{"id":8141,"date":"2024-06-21T22:01:01","date_gmt":"2024-06-21T14:01:01","guid":{"rendered":""},"modified":"2024-06-21T22:01:01","modified_gmt":"2024-06-21T14:01:01","slug":"\u6d6e\u70b9\u6570\u89c4\u8303\u5316\u8868\u793a_32\u4f4d\u6d6e\u70b9\u6570\u6700\u5927\u503c","status":"publish","type":"post","link":"https:\/\/mushiming.com\/8141.html","title":{"rendered":"\u6d6e\u70b9\u6570\u89c4\u8303\u5316\u8868\u793a_32\u4f4d\u6d6e\u70b9\u6570\u6700\u5927\u503c"},"content":{"rendered":"

\n <\/path> \n<\/svg> <\/p>\n

\u2003\u2003\u672c\u6587\u4e3b\u8981\u53c2\u8003\u300aIEEE Standard for Floating-Point Arithmetic\u300b<\/strong><\/font><\/p>\n

\u770b\u591a\u51e0\u6b21\u5c31\u61c2\u4e86\uff0c\u4e3b\u8981\u770b\u5b83\u7684\u8868\u793a\u5f62\u5f0f\u548c\u8f6c\u6362\u516c\u5f0f\u3002<\/p>\n

<\/p>\n

1. Floating-point formats<\/h3>\n

\u6d6e\u70b9\u6570\u683c\u5f0f<\/strong><\/p>\n

1.1 Specification levels<\/h4>\n

\u89c4\u8303\u7b49\u7ea7<\/strong><\/p>\n

\u2003\u2003\u6d6e\u70b9\u7b97\u672f\u662f\u5bf9\u4e8e\u5b9e\u9645\u7b97\u672f\u7684\u7cfb\u7edf\u8fd1\u4f3c\uff0c\u5982\u88681.1\u6240\u793a\u3002\u6d6e\u70b9\u7b97\u672f\u53ea\u80fd\u8868\u793a\u8fde\u7eed\u5b9e\u6570<\/strong>\u7684\u4e00\u4e2a\u6709\u9650\u5b50\u96c6<\/strong>\u3002\u56e0\u6b64\u5bf9\u4e8e\u5b9e\u6570\u7684\u67d0\u4e9b\u5c5e\u6027\uff08\u4f8b\u5982\u52a0\u6cd5\u7ed3\u5408\u5f8b\uff08associativity of addition\uff09\uff09\uff0c\u5e76\u4e0d\u603b\u662f\u9002\u7528\u4e8e\u6d6e\u70b9\u7b97\u672f\u3002<\/p>\n


\n \u88681.1 \u89c4\u8303\u5316\u7b49\u7ea7\u53ca\u5176\u683c\u5f0f <\/font>
\n<\/center> <\/p>\n\n\n\n\n\n\n\n\n\n\n\n
<\/th>\n<\/th>\n<\/th>\n<\/tr>\n<\/thead>\n
Level 1<\/td>\n { \u2212 \u221e \u2005\u200a \u2026 \u2005\u200a 0 \u2005\u200a \u2026 \u2005\u200a + \u221e } \\{-\\infty \\; \\ldots \\; 0 \\; \\ldots\\; +\\infty\\} <\/span><\/span>{
\n <\/span>\u2212<\/span>\u221e<\/span><\/span><\/span>\u2026<\/span><\/span><\/span>0<\/span><\/span><\/span>\u2026<\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u221e<\/span>}<\/span><\/span><\/span><\/span><\/span><\/td>\n		\u6269\u5c55\u5b9e\u6570<\/td>\n<\/tr>\n
\u591a\u5bf9\u4e00 \u2193\u2193<\/td>\n\u820d\u5165 \u2193\u2193<\/td>\n\u2191\u2191 \u6620\u5c04\uff08\u9664\u4e86NaN<\/strong><\/font>\uff09<\/td>\n<\/tr>\n
Level 2<\/td>\n { \u2212 \u221e \u2026 \u2212 0 } \u2005\u200a \u22c3 \u2005\u200a { + 0 \u2026 + \u221e } \u2005\u200a \u22c3 \\{-\\infty \\ldots -0 \\}\\; \\bigcup \\; \\{+0 \\ldots +\\infty \\} \\; \\bigcup <\/span><\/span>{
\n <\/span>\u2212<\/span>\u221e<\/span><\/span>\u2026<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0<\/span>}<\/span><\/span><\/span>\u22c3<\/span><\/span>{
\n <\/span>+<\/span>0<\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>\u221e<\/span>}<\/span><\/span><\/span>\u22c3<\/span><\/span><\/span><\/span><\/span> NaN<\/strong><\/font><\/td>\n		\u6d6e\u70b9\u6570\u636e - - \u4ee3\u6570\u5c01\u95ed\u7684\u7cfb\u7edf<\/td>\n<\/tr>\n
\u4e00\u5bf9\u591a \u2193\u2193<\/td>\n\u89c4\u8303\u5316\u8868\u793a \u2193\u2193<\/td>\n\u2191\u2191 \u591a\u5bf9\u4e00<\/td>\n<\/tr>\n
Level 3<\/td>\n ( s i g n , e x p o n e n t , s i g n i f i c a n d ) \u2005\u200a \u22c3 \u2005\u200a { \u2212 \u221e , + \u221e } \u2005\u200a \u22c3 (sign, exponent, significand) \\; \\bigcup \\; \\{-\\infty,+\\infty \\} \\; \\bigcup <\/span><\/span>(<\/span>s<\/span>i<\/span>g<\/span>n<\/span>,<\/span><\/span>e<\/span>x<\/span>p<\/span>o<\/span>n<\/span>e<\/span>n<\/span>t<\/span>,<\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span>)<\/span><\/span><\/span>\u22c3<\/span><\/span>{
\n <\/span>\u2212<\/span>\u221e<\/span>,<\/span><\/span>+<\/span>\u221e<\/span>}<\/span><\/span><\/span>\u22c3<\/span><\/span><\/span><\/span><\/span> qNaN<\/strong><\/font> \u22c3 \\bigcup <\/span><\/span>\u22c3<\/span><\/span><\/span><\/span><\/span> sNaN<\/strong><\/font><\/td>\n		\u6d6e\u70b9\u6570\u636e\u7684\u8868\u793a<\/td>\n<\/tr>\n
\u4e00\u5bf9\u591a \u2193\u2193<\/td>\n\u6d6e\u70b9\u6570\u636e\u7684\u7f16\u7801\u8868\u793a\u2193\u2193<\/td>\n\u2191\u2191 \u591a\u5bf9\u4e00<\/td>\n<\/tr>\n
Level 4<\/td>\n 0 \u2026 0\\ldots <\/span><\/span>0<\/span>1<\/span>1<\/span>1<\/span>0<\/span>0<\/span>0<\/span><\/span>\u2026<\/span><\/span><\/span><\/span><\/span><\/td>\n\u6bd4\u7279\u5b57\u7b26\u4e32\uff08Bit strings\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u2003\u2003 \u5728\u8be5\u6807\u51c6\u4e2d\uff0c\u652f\u6301\u7b97\u672f\u7684\u6570\u636e\u683c\u5f0f\u662f\u6269\u5c55\u5b9e\u6570\uff0c\u5373\u5b9e\u6570\u96c6\u4ee5\u53ca\u6b63\u8d1f\u65e0\u7a77\uff08 { \u2212 \u221e \u2026 0 \u2026 + \u221e } \\{-\\infty \\ldots 0 \\ldots+\\infty\\} <\/span><\/span>{
\n <\/span>\u2212<\/span>\u221e<\/span><\/span>\u2026<\/span><\/span>0<\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>\u221e<\/span>}<\/span><\/span><\/span><\/span><\/span>\uff09\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u683c\u5f0f\uff0c\u820d\u5165\u8fc7\u7a0b\uff08\u89c1\u540e\u9762\u7b2c?\u8282\uff09\u5c06\u6269\u5c55\u7684\u5b9e\u6570\u6620\u5c04\u5230\u8be5\u683c\u5f0f\u4e2d\u7684\u6d6e\u70b9\u6570\u3002\u6d6e\u70b9\u6570\u636e\u53ef\u4ee5\u662f\u5e26\u7b26\u53f7\u7684\u96f6\uff0c\u6709\u9650\u7684\u975e\u96f6\u6570\u5b57\uff0c\u5e26\u7b26\u53f7\u7684\u65e0\u7a77\u5927\u6216NaN\uff0c\u53ef\u4ee5\u4ee5\u4e00\u79cd\u683c\u5f0f\u6620\u5c04\u5230\u4e00\u4e2a\u6216\u591a\u4e2a\u6d6e\u70b9\u6570\u636e\u8868\u793a\u5f62\u5f0f\u3002<\/p>\n

