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<h3>
Marge Bot pushed to branch master
at <a href="https://gitlab.haskell.org/ghc/ghc">Glasgow Haskell Compiler / GHC</a>
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<h4>
Commits:
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<strong><a href="https://gitlab.haskell.org/ghc/ghc/-/commit/12c06927a03a2fdb516f7008c57d68568b02b576">12c06927</a></strong>
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<span>by Sylvain Henry</span>
<i>at 2020-10-02T13:52:38-04:00</i>
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<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Bignum: implement integerRecipMod (#18427)
</pre>
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<strong><a href="https://gitlab.haskell.org/ghc/ghc/-/commit/8dd4f40512bb18e296280acde0507b4233a27b69">8dd4f405</a></strong>
<div>
<span>by Sylvain Henry</span>
<i>at 2020-10-02T13:52:38-04:00</i>
</div>
<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Bignum: implement integerPowMod (#18427)
Incidentally fix powModInteger which was crashing in integer-gmp for
negative exponents when the modular multiplicative inverse for the base
didn't exist. Now we compute it explicitly with integerRecipMod so that
every backend returns the same result without crashing.
</pre>
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<h4>17 changed files:</h4>
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<li class="file-stats">
<a href="#a1f998e8553841568762af9303c1476e08778e21">
libraries/ghc-bignum/cbits/gmp_wrappers.c
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<li class="file-stats">
<a href="#999bd68489a86559e9a862084e500ffcb808326b">
libraries/ghc-bignum/src/GHC/Num/Backend/Check.hs
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<a href="#e39e8c6b639c1b478a3e6096c6f28dcefa5a9225">
libraries/ghc-bignum/src/GHC/Num/Backend/FFI.hs
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<a href="#233ee515bec9e1a53e1490cca550d836c94c38ad">
libraries/ghc-bignum/src/GHC/Num/Backend/GMP.hs
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<a href="#dcb6aede7f2d4e3b185f11751c4017e9c6dff1b3">
libraries/ghc-bignum/src/GHC/Num/Backend/Native.hs
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<li class="file-stats">
<a href="#51dd5f19656738bf2d7e4b2dc3e742d862435329">
libraries/ghc-bignum/src/GHC/Num/BigNat.hs-boot
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<a href="#84ed6dfb0380e98269259d1b3a64e920ab8b9476">
libraries/ghc-bignum/src/GHC/Num/Integer.hs
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<a href="#0fddd5316dd2410ec91e71bcb3934ad43477b11e">
libraries/ghc-bignum/src/GHC/Num/Integer.hs-boot
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<a href="#e7a247d9c4bd1d57c78b326d4ddcbdc0487410cb">
libraries/ghc-bignum/src/GHC/Num/Natural.hs-boot
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<a href="#ef846b48b51b8e630e61836d776a41049673c8a2">
libraries/integer-gmp/src/GHC/Integer/GMP/Internals.hs
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<li class="file-stats">
<a href="#e7a467a9ebf548b772e4bb5abe937b61495d8e38">
testsuite/tests/lib/integer/all.T
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<a href="#82566519e3b7cd89b06e52dcbb68b698dcb93cec">
testsuite/tests/lib/integer/integerGmpInternals.hs
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<a href="#ea171a03f829cb714c7d613c8f7e161150b6f860">
testsuite/tests/lib/integer/integerGmpInternals.stdout
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<a href="#854e04abf547fe126eb8fef90a557ca1d1161c54">
testsuite/tests/lib/integer/integerPowMod.hs
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<a href="#5b4bacc8d9c2dfe0ee298a058a06a0c4dd7424ec">
testsuite/tests/lib/integer/integerPowMod.stdout
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testsuite/tests/lib/integer/integerRecipMod.hs
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testsuite/tests/lib/integer/integerRecipMod.stdout
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<h4>Changes:</h4>
<li id="a1f998e8553841568762af9303c1476e08778e21">
<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#a1f998e8553841568762af9303c1476e08778e21"><strong>libraries/ghc-bignum/cbits/gmp_wrappers.c</strong></a>
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<td class="diff-line-num unfold js-unfold new_line" data-linenumber="632" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -632,8 +632,7 @@ integer_gmp_powm(mp_limb_t rp[], // result</td>
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632
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<pre style="margin: 0;"> <span id="LC632" class="line" lang="c"> <span class="n" style="color: #333;">assert</span><span class="p">(</span><span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">mp_limb_zero_p</span><span class="p">(</span><span class="n" style="color: #333;">mp</span><span class="p">,</span><span class="n" style="color: #333;">mn</span><span class="p">));</span></span>
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633
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<pre style="margin: 0;"> <span id="LC633" class="line" lang="c"></span>
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<pre style="margin: 0;"> <span id="LC634" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">((</span><span class="n" style="color: #333;">mn</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">1</span> <span class="o" style="font-weight: 600;">||</span> <span class="n" style="color: #333;">mn</span> <span class="o" style="font-weight: 600;">==</span> <span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span> <span class="o" style="font-weight: 600;">&&</span> <span class="n" style="color: #333;">mp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">1</span><span class="p">)</span> <span class="p">{</span></span>
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<pre style="margin: 0;">-<span id="LC635" class="line" lang="c"> <span class="n" style="color: #333;">rp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC636" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">1</span><span class="p">;</span></span>
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<pre style="margin: 0;">+<span id="LC635" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;"> <span id="LC636" class="line" lang="c"> <span class="p">}</span></span>
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<pre style="margin: 0;"> <span id="LC637" class="line" lang="c"></span>
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<pre style="margin: 0;"> <span id="LC638" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="n" style="color: #333;">mp_limb_zero_p</span><span class="p">(</span><span class="n" style="color: #333;">ep</span><span class="p">,</span><span class="n" style="color: #333;">en</span><span class="p">))</span> <span class="p">{</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -659,11 +658,6 @@ integer_gmp_powm(mp_limb_t rp[], // result</td>
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<pre style="margin: 0;"> <span id="LC658" class="line" lang="c"></span>
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<pre style="margin: 0;"> <span id="LC659" class="line" lang="c"> <span class="n" style="color: #333;">mpz_clear</span> <span class="p">(</span><span class="n" style="color: #333;">r</span><span class="p">);</span></span>
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<pre style="margin: 0;"> <span id="LC660" class="line" lang="c"></span>
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<pre style="margin: 0;">-<span id="LC662" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">rn</span><span class="p">)</span> <span class="p">{</span></span>
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<pre style="margin: 0;">-<span id="LC663" class="line" lang="c"> <span class="n" style="color: #333;">rp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC664" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">1</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC665" class="line" lang="c"> <span class="p">}</span></span>
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<pre style="margin: 0;">-<span id="LC666" class="line" lang="c"></span>
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<pre style="margin: 0;"> <span id="LC661" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">rn</span><span class="p">;</span></span>
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<pre style="margin: 0;"> <span id="LC662" class="line" lang="c"><span class="p">}</span></span>
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<pre style="margin: 0;"> <span id="LC663" class="line" lang="c"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -720,8 +714,7 @@ integer_gmp_powm_sec(mp_limb_t rp[], // result</td>
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720
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<pre style="margin: 0;"> <span id="LC714" class="line" lang="c"> <span class="n" style="color: #333;">assert</span><span class="p">(</span><span class="n" style="color: #333;">mp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">&</span> <span class="mi" style="color: #099;">1</span><span class="p">);</span></span>
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715
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<pre style="margin: 0;"> <span id="LC715" class="line" lang="c"></span>
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716
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<pre style="margin: 0;"> <span id="LC716" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">((</span><span class="n" style="color: #333;">mn</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">1</span> <span class="o" style="font-weight: 600;">||</span> <span class="n" style="color: #333;">mn</span> <span class="o" style="font-weight: 600;">==</span> <span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span> <span class="o" style="font-weight: 600;">&&</span> <span class="n" style="color: #333;">mp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">1</span><span class="p">)</span> <span class="p">{</span></span>
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<pre style="margin: 0;">-<span id="LC723" class="line" lang="c"> <span class="n" style="color: #333;">rp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC724" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">1</span><span class="p">;</span></span>
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<pre style="margin: 0;">+<span id="LC717" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;"> <span id="LC718" class="line" lang="c"> <span class="p">}</span></span>
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<pre style="margin: 0;"> <span id="LC719" class="line" lang="c"></span>
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<pre style="margin: 0;"> <span id="LC720" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="n" style="color: #333;">mp_limb_zero_p</span><span class="p">(</span><span class="n" style="color: #333;">ep</span><span class="p">,</span><span class="n" style="color: #333;">en</span><span class="p">))</span> <span class="p">{</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -753,11 +746,6 @@ integer_gmp_powm_sec(mp_limb_t rp[], // result</td>
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<pre style="margin: 0;"> <span id="LC746" class="line" lang="c"></span>
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<pre style="margin: 0;"> <span id="LC747" class="line" lang="c"> <span class="n" style="color: #333;">mpz_clear</span> <span class="p">(</span><span class="n" style="color: #333;">r</span><span class="p">);</span></span>
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748
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<pre style="margin: 0;"> <span id="LC748" class="line" lang="c"></span>
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<pre style="margin: 0;">-<span id="LC756" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">rn</span><span class="p">)</span> <span class="p">{</span></span>
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<pre style="margin: 0;">-<span id="LC757" class="line" lang="c"> <span class="n" style="color: #333;">rp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC758" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">1</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC759" class="line" lang="c"> <span class="p">}</span></span>
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<pre style="margin: 0;">-<span id="LC760" class="line" lang="c"></span>
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749
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<pre style="margin: 0;"> <span id="LC749" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">rn</span><span class="p">;</span></span>
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750
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<pre style="margin: 0;"> <span id="LC750" class="line" lang="c"><span class="p">}</span></span>
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751
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<pre style="margin: 0;"> <span id="LC751" class="line" lang="c"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -779,8 +767,7 @@ integer_gmp_invert(mp_limb_t rp[], // result</td>
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779
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767
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<pre style="margin: 0;"> <span id="LC767" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="n" style="color: #333;">mp_limb_zero_p</span><span class="p">(</span><span class="n" style="color: #333;">xp</span><span class="p">,</span><span class="n" style="color: #333;">xn</span><span class="p">)</span></span>
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780
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768
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<pre style="margin: 0;"> <span id="LC768" class="line" lang="c"> <span class="o" style="font-weight: 600;">||</span> <span class="n" style="color: #333;">mp_limb_zero_p</span><span class="p">(</span><span class="n" style="color: #333;">mp</span><span class="p">,</span><span class="n" style="color: #333;">mn</span><span class="p">)</span></span>
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781
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769
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<pre style="margin: 0;"> <span id="LC769" class="line" lang="c"> <span class="o" style="font-weight: 600;">||</span> <span class="p">((</span><span class="n" style="color: #333;">mn</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">1</span> <span class="o" style="font-weight: 600;">||</span> <span class="n" style="color: #333;">mn</span> <span class="o" style="font-weight: 600;">==</span> <span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span> <span class="o" style="font-weight: 600;">&&</span> <span class="n" style="color: #333;">mp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">==</span> <span class="mi" style="color: #099;">1</span><span class="p">))</span> <span class="p">{</span></span>
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782
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<pre style="margin: 0;">-<span id="LC782" class="line" lang="c"> <span class="n" style="color: #333;">rp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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<pre style="margin: 0;">-<span id="LC783" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">1</span><span class="p">;</span></span>
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<pre style="margin: 0;">+<span id="LC770" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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784
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771
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<pre style="margin: 0;"> <span id="LC771" class="line" lang="c"> <span class="p">}</span></span>
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772
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<pre style="margin: 0;"> <span id="LC772" class="line" lang="c"></span>
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786
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773
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<pre style="margin: 0;"> <span id="LC773" class="line" lang="c"> <span class="k" style="font-weight: 600;">const</span> <span class="n" style="color: #333;">mpz_t</span> <span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">CONST_MPZ_INIT</span><span class="p">(</span><span class="n" style="color: #333;">xp</span><span class="p">,</span> <span class="n" style="color: #333;">xn</span><span class="p">);</span></span>
