update Hacking_of_LHa

diff --git a/Hacking_of_LHa b/Hacking_of_LHa
index d57c0f3..67f4070 100644 (file)
--- a/Hacking_of_LHa
+++ b/Hacking_of_LHa
@@ -5108,29 +5108,44 @@ Huffman
                            :       |
             .        ... ³¬ÁØ:11   |
            / \                     |
-          x   x      ... ³¬ÁØ:12  .' <- ɽ°ú¤­¤Î·ë²Ì x ¤¬(>=NC)¤Î¾ì¹ç¡¢
+          x   y      ... ³¬ÁØ:12  .' <- ɽ°ú¤­¤Î·ë²Ì x ¤¬(>=NC)¤Î¾ì¹ç¡¢
              / \                        Ìڤγ¤­¤¬¤¢¤ë¤³¤È¤ò¼¨¤¹
-            .   .    ... ³¬ÁØ:13  `.
+            z   .    ... ³¬ÁØ:13  `.
                                    |
                            :        >   left[]/right[]¤Çɽ¸½ (³¬ÁØ12¤¬root)
                      ... ³¬ÁØ:16  .'
-
-    ³¬ÁØ 1 ¡Á 12 (1¡Á12bit)¤ÎHuffmanÌڤˤĤ¤¤Æ¤Ï¡¢É½°ú¤­¤ÇÉü¹æ
-    ³¬ÁØ 13 °Ê¾å¤ÎHuffmanÉä¹æ¤Ë¤Ä¤¤¤Æ¤Ï¡¢ÀèƬ 12 bit¤òɽ°ú¤­¤·¡¢¤½¤ÎÃÍ
-    ¤ÏNC ¤è¤êÂ礭¤¤ÃͤȤʤ롣
-
-    ɽ°ú¤­¤·¤¿·ë²Ì¤¬ >= NC ¤Î¾ì¹ç¡¢¤½¤ÎÃͤÏÀá¤ò¼¨¤·¡¢left[ɽ°ú¤­¤ÎÃÍ],
-    right[ɽ°ú¤­¤ÎÃÍ]¤¬¤½¤Î²¼¤ÎÀá¤ò»Ø¤¹¡£
 ----------------------------------------------------------------------------
 
 ³¬ÁØ12¤è¤ê²¼(13 °Ê¾å¤Î bit ¿ô¤Î Huffman Éä¹æ)¤Î Huffman ÌڤˤĤ¤¤Æ
-left[], right[] ¤Çɽ¤·¤Æ¤¤¤ë¤è¤¦¤À¡£¤³¤ÎÌڤΥΡ¼¥É¤ÎÃÍ¤Ï NC °Ê¾å¤Î¿ôÃÍ
-¤òÏ¢È֤dzä¤êÅö¤Æ¤Æ¤¤¤ë¤è¤¦¤À(¤³¤ì¤Ë¤Ä¤¤¤Æ¤Ï¸å½Ò¤¹¤ë)¡£
+left[], right[] ¤Çɽ¤·¤Æ¤¤¤ë¤è¤¦¤À¡£
+
+¾å¤ÎÎã¤Ç¡¢13 ¥Ó¥Ã¥È¤Î Huffman Éä¹æ¤ÇÉä¹æ²½¤µ¤ì¤ëÊ£¹ç¸ì z ¤Ë¤Ä¤¤¤Æ¤Ï¡¢
+y ¤Ë¤½¤ÎÌڤΥ롼¥È¥Î¡¼¥È¤ÎÃÍ(y > NC)¤¬³ä¤êÅö¤Æ¤é¤ì¤ë¡£
+
+¿Þ¤«¤éÌÀ¤é¤«¤À¤¬¡¢Ê£¹ç¸ì¤½¤Î¤â¤Î¤ò»Ø¤¹ 12 bit ¤ÎÉä¹æ(¤¿¤È¤¨¤Ð x)¤È¡¢ÌÚ
+¤Î¥ë¡¼¥È¥Î¡¼¥É¤ò»Ø¤¹ 12 bit ¤ÎÉä¹æ(¤¿¤È¤¨¤Ð y)¤¬Æ±¤¸Éä¹æ¤È¤Ê¤ë¤³¤È¤Ï¤Ê
+¤¤¡£¤³¤ì¤ÏHuffman Éä¹æ¤¬¸ìƬ¾ò·ï¤òËþ¤¿¤¹¤«¤é¤Ç¤¢¤ë¡£
+
+¤Ç¤Ï¡¢y ¤Ë³ä¤êÅö¤Æ¤ëÃͤϤɤΤ褦¤Ë·è¤Þ¤ë¤«¤È¤¤¤¦¤È¤ª¤½¤é¤¯ NC °Ê¾å¤Î¿ô
+ÃͤòÏ¢ÈÖ¤«²¿¤«¤Ç³ä¤êÅö¤Æ¤Æ¤¤¤ë¤Î¤Ç¤Ï¤Ê¤¤¤«¤È»×¤ï¤ì¤ë¡£¤³¤ì¤Ë¤Ä¤¤¤Æ¤Ï¤³
+¤ì°Ê¹ß¤Ç³Îǧ¤¹¤ë¡£
 
