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    <p>If the the output is to give a human reader a fast impression of the order of the result, it makes no sense return something like "113/211", so the output should limit itself to using one-digit numbers (and maybe 1/10 and 9/10). If so, you can observe that there are only 27 <em>different</em> fractions.</p> <p>Since the underlying math for generating the output will never change, a solution could be to simply hard-code a binary search tree, so that the function would perform at most log(27) ~= 4 3/4 comparisons. Here is a tested C version of the code</p> <pre><code>char *userTextForDouble(double d, char *rval) { if (d == 0.0) return "0"; // TODO: negative numbers:if (d &lt; 0.0)... if (d &gt;= 1.0) sprintf(rval, "%.0f ", floor(d)); d = d-floor(d); // now only the fractional part is left if (d == 0.0) return rval; if( d &lt; 0.47 ) { if( d &lt; 0.25 ) { if( d &lt; 0.16 ) { if( d &lt; 0.12 ) // Note: fixed from .13 { if( d &lt; 0.11 ) strcat(rval, "1/10"); // .1 else strcat(rval, "1/9"); // .1111.... } else // d &gt;= .12 { if( d &lt; 0.14 ) strcat(rval, "1/8"); // .125 else strcat(rval, "1/7"); // .1428... } } else // d &gt;= .16 { if( d &lt; 0.19 ) { strcat(rval, "1/6"); // .1666... } else // d &gt; .19 { if( d &lt; 0.22 ) strcat(rval, "1/5"); // .2 else strcat(rval, "2/9"); // .2222... } } } else // d &gt;= .25 { if( d &lt; 0.37 ) // Note: fixed from .38 { if( d &lt; 0.28 ) // Note: fixed from .29 { strcat(rval, "1/4"); // .25 } else // d &gt;=.28 { if( d &lt; 0.31 ) strcat(rval, "2/7"); // .2857... else strcat(rval, "1/3"); // .3333... } } else // d &gt;= .37 { if( d &lt; 0.42 ) // Note: fixed from .43 { if( d &lt; 0.40 ) strcat(rval, "3/8"); // .375 else strcat(rval, "2/5"); // .4 } else // d &gt;= .42 { if( d &lt; 0.44 ) strcat(rval, "3/7"); // .4285... else strcat(rval, "4/9"); // .4444... } } } } else { if( d &lt; 0.71 ) { if( d &lt; 0.60 ) { if( d &lt; 0.55 ) // Note: fixed from .56 { strcat(rval, "1/2"); // .5 } else // d &gt;= .55 { if( d &lt; 0.57 ) strcat(rval, "5/9"); // .5555... else strcat(rval, "4/7"); // .5714 } } else // d &gt;= .6 { if( d &lt; 0.62 ) // Note: Fixed from .63 { strcat(rval, "3/5"); // .6 } else // d &gt;= .62 { if( d &lt; 0.66 ) strcat(rval, "5/8"); // .625 else strcat(rval, "2/3"); // .6666... } } } else { if( d &lt; 0.80 ) { if( d &lt; 0.74 ) { strcat(rval, "5/7"); // .7142... } else // d &gt;= .74 { if(d &lt; 0.77 ) // Note: fixed from .78 strcat(rval, "3/4"); // .75 else strcat(rval, "7/9"); // .7777... } } else // d &gt;= .8 { if( d &lt; 0.85 ) // Note: fixed from .86 { if( d &lt; 0.83 ) strcat(rval, "4/5"); // .8 else strcat(rval, "5/6"); // .8333... } else // d &gt;= .85 { if( d &lt; 0.87 ) // Note: fixed from .88 { strcat(rval, "6/7"); // .8571 } else // d &gt;= .87 { if( d &lt; 0.88 ) // Note: fixed from .89 { strcat(rval, "7/8"); // .875 } else // d &gt;= .88 { if( d &lt; 0.90 ) strcat(rval, "8/9"); // .8888... else strcat(rval, "9/10"); // .9 } } } } } } return rval; } </code></pre>
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    1. POHow to convert floats to human-readable fractions?
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    1. COThis is the kind of lateral thinking we need more of! Excellent suggestion.
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    2. COIts a bit ugly but very fast and practical way
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    3. COThis is an interesting approach that's wonderfully simple. To save space you could instead binary search an array, or create a binary tree, but your approach is probably a little faster (you could save space by using a single call to strcat before return and assign a var where it's now called) . Also I would have included 3/10 and 7/10, but maybe that's just me.
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