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<title>Approximate Comparison of Floating Point Numbers - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">4.8 Approximate Comparison of Floating Point Numbers</h3>
<p>It is sometimes useful to be able to compare two floating point numbers
approximately, to allow for rounding and truncation errors. The following
function implements the approximate floating-point comparison algorithm
proposed by D.E. Knuth in Section 4.2.2 of <cite>Seminumerical
Algorithms</cite> (3rd edition).
<div class="defun">
— Function: int <b>gsl_fcmp</b> (<var>double x, double y, double epsilon</var>)<var><a name="index-gsl_005ffcmp-132"></a></var><br>
<blockquote><p><a name="index-approximate-comparison-of-floating-point-numbers-133"></a><a name="index-safe-comparison-of-floating-point-numbers-134"></a><a name="index-floating-point-numbers_002c-approximate-comparison-135"></a>This function determines whether x and y are approximately
equal to a relative accuracy <var>epsilon</var>.
<p>The relative accuracy is measured using an interval of size 2
\delta, where \delta = 2^k \epsilon and k is the
maximum base-2 exponent of x and y as computed by the
function <code>frexp</code>.
<p>If x and y lie within this interval, they are considered
approximately equal and the function returns 0. Otherwise if x <
y, the function returns -1, or if x > y, the function returns
+1.
<p>Note that x and y are compared to relative accuracy, so
this function is not suitable for testing whether a value is
approximately zero.
<p>The implementation is based on the package <code>fcmp</code> by T.C. Belding.
</p></blockquote></div>
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