\u2003\u2003 \u6d6e\u70b9\u6570\u636e\u7684\u8868\u793a\u683c\u5f0f\uff08\u5c31\u662fLevel 3\uff09\u5305\u62ec\u4ee5\u4e0b3\u5927\u90e8\u5206\uff1a<\/p>\n

\n
    \n
  1. \u4e09\u5143\u7ec4 ( s i g n , e x p o n e n t , s i g n i f i c a n d ) (sign, exponent, significand) <\/span><\/span>(<\/span>s<\/span>i<\/span>g<\/span>n<\/span>,<\/span><\/span>e<\/span>x<\/span>p<\/span>o<\/span>n<\/span>e<\/span>n<\/span>t<\/span>,<\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span>\uff1b \u5bf9\u4e8e\u57fa\u6570 b b <\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\uff0c\u7528\u4e09\u5143\u7ec4\u8868\u793a\u7684\u6d6e\u70b9\u6570\u5c31\u662f ( \u2212 1 ) s i g n \u00d7 b e x p o n e n t \u00d7 s i g n i f i c a n d \\LARGE (-1)^{sign} {\\times} b^{exponent}{\\times}significand <\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>b<\/span><\/span>e<\/span>x<\/span>p<\/span>o<\/span>n<\/span>e<\/span>n<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span><\/span><\/span><\/span><\/span><\/li>\n
  2. \u2212 \u221e , + \u221e -\\infty,+\\infty <\/span><\/span>\u2212<\/span>\u221e<\/span>,<\/span><\/span>+<\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/li>\n
  3. qNaN\uff08quiet\uff0c\u4e0d\u629b\u5f02\u5e38\uff09\uff0csNaN\uff08signaling\uff0c\u629b\u5f02\u5e38\uff09<\/li>\n<\/ol>\n<\/blockquote>\n

    \u2003\u2003\u201c\u6d6e\u70b9\u6570\u7684\u7f16\u7801\u201d\u5c06\u6d6e\u70b9\u6570\u636e\u7684\u8868\u793a\u6620\u5c04\u4e3a\u6bd4\u7279\u5b57\u7b26\u4e32\u3002\u201c\u7f16\u7801\u201d\u53ef\u80fd\u4f1a\u5c06\u4e00\u4e9b\u6d6e\u70b9\u6570\u636e\u6620\u5c04\u5230\u591a\u4e2a\u6bd4\u7279\u5b57\u7b26\u4e32\u3002\u5e94\u8be5\u4f7f\u7528\u591a\u4e2aNaN\u6bd4\u7279\u5b57\u7b26\u4e32\u6765\u5b58\u50a8\u56de\u987e\u6027\u8bca\u65ad\u4fe1\u606f\uff08\u89c1\u540e\u9762\u7b2c?\u8282\uff09\u3002<\/p>\n

    <\/p>\n

    1.2 Sets of floating-point data<\/h4>\n

    \u6d6e\u70b9\u6570\u636e\u96c6<\/strong><\/p>\n

    \u2003\u2003\u6709\u9650\u7684\u6d6e\u70b9\u6570\u96c6\u5408\u53ef\u4ee5\u7528\u7279\u5b9a\u7684\u683c\u5f0f\u8868\u793a\uff0c\u7531\u4ee5\u4e0b\u6574\u6570\u53c2\u6570\u51b3\u5b9a:<\/p>\n

      \n
    • b \\Large b <\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\uff1a\u57fa\u6570\uff0c2\u6216\u800510\u3002<\/li>\n
    • p \\Large p <\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\uff1a s i g n i f i c a n d significand <\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span><\/span><\/span><\/span><\/span>\uff08\u6709\u6548\u4f4d\uff09\u4e2d\u6570\u5b57\u7684\u4e2a\u6570\u3002\uff08precision\u7cbe\u5ea6\uff09<\/li>\n
    • e m a x \\Large emax <\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span>\uff1a\u6700\u5927\u6307\u6570 e e <\/span><\/span>e<\/span><\/span><\/span><\/span><\/span><\/li>\n
    • e m i n \\Large emin <\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span>\uff1a\u6700\u5c0f\u6307\u6570 e e <\/span><\/span>e<\/span><\/span><\/span><\/span><\/span>\uff0c \u5bf9\u4e8e\u6240\u6709\u683c\u5f0f\uff0c e m i n emin <\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span> \u5e94\u4e3a 1 \u2212 e m a x 1-emax <\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

      \u2003\u2003 \u5bf9\u4e8e\u6bcf\u79cd\u57fa\u7840\u683c\u5f0f\uff0c\u4ee5\u4e0a\u53c2\u6570\u7684\u503c\u90fd\u5728\u88681.2\u4e2d\u7ed9\u51fa\u4e86\u3002<\/p>\n


