View source for intermediate float bug

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This problem only affects old versions of davinci.  If you're using davinci 2.18 (in which real numbers default to double) you can ignore this page, and if you're not you should certainly [http://davinci.asu.edu/index.php?title=Download_Davinci update.]

This page describes the intermediate float bug in Davinci, and how to work around it. See [[Syntax]] for a description of the ranges of float and double formats.

==The problem==
In most cases, single-precision floating point format ([[float]] in Davinci) is sufficient. A number stored as a float is typically accurate to seven significant figures. However, great care must be taken when double precision ([[double]] in Davinci) is required. A number stored as a double is typically accurate to fifteen significant figures.

'''Any''' decimal number entered into Davinci is first read as a single-precision [[float]].

 dv> format(2.5)
 "float"

This means that entering a number with the [[double]] function only actually converts a single-precision float number to double, and the double is stored with double precision but is only really accurate to single precision.

 dv> SCALE&#61;16
 16
 dv> a &#61; 4.2
 4.199999809265137
 dv> format(a)
 "float"
 dv> b &#61; double(4.2)
 4.199999809265137
 dv> format(b)
 "double"

==The solution==
====Tricks with integers====
In general, this bug is very hard to avoid. Low-magnitude integers convert exactly to floats (single or double precision), so mathematical tricks help with a few values.

 dv> e &#61; exp(double(1))
 2.718281828459045
 dv> pi &#61; 4*atan(double(1))
 3.141592653589793

For tricks like that to work, the integer must be converted to a double before it is used in computations. Note the difference in the following apparently similar commands. The first value is correct to all 15 places past the decimal; the second value is only correct to 7 places past the decimal, despite also being a double.

 dv> sqrt(double(2))
 1.414213562373095
 dv> double(sqrt(2))
 1.414213538169861

====Complete solution: strings and the atod function====
Using [[double]] on an integer, as above, is only really useful when dealing numbers that can be expressed as some simple function of integers. Fortunately there is a trick that works on all numbers. The function [[atod]] converts a string directly to a double format, without an intermediate float. To ensure correct double-precision values, the atod function should be used on a string specifying the number's value.

 dv> 4.2
 4.199999809265137
 dv> double(4.2)
 4.199999809265137
 dv> atod("4.2")
 4.200000000000000

==Workaround examples==

The following functions were consciously designed to avoid the intermediate float bug. Take a look at their code to see examples of the workarounds.

====Functions using atod====
*[[erf]]
*[[gamma]]
*[[invnorm]]

In addition, the values in the physical constants structure (con) and the solar system structures (Sun, Earth, Moon, Mars, Phobos, Deimos) are defined using [[atod]]. See [[conhelp]] and [[solsys]].

====Functions using some sort of integer trick====
*[[cbrt]]
*[[erf]]
*[[fact]]
*[[fib]]
*[[gamma]]
*[[inverf]]
*[[log2]]
*[[normcdf]]
*[[normpdf]]

[[Category:Glossary]]