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Suppose I have a string containing the C-representation of a floating point number, for example

s = "1.23e-5"

and I want to convert this to a Mathematica number. How can I do this?

ToExpression[s] gives Plus[-5, Times[1.23`, e]].

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The only way I know how to do this is ImportString["1.23e-5","Table"][[1,1]] which seems like rather a large hack! –  Ian Hinder Feb 14 '12 at 13:13

7 Answers 7

up vote 41 down vote accepted

I think probably the cleanest way to do this (at least, if you have only a single string, or are faced with a separate string for each number you wish to convert as a result of some other process) is to use the undocumented function Internal`StringToDouble, i.e.:

s = "1.23e-5";
Internal`StringToDouble[s]

which gives:

0.0000123

However, if you are trying to convert many such numbers at once, the standard, documented methods (Import, Read, etc.), are likely to represent better approaches.

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10  
Another one from Mr.Undocumented! –  rm -rf Feb 14 '12 at 15:32
3  
Always try to avoid ToExpression! –  FJRA Feb 14 '12 at 17:37
1  
This seems like functionality that should be available (officially) in Mathematica. Will Wolfram accept feature-requests? –  Ian Hinder Feb 23 '12 at 16:06
    
@FJRA Why should ToExpression be avoided? –  George Wolfe Oct 17 '12 at 16:19
3  
@GeorgeWolfe because it might lead you to a code leak. What if there is dangerous code within the string? Or something innocent like a equal sign (=) may set any of your variables. –  FJRA Oct 18 '12 at 20:34
s = "1.23e-5"

# &[Read[#, Number], Close@#]&[ StringToStream@s ]

Which is not as good as what you started with. Note that it is important to close the stream.


Szabolcs says this is difficult to read. That was surely not my intention. You could also write it verbosely like this:

fromC =
    Module[{output, stream},
      stream = StringToStream[#];
      output = Read[stream, Number];
      Close[stream];
      output
    ] &;

fromC[s]
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First[ImportString["1.23e-5", "List"]] might be slightly less hack-y than your suggestion in the comments...

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What about a string like "2.12e"? You can see in MMA examples where such strings are generated as CForm/FortranForm ScientificForm[2.12, NumberFormat -> (Row[{#1, "e", #3}] &)] –  PlatoManiac Feb 14 '12 at 13:47
    
@Plato is that a standard form? It looks like an error. –  Mr.Wizard Feb 14 '12 at 13:53
    
@Plato: That's funny; I don't think I've ever seen a superfluous e being added to numbers between $1$ and $10$, I must say. Neither CForm[] nor FortranForm[] do this, and ScientificForm[] will only do that if you mess with options like you have. –  J. M. Feb 14 '12 at 13:54
    
@J.M. You are right! It does not generate numbers that ends with such a "e" as I wrote. Actually I got misled by the documentation of ScientificForm. You can also check there the NumberFormat example in the Options section of the documentation for ScientificForm. There they show how to produce Fortran-like forms. Test with a number like "2.12" and see the foolish "e" appears. But it is indeed not a general truth about the CFormor FortranForm. –  PlatoManiac Feb 14 '12 at 14:07
    
@Plato: Okay, but I think that's a rather contrived example. I don't think I've seen an entity like 2.12e in applications... –  J. M. Feb 14 '12 at 14:19

On version 7 Internal`StringToDouble fails on long strings, and fails to recognize exponents:

Internal`StringToDouble["3.1415926535897932385"]

Internal`StringToDouble /@ {"3.14159", "3.14159e-02", "3.14159e+02"}
$Failed["Bignum"]

{3.14159, 3.14159, 3.14159}

This sent me looking for another way to convert numeric strings. Using Trace on ImportString I found another internal function that does what I need: System`Convert`TableDump`ParseTable.

Being an internal function is it not error tolerant and if fed bad arguments it will crash the kernel. The syntax is as follows:

System`Convert`TableDump`ParseTable[
  table,
  {{pre, post}, {neg, pos}, dot},
  False
]
table  :   table of strings, depth = 2; need not be rectangular.  
pre    :   List of literal strings to ignore if preceding the digits (only first match tried).  
post   :   List of literal strings to ignore if following the digits (only first match tried).  
neg    :   literal string to interpret a negative sign (`-`).  
pos    :   literal string to interpret a positive sign (`+`).  
dot    :   literal string to interpret as decimal point.

(Using True in place of False causes a call to System`Convert`TableDump`TryDate that I do not yet understand.)