      \n \u88681.2 <\/font>
      \n<\/center> <\/p>\n\n\n\n\n\n\n
      <\/th>\n \u4e8c\u8fdb\u5236\u683c\u5f0f\uff08b=2\uff09<\/font><\/th>\n \u5341\u8fdb\u5236\u683c\u5f0f\uff08b=10\uff09<\/font><\/th>\n<\/tr>\n
      \u53c2\u6570<\/th>\n\u4e8c\u8fdb\u523632\u4f4d<\/th>\n\u4e8c\u8fdb\u523664\u4f4d<\/th>\n\u4e8c\u8fdb\u5236128\u4f4d<\/th>\n\u5341\u8fdb\u523664\u4f4d<\/th>\n\u5341\u8fdb\u5236128\u4f4d<\/th>\n<\/tr>\n
      p<\/font><\/th>\n24<\/th>\n53<\/th>\n113<\/th>\n16<\/th>\n34<\/th>\n<\/tr>\n
      emax<\/font><\/th>\n+127<\/th>\n+1023<\/th>\n+16383<\/th>\n+384<\/th>\n+6144<\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u2003\u2003 \u6d6e\u70b9\u6570\u636e\u8868\u793a\u5f62\u5f0f\uff1a<\/strong><\/font><\/p>\n

      \n

      ============================<\/code>\uff081\uff09============================<\/code><\/p>\n

        \n
      • \u6709\u7b26\u53f7\u548c\u975e\u96f6\u7684\u6d6e\u70b9\u6570\u683c\u5f0f\u4e3a ( \u2212 1 ) s \u00d7 b e \u00d7 m \\LARGE (-1)^{s} \\times b^e \\times m <\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>b<\/span><\/span>e<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \uff0c\u5176\u4e2d\n
          \n
        • s s <\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u662f0\u6216\u80051<\/li>\n
        • e e <\/span><\/span>e<\/span><\/span><\/span><\/span><\/span>\u662f\u4efb\u610f\u6574\u6570\uff0c e m i n \u2a7d e \u2a7d e m a x emin \\leqslant e \\leqslant emax <\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span><\/li>\n
        • m m <\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6570\u5b57\uff08\u5c0f\u6570\uff09\uff0c\u7528\u4e00\u4e2a\u6bd4\u7279\u5b57\u7b26\u4e32\u8868\u793a\uff0c\u8be5\u5b57\u7b26\u4e32\u683c\u5f0f\u5982\u4e0b\uff1a
          d 0 . d 1 d 2 . . . d p \u2212 1 d_0. d_1d_2...d_{p-1} <\/span><\/span>d<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span>d<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span>.<\/span>.<\/span>d<\/span><\/span>p<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5176\u4e2d d i d_i <\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6574\u6570\u6570\u5b57\u6ee1\u8db3 0 \u2a7d d i < b 0 \\leqslant d_i <b <\/span><\/span>0<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\uff08\u56e0\u6b64 0 \u2a7d m < b 0 \\leqslant m <b <\/span><\/span>0<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>m<\/span><\/span><<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\uff09<\/li>\n<\/ul>\n<\/li>\n
        • \u4e24\u4e2a\u65e0\u9650\u503c\uff0c + \u221e +\\infty <\/span><\/span>+<\/span>\u221e<\/span><\/span><\/span><\/span><\/span>\u548c \u2212 \u221e -\\infty <\/span><\/span>\u2212<\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/li>\n
        • \u4e24\u4e2a NaNs<\/font>\uff0cqNaN\u548csNaN<\/font><\/li>\n<\/ul>\n

          <\/p>\n

          \u5728\u4e0a\u8ff0\u63cf\u8ff0\u4e2d\uff0c\u7b26\u53f7 m m <\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>\u88ab\u89c6\u4e3a\u4e00\u79cd\u79d1\u5b66\u5f62\u5f0f\uff0c\u5c0f\u6570\u70b9\u7d27\u63a5\u5728\u7b2c\u4e00\u4e2a\u6570\u5b57\u4e4b\u540e\u3002<\/p>\n<\/blockquote>\n

          \n

          ============================<\/code>\uff082\uff09============================<\/code>
          \u4e3a\u4e86\u67d0\u4e9b\u76ee\u7684\uff0c\u628a s i g n i f i c a n d significand <\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span><\/span><\/span><\/span><\/span> \u770b\u4f5c\u4e00\u4e2a\u6574\u6570\u4e5f\u5f88\u65b9\u4fbf\uff0c\u5f53 m m <\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6574\u6570\u65f6(\u5404\u79cd\u8fdb\u5236\u7684\u6574\u6570)\uff1a<\/p>\n

            \n
          • \u6709\u7b26\u53f7\u548c\u975e\u96f6\u7684\u6d6e\u70b9\u6570\u683c\u5f0f\u4e3a ( \u2212 1 ) s \u00d7 b q \u00d7 c \\LARGE(-1)^{s} \\times b^q \\times c <\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>b<\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span> \uff0c\u5176\u4e2d\n
              \n
            • s s <\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u662f0\u6216\u80051<\/li>\n
            • q q <\/span><\/span>q<\/span><\/span><\/span><\/span><\/span>\u662f\u4efb\u610f\u6574\u6570\uff0c e m i n \u2a7d q + p \u2212 1 \u2a7d e m a x emin \\leqslant q+p-1 \\leqslant emax <\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>q<\/span><\/span>+<\/span><\/span><\/span><\/span>p<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span><\/li>\n
            • c c <\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6570\u5b57\uff0c\u7528\u4e00\u4e2a\u6bd4\u7279\u5b57\u7b26\u4e32\u8868\u793a\uff0c\u8be5\u5b57\u7b26\u4e32\u683c\u5f0f\u5982\u4e0b\uff1a
              d 0 d 1 d 2 . . . d p \u2212 1 d_0d_1d_2...d_{p-1} <\/span><\/span>d<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span>.<\/span>.<\/span>d<\/span><\/span>p<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5176\u4e2d d i d_i <\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6574\u6570\u6570\u5b57\u6ee1\u8db3 0 \u2a7d d i < b 0 \\leqslant d_i <b <\/span><\/span>0<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\uff08\u56e0\u6b64 c c <\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\u662f\u4e00\u4e2a\u6574\u6570\uff0c 0 \u2a7d c < b p 0 \\leqslant c <b^p <\/span><\/span>0<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>c<\/span><\/span><<\/span><\/span><\/span><\/span>b<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

              <\/p>\n

              \u8fd9\u79cd\u63cf\u8ff0\u628a s i g n i f i c a n d significand <\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span><\/span><\/span><\/span><\/span> \u5f53\u505a\u4e00\u4e2a\u6574\u6570 c c <\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\uff0c\u5bf9\u5e94\u7684 e x p o n e n t exponent <\/span><\/span>e<\/span>x<\/span>p<\/span>o<\/span>n<\/span>e<\/span>n<\/span>t<\/span><\/span><\/span><\/span><\/span> \u4e3a q q <\/span><\/span>q<\/span><\/span><\/span><\/span><\/span>\u3002\uff08\u5bf9\u4e8e\u6709\u9650\u6d6e\u70b9\u6570\uff0c e = q + p \u2212 1 e=q+p-1 <\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>q<\/span><\/span>+<\/span><\/span><\/span><\/span>p<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\uff0c m = c \u00d7 b 1 \u2212 p m=c\\times b^{1-p} <\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>c<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>b<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff09<\/p>\n<\/blockquote>\n

