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Floating-Point Reliable Library, version 3.1.4.
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floating-point arithmetic, version 3.1.4.">
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<a name="Basic-Arithmetic-Functions"></a>
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<div class="header">
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<p>
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Next: <a href="Comparison-Functions.html#Comparison-Functions" accesskey="n" rel="next">Comparison Functions</a>, Previous: <a href="Conversion-Functions.html#Conversion-Functions" accesskey="p" rel="prev">Conversion 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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<hr>
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<a name="index-Basic-arithmetic-functions"></a>
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<a name="index-Float-arithmetic-functions"></a>
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<a name="index-Arithmetic-functions"></a>
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<a name="Basic-Arithmetic-Functions-1"></a>
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<h3 class="section">5.5 Basic Arithmetic Functions</h3>
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<dl>
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<dt><a name="index-mpfr_005fadd"></a>Function: <em>int</em> <strong>mpfr_add</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fadd_005fui"></a>Function: <em>int</em> <strong>mpfr_add_ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fadd_005fsi"></a>Function: <em>int</em> <strong>mpfr_add_si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fadd_005fd"></a>Function: <em>int</em> <strong>mpfr_add_d</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, double <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fadd_005fz"></a>Function: <em>int</em> <strong>mpfr_add_z</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpz_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fadd_005fq"></a>Function: <em>int</em> <strong>mpfr_add_q</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpq_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var> + <var>op2</var></em> rounded in the direction
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<var>rnd</var>. The IEEE-754 rules are used, in particular for signed zeros.
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But for types having no signed zeros, 0 is considered unsigned
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(i.e., (+0) + 0 = (+0) and (−0) + 0 = (−0)).
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The <code>mpfr_add_d</code> function assumes that the radix of the <code>double</code> type
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is a power of 2, with a precision at most that declared by the C implementation
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(macro <code>IEEE_DBL_MANT_DIG</code>, and if not defined 53 bits).
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fsub"></a>Function: <em>int</em> <strong>mpfr_sub</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fui_005fsub"></a>Function: <em>int</em> <strong>mpfr_ui_sub</strong> <em>(mpfr_t <var>rop</var>, unsigned long int <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsub_005fui"></a>Function: <em>int</em> <strong>mpfr_sub_ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsi_005fsub"></a>Function: <em>int</em> <strong>mpfr_si_sub</strong> <em>(mpfr_t <var>rop</var>, long int <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsub_005fsi"></a>Function: <em>int</em> <strong>mpfr_sub_si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fd_005fsub"></a>Function: <em>int</em> <strong>mpfr_d_sub</strong> <em>(mpfr_t <var>rop</var>, double <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsub_005fd"></a>Function: <em>int</em> <strong>mpfr_sub_d</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, double <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fz_005fsub"></a>Function: <em>int</em> <strong>mpfr_z_sub</strong> <em>(mpfr_t <var>rop</var>, mpz_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsub_005fz"></a>Function: <em>int</em> <strong>mpfr_sub_z</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpz_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsub_005fq"></a>Function: <em>int</em> <strong>mpfr_sub_q</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpq_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var> - <var>op2</var></em> rounded in the direction
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<var>rnd</var>. The IEEE-754 rules are used, in particular for signed zeros.
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But for types having no signed zeros, 0 is considered unsigned
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(i.e., (+0) − 0 = (+0), (−0) − 0 = (−0),
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0 − (+0) = (−0) and 0 − (−0) = (+0)).
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The same restrictions than for <code>mpfr_add_d</code> apply to <code>mpfr_d_sub</code>
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and <code>mpfr_sub_d</code>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fmul"></a>Function: <em>int</em> <strong>mpfr_mul</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fmul_005fui"></a>Function: <em>int</em> <strong>mpfr_mul_ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fmul_005fsi"></a>Function: <em>int</em> <strong>mpfr_mul_si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fmul_005fd"></a>Function: <em>int</em> <strong>mpfr_mul_d</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, double <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fmul_005fz"></a>Function: <em>int</em> <strong>mpfr_mul_z</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpz_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fmul_005fq"></a>Function: <em>int</em> <strong>mpfr_mul_q</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpq_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var> times <var>op2</var></em> rounded in the
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direction <var>rnd</var>.
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When a result is zero, its sign is the product of the signs of the operands
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(for types having no signed zeros, 0 is considered positive).
