Divide {<spanclass="parameter">sp</span>, <spanclass="parameter">n</span>} by <spanclass="code">3</span>, expecting it to divide exactly, and writing the result to {<spanclass="parameter">rp</span>, <spanclass="parameter">n</span>}.
</pre></div></div></div><scripttype="text/javascript">AddLanguageTabSet("ID0EDCA");</script><h4class="subHeading">Parameters</h4><dl><dt><spanclass="parameter">rp</span></dt><dd>Type:<ahref="4609ac5e-5cf9-cd20-2fa9-8040101c165c.htm">Math.Gmp.Native<spanid="LST9DAD6B4F_1"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_1?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mp_ptr</a><br/>The result integer.</dd><dt><spanclass="parameter">sp</span></dt><dd>Type:<ahref="4609ac5e-5cf9-cd20-2fa9-8040101c165c.htm">Math.Gmp.Native<spanid="LST9DAD6B4F_2"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_2?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mp_ptr</a><br/>The operand integer.</dd><dt><spanclass="parameter">n</span></dt><dd>Type:<ahref="4b58a584-7a0e-b600-18fa-ebd493861eb3.htm">Math.Gmp.Native<spanid="LST9DAD6B4F_3"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_3?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mp_size_t</a><br/>The number of limbs in <spanclass="parameter">sp</span>.</dd><dt><spanclass="parameter">carry</span></dt><dd>Type:<ahref="bf1f694d-f9b2-6413-12e5-ebae603d5b49.htm">Math.Gmp.Native<spanid="LST9DAD6B4F_4"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_4?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mp_limb_t</a><br/>The initial carry.</dd></dl><h4class="subHeading">Return Value</h4>Type:<ahref="bf1f694d-f9b2-6413-12e5-ebae603d5b49.htm">mp_limb_t</a><br/>If <spanclass="code">3</span> divides exactly, the return value is zero and the result is the quotient. If not, the return value is non-zero and the result won’t be anything useful.</div><divclass="collapsibleAreaRegion"><spanclass="collapsibleRegionTitle"onclick="SectionExpandCollapse('ID2RB')"onkeypress="SectionExpandCollapse_CheckKey('ID2RB', event)"tabindex="0"><imgid="ID2RBToggle"class="collapseToggle"src="../icons/SectionExpanded.png"/>Remarks</span></div><divid="ID2RBSection"class="collapsibleSection"><p><spanclass="selflink">mpn_divexact_by3c(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)</span> takes an initial carry parameter, which can be the return value from a previous call,
so a large calculation can be done piece by piece from low to high.
<ahref="75f2a84e-44f3-b7cc-e6ad-392111d5b9cc.htm">mpn_divexact_by3(mp_ptr, mp_ptr, mp_size_t)</a> is simply a macro calling <spanclass="selflink">mpn_divexact_by3c(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)</span> with a <spanclass="code">0</span> carry parameter.
</p><p>
These routines use a multiply-by-inverse and will be faster than <ahref="f5c3f25d-1ad5-b3be-fc4b-280a62869912.htm">mpn_divrem_1(mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_limb_t)</a> on CPUs with
fast multiplication but slow division.
</p><p>
The source <spanclass="code">a</span>, result <spanclass="code">q</span>, size <spanclass="code">n</span>, initial carry <spanclass="code">i</span>, and return value <spanclass="code">c</span> satisfy
<spanclass="code">c * b^n + a - i = 3 * q</span>, where <spanclass="code">b = 2^<ahref="f88c76a8-118a-5cbd-0df1-e30adcacb8ae.htm">mp_bits_per_limb</a></span>.
The return <spanclass="code">c</span> is always <spanclass="code">0</span>, <spanclass="code">1</span> or <spanclass="code">2,</span> and the initial carry <spanclass="code">i</span> must also be <spanclass="code">0</span>,
<spanclass="code">1</span> or <spanclass="code">2</span> (these are both borrows really). When <spanclass="code">c = 0</span> clearly <spanclass="code">q = (a - i) / 3</span>.