              <\/p>\n

              \u2003\u2003\u6700\u5c0f\u7684\u6b63normal<\/em><\/font>\uff08\u6b63\u89c4\u6570\uff09\u6d6e\u70b9\u6570\u662f b e m i n b^{emin} <\/span><\/span>b<\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \uff0c\u6700\u5927\u7684\u662f b e m a x \u00d7 ( b \u2212 b 1 \u2212 p ) b^{emax}\\times (b-b^{1-p}) <\/span><\/span>b<\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>b<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>b<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u3002\u5bf9\u4e8e\u8fd9\u79cd\u683c\u5f0f\u5316\u7684\u975e\u96f6\u6d6e\u70b9\u6570\uff0c\u91cf\u7ea7\u5c0f\u4e8e b e m i n b^{emin} <\/span><\/span>b<\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u88ab\u79f0\u4e3asubnormal<\/em><\/font>\uff08\u6b21\u6b63\u89c4\u6570\uff09\uff0c\u56e0\u4e3a\u5b83\u7684\u91cf\u7ea7\u5728\u96f6\u548c\u6700\u5c0f\u6b63\u89c4\u6570\u7684\u91cf\u7ea7\u4e4b\u95f4\u3002\u4ed6\u4eec\u7684\u6709\u6548\u4f4d\u6570\uff08 s i g n i f i c a n d significand <\/span><\/span>s<\/span>i<\/span>g<\/span>n<\/span>i<\/span>f<\/span>i<\/span>c<\/span>a<\/span>n<\/span>d<\/span><\/span><\/span><\/span><\/span> digits\uff09\u901a\u5e38\u6bd4 p p <\/span><\/span>p<\/span><\/span><\/span><\/span><\/span> \u8981\u5c11\u3002\u6bcf\u4e00\u4e2a\u6709\u9650\u6d6e\u70b9\u6570\u5b57\u90fd\u662f\u6700\u5c0f\u6b21\u6b63\u89c4\u6570\u7684\u6574\u6570\u500d b e m i n \u00d7 b 1 \u2212 p b^{emin}\\times b^{1-p} <\/span><\/span>b<\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>b<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

              \u2003\u2003\u5bf9\u4e8e\u503c\u4e3a0\u7684\u6d6e\u70b9\u6570\uff0c\u7b26\u53f7\u4f4d s s <\/span><\/span>s<\/span><\/span><\/span><\/span><\/span> \u63d0\u4f9b\u4e86\u989d\u5916\u7684\u4fe1\u606f\u4f4d\u3002\u5c3d\u7ba1\u6240\u6709\u683c\u5f0f\u5bf9 + 0 +0 <\/span><\/span>+<\/span>0<\/span><\/span><\/span><\/span><\/span> \u548c \u2212 0 -0 <\/span><\/span>\u2212<\/span>0<\/span><\/span><\/span><\/span><\/span> \u90fd\u6709\u4e0d\u540c\u7684\u8868\u793a\uff0c\u4f46 0 0 <\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u7684\u7b26\u53f7\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u5f88\u91cd\u8981\uff0c\u6bd4\u5982 0 0 <\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u9664\u4ee5xxx\uff0c\u4f46\u5728\u5176\u4ed6\u60c5\u51b5\u4e0b\u5219\u4e0d\u91cd\u8981(\u540e\u9762\u518d\u8bb2)\u3002\u4e8c\u8fdb\u5236\u8f6c\u6362\u683c\u5f0f\u5bf9\u4e8e + 0 +0 <\/span><\/span>+<\/span>0<\/span><\/span><\/span><\/span><\/span> \u548c \u2212 0 -0 <\/span><\/span>\u2212<\/span>0<\/span><\/span><\/span><\/span><\/span> \u53ea\u6709\u4e00\u79cd\u8868\u793a\uff0c\u4f46\u662f\u5341\u8fdb\u5236\u683c\u5f0f\u6709\u5f88\u591a\u3002\u5728\u6b64\u6807\u51c6\u4e2d\uff0c\u5f53\u7b26\u53f7\u4e0d\u91cd\u8981\u65f6\uff0c 0 0 <\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u548c \u221e \\infty <\/span><\/span>\u221e<\/span><\/span><\/span><\/span><\/span> \u4e0d\u5e26\u7b26\u53f7\u3002<\/p>\n

              <\/p>\n

              1.3 Binary interchange format encodings<\/h4>\n

              \u6d6e\u70b9\u6570\u636e\u7684\u201c\u4e8c\u8fdb\u5236\u8f6c\u6362\u683c\u5f0f\u201d\u7f16\u7801<\/strong><\/p>\n

              \u2003\u2003\u6bcf\u4e2a\u6d6e\u70b9\u6570\u53ea\u6709\u4e00\u79cd\u4e8c\u8fdb\u5236\u4ea4\u6362\u683c\u5f0f\u7684\u7f16\u7801\u3002\u4e3a\u4e86\u4f7f\u7f16\u7801\u5177\u6709\u552f\u4e00\u6027\uff0c\u5bf9\u4e8e1.2\u4e2d\u7684\u53c2\u6570\uff0c\u901a\u8fc7\u51cf\u5c0f e e <\/span><\/span>e<\/span><\/span><\/span><\/span><\/span> \u4f7f\u6709\u6548\u4f4d\uff08significand\uff09 m m <\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u6700\u5927\u5316\uff0c\u76f4\u5230 e = e m i n e=emin <\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span> \u6216 m \u2a7e 1 m\\geqslant1 <\/span><\/span>m<\/span><\/span>\u2a7e<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u5b8c\u6210\u540e\uff0c\u5982\u679c e = e m i n e=emin <\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e14 0 < m < 1 0<m<1 <\/span><\/span>0<\/span><\/span><<\/span><\/span><\/span><\/span>m<\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \uff0c\u5219\u6d6e\u70b9\u6570\u4e3a\u6b21\u6b63\u89c4\u6570\uff08subnormal\uff09\u3002\u6b21\u6b63\u89c4\u6570\uff08\u4ee5\u53ca\u96f6\uff09\u7528\u4e00\u4e2a\u8868\u7559\u7684\u504f\u7f6e\u6307\u6570\u503c\u6765\u7f16\u7801\u3002\uff08Subnormal numbers (and zero) are encoded with a reserved biased exponent value\uff09<\/p>\n

              \u2003\u2003\u6d6e\u70b9\u6570\u7684\u4e8c\u8fdb\u5236\u5f62\u5f0f\u7531 k k <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6bd4\u7279\u7684\u7f16\u7801\u8868\u793a\uff0c\u4e3b\u8981\u67093\u4e2a\u90e8\u5206\uff1a<\/p>\n