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<td class="diff-line-num unfold js-unfold new_line" data-linenumber="787" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -800,11 +787,6 @@ integer_gmp_invert(mp_limb_t rp[], // result</td>
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800
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787
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<pre style="margin: 0;"> <span id="LC787" class="line" lang="c"></span>
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801
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788
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<pre style="margin: 0;"> <span id="LC788" class="line" lang="c"> <span class="n" style="color: #333;">mpz_clear</span> <span class="p">(</span><span class="n" style="color: #333;">r</span><span class="p">);</span></span>
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802
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789
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<pre style="margin: 0;"> <span id="LC789" class="line" lang="c"></span>
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803
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<pre style="margin: 0;">-<span id="LC803" class="line" lang="c"> <span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">rn</span><span class="p">)</span> <span class="p">{</span></span>
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804
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<pre style="margin: 0;">-<span id="LC804" class="line" lang="c"> <span class="n" style="color: #333;">rp</span><span class="p">[</span><span class="mi" style="color: #099;">0</span><span class="p">]</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">0</span><span class="p">;</span></span>
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805
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<pre style="margin: 0;">-<span id="LC805" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="mi" style="color: #099;">1</span><span class="p">;</span></span>
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806
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<pre style="margin: 0;">-<span id="LC806" class="line" lang="c"> <span class="p">}</span></span>
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807
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<pre style="margin: 0;">-<span id="LC807" class="line" lang="c"></span>
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808
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790
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<pre style="margin: 0;"> <span id="LC790" class="line" lang="c"> <span class="k" style="font-weight: 600;">return</span> <span class="n" style="color: #333;">rn</span><span class="p">;</span></span>
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<pre style="margin: 0;"> <span id="LC791" class="line" lang="c"><span class="p">}</span></span>
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<pre style="margin: 0;"> <span id="LC792" class="line" lang="c"></span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#999bd68489a86559e9a862084e500ffcb808326b"><strong>libraries/ghc-bignum/src/GHC/Num/Backend/Check.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -17,6 +17,7 @@ import GHC.Types</td>
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<pre style="margin: 0;"> <span id="LC17" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.WordArray</span></span>
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<pre style="margin: 0;"> <span id="LC18" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Primitives</span></span>
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<pre style="margin: 0;"> <span id="LC19" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC20" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC21" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="k" style="font-weight: 600;">qualified</span> <span class="nn" style="color: #555;">GHC.Num.Backend.Native</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">Native</span></span>
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<pre style="margin: 0;"> <span id="LC22" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="k" style="font-weight: 600;">qualified</span> <span class="nn" style="color: #555;">GHC.Num.Backend.Selected</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">Other</span></span>
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<pre style="margin: 0;"> <span id="LC23" class="line" lang="haskell"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -469,3 +470,32 @@ integer_gcde a b =</td>
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<pre style="margin: 0;"> <span id="LC470" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">then</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">g0</span><span class="p">,</span> <span class="n" style="color: #333;">x0</span><span class="p">,</span> <span class="n" style="color: #333;">y0</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC471" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">else</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">unexpectedValue</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;"> <span id="LC472" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">integerZero</span><span class="p">,</span> <span class="n" style="color: #333;">integerZero</span><span class="p">,</span> <span class="n" style="color: #333;">integerZero</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC473" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC474" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span></span>
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<pre style="margin: 0;">+<span id="LC475" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC476" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC477" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC478" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span></span>
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<pre style="margin: 0;">+<span id="LC479" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">let</span></span>
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<pre style="margin: 0;">+<span id="LC480" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">r0</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Other</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_recip_mod</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span></span>
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481
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<pre style="margin: 0;">+<span id="LC481" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">r1</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Native</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_recip_mod</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span></span>
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482
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<pre style="margin: 0;">+<span id="LC482" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">in</span> <span class="kr" style="font-weight: 600;">case</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r0</span><span class="p">,</span> <span class="n" style="color: #333;">r1</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">of</span></span>
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483
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<pre style="margin: 0;">+<span id="LC483" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">),</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">r0</span></span>
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484
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<pre style="margin: 0;">+<span id="LC484" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">y0</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">),</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">y1</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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485
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<pre style="margin: 0;">+<span id="LC485" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">isTrue</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">naturalEq</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">y0</span> <span class="n" style="color: #333;">y1</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">r0</span></span>
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486
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<pre style="margin: 0;">+<span id="LC486" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">unexpectedValue</span> <span class="kr" style="font-weight: 600;">of</span></span>
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487
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<pre style="margin: 0;">+<span id="LC487" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC488" class="line" lang="haskell"></span>
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489
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<pre style="margin: 0;">+<span id="LC489" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span></span>
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490
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<pre style="margin: 0;">+<span id="LC490" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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491
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<pre style="margin: 0;">+<span id="LC491" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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492
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<pre style="margin: 0;">+<span id="LC492" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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493
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<pre style="margin: 0;">+<span id="LC493" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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494
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<pre style="margin: 0;">+<span id="LC494" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span></span>
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495
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<pre style="margin: 0;">+<span id="LC495" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">let</span></span>
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496
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<pre style="margin: 0;">+<span id="LC496" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">r0</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Other</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_powmod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span></span>
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497
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<pre style="margin: 0;">+<span id="LC497" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">r1</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Native</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_powmod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span></span>
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498
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<pre style="margin: 0;">+<span id="LC498" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">in</span> <span class="kr" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">isTrue</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">naturalEq</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r0</span> <span class="n" style="color: #333;">r1</span><span class="p">)</span></span>
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499
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<pre style="margin: 0;">+<span id="LC499" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">then</span> <span class="n" style="color: #333;">r0</span></span>
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<pre style="margin: 0;">+<span id="LC500" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">else</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">unexpectedValue</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC501" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">naturalZero</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#e39e8c6b639c1b478a3e6096c6f28dcefa5a9225"><strong>libraries/ghc-bignum/src/GHC/Num/Backend/FFI.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -20,6 +20,8 @@ import GHC.Types</td>
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<pre style="margin: 0;"> <span id="LC20" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.WordArray</span></span>
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<pre style="margin: 0;"> <span id="LC21" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Primitives</span></span>
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<pre style="margin: 0;"> <span id="LC22" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="k" style="font-weight: 600;">qualified</span> <span class="nn" style="color: #555;">GHC.Num.Backend.Native</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">Native</span></span>
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<pre style="margin: 0;">+<span id="LC23" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC24" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC25" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC26" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">default</span> <span class="nb" style="color: #0086b3;">()</span></span>
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<pre style="margin: 0;"> <span id="LC27" class="line" lang="haskell"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -596,3 +598,35 @@ integer_gcde = Native.integer_gcde</td>
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<pre style="margin: 0;"> <span id="LC598" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- for now we use Native's implementation. If some FFI backend user needs a</span></span>
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<pre style="margin: 0;"> <span id="LC599" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- specific implementation, we'll need to determine a prototype to pass and</span></span>
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<pre style="margin: 0;"> <span id="LC600" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- return BigNat signs and sizes via FFI.</span></span>
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<pre style="margin: 0;">+<span id="LC601" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC602" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC603" class="line" lang="haskell"><span class="cd">-- | Computes the modular inverse of two non-zero integers.</span></span>
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<pre style="margin: 0;">+<span id="LC604" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC605" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- I.e. y = integer_recip_mod x m</span></span>
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<pre style="margin: 0;">+<span id="LC606" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- = x^(-1) `mod` m</span></span>
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607
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<pre style="margin: 0;">+<span id="LC607" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC608" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- with 0 < y < abs m</span></span>
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<pre style="margin: 0;">+<span id="LC609" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span></span>
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<pre style="margin: 0;">+<span id="LC610" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC611" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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612
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<pre style="margin: 0;">+<span id="LC612" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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613
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<pre style="margin: 0;">+<span id="LC613" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Native</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_recip_mod</span></span>
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614
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<pre style="margin: 0;">+<span id="LC614" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- for now we use Native's implementation. If some FFI backend user needs a</span></span>
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615
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<pre style="margin: 0;">+<span id="LC615" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- specific implementation, we'll need to determine a prototype to pass and</span></span>
