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Diffstat (limited to 'services/nuldoc/public/blog/posts/2025-10-31/representing-single-value-with-half-open-float-interval/index.html')
| -rw-r--r-- | services/nuldoc/public/blog/posts/2025-10-31/representing-single-value-with-half-open-float-interval/index.html | 59 |
1 files changed, 31 insertions, 28 deletions
diff --git a/services/nuldoc/public/blog/posts/2025-10-31/representing-single-value-with-half-open-float-interval/index.html b/services/nuldoc/public/blog/posts/2025-10-31/representing-single-value-with-half-open-float-interval/index.html index 10500010..deff05d3 100644 --- a/services/nuldoc/public/blog/posts/2025-10-31/representing-single-value-with-half-open-float-interval/index.html +++ b/services/nuldoc/public/blog/posts/2025-10-31/representing-single-value-with-half-open-float-interval/index.html @@ -152,8 +152,9 @@ <code>1</code> と <code>p</code> のビット列での表現を見てみよう。 </p> <div class="codeblock"> - <pre class="shiki github-light" style="background-color:#f5f5f5;color:#24292e" tabindex="0"><code><span class="line"><span>1 = 0011111111110000000000000000000000000000000000000000000000000000</span></span> -<span class="line"><span>p = 0011111111110000000000000000000000000000000000000000000000000001</span></span></code></pre> + <pre class="highlight" style="background-color:#f5f5f5"><code>1 = 0011111111110000000000000000000000000000000000000000000000000000 +p = 0011111111110000000000000000000000000000000000000000000000000001 +</code></pre> </div> <p> <code>p</code> が <code>1</code> よりも一つ分だけ大きいのがわかるだろうか (ここでは <code>binary64</code> の具体的な表現について言及していないのでそうなる保証はないのだが、あくまで雰囲気として)。 @@ -182,37 +183,39 @@ <code>binary64</code> を 64 bit の整数に変換できるなら、他の言語でもほとんど同じ方法で実装できるはずだ。 </p> <div class="codeblock"> - <pre class="shiki github-light" style="background-color:#f5f5f5;color:#24292e" tabindex="0"><code><span class="line"><span style="color:#D73A49"> public</span><span style="color:#D73A49"> static</span><span style="color:#D73A49"> function</span><span style="color:#6F42C1"> nextUp</span><span style="color:#24292E">(</span><span style="color:#D73A49">float</span><span style="color:#24292E"> $x)</span><span style="color:#D73A49">:</span><span style="color:#D73A49"> float</span></span> -<span class="line"><span style="color:#24292E"> {</span></span> -<span class="line"><span style="color:#6A737D"> // NaN (Not a Number) なら NaN を返す。</span></span> -<span class="line"><span style="color:#D73A49"> if</span><span style="color:#24292E"> (</span><span style="color:#005CC5">is_nan</span><span style="color:#24292E">($x)) {</span></span> -<span class="line"><span style="color:#D73A49"> return</span><span style="color:#005CC5"> NAN</span><span style="color:#24292E">;</span></span> -<span class="line"><span style="color:#24292E"> }</span></span> -<span class="line"><span style="color:#6A737D"> // 正の無限大なら正の無限大を返す。</span></span> -<span class="line"><span style="color:#D73A49"> if</span><span style="color:#24292E"> (</span><span style="color:#005CC5">is_infinite</span><span style="color:#24292E">($x) </span><span style="color:#D73A49">&&</span><span style="color:#24292E"> $x </span><span style="color:#D73A49">></span><span style="color:#005CC5"> 0</span><span style="color:#24292E">) {</span></span> -<span class="line"><span style="color:#D73A49"> return</span><span style="color:#005CC5"> INF</span><span style="color:#24292E">;</span></span> -<span class="line"><span style="color:#24292E"> }</span></span> -<span class="line"><span style="color:#6A737D"> // 0 なら minValue() を返す (後述)。</span></span> -<span class="line"><span style="color:#D73A49"> if</span><span style="color:#24292E"> ($x </span><span style="color:#D73A49">===</span><span style="color:#005CC5"> 0.0</span><span style="color:#24292E">) {</span></span> -<span class="line"><span style="color:#D73A49"> return</span><span style="color:#D73A49"> self::</span><span style="color:#6F42C1">minValue</span><span style="color:#24292E">();</span></span> -<span class="line"><span style="color:#24292E"> }</span></span> -<span class="line"><span style="color:#6A737D"> // binary64 を 64 bit 整数に変換する。