                \n
              1. 1\u4e2a\u6bd4\u7279\uff0c\u7b26\u53f7\u4f4dS<\/strong><\/li>\n
              2. w\u4e2a\u6bd4\u7279\uff0c\u504f\u7f6e\u7684\u6307\u6570\uff08biased exponent\uff09\uff0c E = e + b i a s E=e+bias <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span><\/span><\/span><\/span><\/li>\n
              3. \uff08t=p-1\uff09\u4e2a\u6bd4\u7279\uff0c\u5c3e\u90e8\u6709\u6548\u4f4d\uff08trailing significand field\uff09\u6570\u5b57\u5b57\u7b26\u4e32 T = d 1 d 2 . . . d p \u2212 1 T=d_1d_2...d_{p-1} <\/span><\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span>.<\/span>.<\/span>d<\/span><\/span>p<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \uff1b<\/li>\n<\/ol>\n

                \"\u6d6e\u70b9\u6570\u89c4\u8303\u5316\u8868\u793a_32\u4f4d\u6d6e\u70b9\u6570\u6700\u5927\u503c<\/p>\n


                \n \u56fe1.1 \u6d6e\u70b9\u6570\u7684\u7f16\u7801<\/font>
                \n<\/center> <\/p>\n

                <\/p>\n

                \u2003\u2003\u4e8c\u8fdb\u5236\u8f6c\u6362\u683c\u5f0f\u7684 k , \u2005\u200a p , \u2005\u200a t , \u2005\u200a w , \u2005\u200a b i a s k, \\; p,\\; t,\\; w,\\; bias <\/span><\/span>k<\/span>,<\/span><\/span><\/span>p<\/span>,<\/span><\/span><\/span>t<\/span>,<\/span><\/span><\/span>w<\/span>,<\/span><\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u5982\u88681.3\u6240\u793a<\/p>\n


                \n \u88681.3 \u4e8c\u8fdb\u5236\u4ea4\u6362\u683c\u5f0f\u7684\u53c2\u6570<\/font>
                \n<\/center> <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
                \u53c2\u6570<\/th>\n\u4e8c\u8fdb\u523616\u4f4d<\/th>\n\u4e8c\u8fdb\u523632\u4f4d<\/th>\n\u4e8c\u8fdb\u523664\u4f4d<\/th>\n\u4e8c\u8fdb\u5236128\u4f4d<\/th>\n\u4e8c\u8fdb\u5236 k k <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u4f4d ( k \u2a7e 128 ) (k\\geqslant128) <\/span><\/span>(<\/span>k<\/span><\/span>\u2a7e<\/span><\/span><\/span><\/span>1<\/span>2<\/span>8<\/span>)<\/span><\/span><\/span><\/span><\/span><\/th>\n<\/tr>\n<\/thead>\n
                k k <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\uff0c\u6570\u636e\u5bbd\u5ea6<\/td>\n16<\/td>\n32<\/td>\n64<\/td>\n128<\/td>\n32\u7684\u500d\u6570<\/td>\n<\/tr>\n
                p p <\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\uff0c\u7cbe\u5ea6<\/td>\n11<\/td>\n24<\/td>\n53<\/td>\n113<\/td>\n k \u2212 r o u n d ( 4 \u00d7 l o g 2 ( k ) ) + 13 k-round(4\\times log_2(k))+13 <\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>k<\/span>)<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>3<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                e m a x emax <\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span>\uff0c\u6307\u6570 e e <\/span><\/span>e<\/span><\/span><\/span><\/span><\/span>\u7684\u6700\u5927\u503c<\/td>\n15<\/td>\n127<\/td>\n1023<\/td>\n16383<\/td>\n 2 ( k \u2212 p \u2212 1 ) \u2212 1 2^{(k-p-1)}-1 <\/span><\/span>2<\/span><\/span>(<\/span>k<\/span>\u2212<\/span>p<\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                \u2013<\/td>\n\u2013<\/td>\n\u2013<\/td>\n\u2013<\/td>\n\u2013<\/td>\n\u2013<\/td>\n<\/tr>\n
                b i a s bias <\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span><\/span><\/span><\/span>\uff0c E \u2212 e E-e <\/span><\/span>E<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>e<\/span><\/span><\/span><\/span><\/span><\/td>\n15<\/td>\n127<\/td>\n1023<\/td>\n16383<\/td>\n e m a x emax <\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                \u7b26\u53f7\u4f4d<\/td>\n1<\/td>\n1<\/td>\n1<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n
                w w <\/span><\/span>w<\/span><\/span><\/span><\/span><\/span>\uff0c\u6307\u6570\u4f4d\u7684\u5bbd\u5ea6<\/td>\n5<\/td>\n8<\/td>\n11<\/td>\n15<\/td>\n r o u n d ( 4 \u00d7 l o g 2 ( k ) ) \u2212 13 round(4\\times log_2(k))-13 <\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>k<\/span>)<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>3<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                t t <\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\uff0c\u5c3e\u90e8\u6709\u6548\u4f4d\u7684\u5bbd\u5ea6<\/td>\n10<\/td>\n23<\/td>\n52<\/td>\n112<\/td>\n k \u2212 w \u2212 1 k-w-1 <\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>w<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                k k <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\uff0c\u6570\u636e\u5bbd\u5ea6<\/td>\n16<\/td>\n32<\/td>\n64<\/td>\n128<\/td>\n 1 + w + t 1+w+t <\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>w<\/span><\/span>+<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                \u8fd9\u91cc r o u n d round <\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u56db\u820d\u4e94\u5165<\/p>\n

                <\/p>\n

                \u6307\u6570\u9879 E E <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span> \u5177\u6709\u5173\u952e\u4f5c\u7528<\/strong><\/font>(\u51b3\u5b9a\u4e86\u6d6e\u70b9\u6570\u7684\u6027\u8d28\uff0c\u4ee5\u53ca\u8ba1\u7b97\u516c\u5f0f)
                \u6027\u8d28\uff1a<\/strong><\/font>
                \uff081\uff09 \u5f53 E \u2208 [ 1 , 2 w \u2212 2 ] E\\in [1,2^w-2] <\/span><\/span>E<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span>]<\/span><\/span><\/span><\/span><\/span> \u65f6\uff0c\u7528\u4e8e\u7f16\u7801\u89c4\u8303\u6570\uff08normal numbers\uff09<\/font>
                \uff082\uff09 \u5f53 E = 0 E=0 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6\uff0c\u7528\u4e8e\u7f16\u7801 \u00b1 0 \\pm0 <\/span><\/span>\u00b1<\/span>0<\/span><\/span><\/span><\/span><\/span> \u548c\u6b21\u89c4\u8303\u6570\uff08subnormal numbers\uff09<\/font>
                \uff083\uff09 \u5f53 E = 2 w \u2212 1 E = 2^w-1 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6\uff0c\u7528\u4e8e\u7f16\u7801 \u00b1 \u221e \\pm\\infty <\/span><\/span>\u00b1<\/span>\u221e<\/span><\/span><\/span><\/span><\/span> \u548c NaNs<\/font><\/font><\/p>\n