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 ¤¤¤¦¤³¤È¤Ï½Ð¸½ÉÑÅÙ¤¬Ä㤤¤Ï¤º¤Ç¤¢¤ë¤«¤é¡¢left[], right[] ¤ÇÌÚ¤òé¤ë²ó¿ô
 ¤Ï¾¯¤Ê¤¤¤Ï¤º¤Ç¤¢¤ë¡£¤³¤ì¤ÏÍý¤Ë¤«¤Ê¤Ã¤Æ¤¤¤ë¡£
 
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+³¬ÁØ13°Ê¾å¤Î¥Î¡¼¥É¤Î¿ô¤È¤Ê¤ë¤¬¡¢³¬ÁØ n ¤ÎÆóʬÌڤΥΡ¼¥É¤Î¿ô¤¬2^(n+1) -
+1 ¤Ç¤¢¤ë(³¬ÁØ n ¤ÎÍդοô¤Ï 2^n ¤Ç¡¢Àá¤Î¿ô¤Ï 2^n-1)¤«¤é¡¢
+
+    ³¬ÁØ 12 ¤Î¥Î¡¼¥É¤Î¿ô¤Ï¡¢(2^(12+1)-1) = 8191
+    ³¬ÁØ 16 ¤Î¥Î¡¼¥É¤Î¿ô¤Ï¡¢(2^(16+1)-1) = 131071
+
+¤È¤Ê¤ê¡¢¤½¤Îº¹¤Ï 131071 - 8191 = 122880 ¤È¤Ê¤ë¡£Ã±½ã¤Ë¹Í¤¨¤ë¤È¡¢ºÇ°­¤Î
+¾ì¹ç¤òÁÛÄꤷ¤Æleft[], right[] ¹ç·×¤Ç 122880 ¤Î¥µ¥¤¥º¤¬É¬ÍפǤ¢¤ë¤³¤È¤Ë
+¤Ê¤ë¡£¤½¤¦¤¹¤ë¤ÈÎΰè¤òÀáÌ󤹤ë¤È¤¤¤¦ÌÜŪ¤«¤é¤Ï¸µ¤â»Ò¤â¤Ê¤¤¤³¤È¤È¤Ê¤ë¡£
+¤Ê¤¼¤À¤í¤¦¡©¡Ê¡¦¡¦¡¦²¿¤«´Ö°ã¤Ã¤Æ¤¤¤ë¤Î¤À¤í¤¦¤«¡©¡Ë
+
 ³¤­¤ò¸«¤Æ¤¤¤³¤¦¡¢(E) ¤Î½èÍý
 
     /* (E) */
@@ -5141,7 +5156,27 @@ left[], right[] 
         for (i = j; i < k; i++)
             table[i] = 0;
 