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<pre style="margin: 0;">+<span id="LC616" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- return BigNat signs and sizes via FFI.</span></span>
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617
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<pre style="margin: 0;">+<span id="LC617" class="line" lang="haskell"></span>
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618
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<pre style="margin: 0;">+<span id="LC618" class="line" lang="haskell"><span class="cd">-- | Computes the modular exponentiation.</span></span>
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619
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<pre style="margin: 0;">+<span id="LC619" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC620" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- I.e. y = integer_powmod b e m</span></span>
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<pre style="margin: 0;">+<span id="LC621" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- = b^e `mod` m</span></span>
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<pre style="margin: 0;">+<span id="LC622" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC623" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- with 0 <= y < abs m</span></span>
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<pre style="margin: 0;">+<span id="LC624" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span></span>
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<pre style="margin: 0;">+<span id="LC625" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC626" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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627
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<pre style="margin: 0;">+<span id="LC627" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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628
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<pre style="margin: 0;">+<span id="LC628" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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629
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<pre style="margin: 0;">+<span id="LC629" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Native</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_powmod</span></span>
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<pre style="margin: 0;">+<span id="LC630" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- for now we use Native's implementation. If some FFI backend user needs a</span></span>
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631
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<pre style="margin: 0;">+<span id="LC631" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- specific implementation, we'll need to determine a prototype to pass and</span></span>
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<pre style="margin: 0;">+<span id="LC632" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- return BigNat signs and sizes via FFI.</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#233ee515bec9e1a53e1490cca550d836c94c38ad"><strong>libraries/ghc-bignum/src/GHC/Num/Backend/GMP.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -28,6 +28,7 @@ import GHC.Types</td>
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<pre style="margin: 0;"> <span id="LC28" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Magic</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">runRW</span><span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC29" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC30" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">BigNat</span></span>
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<pre style="margin: 0;">+<span id="LC31" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC32" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC33" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">default</span> <span class="nb" style="color: #0086b3;">()</span></span>
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<pre style="margin: 0;"> <span id="LC34" class="line" lang="haskell"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -354,8 +355,37 @@ bignat_powmod</td>
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<pre style="margin: 0;"> <span id="LC355" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">WordArray</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;"> <span id="LC356" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">State</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">RealWorld</span></span>
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<pre style="margin: 0;"> <span id="LC357" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">State</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">RealWorld</span></span>
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<pre style="margin: 0;">-<span id="LC357" class="line" lang="haskell"><span class="n" style="color: #333;">bignat_powmod</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="n" style="color: #333;">s</span> <span class="o" style="font-weight: 600;">=</span></span>
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<pre style="margin: 0;">-<span id="LC358" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">ioInt</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">integer_gmp_powm</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">b</span> <span class="p">(</span><span class="n" style="color: #333;">wordArraySize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">wordArraySize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="n" style="color: #333;">m</span> <span class="p">(</span><span class="n" style="color: #333;">wordArraySize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">m</span><span class="p">))</span> <span class="n" style="color: #333;">s</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC358" class="line" lang="haskell"><span class="n" style="color: #333;">bignat_powmod</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="n" style="color: #333;">s</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">sbignat_powmod</span> <span class="n" style="color: #333;">r</span> <span class="p">(</span><span class="n" style="color: #333;">wordArraySize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="n" style="color: #333;">s</span></span>
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<pre style="margin: 0;">+<span id="LC359" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC360" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span></span>
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<pre style="margin: 0;">+<span id="LC361" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC362" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC363" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC364" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC365" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">naturalFromBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">withNewWordArray</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">szm</span> <span class="n" style="color: #333;">io</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC366" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC367" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">be</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">naturalToBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">e</span></span>
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<pre style="margin: 0;">+<span id="LC368" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">bm</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">naturalToBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">m</span></span>
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369
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<pre style="margin: 0;">+<span id="LC369" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">sb</span><span class="p">,</span> <span class="n" style="color: #333;">bb</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">integerToBigNatSign</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b</span></span>
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<pre style="margin: 0;">+<span id="LC370" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">szb</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">bigNatSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">bb</span></span>
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371
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<pre style="margin: 0;">+<span id="LC371" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">szm</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">bigNatSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">bm</span></span>
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<pre style="margin: 0;">+<span id="LC372" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">ssb</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">sb</span> <span class="kr" style="font-weight: 600;">of</span> <span class="c1" style="color: #998; font-style: italic;">-- signed size of b</span></span>
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<pre style="margin: 0;">+<span id="LC373" class="line" lang="haskell"> <span class="mi" style="color: #099;">0</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">szb</span></span>
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<pre style="margin: 0;">+<span id="LC374" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">negateInt</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">szb</span></span>
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<pre style="margin: 0;">+<span id="LC375" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC376" class="line" lang="haskell"> <span class="n" style="color: #333;">io</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">s</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">sbignat_powmod</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">ssb</span> <span class="n" style="color: #333;">bb</span> <span class="n" style="color: #333;">be</span> <span class="n" style="color: #333;">bm</span> <span class="n" style="color: #333;">s</span></span>
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<pre style="margin: 0;">+<span id="LC377" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC378" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC379" class="line" lang="haskell"><span class="n" style="color: #333;">sbignat_powmod</span></span>
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380
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<pre style="margin: 0;">+<span id="LC380" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">MutableWordArray</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">RealWorld</span></span>
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381
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<pre style="margin: 0;">+<span id="LC381" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Int</span><span class="o" style="font-weight: 600;">#</span></span>
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382
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<pre style="margin: 0;">+<span id="LC382" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">WordArray</span><span class="o" style="font-weight: 600;">#</span></span>
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383
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<pre style="margin: 0;">+<span id="LC383" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">WordArray</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;">+<span id="LC384" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">WordArray</span><span class="o" style="font-weight: 600;">#</span></span>
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385
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<pre style="margin: 0;">+<span id="LC385" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">State</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">RealWorld</span></span>
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386
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<pre style="margin: 0;">+<span id="LC386" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">State</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">RealWorld</span></span>
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387
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<pre style="margin: 0;">+<span id="LC387" class="line" lang="haskell"><span class="n" style="color: #333;">sbignat_powmod</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">b_signed_size</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="n" style="color: #333;">s</span> <span class="o" style="font-weight: 600;">=</span></span>
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388
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<pre style="margin: 0;">+<span id="LC388" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">ioInt</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">integer_gmp_powm</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">b_signed_size</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">wordArraySize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="n" style="color: #333;">m</span> <span class="p">(</span><span class="n" style="color: #333;">wordArraySize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">m</span><span class="p">))</span> <span class="n" style="color: #333;">s</span> <span class="kr" style="font-weight: 600;">of</span></span>
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359
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389
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<pre style="margin: 0;"> <span id="LC389" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">s'</span><span class="p">,</span> <span class="n" style="color: #333;">n</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">mwaSetSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="p">(</span><span class="n" style="color: #333;">narrowGmpSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">n</span><span class="p">)</span> <span class="n" style="color: #333;">s'</span></span>
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390
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<pre style="margin: 0;"> <span id="LC390" class="line" lang="haskell"></span>
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391
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<pre style="margin: 0;"> <span id="LC391" class="line" lang="haskell"><span class="n" style="color: #333;">integer_gcde</span></span>
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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="423" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -423,6 +453,32 @@ integer_gcde a b = case runRW# io of (# _, a #) -> a</td>
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<pre style="margin: 0;"> <span id="LC453" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC454" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC455" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC456" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span></span>
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<pre style="margin: 0;">+<span id="LC457" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC458" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC459" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC460" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span></span>
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<pre style="margin: 0;">+<span id="LC461" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">let</span></span>
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462
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<pre style="margin: 0;">+<span id="LC462" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">sign_x</span><span class="p">,</span> <span class="n" style="color: #333;">bx</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">integerToBigNatSign</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">x</span></span>
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<pre style="margin: 0;">+<span id="LC463" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">bm</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">naturalToBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC464" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">br</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">sbignat_recip_mod</span> <span class="n" style="color: #333;">sign_x</span> <span class="n" style="color: #333;">bx</span> <span class="n" style="color: #333;">bm</span></span>