                \u8ba1\u7b97\u516c\u5f0f\uff1a<\/strong><\/font>
                \uff08 r r <\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u662f\u6d6e\u70b9\u6570\u636e\u7684\u8868\u793a\u5f62\u5f0f \uff0c v v <\/span><\/span>v<\/span><\/span><\/span><\/span><\/span> \u662f\u6d6e\u70b9\u6570\u636e\u4ee3\u8868\u7684\u503c\uff09\uff1a<\/p>\n

                \uff08a\uff09<\/strong> \u5982\u679c E = 2 w \u2212 1 E=2^w-1 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\uff0c\u5e76\u4e14 T \u2260 0 T\\neq0 <\/span><\/span>T<\/span><\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>
                \u5219 r r <\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f qNaN<\/font> \u6216\u8005 sNaN<\/font>\uff0c v v <\/span><\/span>v<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f NaN<\/font>\uff08\u65e0\u8bba\u7b26\u53f7\u4f4d\uff09<\/p>\n

                \uff08b\uff09<\/strong> \u5982\u679c E = 2 w \u2212 1 E=2^w-1 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\uff0c\u5e76\u4e14 T = 0 T=0 <\/span><\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>
                \u5219 r r <\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u548c v v <\/span><\/span>v<\/span><\/span><\/span><\/span><\/span> \u90fd\u662f ( \u2212 1 ) S \u00d7 ( + \u221e ) \\large(-1)^S\\times(+\\infty) <\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>+<\/span>\u221e<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \uff08c\uff09<\/strong> \u5982\u679c 1 \u2a7d E \u2a7d 2 w \u2212 2 1\\leqslant E \\leqslant2^w-2 <\/span><\/span>1<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>E<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u2003 \uff08\u8fd9\u79cd\u60c5\u51b5\u5c45\u591a\uff09<\/strong><\/font>
                \u5219 r r <\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f ( S , ( E \u2212 b i a s ) , ( 1 + 2 1 \u2212 p \u00d7 T ) ) \\large(S, (E-bias),(1+2^{1-p}\\times T)) <\/span><\/span>(<\/span>S<\/span>,<\/span><\/span>(<\/span>E<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span>)<\/span>,<\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>T<\/span>)<\/span>)<\/span><\/span><\/span><\/span><\/span>\uff0c v = ( \u2212 1 ) S \u00d7 2 E \u2212 b i a s \u00d7 ( 1 + 2 1 \u2212 p \u00d7 T ) \\large v=(-1)^S\\times 2^{E-bias}\\times(1+2^{1-p}\\times T) <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>E<\/span>\u2212<\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>T<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \uff08d\uff09<\/strong> \u5982\u679c E = 0 E=0 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\uff0c\u5e76\u4e14 T \u2260 0 T\\neq0 <\/span><\/span>T<\/span><\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>
                \u5219 r r <\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f ( S , e m i n , ( 0 + 2 1 \u2212 p \u00d7 T ) ) \\large(S, emin,(0+2^{1-p}\\times T)) <\/span><\/span>(<\/span>S<\/span>,<\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span>,<\/span><\/span>(<\/span>0<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>T<\/span>)<\/span>)<\/span><\/span><\/span><\/span><\/span>\uff0c v = ( \u2212 1 ) S \u00d7 2 e m i n \u00d7 ( 0 + 2 1 \u2212 p \u00d7 T ) \\large v=(-1)^S\\times 2^{emin}\\times(0+2^{1-p}\\times T) <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>0<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>T<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \uff08e\uff09<\/strong> \u5982\u679c E = 0 E=0 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\uff0c\u5e76\u4e14 T = 0 T=0 <\/span><\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>
                \u5219 r r <\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f ( S , e m i n , 0 ) \\large(S,emin,0) <\/span><\/span>(<\/span>S<\/span>,<\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span>,<\/span><\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span>\uff0c v = ( \u2212 1 ) S \u00d7 ( + 0 ) \\large v=(-1)^S\\times (+0) <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>+<\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/p>\n

                \u6ce8\u610f\uff0c<\/strong> \u5f53 k k <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u662f64\u6216\u4ee5\u4e0a\uff0832\u7684\u500d\u6570\uff09\u65f6\uff0c\u5404\u53c2\u6570\u6ee1\u8db3\u4e0b\u5217\u516c\u5f0f\uff1a
                k = 1 + w + t = w + p = 32 \u00d7 c e i l i n g ( ( p + r o u n d ( 4 \u00d7 l o g 2 ( p + r o u n d ( 4 \u00d7 l o g 2 ( p ) ) \u2212 13 ) ) \u2212 13 ) \/ 32 ) k=1+w+t=w+p=32\\times ceiling((p+round(4\\times log_2(p+round(4\\times log_2(p))-13))-13)\/32) <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>w<\/span><\/span>+<\/span><\/span><\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>w<\/span><\/span>+<\/span><\/span><\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>c<\/span>e<\/span>i<\/span>l<\/span>i<\/span>n<\/span>g<\/span>(<\/span>(<\/span>p<\/span><\/span>+<\/span><\/span><\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>p<\/span><\/span>+<\/span><\/span><\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>p<\/span>)<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>3<\/span>)<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>3<\/span>)<\/span>\/<\/span>3<\/span>2<\/span>)<\/span><\/span><\/span><\/span><\/span>
                w = k \u2212 t \u2212 1 = k \u2212 p = r o u n d ( 4 \u00d7 l o g 2 ( k ) ) \u2212 13 w=k-t-1=k-p=round(4\\times log_2(k))-13 <\/span><\/span>w<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>t<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>k<\/span>)<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>3<\/span><\/span><\/span><\/span><\/span>
                t = k \u2212 w \u2212 1 = p \u2212 1 = k \u2212 r o u n d ( 4 \u00d7 l o g 2 ( k ) ) + 12 t=k-w-1=p-1=k-round(4\\times log_2(k))+12 <\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>w<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>p<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>k<\/span>)<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>2<\/span><\/span><\/span><\/span><\/span>
                p = k \u2212 w = t + 1 = k \u2212 r o u n d ( 4 \u00d7 l o g 2 ( k ) ) + 13 p=k-w=t+1=k-round(4\\times log_2(k))+13 <\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>w<\/span><\/span>=<\/span><\/span><\/span><\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>r<\/span>o<\/span>u<\/span>n<\/span>d<\/span>(<\/span>4<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>l<\/span>o<\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>k<\/span>)<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>3<\/span><\/span><\/span><\/span><\/span>
                e m a x = b i a s = 2 ( w \u2212 1 ) \u2212 1 emax=bias=2^{(w-1)}-1 <\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>(<\/span>w<\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>
                e m i n = 1 \u2212 e m a x = 2 \u2212 2 ( w \u2212 1 ) emin=1-emax=2-2^{(w-1)} <\/span><\/span>e<\/span>m<\/span>i<\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>e<\/span>m<\/span>a<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span>(<\/span>w<\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/p>\n