-¼¡¤Ë (F) ¤Î½èÍý¡£²¼µ­¤ÎÄ̤ê (F.1), (F.2) ¤ÈºÙʬ²½¤·¤Æ¤ß¤¿¡£
+table[] ¤Î½é´üÃͤȤ·¤Æ 0 ¤òÀßÄꤷ¤Æ¤¤¤ë¡£
+
+Huffman Éä¹æ¤Ç¤¢¤ë j ¤Ë¤Ï¡¢start[tablebits + 1] ¤Ä¤Þ¤ê¡¢¥Ó¥Ã¥ÈĹ
+tablebits ¤ÎºÇÂç¤Î Huffman Éä¹æ+1¤¬ÀßÄꤵ¤ì¤ë¡£(·«¤êÊÖ¤·¤Ë¤Ê¤ë¤¬¡¢¥Ó¥Ã
+¥ÈĹ i ¤Î Huffman Éä¹æ¤Ï¡¢start[i] ¤«¤é start[i+1]-1¤ÎÈϰϤÎÉä¹æ¤Ç¤¢¤ë)
+m ¤Ç±¦¥·¥Õ¥È¤·¤Æ¤¤¤ë¤Î¤Ï¡¢(D) ¤Ç¤Ï¡¢tablebits ¤Þ¤Ç¤Î start[i] ¤·¤« ±¦
+¥·¥Õ¥È¤·¤Æ¤¤¤Ê¤¤¤¿¤á¤Ç¤¢¤ë¡£
+
+k ¤Ï¡¢1 << tablebits ¤«¤é tablebits + 1 ÈÖÌܤΥӥåȤ¬Î©¤Ã¤¿¿ôÃͤȤʤ롣
+¤³¤ÎÃͤϤĤޤê¤Ï tablebits ¥Ó¥Ã¥È¤Î Huffman Éä¹æ¤ÎºÇÂçÃÍ + 1 ¤Ç¤¢¤ë¡£
+
+¤½¤·¤Æ¡¢start[j...k] ¤ÎÈϰϤˤĤ¤¤Æ 0 ¤òÀßÄꤷ¤Æ¤¤¤ë¡£·ë¶É tablebits ¤Î
+¥Ó¥Ã¥ÈŤÎÈϰϤdzä¤êÅö¤Æ¤é¤ì¤ë¤³¤È¤¬¤Ê¤¤ Huffman Éä¹æ¤ËÂФ·¤Æ 0 ¤Ç½é´ü
+²½¤·¤Æ¤¤¤ë¤È¤¤¤¦¤³¤È¤Î¤è¤¦¤À¡£
+
+¤Á¤ç¤Ã¤Èµ¿Ìä¤Ê¤Î¤À¤¬¡¢if (j != 0) ¤ÏɬÍפʤΤÀ¤í¤¦¤«¡©¤Ä¤Þ¤ê¡¢j = 0 ¤È
+¤·¤Æ¡¢table[] ¤ÎÁ´Í×ÁǤˤĤ¤¤Æ 0 ¤Ç½é´ü²½¤·¤Æ¤â²¿¤âÌäÂê¤Ï¤Ê¤¤¤Î¤Ç¤Ï¤Ê¤¤
+¤«¡©¤½¤·¤Æ¤½¤ì¤Ê¤é make_table() ¤Ë table[] ¤Î¥µ¥¤¥º(sizeof)¤òÅϤ·
+memset() ¤Ë¤Æ 0 ¤Ç½é´ü²½¤·¤¿Êý¤¬Â®¤¤¤Î¤Ç¤Ï¤Ê¤¤¤À¤í¤¦¤«¡©
+
+¼¡¤Ë (F) ¤Î½èÍý¡£¾¯¤·Â礭¤¤¤Î¤Ç²¼µ­¤ÎÄ̤ê (F.1), (F.2) ¤ÈºÙʬ²½¤·¤Æ¤ß¤¿¡£
 
     /* (F) */
     /* create table and tree */
@@ -5182,7 +5217,10 @@ left[], right[] 
 
 ¤³¤ÎÉôʬ¤Ï°ì»þÊÑ¿ô¤ÎÎ̤¬Â¿¤¤¡¢i,j,k,l,m,n,p ¤Þ¤Ç»È¤ï¤ì¤Æ¤¤¤ë¡£
 (¤·¤«¤â¡¢Á°¤Î½èÍý¤Þ¤Ç¤ÈÊÑ¿ô¤ÎÍÑÅÓ¤¬°ã¤Ã¤Æ¤¿¤ê¤¹¤ë¤Î¤Ç¡¢Ê£»¨¤Ë¤Ê¤Ã¤Æ¤¤¤ë)
-°ìö¡¢°Ê²¼¤ËÀ°Íý¤·¤Æ¤ß¤¿¡£
+
+°ìö¡¢°Ê²¼¤ËÀ°Íý¤·¤Æ¤ß¤¿¡£(¤É¤ÎÊÑ¿ô¤Îź¤¨»ú¤Ë»È¤ï¤ì¤Æ¤¤¤ë¤«¤Ê¤É¤«¤é¤Ò¤È
+¤á¤ÇȽÃǤ·¤Æ¤ß¤¿·ë²Ì¤Ç¤¢¤ë¡£¤½¤·¤Æ¡¢n, p ¤Ë¤Ä¤¤¤Æ¤Ï¤Ò¤È¤á¤Ç¤Ï¤ï¤«¤é¤Ê¤«¤Ã
+¤¿)¡£
 
     i: Huffman Éä¹æ
     j: Éü¹æʸ»ú
@@ -5192,8 +5230,6 @@ left[], right[] 
     n: ??
     p: ??
 