</span></span> -<span class="line"><span style="color:#24292E"> $u </span><span style="color:#D73A49">=</span><span style="color:#D73A49"> self::</span><span style="color:#6F42C1">floatToInt</span><span style="color:#24292E">($x);</span></span> -<span class="line"><span style="color:#6A737D"> // 正なら整数に +1 して binary64 に戻す。</span></span> -<span class="line"><span style="color:#6A737D"> // 負なら整数に -1 して binary64 に戻す。</span></span> -<span class="line"><span style="color:#D73A49"> return</span><span style="color:#24292E"> $x </span><span style="color:#D73A49">></span><span style="color:#005CC5"> 0.0</span><span style="color:#D73A49"> ?</span><span style="color:#D73A49"> self::</span><span style="color:#6F42C1">intToFloat</span><span style="color:#24292E">($u </span><span style="color:#D73A49">+</span><span style="color:#005CC5"> 1</span><span style="color:#24292E">) </span><span style="color:#D73A49">:</span><span style="color:#D73A49"> self::</span><span style="color:#6F42C1">intToFloat</span><span style="color:#24292E">($u </span><span style="color:#D73A49">-</span><span style="color:#005CC5"> 1</span><span style="color:#24292E">);</span></span> -<span class="line"><span style="color:#24292E"> }</span></span></code></pre> + <pre class="highlight" style="background-color:#f5f5f5"><code> <span style="color: #cf222e">public</span> <span style="color: #cf222e">static</span> <span style="color: #cf222e">function</span> <span style="color: #24292f;background-color: #f6f8fa">nextUp</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #cf222e">float</span> <span style="color: #0550ae">$x</span><span style="color: #24292f;background-color: #f6f8fa">):</span> <span style="color: #cf222e">float</span> + <span style="color: #24292f;background-color: #f6f8fa">{</span> + <span style="color: #6e7781">// NaN (Not a Number) なら NaN を返す。</span> + <span style="color: #cf222e">if</span> <span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #953800">is_nan</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">$x</span><span style="color: #24292f;background-color: #f6f8fa">))</span> <span style="color: #24292f;background-color: #f6f8fa">{</span> + <span style="color: #cf222e">return</span> <span style="color: #953800">NAN</span><span style="color: #24292f;background-color: #f6f8fa">;</span> + <span style="color: #24292f;background-color: #f6f8fa">}</span> + <span style="color: #6e7781">// 正の無限大なら正の無限大を返す。</span> + <span style="color: #cf222e">if</span> <span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #953800">is_infinite</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">$x</span><span style="color: #24292f;background-color: #f6f8fa">)</span> <span style="color: #0550ae">&&</span> <span style="color: #0550ae">$x</span> <span style="color: #0550ae">></span> <span style="color: #0550ae">0</span><span style="color: #24292f;background-color: #f6f8fa">)</span> <span style="color: #24292f;background-color: #f6f8fa">{</span> + <span style="color: #cf222e">return</span> <span style="color: #953800">INF</span><span style="color: #24292f;background-color: #f6f8fa">;</span> + <span style="color: #24292f;background-color: #f6f8fa">}</span> + <span style="color: #6e7781">// 0 なら minValue() を返す (後述)。</span> + <span style="color: #cf222e">if</span> <span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">$x</span> <span style="color: #0550ae">===</span> <span style="color: #0550ae">0.0</span><span style="color: #24292f;background-color: #f6f8fa">)</span> <span style="color: #24292f;background-color: #f6f8fa">{</span> + <span style="color: #cf222e">return</span> <span style="color: #cf222e">self</span><span style="color: #0550ae">::</span><span style="color: #8250df">minValue</span><span style="color: #24292f;background-color: #f6f8fa">();</span> + <span style="color: #24292f;background-color: #f6f8fa">}</span> + <span style="color: #6e7781">// binary64 を 64 bit 整数に変換する。