                1.4 Decimal interchange format encodings<\/h4>\n

                \u5341\u8fdb\u5236\u8f6c\u6362\u683c\u5f0f\u7f16\u7801<\/strong><\/p>\n

                \u6709\u7a7a\u518d\u8bf4<\/strong><\/font><\/p>\n

                <\/p>\n

                1.5 Extended and extendable precisions<\/h4>\n

                \u6269\u5c55\u7684\u548c\u53ef\u6269\u5c55\u7684\u7cbe\u5ea6<\/strong><\/p>\n

                \u6709\u7a7a\u518d\u8bf4<\/strong><\/font><\/p>\n

                <\/p>\n

                2. \u4e3e\u4e2a\u4f8b\u5b50<\/h3>\n

                \u6709\u51e0\u4e2a\u683c\u5f0f\u8f6c\u6362\u7684\u7f51\u7ad9\u53ef\u4ee5\u53c2\u8003
                (1): https:\/\/www.h-schmidt.net\/FloatConverter\/IEEE754.html
                (2): http:\/\/www.styb.cn\/cms\/ieee_754.php
                (3): http:\/\/weitz.de\/ieee\/<\/p>\n

                2.1 \u7f16\u7801\u7684\u6d6e\u70b9\u6570\u8f6c\u5341\u8fdb\u5236\u5c0f\u6570<\/h4>\n

                \u2003\u2003\u5047\u8bbe\u5185\u5b58\u4e2d\u5b58\u4e86\u4e00\u4e2a32\u4f4d\u6d6e\u70b9\u6570\uff0c\u5341\u516d\u8fdb\u5236\uff1a0x<\/code>\uff0c\u4e8c\u8fdb\u5236\uff1a0<\/strong><\/strong><\/font>000000000000<\/strong><\/font>
                \u2003\u2003\u56fe\u793a\u5982\u4e0b\uff1a<\/p>\n

                \"\u6d6e\u70b9\u6570\u89c4\u8303\u5316\u8868\u793a_32\u4f4d\u6d6e\u70b9\u6570\u6700\u5927\u503c
                \u6839\u636e\u4e0a\u9762\u7684\u88681.3<\/code>\u53ef\u5f9732\u4f4d\u4e8c\u8fdb\u5236\u6d6e\u70b9\u6570\u7684\u53c2\u6570\uff1a
                p = 24 p=24 <\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>4<\/span><\/span><\/span><\/span><\/span>\uff0c b i a s = 127 bias=127 <\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>2<\/span>7<\/span><\/span><\/span><\/span><\/span>\uff0c w = 8 w=8 <\/span><\/span>w<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\uff0c t = 23 t=23 <\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>3<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u8fd9\u91cc E E <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span>\u662f\u4e8c\u8fdb\u5236\u7684<\/code>\uff0c\u5373\u5341\u8fdb\u5236\u7684128\uff0c\u6ee1\u8db3 1 \u2a7d E \u2a7d 2 w \u2212 2 1\\leqslant E \\leqslant2^w-2 <\/span><\/span>1<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>E<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\uff0c\u53ef\u4ee5\u5957\u516c\u5f0f(c)<\/code>\uff1a v = ( \u2212 1 ) S \u00d7 2 E \u2212 b i a s \u00d7 ( 1 + 2 1 \u2212 p \u00d7 T ) \\large v=(-1)^S\\times 2^{E-bias}\\times(1+2^{1-p}\\times T) <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>E<\/span>\u2212<\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>T<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5373 v = ( \u2212 1 ) 0 \u00d7 2 128 \u2212 127 \u00d7 ( 1 + 2 1 \u2212 24 \u00d7 000000000000 ) \\large v=(-1)^0\\times 2^{128-127}\\times(1+2^{1-24}\\times 000000000000) <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>2<\/span>8<\/span>\u2212<\/span>1<\/span>2<\/span>7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>2<\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>1<\/span>0<\/span>1<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u7531\u4e8e\u8fd9\u91cc\u662f\u4e8c\u8fdb\u5236\uff0c\u4e58\u4ee5 2 n 2^n <\/span><\/span>2<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5c31\u662f\u5c0f\u6570\u70b9\u5411\u53f3\u79fb\u52a8 n n <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u4f4d\uff0c\u82e5 n n <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u662f\u8d1f\u6570\u5219\u5411\u5de6\u79fb\u52a8 n n <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u4f4d\u3002<\/p>\n

                \u4e8e\u662f v = 1 \u00d7 2 \u00d7 ( 1 + 0.101 ) = 1 \u00d7 2 \u00d7 ( 1.1101 ) = 11.101 \\large v=1 \\times 2 \\times(1+0.101)=1 \\times 2 \\times(1.1101)=11.101 <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0<\/span>.<\/span>1<\/span>0<\/span>1<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span>.<\/span>1<\/span>1<\/span>0<\/span>1<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>1<\/span>.<\/span>1<\/span>0<\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u518d\u8f6c\u4e3a\u5341\u8fdb\u5236\uff1a v = 1 \u22c5 2 1 + 1 \u22c5 2 0 + 1 \u22c5 2 \u2212 1 + 0 \u22c5 2 \u2212 2 + 1 \u22c5 2 \u2212 3 = 3.625 \\large v=1\\cdot2^1+1\\cdot2^0+1\\cdot2^{-1}+0\\cdot2^{-2}+1\\cdot2^{-3}=3.625 <\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>0<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>\u2212<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span>.<\/span>6<\/span>2<\/span>5<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u7ed3\u679c\u662f3.625<\/strong><\/p>\n

                <\/p>\n

                2.2 \u5341\u8fdb\u5236\u5c0f\u6570\u8f6c\u4e3a\u4e8c\u8fdb\u5236\u6d6e\u70b9\u6570\u7f16\u7801<\/h4>\n

                \u73b0\u5728\u6709\u4e00\u4e2a\u5341\u8fdb\u5236\u7684\u5c0f\u657013.78125<\/code> \uff0c\u8981\u8f6c\u621032\u4f4d\u7684\u4e8c\u8fdb\u5236\u6d6e\u70b9\u6570\u7f16\u7801\u3002
                \u5148\u770b\u6574\u6570\u90e8\u5206\uff1a<\/strong><\/p>\n

                13 \u00f7 2 = 6 13\\div 2 = 6 <\/span><\/span>1<\/span>3<\/span><\/span>\u00f7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>6<\/span><\/span><\/span><\/span><\/span> \u4f59 1<\/strong><\/font>
                6 \u00f7 2 = 3 6\\div 2 = 3 <\/span><\/span>6<\/span><\/span>\u00f7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u4f59 0<\/strong><\/font>
                3 \u00f7 2 = 1 3\\div 2 = 1 <\/span><\/span>3<\/span><\/span>\u00f7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4f59 1<\/strong><\/font>
                1 \u00f7 2 = 0 1\\div 2 = 0 <\/span><\/span>1<\/span><\/span>\u00f7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4f59 1<\/strong><\/font><\/p>\n

