# Questions tagged [machine-precision]

For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.

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### Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
1answer
510 views

### Reasonable choice of MachinePrecision, AccuracyGoal and PrecisionGoal for NDSolve

I am trying to use this model for later use in FindFit: ...
1answer
922 views

### How to increase significant digits in Mathematica

How can I increase the number of significant digits in Mathematica? When I import a matrix, an element like 112.5276 is rounded to 112.528. I would like to increase the number of significant digits ...
2answers
114 views

### Decimal output from a simple equation

Let x= 0.0000000000000000036; y = 1 - x If i type this in Mathematica the answer of y is 1. I want the answer to be as it ...
1answer
159 views

### How to map HoldForm?

I'm trying to compare between Sqrt[3.] and Sqrt. To display the result, I mapped HoldForm to display the expressions on the left hand column (code at end), but it seems like Sqrt[3.] had been ...
1answer
157 views

### Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
1answer
84 views

### Unexpected behavior of subtraction with approximate numbers [duplicate]

I'm using the Table command to generate a list of values: FullForm /@ Table[10. - x, {x, 2.7, 2.8, .1}] and I get the ...
2answers
3k views

### Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays 0.333333 as the result. When I copy that output to use elsewhere, the paste ...
1answer
1k views

### How to get more accurate orthonormal eigenvectors?

I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
0answers
66 views

### Number precision in a list [duplicate]

I have list with elements: ...
2answers
216 views

### The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
2answers
1k views

### Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
1answer
2k views

### Plot periodic function from Dirac delta function [duplicate]

Sorry for my bad english. I need to plot periodic function from dirac delta: δT(t)=∑δ(t–n*T), where T - is a constant, and n=-20..20 And after them, plot new function fd=f(t)*δT(t) - discrete signal ...
1answer
1k views

1answer
804 views

### How to Chop correctly?

I want to count degeneracies in a list called spectrum. The list contains numbers of double (~ 15digits) precision. So it makes no sense if the noise below this ...
2answers
1k views

### FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
0answers
2k views

### Set Global Maximum Precision

I'm sure this has been asked before, but I've looked around and can't figure it out: How do I set a global maximum precision for a notebook (or in general, globally)? I have a large notebook in ...
2answers
3k views

### Precision of number not maintained when saved via Export

Assume that the output of my calculation is a and is a number such as: a = 100.1252135246354847; ...
1answer
775 views

### Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
3answers
871 views

### Mathematica Plot: Inconsistency when plotting large values

I am working with a function in Mathematica and I am getting some inconsistencies when I plot it. As I really need to understand were this comes from I would appreciate any help. I am working with a ...
1answer
2k views

### Infinite expression 1/0. encountered - caused by precision?

Planck's law dependent on frequency rho is as follows: B[T_, h_, rho_, k_, c_] := (2 h rho^3)/c^2 1/(Exp[h rho/(T k)] - 1) As you can see, the denominator can ...
1answer
1k views

### Quadruple-precision (128 bit) arithmetic

Is it possible to force Mathematica to perform computations with hardware supported quadruple-precision? The following test suggest, that all of the computations with fixed precision, different than <...
1answer
156 views

### Using Differences on data: trouble with floats and doubles

Consider the following data set (after I have run FullForm), which is imported from a file (stored typically as 10.040): ...