</span> + <span style="color: #0550ae">$u</span> <span style="color: #0550ae">=</span> <span style="color: #cf222e">self</span><span style="color: #0550ae">::</span><span style="color: #8250df">floatToInt</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">$x</span><span style="color: #24292f;background-color: #f6f8fa">);</span> + <span style="color: #6e7781">// 正なら整数に +1 して binary64 に戻す。</span> + <span style="color: #6e7781">// 負なら整数に -1 して binary64 に戻す。</span> + <span style="color: #cf222e">return</span> <span style="color: #0550ae">$x</span> <span style="color: #0550ae">></span> <span style="color: #0550ae">0.0</span> <span style="color: #0550ae">?</span> <span style="color: #cf222e">self</span><span style="color: #0550ae">::</span><span style="color: #8250df">intToFloat</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">$u</span> <span style="color: #0550ae">+</span> <span style="color: #0550ae">1</span><span style="color: #24292f;background-color: #f6f8fa">)</span> <span style="color: #0550ae">:</span> <span style="color: #cf222e">self</span><span style="color: #0550ae">::</span><span style="color: #8250df">intToFloat</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">$u</span> <span style="color: #0550ae">-</span> <span style="color: #0550ae">1</span><span style="color: #24292f;background-color: #f6f8fa">);</span> + <span style="color: #24292f;background-color: #f6f8fa">}</span> +</code></pre> </div> <p> <code>0</code> のときに返している <code>minValue()</code> は次のような値である。 </p> <div class="codeblock"> - <pre class="shiki github-light" style="background-color:#f5f5f5;color:#24292e" tabindex="0"><code><span class="line"><span style="color:#D73A49"> public</span><span style="color:#D73A49"> static</span><span style="color:#D73A49"> function</span><span style="color:#6F42C1"> minValue</span><span style="color:#24292E">()</span><span style="color:#D73A49">:</span><span style="color:#D73A49"> float</span></span> -<span class="line"><span style="color:#24292E"> {</span></span> -<span class="line"><span style="color:#6A737D"> // 整数の 1 を binary64 と解釈した値を返す。</span></span> -<span class="line"><span style="color:#6A737D"> // binary64 で表せる最小の正の非正規化数。</span></span> -<span class="line"><span style="color:#D73A49"> return</span><span style="color:#D73A49"> self::</span><span style="color:#6F42C1">intToFloat</span><span style="color:#24292E">(</span><span style="color:#005CC5">1</span><span style="color:#24292E">);</span></span> -<span class="line"><span style="color:#24292E"> }</span></span></code></pre> + <pre class="highlight" style="background-color:#f5f5f5"><code> <span style="color: #cf222e">public</span> <span style="color: #cf222e">static</span> <span style="color: #cf222e">function</span> <span style="color: #24292f;background-color: #f6f8fa">minValue</span><span style="color: #24292f;background-color: #f6f8fa">():</span> <span style="color: #cf222e">float</span> + <span style="color: #24292f;background-color: #f6f8fa">{</span> + <span style="color: #6e7781">// 整数の 1 を binary64 と解釈した値を返す。</span> + <span style="color: #6e7781">// binary64 で表せる最小の正の非正規化数。</span> + <span style="color: #cf222e">return</span> <span style="color: #cf222e">self</span><span style="color: #0550ae">::</span><span style="color: #8250df">intToFloat</span><span style="color: #24292f;background-color: #f6f8fa">(</span><span style="color: #0550ae">1</span><span style="color: #24292f;background-color: #f6f8fa">);</span> + <span style="color: #24292f;background-color: #f6f8fa">}</span> +</code></pre> </div> </section> <section id="section--outro"> |