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<pre style="margin: 0;">+<span id="LC465" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">in</span> <span class="kr" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">isTrue</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">bigNatIsZero</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">br</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC466" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">then</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC467" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">else</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">naturalFromBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">br</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC470" class="line" lang="haskell"><span class="cd">-- | Return 0 for invalid inputs</span></span>
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<pre style="margin: 0;">+<span id="LC471" class="line" lang="haskell"><span class="n" style="color: #333;">sbignat_recip_mod</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Int</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;">+<span id="LC472" class="line" lang="haskell"><span class="n" style="color: #333;">sbignat_recip_mod</span> <span class="n" style="color: #333;">sign_x</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">withNewWordArray</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">szm</span> <span class="n" style="color: #333;">io</span></span>
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<pre style="margin: 0;">+<span id="LC473" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC474" class="line" lang="haskell"> <span class="n" style="color: #333;">io</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">s</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">ioInt</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">integer_gmp_invert</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">ssx</span> <span class="n" style="color: #333;">m</span> <span class="n" style="color: #333;">szm</span><span class="p">)</span> <span class="n" style="color: #333;">s</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC475" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">s</span><span class="p">,</span> <span class="n" style="color: #333;">rn</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">mwaSetSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="p">(</span><span class="n" style="color: #333;">narrowGmpSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">rn</span><span class="p">)</span> <span class="n" style="color: #333;">s</span></span>
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<pre style="margin: 0;">+<span id="LC476" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">szx</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">bigNatSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">x</span></span>
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<pre style="margin: 0;">+<span id="LC477" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">szm</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">bigNatSize</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC478" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">ssx</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">sign_x</span> <span class="kr" style="font-weight: 600;">of</span> <span class="c1" style="color: #998; font-style: italic;">-- signed size of x</span></span>
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<pre style="margin: 0;">+<span id="LC479" class="line" lang="haskell"> <span class="mi" style="color: #099;">0</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">szx</span></span>
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<pre style="margin: 0;">+<span id="LC480" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">negateInt</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">szx</span></span>
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<pre style="margin: 0;">+<span id="LC481" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC482" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">----------------------------------------------------------------------</span></span>
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<pre style="margin: 0;"> <span id="LC483" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- FFI ccall imports</span></span>
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<pre style="margin: 0;"> <span id="LC484" class="line" lang="haskell"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -444,6 +500,11 @@ foreign import ccall unsafe "integer_gmp_gcdext" integer_gmp_gcdext#</td>
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<pre style="margin: 0;"> <span id="LC500" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">ByteArray</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">GmpSize</span><span class="o" style="font-weight: 600;">#</span></span>
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501
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<pre style="margin: 0;"> <span id="LC501" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">IO</span> <span class="nb" style="color: #0086b3;">()</span></span>
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502
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<pre style="margin: 0;"> <span id="LC502" class="line" lang="haskell"></span>
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503
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<pre style="margin: 0;">+<span id="LC503" class="line" lang="haskell"><span class="n" style="color: #333;">foreign</span> <span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">ccall</span> <span class="n" style="color: #333;">unsafe</span> <span class="s" style="color: #d14;">"integer_gmp_invert"</span></span>
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504
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<pre style="margin: 0;">+<span id="LC504" class="line" lang="haskell"> <span class="n" style="color: #333;">integer_gmp_invert</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">MutableByteArray</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">RealWorld</span></span>
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505
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<pre style="margin: 0;">+<span id="LC505" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">ByteArray</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">GmpSize</span><span class="o" style="font-weight: 600;">#</span></span>
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506
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<pre style="margin: 0;">+<span id="LC506" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">ByteArray</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">GmpSize</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">IO</span> <span class="kt" style="color: #458; font-weight: 600;">GmpSize</span></span>
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507
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<pre style="margin: 0;">+<span id="LC507" class="line" lang="haskell"></span>
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508
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<pre style="margin: 0;"> <span id="LC508" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- mp_limb_t mpn_add_1 (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t n,</span></span>
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509
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<pre style="margin: 0;"> <span id="LC509" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- mp_limb_t s2limb)</span></span>
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510
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<pre style="margin: 0;"> <span id="LC510" class="line" lang="haskell"><span class="n" style="color: #333;">foreign</span> <span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">ccall</span> <span class="n" style="color: #333;">unsafe</span> <span class="s" style="color: #d14;">"gmp.h __gmpn_add_1"</span></span>
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<li id="dcb6aede7f2d4e3b185f11751c4017e9c6dff1b3">
<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#dcb6aede7f2d4e3b185f11751c4017e9c6dff1b3"><strong>libraries/ghc-bignum/src/GHC/Num/Backend/Native.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -14,7 +14,7 @@ module GHC.Num.Backend.Native where</td>
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<pre style="margin: 0;"> <span id="LC14" class="line" lang="haskell"><span class="o" style="font-weight: 600;">#</span><span class="n" style="color: #333;">include</span> <span class="s" style="color: #d14;">"MachDeps.h"</span></span>
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<pre style="margin: 0;"> <span id="LC15" class="line" lang="haskell"><span class="o" style="font-weight: 600;">#</span><span class="n" style="color: #333;">include</span> <span class="s" style="color: #d14;">"WordSize.h"</span></span>
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<pre style="margin: 0;"> <span id="LC16" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC17" class="line" lang="haskell"><span class="o" style="font-weight: 600;">#</span><span class="kr" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">defined</span><span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">BIGNUM_NATIVE</span><span class="p">)</span> <span class="o" style="font-weight: 600;">||</span> <span class="n" style="color: #333;">defined</span><span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">BIGNUM_CHECK</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC17" class="line" lang="haskell"><span class="o" style="font-weight: 600;">#</span><span class="kr" style="font-weight: 600;">if</span> <span class="n" style="color: #333;">defined</span><span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">BIGNUM_NATIVE</span><span class="p">)</span> <span class="o" style="font-weight: 600;">||</span> <span class="n" style="color: #333;">defined</span><span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">BIGNUM_CHECK</span><span class="p">)</span><span class="idiff left"> </span><span class="o" style="font-weight: 600;"><span class="idiff">||</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">defined</span></span><span class="p"><span class="idiff">(</span></span><span class="kt" style="color: #458; font-weight: 600;"><span class="idiff">BIGNUM_FFI</span></span><span class="p"><span class="idiff right">)</span></span></span>
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<pre style="margin: 0;"> <span id="LC18" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">BigNat</span></span>
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19
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<pre style="margin: 0;"> <span id="LC19" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC20" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -737,3 +737,40 @@ integer_gcde a b = f (# a,integerOne,integerZero #) (# b,integerZero,integerOne</td>
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<pre style="margin: 0;"> <span id="LC737" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="kt" style="color: #458; font-weight: 600;">True</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">integerQuotRem</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">old_g</span> <span class="n" style="color: #333;">g</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;"> <span id="LC738" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">q</span><span class="p">,</span> <span class="n" style="color: #333;">r</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">new</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="p">,</span> <span class="n" style="color: #333;">old_s</span> <span class="p">`</span><span class="n" style="color: #333;">integerSub</span><span class="p">`</span> <span class="p">(</span><span class="n" style="color: #333;">q</span> <span class="p">`</span><span class="n" style="color: #333;">integerMul</span><span class="p">`</span> <span class="n" style="color: #333;">s</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC739" class="line" lang="haskell"> <span class="p">,</span> <span class="n" style="color: #333;">old_t</span> <span class="p">`</span><span class="n" style="color: #333;">integerSub</span><span class="p">`</span> <span class="p">(</span><span class="n" style="color: #333;">q</span> <span class="p">`</span><span class="n" style="color: #333;">integerMul</span><span class="p">`</span> <span class="n" style="color: #333;">t</span><span class="p">)</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC740" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC741" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span></span>
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<pre style="margin: 0;">+<span id="LC742" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC743" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC744" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC745" class="line" lang="haskell"><span class="n" style="color: #333;">integer_recip_mod</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span></span>
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<pre style="margin: 0;">+<span id="LC746" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">let</span> <span class="n" style="color: #333;">m'</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">integerFromNatural</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC747" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">in</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">integer_gcde</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m'</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC748" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">g</span><span class="p">,</span> <span class="n" style="color: #333;">a</span><span class="p">,</span> <span class="n" style="color: #333;">_b</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC749" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- gcd(x,m) = ax+mb = 1</span></span>
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<pre style="margin: 0;">+<span id="LC750" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- ==> ax - 1 = -mb</span></span>
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<pre style="margin: 0;">+<span id="LC751" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- ==> ax = 1 [m]</span></span>
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<pre style="margin: 0;">+<span id="LC752" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">g</span> <span class="p">`</span><span class="n" style="color: #333;">integerEq</span><span class="p">`</span> <span class="n" style="color: #333;">integerOne</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">integerToNatural</span> <span class="p">(</span><span class="n" style="color: #333;">a</span> <span class="p">`</span><span class="n" style="color: #333;">integerMod</span><span class="p">`</span> <span class="n" style="color: #333;">m'</span><span class="p">)</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC753" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- a `mod` m > 0 because m > 0</span></span>
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<pre style="margin: 0;">+<span id="LC754" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="kt" style="color: #458; font-weight: 600;">True</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC756" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span></span>
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<pre style="margin: 0;">+<span id="LC757" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC758" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC759" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC760" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC761" class="line" lang="haskell"><span class="n" style="color: #333;">integer_powmod</span> <span class="n" style="color: #333;">b0</span> <span class="n" style="color: #333;">e0</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">go</span> <span class="n" style="color: #333;">b0</span> <span class="n" style="color: #333;">e0</span> <span class="n" style="color: #333;">integerOne</span></span>
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<pre style="margin: 0;">+<span id="LC762" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC763" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">m'</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">integerFromNatural</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC764" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC765" class="line" lang="haskell"> <span class="n" style="color: #333;">go</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">r</span></span>
