This little C program converts a decimal value — represented as a string — into a double-precision floating-point number:

#include <string.h>

int main (void)
{
 double intPart = 0, fracPart = 0, conversion;
 unsigned int i;
 char decimal[] = "3.14159";

 i = 0; /* Left to right */
 while (decimal[i] != '.') {
    intPart = intPart*10 + (decimal[i] - '0');
    i++;
   }

 i = strlen(decimal)-1; /* Right to left */
 while (decimal[i] != '.') {
    fracPart = (fracPart + (decimal[i] - '0'))/10;
    i--;
   }

 conversion = intPart + fracPart;
}

The conversion is done using the elegant Horner’s method, summing each digit according to its decimal place value. So why do I call it “quick and dirty?” Because the binary floating-point value it produces is not necessarily the closest approximation to the input decimal value — the so-called correctly rounded result. (Remember that most real numbers cannot be represented exactly in floating-point.) Most of the time it will produce the correctly rounded result, but sometimes it won’t — the result will be off in its least significant bit(s). There’s just not enough precision in floating-point to guarantee the result is correct every time.

I will demonstrate this program with different input values, some of which convert correctly, and some of which don’t. In the end, you’ll appreciate one reason why library functions like strtod() exist — to perform efficient, correctly rounded conversion.

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Are there any multiple digit hexadecimal number palindromes that are also palindromic in binary and decimal? I have been searching but have not found any.

I started my search with my program that finds multiple-base palindromes. I generated palindromes in binary, and then checked them to see if they were also palindromes in hexadecimal and decimal. I looked for decimal/binary/hexadecimal palindromes up to 16 hex digits long, but did not find any.

To continue my search into bigger numbers, I wrote a program that uses arbitrary-precision integer arithmetic and a more efficient algorithm. Despite being able to search much further, I still have not found any.

In this article, I’ll analyze the size of the palindrome “search space”, explain my improved algorithm, and discuss the state of my search.

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In case you haven’t heard, Mattel® has created Computer Engineer Barbie®, based on popular vote. Here’s the laptop she is holding:

Binary Code on Barbie's Laptop

It spells “Barbie” — repeatedly, in ASCII code.

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In my article “When Floats Don’t Behave Like Floats” I explained how calculations involving single-precision floating-point variables may be done, under the covers, in double or extended precision. This leads to anomalies in expected results, which I demonstrated with two C programs — compiled with Microsoft Visual C++ and run on a 32-bit Intel Core Duo processor.

In this article, I’ll do a similar analysis for double-precision floating-point variables, showing how similar anomalies arise when extended precision calculations are done. I modified my two example programs to use doubles instead of floats. Interestingly, the doubles version of program 2 does not exhibit the anomaly. I’ll explain.

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