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The same restrictions than for <code>mpfr_add_d</code> apply to <code>mpfr_mul_d</code>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fsqr"></a>Function: <em>int</em> <strong>mpfr_sqr</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 <em>the square of <var>op</var></em>
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rounded in the direction <var>rnd</var>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fdiv"></a>Function: <em>int</em> <strong>mpfr_div</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fui_005fdiv"></a>Function: <em>int</em> <strong>mpfr_ui_div</strong> <em>(mpfr_t <var>rop</var>, unsigned long int <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fdiv_005fui"></a>Function: <em>int</em> <strong>mpfr_div_ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fsi_005fdiv"></a>Function: <em>int</em> <strong>mpfr_si_div</strong> <em>(mpfr_t <var>rop</var>, long int <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fdiv_005fsi"></a>Function: <em>int</em> <strong>mpfr_div_si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fd_005fdiv"></a>Function: <em>int</em> <strong>mpfr_d_div</strong> <em>(mpfr_t <var>rop</var>, double <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fdiv_005fd"></a>Function: <em>int</em> <strong>mpfr_div_d</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, double <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fdiv_005fz"></a>Function: <em>int</em> <strong>mpfr_div_z</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpz_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fdiv_005fq"></a>Function: <em>int</em> <strong>mpfr_div_q</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpq_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var>/<var>op2</var></em> rounded in the direction <var>rnd</var>.
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When a result is zero, its sign is the product of the signs of the operands
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(for types having no signed zeros, 0 is considered positive).
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The same restrictions than for <code>mpfr_add_d</code> apply to <code>mpfr_d_div</code>
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and <code>mpfr_div_d</code>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fsqrt"></a>Function: <em>int</em> <strong>mpfr_sqrt</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_005fsqrt_005fui"></a>Function: <em>int</em> <strong>mpfr_sqrt_ui</strong> <em>(mpfr_t <var>rop</var>, unsigned long int <var>op</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em>the square root of <var>op</var></em>
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rounded in the direction <var>rnd</var>. Set <var>rop</var> to −0 if
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<var>op</var> is −0, to be consistent with the IEEE 754 standard.
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Set <var>rop</var> to NaN if <var>op</var> is negative.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005frec_005fsqrt"></a>Function: <em>int</em> <strong>mpfr_rec_sqrt</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 <em>the reciprocal square root of <var>op</var></em>
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rounded in the direction <var>rnd</var>. Set <var>rop</var> to +Inf if <var>op</var> is
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±0, +0 if <var>op</var> is +Inf, and NaN if <var>op</var> is negative. Warning!
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Therefore the result on −0 is different from the one of the rSqrt
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function recommended by the IEEE 754-2008 standard (Section 9.2.1), which
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is −Inf instead of +Inf.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fcbrt"></a>Function: <em>int</em> <strong>mpfr_cbrt</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_005froot"></a>Function: <em>int</em> <strong>mpfr_root</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op</var>, unsigned long int <var>k</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to the cubic root (resp. the <var>k</var>th root)
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of <var>op</var> rounded in the direction <var>rnd</var>.
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For <var>k</var> odd (resp. even) and <var>op</var> negative (including −Inf),
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set <var>rop</var> to a negative number (resp. NaN).
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The <var>k</var>th root of −0 is defined to be −0,
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whatever the parity of <var>k</var>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fpow"></a>Function: <em>int</em> <strong>mpfr_pow</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fpow_005fui"></a>Function: <em>int</em> <strong>mpfr_pow_ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fpow_005fsi"></a>Function: <em>int</em> <strong>mpfr_pow_si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fpow_005fz"></a>Function: <em>int</em> <strong>mpfr_pow_z</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpz_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fui_005fpow_005fui"></a>Function: <em>int</em> <strong>mpfr_ui_pow_ui</strong> <em>(mpfr_t <var>rop</var>, unsigned long int <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fui_005fpow"></a>Function: <em>int</em> <strong>mpfr_ui_pow</strong> <em>(mpfr_t <var>rop</var>, unsigned long int <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var> raised to <var>op2</var></em>,
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rounded in the direction <var>rnd</var>.
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Special values are handled as described in the ISO C99 and IEEE 754-2008
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standards for the <code>pow</code> function:
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</p><ul>
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<li> <code>pow(±0, <var>y</var>)</code> returns plus or minus infinity for <var>y</var> a negative odd integer.