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<pre style="margin: 0;">+<span id="LC766" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">isTrue</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">e</span> <span class="p">`</span><span class="n" style="color: #333;">naturalTestBit</span><span class="o" style="font-weight: 600;">#</span><span class="p">`</span> <span class="mi" style="color: #099;">0</span><span class="o" style="font-weight: 600;">##</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC767" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">go</span> <span class="n" style="color: #333;">b'</span> <span class="n" style="color: #333;">e'</span> <span class="p">((</span><span class="n" style="color: #333;">r</span> <span class="p">`</span><span class="n" style="color: #333;">integerMul</span><span class="p">`</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="p">`</span><span class="n" style="color: #333;">integerMod</span><span class="p">`</span> <span class="n" style="color: #333;">m'</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC768" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC769" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">naturalIsZero</span> <span class="n" style="color: #333;">e</span></span>
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<pre style="margin: 0;">+<span id="LC770" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">integerToNatural</span> <span class="n" style="color: #333;">r</span> <span class="c1" style="color: #998; font-style: italic;">-- r >= 0 by integerMod above</span></span>
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<pre style="margin: 0;">+<span id="LC771" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC772" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="kt" style="color: #458; font-weight: 600;">True</span></span>
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<pre style="margin: 0;">+<span id="LC773" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">go</span> <span class="n" style="color: #333;">b'</span> <span class="n" style="color: #333;">e'</span> <span class="n" style="color: #333;">r</span></span>
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<pre style="margin: 0;">+<span id="LC774" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC775" class="line" lang="haskell"> <span class="n" style="color: #333;">b'</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="n" style="color: #333;">b</span> <span class="p">`</span><span class="n" style="color: #333;">integerMul</span><span class="p">`</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="p">`</span><span class="n" style="color: #333;">integerRem</span><span class="p">`</span> <span class="n" style="color: #333;">m'</span></span>
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<pre style="margin: 0;">+<span id="LC776" class="line" lang="haskell"> <span class="n" style="color: #333;">e'</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">e</span> <span class="p">`</span><span class="n" style="color: #333;">naturalShiftR</span><span class="o" style="font-weight: 600;">#</span><span class="p">`</span> <span class="mi" style="color: #099;">1</span><span class="o" style="font-weight: 600;">##</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#51dd5f19656738bf2d7e4b2dc3e742d862435329"><strong>libraries/ghc-bignum/src/GHC/Num/BigNat.hs-boot</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -5,11 +5,13 @@</td>
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<pre style="margin: 0;"> <span id="LC5" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">module</span> <span class="nn" style="color: #555;">GHC.Num.BigNat</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;"> <span id="LC6" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC7" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.WordArray</span></span>
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<pre style="margin: 0;">+<span id="LC8" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Primitives</span></span>
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<pre style="margin: 0;"> <span id="LC9" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Prim</span></span>
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<pre style="margin: 0;"> <span id="LC10" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC11" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">type</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">WordArray</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;"> <span id="LC12" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">data</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">BN</span><span class="o" style="font-weight: 600;">#</span> <span class="p">{</span> <span class="n" style="color: #333;">unBigNat</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="p">}</span></span>
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<pre style="margin: 0;"> <span id="LC13" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC14" class="line" lang="haskell"><span class="n" style="color: #333;">bigNatIsZero</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;"> <span id="LC15" class="line" lang="haskell"><span class="n" style="color: #333;">bigNatSize</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Int</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;"> <span id="LC16" class="line" lang="haskell"><span class="n" style="color: #333;">bigNatSubUnsafe</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;"> <span id="LC17" class="line" lang="haskell"><span class="n" style="color: #333;">bigNatMulWord</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Word</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span></span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#84ed6dfb0380e98269259d1b3a64e920ab8b9476"><strong>libraries/ghc-bignum/src/GHC/Num/Integer.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -244,6 +244,11 @@ integerIsZero :: Integer -> Bool</td>
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<pre style="margin: 0;"> <span id="LC244" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsZero</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">IS</span> <span class="mi" style="color: #099;">0</span><span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">True</span></span>
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<pre style="margin: 0;"> <span id="LC245" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsZero</span> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">False</span></span>
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<pre style="margin: 0;"> <span id="LC246" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC247" class="line" lang="haskell"><span class="cd">-- | One predicate</span></span>
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<pre style="margin: 0;">+<span id="LC248" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsOne</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;">+<span id="LC249" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsOne</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">IS</span> <span class="mi" style="color: #099;">1</span><span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">True</span></span>
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250
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<pre style="margin: 0;">+<span id="LC250" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsOne</span> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">False</span></span>
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251
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<pre style="margin: 0;">+<span id="LC251" class="line" lang="haskell"></span>
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247
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252
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<pre style="margin: 0;"> <span id="LC252" class="line" lang="haskell"><span class="cd">-- | Not-equal predicate.</span></span>
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248
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253
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<pre style="margin: 0;"> <span id="LC253" class="line" lang="haskell"><span class="n" style="color: #333;">integerNe</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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249
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254
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<pre style="margin: 0;"> <span id="LC254" class="line" lang="haskell"><span class="n" style="color: #333;">integerNe</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">y</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">isTrue</span><span class="o" style="font-weight: 600;">#</span> <span class="p">(</span><span class="n" style="color: #333;">integerNe</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">y</span><span class="p">)</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1217,3 +1222,50 @@ integerGcde</td>
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1217
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1222
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<pre style="margin: 0;"> <span id="LC1222" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span><span class="p">)</span></span>
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1218
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1223
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<pre style="margin: 0;"> <span id="LC1223" class="line" lang="haskell"><span class="n" style="color: #333;">integerGcde</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">integerGcde</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="kr" style="font-weight: 600;">of</span></span>
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1219
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1224
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<pre style="margin: 0;"> <span id="LC1224" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">g</span><span class="p">,</span><span class="n" style="color: #333;">x</span><span class="p">,</span><span class="n" style="color: #333;">y</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="n" style="color: #333;">g</span><span class="p">,</span><span class="n" style="color: #333;">x</span><span class="p">,</span><span class="n" style="color: #333;">y</span><span class="p">)</span></span>
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1225
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<pre style="margin: 0;">+<span id="LC1225" class="line" lang="haskell"></span>
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1226
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<pre style="margin: 0;">+<span id="LC1226" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC1227" class="line" lang="haskell"><span class="cd">-- | Computes the modular inverse.</span></span>
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1228
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<pre style="margin: 0;">+<span id="LC1228" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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1229
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<pre style="margin: 0;">+<span id="LC1229" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- I.e. y = integerRecipMod# x m</span></span>
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1230
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<pre style="margin: 0;">+<span id="LC1230" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- = x^(-1) `mod` m</span></span>
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1231
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<pre style="margin: 0;">+<span id="LC1231" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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1232
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<pre style="margin: 0;">+<span id="LC1232" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- with 0 < y < |m|</span></span>
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1233
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<pre style="margin: 0;">+<span id="LC1233" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC1234" class="line" lang="haskell"><span class="n" style="color: #333;">integerRecipMod</span><span class="o" style="font-weight: 600;">#</span></span>
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1235
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<pre style="margin: 0;">+<span id="LC1235" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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1236
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<pre style="margin: 0;">+<span id="LC1236" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC1237" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC1238" class="line" lang="haskell"><span class="n" style="color: #333;">integerRecipMod</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC1239" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">integerIsZero</span> <span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1240
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<pre style="margin: 0;">+<span id="LC1240" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">naturalIsZero</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1241
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<pre style="margin: 0;">+<span id="LC1241" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">naturalIsOne</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1242
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<pre style="margin: 0;">+<span id="LC1242" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="kt" style="color: #458; font-weight: 600;">True</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Backend</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_recip_mod</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span></span>
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1243
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<pre style="margin: 0;">+<span id="LC1243" class="line" lang="haskell"></span>
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1244
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<pre style="margin: 0;">+<span id="LC1244" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC1245" class="line" lang="haskell"><span class="cd">-- | Computes the modular exponentiation.</span></span>
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1246
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<pre style="margin: 0;">+<span id="LC1246" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC1247" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- I.e. y = integer_powmod b e m</span></span>
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<pre style="margin: 0;">+<span id="LC1248" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- = b^e `mod` m</span></span>
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<pre style="margin: 0;">+<span id="LC1249" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC1250" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- with 0 <= y < abs m</span></span>
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<pre style="margin: 0;">+<span id="LC1251" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC1252" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- If e is negative, we use `integerRecipMod#` to try to find a modular</span></span>
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<pre style="margin: 0;">+<span id="LC1253" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- multiplicative inverse (which may not exist).</span></span>
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<pre style="margin: 0;">+<span id="LC1254" class="line" lang="haskell"><span class="n" style="color: #333;">integerPowMod</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC1255" class="line" lang="haskell"><span class="n" style="color: #333;">integerPowMod</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">e</span> <span class="o" style="font-weight: 600;">!</span><span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC1256" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">naturalIsZero</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC1257" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">naturalIsOne</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">naturalZero</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1258
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<pre style="margin: 0;">+<span id="LC1258" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">integerIsZero</span> <span class="n" style="color: #333;">e</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">naturalOne</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1259
