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<!-- This manual documents how to install and use the Multiple Precision
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Floating-Point Reliable Library, version 3.1.4.
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Copyright 1991, 1993-2016 Free Software Foundation, Inc.
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Permission is granted to copy, distribute and/or modify this document under
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<title>Integer Related Functions (GNU MPFR 3.1.4)</title>
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<meta name="description" content="How to install and use GNU MPFR, a library for reliable multiple precision
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floating-point arithmetic, version 3.1.4.">
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<meta name="keywords" content="Integer Related Functions (GNU MPFR 3.1.4)">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="MPFR-Interface.html#MPFR-Interface" rel="up" title="MPFR Interface">
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<link href="Rounding-Related-Functions.html#Rounding-Related-Functions" rel="next" title="Rounding Related Functions">
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<a name="Integer-Related-Functions"></a>
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<div class="header">
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<p>
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Next: <a href="Rounding-Related-Functions.html#Rounding-Related-Functions" accesskey="n" rel="next">Rounding Related Functions</a>, Previous: <a href="Formatted-Output-Functions.html#Formatted-Output-Functions" accesskey="p" rel="prev">Formatted Output Functions</a>, Up: <a href="MPFR-Interface.html#MPFR-Interface" accesskey="u" rel="up">MPFR Interface</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="index-Integer-related-functions"></a>
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<a name="Integer-and-Remainder-Related-Functions"></a>
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<h3 class="section">5.10 Integer and Remainder Related Functions</h3>
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<dl>
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<dt><a name="index-mpfr_005frint"></a>Function: <em>int</em> <strong>mpfr_rint</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fceil"></a>Function: <em>int</em> <strong>mpfr_ceil</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>)</em></dt>
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<dt><a name="index-mpfr_005ffloor"></a>Function: <em>int</em> <strong>mpfr_floor</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>)</em></dt>
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<dt><a name="index-mpfr_005fround"></a>Function: <em>int</em> <strong>mpfr_round</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>)</em></dt>
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<dt><a name="index-mpfr_005ftrunc"></a>Function: <em>int</em> <strong>mpfr_trunc</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <var>op</var> rounded to an integer.
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<code>mpfr_rint</code> rounds to the nearest representable integer in the
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given direction <var>rnd</var>, <code>mpfr_ceil</code> rounds
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to the next higher or equal representable integer, <code>mpfr_floor</code> to
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the next lower or equal representable integer, <code>mpfr_round</code> to the
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nearest representable integer, rounding halfway cases away from zero
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(as in the roundTiesToAway mode of IEEE 754-2008),
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and <code>mpfr_trunc</code> to the next representable integer toward zero.
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</p>
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<p>The returned value is zero when the result is exact, positive when it is
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greater than the original value of <var>op</var>, and negative when it is smaller.
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More precisely, the returned value is 0 when <var>op</var> is an integer
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representable in <var>rop</var>, 1 or −1 when <var>op</var> is an integer
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that is not representable in <var>rop</var>, 2 or −2 when <var>op</var> is
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not an integer.
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</p>
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<p>When <var>op</var> is NaN, the NaN flag is set as usual. In the other cases,
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the inexact flag is set when <var>rop</var> differs from <var>op</var>, following
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the ISO C99 rule for the <code>rint</code> function. If you want the behavior to
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be more like IEEE 754 / ISO TS 18661-1, i.e., the usual behavior where the
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round-to-integer function is regarded as any other mathematical function,
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you should use one the <code>mpfr_rint_*</code> functions instead (however it is
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not possible to round to nearest with the even rounding rule yet).
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</p>
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<p>Note that <code>mpfr_round</code> is different from <code>mpfr_rint</code> called with
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the rounding to nearest mode (where halfway cases are rounded to an even
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integer or significand). Note also that no double rounding is performed; for
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instance, 10.5 (1010.1 in binary) is rounded by <code>mpfr_rint</code> with
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rounding to nearest to 12 (1100
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in binary) in 2-bit precision, because the two enclosing numbers representable
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on two bits are 8 and 12, and the closest is 12.
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(If one first rounded to an integer, one would round 10.5 to 10 with
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even rounding, and then 10 would be rounded to 8 again with even rounding.)
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005frint_005fceil"></a>Function: <em>int</em> <strong>mpfr_rint_ceil</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005frint_005ffloor"></a>Function: <em>int</em> <strong>mpfr_rint_floor</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005frint_005fround"></a>Function: <em>int</em> <strong>mpfr_rint_round</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005frint_005ftrunc"></a>Function: <em>int</em> <strong>mpfr_rint_trunc</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <var>op</var> rounded to an integer.
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<code>mpfr_rint_ceil</code> rounds to the next higher or equal integer,
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<code>mpfr_rint_floor</code> to the next lower or equal integer,
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<code>mpfr_rint_round</code> to the nearest integer, rounding halfway cases away
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from zero, and <code>mpfr_rint_trunc</code> to the next integer toward zero.