Example:

System`Convert`TableDump`ParseTable[
  {{"-£1,234.141592653589793e+007"}, {"0.97¢", "140e2kg"}},
  {{{"£"}, {"kg", "¢"}}, {"-", "+"}, "."},
  False
]

{{-1.2341415926535898*^10}, {0.97, 14000.}}

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Ah, kernel spelunking, +1. –  rcollyer Aug 20 '12 at 14:49
2  
Nice work! I'm sure this function will be useful. Regarding Internal`StringToDouble on 7: exponents are recognised if you first use StringReplace[nums, "e"|"E" -> "*^"]. –  Oleksandr R. Aug 21 '12 at 23:54
    
@Oleksandr thanks, and good to know about StringToDouble! –  Mr.Wizard Aug 22 '12 at 4:49
    
ParseTable is great. Very fast and handles integers as well as reals. I've used it a bunch of times when I know my input is clean, thanks a bunch! –  ssch Dec 7 '13 at 14:30
    
@ssch Glad I could help. :-) –  Mr.Wizard Dec 7 '13 at 18:25

Another solution would be to use SemanticImportString (new in 10).

Borrowing some code from Mr.Wizard so that I can compare my solution to his:

strings =
  ToString @ Row[RandomChoice /@ {{"-", ""}, {#}, {"e"}, {"-", ""}, Range@12}] & /@ 
    RandomReal[{0, 10}, 15000];

Needs["GeneralUtilities`"]

Internal`StringToDouble /@ strings // AccurateTiming

System`Convert`TableDump`ParseTable[
  {strings}, {{{}, {}}, {"-", "+"}, "."}, False
] // AccurateTiming

Interpreter["Number"][strings]   // AccurateTiming

SemanticImportString[
     StringJoin[Riffle[strings, ";"]],
     {"Number"}, 
     "List",
     Delimiters -> ";"
] // AccurateTiming

0.00671892

0.00504799

12.980645

0.0426966

Now as you can see there is still an order of magnitude, but at least SemanticImport is strict with things that are not numbers, while Internal`StringToDouble["foo"] returns 0..

Some of the types in Interpreter will benefit from using SemanticImport internally when called on lists of strings in the future.

As far as the current speed of Interpreter there is only so much you can gain if you want to support things like

Interpreter[
    Restricted["Number", {0, 10, 0.5}],
    NumberPoint -> "baz",
    NumberSigns -> {"foo", "bar"}
]["bar5baz5"]

5.5

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Thank you Carlo, this is much appreciated! –  Szabolcs yesterday

May be one can try the following

convert[inp_?StringQ] := ToExpression@StringReplace[inp, "e" -> "*10^"];
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Still this is not fully correct! If numbers like 2.12 is represented as "2.12e" than the expected "2.12e1". MMA does so as I mentioned in the above comment on the answer given by @J.M –  PlatoManiac Feb 14 '12 at 13:51
8  
It works, but let me give one comment: whenever you use ToExpression on data read from a file, you make it possible to inject code into a program even inadvertently (one can never tell what sort of erroneous input the program might get by mistake). I generally try not to use ToExpression for just reading in data (as opposed to converting code) –  Szabolcs Feb 14 '12 at 13:55
    
@Szabolcs thanks for explaining the issue with ToExpression. Your implementation is pretty cool. I did not know about the function StringToStream thanks for introducing... –  PlatoManiac Feb 14 '12 at 14:01

Version 10 introduced Interpreter which would seem suited to this task:

Interpreter[form]
represents an interpreter object that can be applied to a string to try to interpret it as an object of the specified form.

Interpreter["Number"]["1.23e-5"]
0.0000123

Unfortunately it seems that like many new-in-10 functions this is far from optimized. In fact I would say its performance is nothing short of abysmal for this particular task.

Some string data to test with:

strings =
  ToString @ Row[RandomChoice /@ {{"-", ""}, {#}, {"e"}, {"-", ""}, Range@12}] & /@ 
    RandomReal[{0, 10}, 15000];

Timings for Interpreter against StringToDouble and ParseTable (see the other answers):

Needs["GeneralUtilities`"]

Internal`StringToDouble /@ strings // AccurateTiming

System`Convert`TableDump`ParseTable[
  {strings}, {{{}, {}}, {"-", "+"}, "."}, False
] // AccurateTiming

Interpreter["Number"] /@ strings   // AccurateTiming
0.0052075

0.00645107

10.625608

At more than three orders of magnitude slower than the old methods the new function is simply not appropriate for general use. Hopefully it will be improved in a future release.

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1  
I really need a useful function that can parse a number or tell me that the input is not a number (and won't execute arbitrary code like ToExpression). I also tried Interpreter and found it to be unusable slow, unfortunately (I can't wait for half a minute for a file to import). I'm reporting the problem now and hoping for a fix ... –  Szabolcs Aug 9 at 15:32
    
@Szabolcs I think Read is still your best bet. What is the format or structure of the files you need to import? –  Mr.Wizard Aug 9 at 16:42
    
Read is useful when the precise format is known in advance, i.e. you know what type of expect for the next token. Take for example a mixture of strings and number. If reading as a number fails, read as a string. This comment wasn't motivated by the need to read a single file type only. –  Szabolcs Aug 9 at 16:58
    
@Szabolcs I understand that; this is still applicable, as is StringReplace, depending on the specifics. I'd welcome a Question from you on the subject. –  Mr.Wizard Aug 9 at 17:42
    
@Szabolcs I've added an answer to this question that might serve your purpose. –  Carlo yesterday

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