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<pre style="margin: 0;">+<span id="LC1259" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">integerIsZero</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">naturalZero</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1260
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<pre style="margin: 0;">+<span id="LC1260" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">integerIsOne</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">naturalOne</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1261
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<pre style="margin: 0;">+<span id="LC1261" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- when the exponent is negative, try to find the modular multiplicative</span></span>
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1262
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<pre style="margin: 0;">+<span id="LC1262" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- inverse and use it instead</span></span>
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1263
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<pre style="margin: 0;">+<span id="LC1263" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">integerIsNegative</span> <span class="n" style="color: #333;">e</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">integerRecipMod</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">m</span> <span class="kr" style="font-weight: 600;">of</span></span>
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1264
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<pre style="margin: 0;">+<span id="LC1264" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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1265
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<pre style="margin: 0;">+<span id="LC1265" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b'</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">integerPowMod</span><span class="o" style="font-weight: 600;">#</span></span>
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1266
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<pre style="margin: 0;">+<span id="LC1266" class="line" lang="haskell"> <span class="p">(</span><span class="n" style="color: #333;">integerFromNatural</span> <span class="n" style="color: #333;">b'</span><span class="p">)</span></span>
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1267
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<pre style="margin: 0;">+<span id="LC1267" class="line" lang="haskell"> <span class="p">(</span><span class="n" style="color: #333;">integerNegate</span> <span class="n" style="color: #333;">e</span><span class="p">)</span></span>
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1268
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<pre style="margin: 0;">+<span id="LC1268" class="line" lang="haskell"> <span class="n" style="color: #333;">m</span></span>
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1269
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<pre style="margin: 0;">+<span id="LC1269" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC1270" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- e > 0 by cases above</span></span>
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<pre style="margin: 0;">+<span id="LC1271" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">|</span> <span class="kt" style="color: #458; font-weight: 600;">True</span> <span class="o" style="font-weight: 600;">=</span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Backend</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integer_powmod</span> <span class="n" style="color: #333;">b</span> <span class="p">(</span><span class="n" style="color: #333;">integerToNatural</span> <span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#0fddd5316dd2410ec91e71bcb3934ad43477b11e"><strong>libraries/ghc-bignum/src/GHC/Num/Integer.hs-boot</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -7,6 +7,7 @@ module GHC.Num.Integer where</td>
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<pre style="margin: 0;"> <span id="LC7" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Types</span></span>
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<pre style="margin: 0;"> <span id="LC8" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Prim</span></span>
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<pre style="margin: 0;"> <span id="LC9" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">BigNat</span></span>
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10
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<pre style="margin: 0;">+<span id="LC10" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="err" style="color: #a61717; background-color: #e3d2d2;">{-#</span> <span class="nn" style="color: #555;">SOURCE</span> <span class="o" style="font-weight: 600;">#-</span><span class="p">}</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Num</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC11" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC12" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">data</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC13" class="line" lang="haskell"></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -17,14 +18,20 @@ integerEq# :: Integer -> Integer -> Int#</td>
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<pre style="margin: 0;"> <span id="LC18" class="line" lang="haskell"><span class="n" style="color: #333;">integerEq</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;"> <span id="LC19" class="line" lang="haskell"><span class="n" style="color: #333;">integerGt</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;"> <span id="LC20" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsZero</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;">+<span id="LC21" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsOne</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;"> <span id="LC22" class="line" lang="haskell"><span class="n" style="color: #333;">integerIsNegative</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;"> <span id="LC23" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC24" class="line" lang="haskell"><span class="n" style="color: #333;">integerSub</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC25" class="line" lang="haskell"><span class="n" style="color: #333;">integerMul</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC26" class="line" lang="haskell"><span class="n" style="color: #333;">integerMod</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC27" class="line" lang="haskell"><span class="n" style="color: #333;">integerRem</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC28" class="line" lang="haskell"><span class="n" style="color: #333;">integerNegate</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC29" class="line" lang="haskell"><span class="n" style="color: #333;">integerAbs</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC30" class="line" lang="haskell"><span class="n" style="color: #333;">integerDivMod</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC31" class="line" lang="haskell"><span class="n" style="color: #333;">integerQuotRem</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC32" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC33" class="line" lang="haskell"><span class="n" style="color: #333;">integerToBigNatSign</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="kt" style="color: #458; font-weight: 600;">Int</span><span class="o" style="font-weight: 600;">#</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC34" class="line" lang="haskell"><span class="n" style="color: #333;">integerFromBigNatSign</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Int</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC35" class="line" lang="haskell"><span class="n" style="color: #333;">integerFromBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC36" class="line" lang="haskell"><span class="n" style="color: #333;">integerToNatural</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC37" class="line" lang="haskell"><span class="n" style="color: #333;">integerFromNatural</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#e7a247d9c4bd1d57c78b326d4ddcbdc0487410cb"><strong>libraries/ghc-bignum/src/GHC/Num/Natural.hs-boot</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -16,8 +16,12 @@ naturalToWord# :: Natural -> Word#</td>
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<pre style="margin: 0;"> <span id="LC16" class="line" lang="haskell"><span class="n" style="color: #333;">naturalFromWord</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Word</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC17" class="line" lang="haskell"><span class="n" style="color: #333;">naturalFromBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC18" class="line" lang="haskell"><span class="n" style="color: #333;">naturalToBigNat</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">BigNat</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;">+<span id="LC19" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC20" class="line" lang="haskell"><span class="n" style="color: #333;">naturalZero</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC21" class="line" lang="haskell"><span class="n" style="color: #333;">naturalMul</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;"> <span id="LC22" class="line" lang="haskell"><span class="n" style="color: #333;">naturalRem</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">-<span id="LC21" class="line" lang="haskell"><span class="n" style="color: #333;">naturalIsZero</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;"> <span id="LC23" class="line" lang="haskell"><span class="n" style="color: #333;">naturalShiftR</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Word</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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<pre style="margin: 0;">+<span id="LC24" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC25" class="line" lang="haskell"><span class="n" style="color: #333;">naturalIsZero</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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<pre style="margin: 0;"> <span id="LC26" class="line" lang="haskell"><span class="n" style="color: #333;">naturalTestBit</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Word</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span><span class="o" style="font-weight: 600;">#</span></span>
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<pre style="margin: 0;">+<span id="LC27" class="line" lang="haskell"><span class="n" style="color: #333;">naturalEq</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span><span class="o" style="font-weight: 600;">#</span></span></pre>
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<li id="ef846b48b51b8e630e61836d776a41049673c8a2">
<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#ef846b48b51b8e630e61836d776a41049673c8a2"><strong>libraries/integer-gmp/src/GHC/Integer/GMP/Internals.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -32,6 +32,8 @@ module GHC.Integer.GMP.Internals</td>
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<pre style="margin: 0;"> <span id="LC32" class="line" lang="haskell"> <span class="p">,</span> <span class="nf" style="color: #900; font-weight: 600;">gcdExtInteger</span></span>
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<pre style="margin: 0;"> <span id="LC33" class="line" lang="haskell"> <span class="p">,</span> <span class="nf" style="color: #900; font-weight: 600;">lcmInteger</span></span>
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<pre style="margin: 0;"> <span id="LC34" class="line" lang="haskell"> <span class="p">,</span> <span class="nf" style="color: #900; font-weight: 600;">sqrInteger</span></span>
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<pre style="margin: 0;">+<span id="LC35" class="line" lang="haskell"> <span class="p">,</span> <span class="nf" style="color: #900; font-weight: 600;">powModInteger</span></span>
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<pre style="margin: 0;">+<span id="LC36" class="line" lang="haskell"> <span class="p">,</span> <span class="nf" style="color: #900; font-weight: 600;">recipModInteger</span></span>
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<pre style="margin: 0;"> <span id="LC37" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC38" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- ** Additional conversion operations to 'Integer'</span></span>
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<pre style="margin: 0;"> <span id="LC39" class="line" lang="haskell"> <span class="p">,</span> <span class="nf" style="color: #900; font-weight: 600;">wordToNegInteger</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -186,6 +188,18 @@ lcmInteger = I.integerLcm</td>
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<pre style="margin: 0;"> <span id="LC188" class="line" lang="haskell"><span class="n" style="color: #333;">sqrInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC189" class="line" lang="haskell"><span class="n" style="color: #333;">sqrInteger</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerSqr</span></span>
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<pre style="margin: 0;"> <span id="LC190" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC191" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# DEPRECATED recipModInteger "Use integerRecipMod# instead" #-}</span></span>
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<pre style="margin: 0;">+<span id="LC192" class="line" lang="haskell"><span class="n" style="color: #333;">recipModInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC193" class="line" lang="haskell"><span class="n" style="color: #333;">recipModInteger</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerRecipMod</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">x</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerToNatural</span> <span class="n" style="color: #333;">m</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC194" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">y</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerFromNatural</span> <span class="n" style="color: #333;">y</span></span>
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<pre style="margin: 0;">+<span id="LC195" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="mi" style="color: #099;">0</span></span>
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<pre style="margin: 0;">+<span id="LC196" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC197" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# DEPRECATED powModInteger "Use integerPowMod# instead" #-}</span></span>
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<pre style="margin: 0;">+<span id="LC198" class="line" lang="haskell"><span class="n" style="color: #333;">powModInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC199" class="line" lang="haskell"><span class="n" style="color: #333;">powModInteger</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerPowMod</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerToNatural</span> <span class="n" style="color: #333;">m</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC200" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerFromNatural</span> <span class="n" style="color: #333;">r</span></span>
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<pre style="margin: 0;">+<span id="LC201" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="mi" style="color: #099;">0</span></span>
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<pre style="margin: 0;">+<span id="LC202" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC203" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# DEPRECATED wordToNegInteger "Use integerFromWordNeg# instead" #-}</span></span>
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<pre style="margin: 0;"> <span id="LC204" class="line" lang="haskell"><span class="n" style="color: #333;">wordToNegInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Word</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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191
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205
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<pre style="margin: 0;"> <span id="LC205" class="line" lang="haskell"><span class="n" style="color: #333;">wordToNegInteger</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerFromWordNeg</span><span class="o" style="font-weight: 600;">#</span></span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#e7a467a9ebf548b772e4bb5abe937b61495d8e38"><strong>testsuite/tests/lib/integer/all.T</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -8,7 +8,8 @@ test('IntegerConversionRules', [], makefile_test, ['IntegerConversionRules'])</td>