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If the result is not representable, it is rounded in the direction <var>rnd</var>.
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The returned value is the ternary value associated with the considered
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round-to-integer function (regarded in the same way as any other
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mathematical function).
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</p>
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<p>Contrary to <code>mpfr_rint</code>, those functions do perform a double rounding:
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first <var>op</var> is rounded to the nearest integer in the direction given by
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the function name, then this nearest integer (if not representable) is
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rounded in the given direction <var>rnd</var>. Thus these round-to-integer
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functions behave more like the other mathematical functions, i.e., the
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returned result is the correct rounding of the exact result of the function
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in the real numbers.
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</p>
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<p>For example, <code>mpfr_rint_round</code> with rounding to nearest and a precision
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of two bits rounds 6.5 to 7 (halfway cases away from zero), then 7 is
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rounded to 8 by the round-even rule, despite the fact that 6 is also
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representable on two bits, and is closer to 6.5 than 8.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005ffrac"></a>Function: <em>int</em> <strong>mpfr_frac</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to the fractional part of <var>op</var>, having the same sign as
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<var>op</var>, rounded in the direction <var>rnd</var> (unlike in <code>mpfr_rint</code>,
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<var>rnd</var> affects only how the exact fractional part is rounded, not how
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the fractional part is generated).
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fmodf"></a>Function: <em>int</em> <strong>mpfr_modf</strong> <em>(mpfr_t <var>iop</var>, mpfr_t <var>fop</var>, mpfr_t <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set simultaneously <var>iop</var> to the integral part of <var>op</var> and <var>fop</var> to
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the fractional part of <var>op</var>, rounded in the direction <var>rnd</var> with the
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corresponding precision of <var>iop</var> and <var>fop</var> (equivalent to
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<code>mpfr_trunc(<var>iop</var>, <var>op</var>, <var>rnd</var>)</code> and
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<code>mpfr_frac(<var>fop</var>, <var>op</var>, <var>rnd</var>)</code>). The variables <var>iop</var> and
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<var>fop</var> must be different. Return 0 iff both results are exact (see
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<code>mpfr_sin_cos</code> for a more detailed description of the return value).
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005ffmod"></a>Function: <em>int</em> <strong>mpfr_fmod</strong> <em>(mpfr_t <var>r</var>, mpfr_t <var>x</var>, mpfr_t <var>y</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fremainder"></a>Function: <em>int</em> <strong>mpfr_remainder</strong> <em>(mpfr_t <var>r</var>, mpfr_t <var>x</var>, mpfr_t <var>y</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fremquo"></a>Function: <em>int</em> <strong>mpfr_remquo</strong> <em>(mpfr_t <var>r</var>, long* <var>q</var>, mpfr_t <var>x</var>, mpfr_t <var>y</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>r</var> to the value of <em><var>x</var> - <var>n</var><var>y</var></em>, rounded
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according to the direction <var>rnd</var>, where <var>n</var> is the integer quotient
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of <var>x</var> divided by <var>y</var>, defined as follows: <var>n</var> is rounded
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toward zero for <code>mpfr_fmod</code>, and to the nearest integer (ties rounded
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to even) for <code>mpfr_remainder</code> and <code>mpfr_remquo</code>.
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</p>
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<p>Special values are handled as described in Section F.9.7.1 of
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the ISO C99 standard:
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If <var>x</var> is infinite or <var>y</var> is zero, <var>r</var> is NaN.
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If <var>y</var> is infinite and <var>x</var> is finite, <var>r</var> is <var>x</var> rounded
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to the precision of <var>r</var>.
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If <var>r</var> is zero, it has the sign of <var>x</var>.
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The return value is the ternary value corresponding to <var>r</var>.
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</p>
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<p>Additionally, <code>mpfr_remquo</code> stores
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the low significant bits from the quotient <var>n</var> in <var>*q</var>
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(more precisely the number of bits in a <code>long</code> minus one),
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with the sign of <var>x</var> divided by <var>y</var>
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(except if those low bits are all zero, in which case zero is returned).
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Note that <var>x</var> may be so large in magnitude relative to <var>y</var> that an
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exact representation of the quotient is not practical.
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The <code>mpfr_remainder</code> and <code>mpfr_remquo</code> functions are useful for
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additive argument reduction.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005finteger_005fp"></a>Function: <em>int</em> <strong>mpfr_integer_p</strong> <em>(mpfr_t <var>op</var>)</em></dt>
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<dd><p>Return non-zero iff <var>op</var> is an integer.
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</p></dd></dl>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Rounding-Related-Functions.html#Rounding-Related-Functions" accesskey="n" rel="next">Rounding Related Functions</a>, Previous: <a href="Formatted-Output-Functions.html#Formatted-Output-Functions" accesskey="p" rel="prev">Formatted Output Functions</a>, Up: <a href="MPFR-Interface.html#MPFR-Interface" accesskey="u" rel="up">MPFR Interface</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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