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</li><li> <code>pow(±0, <var>y</var>)</code> returns plus infinity for <var>y</var> negative and not an odd integer.
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</li><li> <code>pow(±0, <var>y</var>)</code> returns plus or minus zero for <var>y</var> a positive odd integer.
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</li><li> <code>pow(±0, <var>y</var>)</code> returns plus zero for <var>y</var> positive and not an odd integer.
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</li><li> <code>pow(-1, ±Inf)</code> returns 1.
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</li><li> <code>pow(+1, <var>y</var>)</code> returns 1 for any <var>y</var>, even a NaN.
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</li><li> <code>pow(<var>x</var>, ±0)</code> returns 1 for any <var>x</var>, even a NaN.
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</li><li> <code>pow(<var>x</var>, <var>y</var>)</code> returns NaN for finite negative <var>x</var> and finite non-integer <var>y</var>.
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</li><li> <code>pow(<var>x</var>, -Inf)</code> returns plus infinity for <em>0 < abs(x) < 1</em>, and plus zero for <em>abs(x) > 1</em>.
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</li><li> <code>pow(<var>x</var>, +Inf)</code> returns plus zero for <em>0 < abs(x) < 1</em>, and plus infinity for <em>abs(x) > 1</em>.
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</li><li> <code>pow(-Inf, <var>y</var>)</code> returns minus zero for <var>y</var> a negative odd integer.
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</li><li> <code>pow(-Inf, <var>y</var>)</code> returns plus zero for <var>y</var> negative and not an odd integer.
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</li><li> <code>pow(-Inf, <var>y</var>)</code> returns minus infinity for <var>y</var> a positive odd integer.
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</li><li> <code>pow(-Inf, <var>y</var>)</code> returns plus infinity for <var>y</var> positive and not an odd integer.
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</li><li> <code>pow(+Inf, <var>y</var>)</code> returns plus zero for <var>y</var> negative, and plus infinity for <var>y</var> positive.
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</li></ul>
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</dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fneg"></a>Function: <em>int</em> <strong>mpfr_neg</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_005fabs"></a>Function: <em>int</em> <strong>mpfr_abs</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 <em>-<var>op</var></em> and the absolute value of <var>op</var>
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respectively, rounded in the direction <var>rnd</var>.
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Just changes or adjusts
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the sign if <var>rop</var> and <var>op</var> are the same variable,
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otherwise a rounding might occur if the precision of <var>rop</var> is less than
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that of <var>op</var>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fdim"></a>Function: <em>int</em> <strong>mpfr_dim</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, mpfr_t <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to the positive difference of <var>op1</var> and <var>op2</var>, i.e.,
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<em><var>op1</var> - <var>op2</var></em> rounded in the direction <var>rnd</var>
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if <em><var>op1</var> > <var>op2</var></em>, +0 if <em><var>op1</var> <= <var>op2</var></em>,
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and NaN if <var>op1</var> or <var>op2</var> is NaN.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fmul_005f2ui"></a>Function: <em>int</em> <strong>mpfr_mul_2ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fmul_005f2si"></a>Function: <em>int</em> <strong>mpfr_mul_2si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var> times 2 raised
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to <var>op2</var></em>
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rounded in the direction <var>rnd</var>. Just increases the exponent by <var>op2</var>
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when <var>rop</var> and <var>op1</var> are identical.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpfr_005fdiv_005f2ui"></a>Function: <em>int</em> <strong>mpfr_div_2ui</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, unsigned long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dt><a name="index-mpfr_005fdiv_005f2si"></a>Function: <em>int</em> <strong>mpfr_div_2si</strong> <em>(mpfr_t <var>rop</var>, mpfr_t <var>op1</var>, long int <var>op2</var>, mpfr_rnd_t <var>rnd</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em><var>op1</var> divided by 2 raised
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to <var>op2</var></em>
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rounded in the direction <var>rnd</var>. Just decreases the exponent by <var>op2</var>
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when <var>rop</var> and <var>op1</var> are identical.
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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="Comparison-Functions.html#Comparison-Functions" accesskey="n" rel="next">Comparison Functions</a>, Previous: <a href="Conversion-Functions.html#Conversion-Functions" accesskey="p" rel="prev">Conversion 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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