When <spanclass="code">c != 0</span>, the remainder <spanclass="code">(a - i) mod 3</span> is given by <spanclass="code">3 - c</span>, because
<spanclass="code">b ≡ 1 mod 3</span> (when <ahref="f88c76a8-118a-5cbd-0df1-e30adcacb8ae.htm">mp_bits_per_limb</a> is even, which is always so currently).
mp_ptr rp = <spanclass="highlight-keyword">new</span> mp_ptr(<spanclass="highlight-keyword">new</span><spanclass="highlight-keyword">uint</span>[<spanclass="highlight-number">2</span>]);
mp_ptr result = <spanclass="highlight-keyword">new</span> mp_ptr(<spanclass="highlight-keyword">new</span><spanclass="highlight-keyword">uint</span>[] { <spanclass="highlight-number">0xaaaaaaaa</span>, <spanclass="highlight-number">0x5555aaaa</span> });
<spanclass="highlight-comment">// Set rp = sp / 3.</span>
gmp_lib.free(rp, sp, result)</pre></div><divid="ID0EDAABA_code_Div3"class="codeSnippetContainerCode"style="display: none"><p>No code example is currently available or this language may not be supported.</p></div><divid="ID0EDAABA_code_Div4"class="codeSnippetContainerCode"style="display: none"><p>No code example is currently available or this language may not be supported.</p></div></div></div><scripttype="text/javascript">AddLanguageTabSet("ID0EDAABA");</script></div><divclass="collapsibleAreaRegion"id="seeAlsoSection"><spanclass="collapsibleRegionTitle"onclick="SectionExpandCollapse('ID4RB')"onkeypress="SectionExpandCollapse_CheckKey('ID4RB', event)"tabindex="0"><imgid="ID4RBToggle"class="collapseToggle"src="../icons/SectionExpanded.png"/>See Also</span></div><divid="ID4RBSection"class="collapsibleSection"><h4class="subHeading">Reference</h4><divclass="seeAlsoStyle"><ahref="3af6b34c-3242-2b75-e7c7-ab79af8a4b0f.htm">gmp_lib Class</a></div><divclass="seeAlsoStyle"><ahref="d9c51b9f-0c54-770b-28ea-6eebd8fef368.htm">Math.Gmp.Native Namespace</a></div><divclass="seeAlsoStyle"><ahref="b9df04c4-224e-f2ad-8e90-fbb3b30bd76d.htm">gmp_lib<spanid="LST9DAD6B4F_5"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_5?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_add(mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t)</a></div><divclass="seeAlsoStyle"><ahref="5562b14f-48a4-be75-2eb0-6a129cd0d5ab.htm">gmp_lib<spanid="LST9DAD6B4F_6"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_6?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_add_1(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)</a></div><divclass="seeAlsoStyle"><ahref="339edb73-5781-7d73-97b6-9b73451a698f.htm">gmp_lib<spanid="LST9DAD6B4F_7"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_7?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_add_n(mp_ptr, mp_ptr, mp_ptr, mp_size_t)</a></div><divclass="seeAlsoStyle"><ahref="77fdf32b-986d-4df3-3c76-022e3e3fbb98.htm">gmp_lib<spanid="LST9DAD6B4F_8"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_8?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_addmul_1(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)</a></div><divclass="seeAlsoStyle"><ahref="1d6343a5-d42c-c362-714e-e10730e6a6d5.htm">gmp_lib<spanid="LST9DAD6B4F_9"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_9?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_divexact_1(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)</a></div><divclass="seeAlsoStyle"><ahref="75f2a84e-44f3-b7cc-e6ad-392111d5b9cc.htm">gmp_lib<spanid="LST9DAD6B4F_10"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_10?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_divexact_by3(mp_ptr, mp_ptr, mp_size_t)</a></div><divclass="seeAlsoStyle"><ahref="9074a45b-0d68-cf18-75fe-076e720a9a61.htm">gmp_lib<spanid="LST9DAD6B4F_11"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_11?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_divmod_1(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)</a></div><divclass="seeAlsoStyle"><ahref="f5c3f25d-1ad5-b3be-fc4b-280a62869912.htm">gmp_lib<spanid="LST9DAD6B4F_12"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_12?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_divrem_1(mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_limb_t)</a></div><divclass="seeAlsoStyle"><ahref="9aa24cc8-8cf5-4b8a-cd1b-5ded400efa50.htm">gmp_lib<spanid="LST9DAD6B4F_13"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_13?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_mod_1(mp_ptr, mp_size_t, mp_limb_t)</a></div><divclass="seeAlsoStyle"><ahref="68d3161d-2909-1909-cda7-e87949ee27ce.htm">gmp_lib<spanid="LST9DAD6B4F_14"></span><scripttype="text/javascript">AddLanguageSpecificTextSet("LST9DAD6B4F_14?cs=.|vb=.|cpp=::|nu=.|fs=.");</script>mpn_mul(mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t)</a></div><divclass="seeAlsoStyle"><ahref="b819fb3b-5d3e-ff23-1687-0e71af684bd7.htm">gmp_lib<spanid="LST9DAD6B4F_15"></span><scripttype="text/
