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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>
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<p>It is sometimes useful to be able to compare two floating point numbers
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approximately, to allow for rounding and truncation errors. The following
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function implements the approximate floating-point comparison algorithm
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proposed by D.E. Knuth in Section 4.2.2 of <cite>Seminumerical
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Algorithms</cite> (3rd edition).
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— Function: int <b>gsl_fcmp</b> (<var>double x, double y, double epsilon</var>)<var><a name="index-gsl_005ffcmp-128"></a></var><br>
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<blockquote><p><a name="index-approximate-comparison-of-floating-point-numbers-129"></a><a name="index-safe-comparison-of-floating-point-numbers-130"></a><a name="index-floating-point-numbers_002c-approximate-comparison-131"></a>This function determines whether x and y are approximately
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equal to a relative accuracy <var>epsilon</var>.
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<p>The relative accuracy is measured using an interval of size 2
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\delta, where \delta = 2^k \epsilon and k is the
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maximum base-2 exponent of x and y as computed by the
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function <code>frexp()</code>.
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<p>If x and y lie within this interval, they are considered
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approximately equal and the function returns 0. Otherwise if x <
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y, the function returns -1, or if x > y, the function returns
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<p>The implementation is based on the package <code>fcmp</code> by T.C. Belding.
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</p></blockquote></div>
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