-n, p ¤Ë¤Ä¤¤¤Æ¤Ï¤Ò¤È¤á¤Ç¤Ï¤ï¤«¤é¤Ê¤«¤Ã¤¿¡£
-
 ¤³¤ì¤òƧ¤Þ¤¨¤Æ½èÍýÆâÍƤò¸«¤Æ¤ß¤è¤¦¡£¤Þ¤º¡¢(F)Á´ÂΤˤĤ¤¤Æ
 
     /* (F) */
@@ -5215,7 +5251,7 @@ bitlen[] 
 ¤Îʸ»ú¤Ï¥¹¥­¥Ã¥×¤·¤Æ¤¤¤ë¡£¤³¤³¤Ï¡¢Îɤ¤¤À¤í¤¦¡£
 
 (F.1), (F.2) ¤Ï¡¢HuffmanÉä¹æ²½¤µ¤ì¤Æ¤¤¤ëʸ»ú j ¤Ë¤Ä¤¤¤Æ
-¤Î½èÍý¤È¤Ê¤ë¡£(ºÇ¸å¤Îstart[k] = l ¤Ï¸å²ó¤·)
+¤Î½èÍý¤È¤Ê¤ë¡£(ºÇ¸å¤Îstart[k] = l ¤Ï¸å¤Ç¹Í¤¨¤è¤¦)
 
 ½èÍý¤ÎÌÜŪ¤«¤éÂ绨ÇĤË
 
@@ -5247,8 +5283,8 @@ bitlen[] 
       a /\              b: 10
         b c             c: 11
 
-ʸ»úa¤Ï¡¢1¥Ó¥Ã¥È¤Ç¡¢00...10 ¤ÎÈÏ°Ï
-ʸ»úb¤Ï¡¢2¥Ó¥Ã¥È¤Ç¡¢10...11 ¤ÎÈÏ°Ï
+ʸ»úa¤Ï¡¢1¥Ó¥Ã¥È¤Ç¡¢00...10 ¤ÎÈÏ°Ï(¤Ä¤Þ¤ê¡¢00¤È01)
+ʸ»úb¤Ï¡¢2¥Ó¥Ã¥È¤Ç¡¢10...11 ¤ÎÈÏ°Ï(¤Ä¤Þ¤ê¡¢10)
 ʸ»úc¤Ï¡¢2¥Ó¥Ã¥È¤Ç¡¢11
 
 ¤È¤Ê¤ë¡£¤³¤³¤Ç¡¢Ê¸»ú c ¤Ë¤Ä¤¤¤Æ¤Ï¤³¤Î¥ë¡¼¥×¤Ç¤Ï¥Æ¡¼¥Ö¥ë¤ËÃͤ¬¥»¥Ã¥È¤µ¤ì
@@ -5282,7 +5318,7 @@ bitlen[] 
             *p = j;
         }
 
-¤Þ¤º¡¢
+¤Á¤ç¤Ã¤ÈÊ£»¨¤À¤¬Æñ¤·¤¤¤³¤È¤Ï¤Ê¤¤¡£¤Þ¤º¡¢
 
     p = &table[(i = start[k]) >> m];
 
@@ -5291,7 +5327,11 @@ bitlen[] 
     i = start[k];
     p = &table[i >> m]
 
-¤Ç¤¢¤ê¡¢i ¤Ï Huffman Éä¹æ¤Î½é´üÃÍ
+¤Ç¤¢¤ê¡¢i ¤Ï Huffman Éä¹æ¤Î½é´üÃͤǤ¢¤ë¡£i ¤¬ m ¤Ç±¦¥·¥Õ¥È¤µ¤ì¤Æ¤¤¤ë¤¬¡¢
+½é´ü²½Éôʬ¤Î (D) ¤Ç¤Ï¡¢tablebits ¤Þ¤Ç¤Î¥¤¥ó¥Ç¥Ã¥¯¥¹¤ËÂФ¹¤ëÃÍ
+(start[1..tablebits])¤·¤«¥·¥Õ¥È¤·¤Æ¤ª¤é¤º¡¢¤³¤Î (F.2) ¤ÎÉôʬ¤Ï k >
+tablebits ¤Ç¤¢¤ë¤«¤é start[k] ¤Ï m ¤Ç¥·¥Õ¥È¤µ¤ì¤Æ¤¤¤Ê¤¤ Huffman Éä¹æ¤È
+¤Ê¤Ã¤Æ¤¤¤ë¡£
 
 p ¤Ï¡¢HuffmanÉä¹æ i ¤Î table ¾å¤Î°ÌÃÖ¤ò»Ø¤¹¡£¸å¤Ç¡¢*p ¤Ë¤ÏÌڤΥ롼¥È°ÌÃÖ
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