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8
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<pre style="margin: 0;"> <span id="LC8" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">gcdInteger</span><span class="p">',</span> <span class="nv" style="color: #008080;">normal</span><span class="p">,</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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9
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<pre style="margin: 0;"> <span id="LC9" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">gcdeInteger</span><span class="p">',</span> <span class="nv" style="color: #008080;">normal</span><span class="p">,</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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10
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<pre style="margin: 0;"> <span id="LC10" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">integerPowMod</span><span class="p">',</span> <span class="o" style="font-weight: 600;">[]</span><span class="p">,</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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11
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<pre style="margin: 0;">-<span id="LC11" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">integerGcdExt</span><span class="p">',</span> <span class="p">[</span><span class="nv" style="color: #008080;">omit_ways</span><span class="p">(['</span><span class="s1" style="color: #d14;">ghci</span><span class="p">'])],</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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<pre style="margin: 0;">+<span id="LC11" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">integerGcdExt</span><span class="p">',</span> <span class="o" style="font-weight: 600;">[]</span><span class="p">,</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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<pre style="margin: 0;">+<span id="LC12" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">integerRecipMod</span><span class="p">',</span> <span class="o" style="font-weight: 600;">[]</span><span class="p">,</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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<pre style="margin: 0;"> <span id="LC13" class="line" lang="perl"></span>
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<pre style="margin: 0;"> <span id="LC14" class="line" lang="perl"><span class="c1" style="color: #998; font-style: italic;"># skip ghci as it doesn't support unboxed tuples</span></span>
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<pre style="margin: 0;"> <span id="LC15" class="line" lang="perl"><span class="nv" style="color: #008080;">test</span><span class="p">('</span><span class="s1" style="color: #d14;">integerImportExport</span><span class="p">',</span> <span class="p">[</span><span class="nv" style="color: #008080;">omit_ways</span><span class="p">(['</span><span class="s1" style="color: #d14;">ghci</span><span class="p">'])],</span> <span class="nv" style="color: #008080;">compile_and_run</span><span class="p">,</span> <span class="p">[''])</span></span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#82566519e3b7cd89b06e52dcbb68b698dcb93cec"><strong>testsuite/tests/lib/integer/integerGmpInternals.hs</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -12,9 +12,6 @@ import GHC.Base</td>
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<pre style="margin: 0;"> <span id="LC12" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Integer</span></span>
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<pre style="margin: 0;"> <span id="LC13" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="k" style="font-weight: 600;">qualified</span> <span class="nn" style="color: #555;">GHC.Num.Integer</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">I</span></span>
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<pre style="margin: 0;"> <span id="LC14" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC15" class="line" lang="haskell"><span class="n" style="color: #333;">recipModInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">-<span id="LC16" class="line" lang="haskell"><span class="n" style="color: #333;">recipModInteger</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">recipModInteger</span></span>
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<pre style="margin: 0;">-<span id="LC17" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC15" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- FIXME: Lacks GMP2 version</span></span>
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<pre style="margin: 0;"> <span id="LC16" class="line" lang="haskell"><span class="n" style="color: #333;">powInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Word</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;"> <span id="LC17" class="line" lang="haskell"><span class="n" style="color: #333;">powInteger</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">e</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">x</span><span class="o" style="font-weight: 600;">^</span><span class="n" style="color: #333;">e</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -25,7 +22,6 @@ main = do</td>
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<pre style="margin: 0;"> <span id="LC22" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">powInteger</span> <span class="mi" style="color: #099;">12345</span> <span class="mi" style="color: #099;">0</span></span>
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<pre style="margin: 0;"> <span id="LC23" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">powInteger</span> <span class="mi" style="color: #099;">12345</span> <span class="mi" style="color: #099;">1</span></span>
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<pre style="margin: 0;"> <span id="LC24" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">powInteger</span> <span class="mi" style="color: #099;">12345</span> <span class="mi" style="color: #099;">30</span></span>
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<pre style="margin: 0;">-<span id="LC28" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="p">[</span> <span class="p">(</span><span class="n" style="color: #333;">x</span><span class="p">,</span><span class="n" style="color: #333;">i</span><span class="p">)</span> <span class="o" style="font-weight: 600;">|</span> <span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;"><-</span> <span class="p">[</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">7</span><span class="o" style="font-weight: 600;">..</span><span class="mi" style="color: #099;">71</span><span class="p">],</span> <span class="kr" style="font-weight: 600;">let</span> <span class="n" style="color: #333;">i</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">recipModInteger</span> <span class="n" style="color: #333;">x</span> <span class="p">(</span><span class="mi" style="color: #099;">2</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">3</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">11</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">11</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">17</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">17</span><span class="p">),</span> <span class="n" style="color: #333;">i</span> <span class="o" style="font-weight: 600;">/=</span> <span class="mi" style="color: #099;">0</span> <span class="p">]</span></span>
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<pre style="margin: 0;"> <span id="LC25" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC26" class="line" lang="haskell"> <span class="n" style="color: #333;">putStrLn</span> <span class="s" style="color: #d14;">"</span><span class="se" style="color: #d14;">\n</span><span class="s" style="color: #d14;"># nextPrimeInteger"</span></span>
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<pre style="margin: 0;"> <span id="LC27" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">nextPrimeInteger</span> <span class="n" style="color: #333;">b</span></span>
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<li id="ea171a03f829cb714c7d613c8f7e161150b6f860">
<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#ea171a03f829cb714c7d613c8f7e161150b6f860"><strong>testsuite/tests/lib/integer/integerGmpInternals.stdout</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -3,7 +3,6 @@</td>
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<pre style="margin: 0;"> <span id="LC3" class="line" lang="plaintext">1</span>
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<pre style="margin: 0;"> <span id="LC4" class="line" lang="plaintext">12345</span>
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<pre style="margin: 0;"> <span id="LC5" class="line" lang="plaintext">555562377826831043419246079513769804614412256811161773362797946971665712715296306339052301636736176350153982639312744140625</span>
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<pre style="margin: 0;">-<span id="LC6" class="line" lang="plaintext">[(-7,149867),(-5,167851),(-1,209813),(1,1),(5,41963),(7,59947),(13,177535),(19,143557),(23,182447),(25,134281),(29,7235),(31,33841),(35,95915),(37,113413),(41,61409),(43,24397),(47,174101),(49,158431),(53,193979),(59,188477),(61,185737),(65,35507),(67,118999),(71,186173)]</span>
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<pre style="margin: 0;"> <span id="LC6" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC7" class="line" lang="plaintext"># nextPrimeInteger</span>
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<pre style="margin: 0;"> <span id="LC8" class="line" lang="plaintext">2988348162058574136915891421498819466320163312926952423791023078876343</span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#854e04abf547fe126eb8fef90a557ca1d1161c54"><strong>testsuite/tests/lib/integer/integerPowMod.hs</strong></a>
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<pre style="margin: 0;">+<span id="LC1" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE UnboxedTuples #-}</span></span>
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<pre style="margin: 0;">+<span id="LC2" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE MagicHash #-}</span></span>
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3
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<pre style="margin: 0;">+<span id="LC3" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC4" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">module</span> <span class="nn" style="color: #555;">Main</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">main</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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2
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5
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<pre style="margin: 0;"> <span id="LC5" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC6" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.List</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">group</span><span class="p">)</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -7,22 +10,33 @@ import Control.Monad</td>
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<pre style="margin: 0;"> <span id="LC10" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC11" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Word</span></span>
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<pre style="margin: 0;"> <span id="LC12" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Base</span></span>
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<pre style="margin: 0;">-<span id="LC10" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Natural</span></span>
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<pre style="margin: 0;">+<span id="LC13" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Natural</span></span>
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<pre style="margin: 0;">+<span id="LC14" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Integer</span></span>
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<pre style="margin: 0;">+<span id="LC15" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC16" class="line" lang="haskell"><span class="n" style="color: #333;">integerPowMod</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Maybe</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">+<span id="LC17" class="line" lang="haskell"><span class="n" style="color: #333;">integerPowMod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">integerPowMod</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">fromIntegral</span> <span class="n" style="color: #333;">m</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC18" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Nothing</span></span>
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<td class="diff-line-num new new_line" data-linenumber="19" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
19
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<pre style="margin: 0;">+<span id="LC19" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">r</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Just</span> <span class="p">(</span><span class="n" style="color: #333;">fromIntegral</span> <span class="n" style="color: #333;">r</span><span class="p">)</span></span>
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11
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20
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<pre style="margin: 0;"> <span id="LC20" class="line" lang="haskell"></span>
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12
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<pre style="margin: 0;"> <span id="LC21" class="line" lang="haskell"><span class="n" style="color: #333;">main</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">IO</span> <span class="nb" style="color: #0086b3;">()</span></span>
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13
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<pre style="margin: 0;"> <span id="LC22" class="line" lang="haskell"><span class="n" style="color: #333;">main</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">do</span></span>
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<pre style="margin: 0;">-<span id="LC14" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">powModNatural</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">-<span id="LC15" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">powModNatural</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">m</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC23" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">naturalPowMod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC24" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">naturalPowMod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">m</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC25" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC26" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC27" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">m</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC28" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC29" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="n" style="color: #333;">b</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC30" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="n" style="color: #333;">b</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="p">(</span><span class="n" style="color: #333;">m</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC31" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC32" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="n" style="color: #333;">e</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC33" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="n" style="color: #333;">e</span> <span class="p">(</span><span class="n" style="color: #333;">m</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC34" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC35" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="n" style="color: #333;">m</span></span>
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<pre style="margin: 0;">+<span id="LC36" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">integerPowMod</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="p">(</span><span class="o" style="font-weight: 600;">-</span><span class="n" style="color: #333;">e</span><span class="p">)</span> <span class="p">(</span><span class="n" style="color: #333;">m</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC37" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC38" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC39" class="line" lang="haskell"> <span class="n" style="color: #333;">b</span><span class="p">,</span><span class="n" style="color: #333;">e</span><span class="p">,</span><span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Num</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=></span> <span class="n" style="color: #333;">a</span></span>