                \u56e0\u6b64\u6574\u6570\u90e8\u5206\u4e8c\u8fdb\u5236\u4e3a1101<\/code><\/p>\n

                <\/p>\n

                \u518d\u770b\u5c0f\u6570\u90e8\u5206\uff1a<\/strong>
                0.78125 \u00d7 2 = 1.5625 0.78125 \\times 2 = 1.5625 <\/span><\/span>0<\/span>.<\/span>7<\/span>8<\/span>1<\/span>2<\/span>5<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>.<\/span>5<\/span>6<\/span>2<\/span>5<\/span><\/span><\/span><\/span><\/span>\uff0c\u6574\u6570\u90e8\u52061<\/strong><\/font>
                0.5625 \u00d7 2 = 1.125 0.5625 \\times 2 = 1.125 <\/span><\/span>0<\/span>.<\/span>5<\/span>6<\/span>2<\/span>5<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>.<\/span>1<\/span>2<\/span>5<\/span><\/span><\/span><\/span><\/span>\uff0c\u6574\u6570\u90e8\u52061<\/strong><\/font>
                0.125 \u00d7 2 = 0.25 0.125 \\times 2 = 0.25 <\/span><\/span>0<\/span>.<\/span>1<\/span>2<\/span>5<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>.<\/span>2<\/span>5<\/span><\/span><\/span><\/span><\/span>\uff0c\u6574\u6570\u90e8\u52060<\/strong><\/font>
                0.25 \u00d7 2 = 0.5 0.25 \\times 2 = 0.5 <\/span><\/span>0<\/span>.<\/span>2<\/span>5<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>.<\/span>5<\/span><\/span><\/span><\/span><\/span>\uff0c\u6574\u6570\u90e8\u52060<\/strong><\/font>
                0.5 \u00d7 2 = 1 0.5 \\times 2 = 1 <\/span><\/span>0<\/span>.<\/span>5<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\uff0c\u6574\u6570\u90e8\u52061<\/strong><\/font><\/p>\n

                \u56e0\u6b64\u5c0f\u6570\u90e8\u5206\u4e3a11001<\/code>\uff0c\u6240\u4ee513.78125<\/code>\u7684\u4e8c\u8fdb\u5236\u8868\u793a\u662f1101.11001<\/code><\/p>\n

                <\/p>\n

                \u518d\u770b\u683c\u5f0f\u8f6c\u6362\uff1a<\/strong><\/p>\n

                \u6839\u636e\u6d6e\u70b9\u6570\u8868\u793a\u5f62\u5f0f(1)<\/code> \uff1a ( \u2212 1 ) s \u00d7 b e \u00d7 m (-1)^{s} \\times b^e \\times m <\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>b<\/span><\/span>e<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>\uff0c\u628a\u4e8c\u8fdb\u5236\u5c0f\u6570\u7528\u8be5\u5f62\u5f0f\u8868\u793a\uff1a<\/p>\n

                1101.11001 = ( \u2212 1 ) 0 \u00d7 2 3 \u00d7 1. 1101.11001 = (-1)^0\\times2^3\\times1. <\/span><\/span>1<\/span>1<\/span>0<\/span>1<\/span>.<\/span>1<\/span>1<\/span>0<\/span>0<\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>.<\/span>1<\/span>0<\/span>1<\/span>1<\/span>1<\/span>0<\/span>0<\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5f97\uff1a S = S= <\/span><\/span>S<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span> 0<\/code>\uff0c e = 3 e=3 <\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>\uff0c m = 1. m=1. <\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>.<\/span>1<\/span>0<\/span>1<\/span>1<\/span>1<\/span>0<\/span>0<\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u67e5\u88681.3<\/code>\u5f9732\u4f4d\u7684\u6d6e\u70b9\u6570\u7684\u53c2\u6570\uff1a p = 24 p=24 <\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>4<\/span><\/span><\/span><\/span><\/span>\uff0c b i a s = 127 bias=127 <\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>2<\/span>7<\/span><\/span><\/span><\/span><\/span>\uff0c w = 8 w=8 <\/span><\/span>w<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\uff0c p = 24 p=24 <\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>4<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u7531 b i a s = E \u2212 e bias=E-e <\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>e<\/span><\/span><\/span><\/span><\/span> \u5f97\uff1a E = b i a s + e = 127 + 3 = 130 E = bias+e=127+3=130 <\/span><\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span>+<\/span><\/span><\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>2<\/span>7<\/span><\/span>+<\/span><\/span><\/span><\/span>3<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>3<\/span>0<\/span><\/span><\/span><\/span><\/span>\uff0c E E <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span> \u7684\u4e8c\u8fdb\u5236\u503c\u4e3a\uff1a<\/code><\/p>\n

                \u7531\u4e8e E E <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span> \u7b26\u5408 1 \u2a7d E \u2a7d 2 w \u2212 2 1\\leqslant E \\leqslant2^w-2 <\/span><\/span>1<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>E<\/span><\/span>\u2a7d<\/span><\/span><\/span><\/span>2<\/span><\/span>w<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \uff0c\u53ef\u4ee5\u5957\u516c\u5f0f(c)<\/code>\uff1a<\/p>\n

                1101.11001 = ( \u2212 1 ) S \u00d7 2 E \u2212 b i a s \u00d7 ( 1 + 2 1 \u2212 p \u00d7 T ) 1101.11001=(-1)^S\\times 2^{E-bias}\\times(1+2^{1-p}\\times T) <\/span><\/span>1<\/span>1<\/span>0<\/span>1<\/span>.<\/span>1<\/span>1<\/span>0<\/span>0<\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>E<\/span>\u2212<\/span>b<\/span>i<\/span>a<\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>T<\/span>)<\/span><\/span><\/span><\/span><\/span>
                = ( \u2212 1 ) 0 \u00d7 2 130 \u2212 127 \u00d7 ( 1 + 2 1 \u2212 24 \u00d7 000000000000 ) =(-1)^0\\times 2^{130-127}\\times(1+2^{1-24}\\times 000000000000) <\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>3<\/span>0<\/span>\u2212<\/span>1<\/span>2<\/span>7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span>1<\/span>\u2212<\/span>2<\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span>1<\/span>1<\/span>1<\/span>0<\/span>0<\/span>1<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u6240\u4ee5 T = T= <\/span><\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span> 000000000000<\/code><\/p>\n

                S S <\/span><\/span>S<\/span><\/span><\/span><\/span><\/span>\u3001 E E <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span>\u3001 T T <\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u90fd\u7b97\u51fa\u6765\u4e86\uff0c\u7531\u56fe1.1<\/code>\u5f9732\u4f4d\u4e8c\u8fdb\u5236\u7ed3\u679c<\/strong>\uff1a0<\/strong><\/strong><\/font>000000000000<\/strong><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"\u6d6e\u70b9\u6570\u89c4\u8303\u5316\u8868\u793a_32\u4f4d\u6d6e\u70b9\u6570\u6700\u5927\u503c\u2003\u2003\u672c\u6587\u4e3b\u8981\u53c2\u8003\u300aIEEEStandardforFloating-PointArithmetic\u300b1.Floating-pointformats\u6d6e\u70b9...","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/8141"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=8141"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/8141\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=8141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=8141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=8141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}