granularity

2 π * x / tanh

Granularity dead zone

2 π * x / tanh low high 3 1 sys

Mathcad 11 granularity appears in the region and alternates => Tested on XP Home, Smath 32 bits is extraodinary granular. That affects all numerical maths in all sorts of error messages. Remember that no numerical maths exist outsides of the 4 basic arithmetic operations [+, -, *, /]. Also, remember that digital computing machineries perform only 2½ tasks, i.e: add [+], peak/poke memory, "the ½ is logical". [-, *, /] don't exist by themselves, only via [add +] I noticed in the Smath forum the "wish list" is as elastic as the one in Mathcad. The top one that Andrey can't escape is the minimal 64 bits extended floating. I'm not clear about Mathcad Primes XXX version: is it 128 extended floating ? ? ?

Mathcad 11

n tested ≡ 21 ≡

x 10 n -^≡ 1.784 10 n 3 -^* ≡

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 !