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18
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<pre style="margin: 0;"> <span id="LC40" class="line" lang="haskell"> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">2988348162058574136915891421498819466320163312926952423791023078876139</span></span>
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19
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41
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<pre style="margin: 0;"> <span id="LC41" class="line" lang="haskell"> <span class="n" style="color: #333;">e</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">2351399303373464486466122544523690094744975233415544072992656881240319</span></span>
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<pre style="margin: 0;"> <span id="LC42" class="line" lang="haskell"> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">10</span><span class="o" style="font-weight: 600;">^</span><span class="p">(</span><span class="mi" style="color: #099;">40</span><span class="o" style="font-weight: 600;">::</span><span class="kt" style="color: #458; font-weight: 600;">Int</span><span class="p">)</span></span></pre>
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<pre style="margin: 0;">-<span id="LC21" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC22" class="line" lang="haskell"> <span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">5328841272400314897981163497728751426</span></span>
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<pre style="margin: 0;">-<span id="LC23" class="line" lang="haskell"> <span class="n" style="color: #333;">y</span> <span class="o" style="font-weight: 600;">=</span> <span class="mi" style="color: #099;">32052182750761975518649228050096851724</span></span>
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24
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<pre style="margin: 0;">-<span id="LC24" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC25" class="line" lang="haskell"> <span class="n" style="color: #333;">b1024</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">roll</span> <span class="p">(</span><span class="n" style="color: #333;">map</span> <span class="n" style="color: #333;">fromIntegral</span> <span class="p">(</span><span class="n" style="color: #333;">take</span> <span class="mi" style="color: #099;">128</span> <span class="p">[</span><span class="mh" style="color: #099;">0x80</span><span class="o" style="font-weight: 600;">::</span><span class="kt" style="color: #458; font-weight: 600;">Int</span> <span class="o" style="font-weight: 600;">..</span> <span class="p">]))</span></span>
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<pre style="margin: 0;">-<span id="LC26" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC27" class="line" lang="haskell"> <span class="n" style="color: #333;">roll</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">[</span><span class="kt" style="color: #458; font-weight: 600;">Word8</span><span class="p">]</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span></span>
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<pre style="margin: 0;">-<span id="LC28" class="line" lang="haskell"> <span class="n" style="color: #333;">roll</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">GHC</span><span class="o" style="font-weight: 600;">.</span><span class="kt" style="color: #458; font-weight: 600;">Base</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">foldr</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">\</span><span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span> <span class="p">`</span><span class="n" style="color: #333;">shiftL</span><span class="p">`</span> <span class="mi" style="color: #099;">8</span> <span class="o" style="font-weight: 600;">.|.</span> <span class="n" style="color: #333;">fromIntegral</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="mi" style="color: #099;">0</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#5b4bacc8d9c2dfe0ee298a058a06a0c4dd7424ec"><strong>testsuite/tests/lib/integer/integerPowMod.stdout</strong></a>
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<pre style="margin: 0;"> <span id="LC1" class="line" lang="plaintext">1527229998585248450016808958343740453059</span>
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<pre style="margin: 0;"> <span id="LC2" class="line" lang="plaintext">682382427572745901624116300491295556924</span>
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3
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<pre style="margin: 0;">+<span id="LC3" class="line" lang="plaintext">Just 1527229998585248450016808958343740453059</span>
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4
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<pre style="margin: 0;">+<span id="LC4" class="line" lang="plaintext">Just 682382427572745901624116300491295556924</span>
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5
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<pre style="margin: 0;">+<span id="LC5" class="line" lang="plaintext">Just 9710805908340105786808462779613285007339</span>
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6
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<pre style="margin: 0;">+<span id="LC6" class="line" lang="plaintext">Nothing</span>
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7
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<pre style="margin: 0;">+<span id="LC7" class="line" lang="plaintext">Just 8472770001414751549983191041656259546941</span>
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8
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<pre style="margin: 0;">+<span id="LC8" class="line" lang="plaintext">Just 9317617572427254098375883699508704443075</span>
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9
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<pre style="margin: 0;">+<span id="LC9" class="line" lang="plaintext">Just 289194091659894213191537220386714992661</span>
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10
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<pre style="margin: 0;">+<span id="LC10" class="line" lang="plaintext">Nothing</span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#7a51550af5693585cf456d0acd81830d64828e0c"><strong>testsuite/tests/lib/integer/integerRecipMod.hs</strong></a>
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<pre style="margin: 0;">+<span id="LC1" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE BangPatterns, CPP, MagicHash, UnboxedTuples, TupleSections #-}</span></span>
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2
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<pre style="margin: 0;">+<span id="LC2" class="line" lang="haskell"></span>
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3
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<pre style="margin: 0;">+<span id="LC3" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">module</span> <span class="nn" style="color: #555;">Main</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">main</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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4
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<pre style="margin: 0;">+<span id="LC4" class="line" lang="haskell"></span>
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5
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<pre style="margin: 0;">+<span id="LC5" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.List</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">group</span><span class="p">)</span></span>
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6
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<pre style="margin: 0;">+<span id="LC6" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Bits</span></span>
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7
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<pre style="margin: 0;">+<span id="LC7" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Word</span></span>
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8
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<pre style="margin: 0;">+<span id="LC8" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Maybe</span></span>
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9
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<pre style="margin: 0;">+<span id="LC9" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Control.Monad</span></span>
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10
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<pre style="margin: 0;">+<span id="LC10" class="line" lang="haskell"></span>
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11
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<pre style="margin: 0;">+<span id="LC11" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Word</span></span>
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12
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<pre style="margin: 0;">+<span id="LC12" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Base</span></span>
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13
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<pre style="margin: 0;">+<span id="LC13" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Integer</span></span>
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14
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<pre style="margin: 0;">+<span id="LC14" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Num.Natural</span></span>
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15
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<pre style="margin: 0;">+<span id="LC15" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="k" style="font-weight: 600;">qualified</span> <span class="nn" style="color: #555;">GHC.Num.Integer</span> <span class="k" style="font-weight: 600;">as</span> <span class="n" style="color: #333;">I</span></span>
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16
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<pre style="margin: 0;">+<span id="LC16" class="line" lang="haskell"></span>
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17
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<pre style="margin: 0;">+<span id="LC17" class="line" lang="haskell"><span class="n" style="color: #333;">recipModInteger</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Integer</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Maybe</span> <span class="kt" style="color: #458; font-weight: 600;">Natural</span></span>
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18
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<pre style="margin: 0;">+<span id="LC18" class="line" lang="haskell"><span class="n" style="color: #333;">recipModInteger</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="kt" style="color: #458; font-weight: 600;">I</span><span class="o" style="font-weight: 600;">.</span><span class="n" style="color: #333;">integerRecipMod</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">x</span> <span class="n" style="color: #333;">m</span> <span class="kr" style="font-weight: 600;">of</span></span>
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19
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<pre style="margin: 0;">+<span id="LC19" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="n" style="color: #333;">y</span> <span class="o" style="font-weight: 600;">|</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Just</span> <span class="n" style="color: #333;">y</span></span>
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20
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<pre style="margin: 0;">+<span id="LC20" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">#</span> <span class="o" style="font-weight: 600;">|</span> <span class="nb" style="color: #0086b3;">()</span> <span class="o" style="font-weight: 600;">#</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Nothing</span></span>
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21
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<pre style="margin: 0;">+<span id="LC21" class="line" lang="haskell"></span>
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22
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<pre style="margin: 0;">+<span id="LC22" class="line" lang="haskell"><span class="n" style="color: #333;">main</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">IO</span> <span class="nb" style="color: #0086b3;">()</span></span>
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23
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<pre style="margin: 0;">+<span id="LC23" class="line" lang="haskell"><span class="n" style="color: #333;">main</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">do</span></span>
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<pre style="margin: 0;">+<span id="LC24" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">let</span></span>
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<pre style="margin: 0;">+<span id="LC25" class="line" lang="haskell"> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">recipModInteger</span> <span class="n" style="color: #333;">x</span> <span class="p">(</span><span class="mi" style="color: #099;">2</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">3</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">11</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">11</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">17</span><span class="o" style="font-weight: 600;">*</span><span class="mi" style="color: #099;">17</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;">+<span id="LC26" class="line" lang="haskell"> <span class="n" style="color: #333;">y</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">fmap</span> <span class="p">(</span><span class="n" style="color: #333;">x</span><span class="p">,)</span> <span class="n" style="color: #333;">y</span></span>
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<pre style="margin: 0;">+<span id="LC27" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC28" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- positive modulo</span></span>
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<pre style="margin: 0;">+<span id="LC29" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">mapMaybe</span> <span class="n" style="color: #333;">f</span> <span class="p">[</span><span class="o" style="font-weight: 600;">-</span><span class="mi" style="color: #099;">7</span><span class="o" style="font-weight: 600;">..</span><span class="mi" style="color: #099;">71</span><span class="p">]</span></span>
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<pre style="margin: 0;">+<span id="LC30" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC31" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- modulo == 1 or 0</span></span>
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<pre style="margin: 0;">+<span id="LC32" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="p">(</span><span class="n" style="color: #333;">recipModInteger</span> <span class="mi" style="color: #099;">77</span> <span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC33" class="line" lang="haskell"> <span class="n" style="color: #333;">print</span> <span class="p">(</span><span class="n" style="color: #333;">recipModInteger</span> <span class="mi" style="color: #099;">77</span> <span class="mi" style="color: #099;">0</span><span class="p">)</span></span></pre>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/compare/3c9beab75aaa5fbbb11132c99e2af114f322152f...8dd4f40512bb18e296280acde0507b4233a27b69#4694c4d20cf7c9f996ad104728cf16177470ad88"><strong>testsuite/tests/lib/integer/integerRecipMod.stdout</strong></a>
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<pre style="margin: 0;">+<span id="LC1" class="line" lang="plaintext">[(-7,149867),(-5,167851),(-1,209813),(1,1),(5,41963),(7,59947),(13,177535),(19,143557),(23,182447),(25,134281),(29,7235),(31,33841),(35,95915),(37,113413),(41,61409),(43,24397),(47,174101),(49,158431),(53,193979),(59,188477),(61,185737),(65,35507),(67,118999),(71,186173)]</span>
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2
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<pre style="margin: 0;">+<span id="LC2" class="line" lang="plaintext">Nothing</span>
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3
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<pre style="margin: 0;">+<span id="LC3" class="line" lang="plaintext">Nothing</span></pre>
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