銆銆鍦↖EEE鏍囧噯754涔嬪墠錛屼笟鐣屽茍娌℃湁涓涓粺涓鐨勬誕鐐規暟鏍囧噯錛岀浉鍙嶏紝寰堝璁＄畻鏈哄埗閫犲晢閮借璁¤嚜宸辯殑嫻偣鏁拌鍒欙紝浠ュ強榪愮畻緇嗚妭銆傞偅鏃訛紝瀹炵幇鐨勯熷害鍜岀畝鏄撴ф瘮鏁板瓧鐨勭簿紜ф洿鍙楅噸瑙嗐?br>銆銆鐩村埌1985騫碔ntel鎵撶畻涓哄叾鐨?086寰鐞嗗櫒寮曡繘涓縐嶆誕鐐規暟鍗忓鐞嗗櫒鐨勬椂鍊欙紝鑱槑鍦版剰璇嗗埌錛屼綔涓鴻璁¤姱鐗囪呯殑鐢靛瓙宸ョ▼甯堝拰鍥轟綋鐗╃悊瀛﹀浠紝涔熻騫朵笉鑳介氳繃鏁板煎垎鏋愭潵閫夋嫨鏈鍚堢悊鐨勬誕鐐規暟浜岃繘鍒舵牸寮忋備簬鏄疘ntel鍦ㄨ鍔犲窞澶у浼厠鍒╁垎鏍＄殑 WilliamKahan鏁欐巿鈹鈹鏈浼樼鐨勬暟鍊煎垎鏋愬涔嬩竴鏉ヤ負8087 FPU璁捐嫻偣鏁版牸寮?鑰岃繖涓浼欏張鎵炬潵涓や釜涓撳鏉ュ崗鍔╀粬錛屼簬鏄氨鏈変簡KCS緇勫悎錛圞ahn, Coonan, andStone錛夈傘浠栦滑鍏卞悓瀹屾垚浜咺ntel鐨勬誕鐐規暟鏍煎紡璁捐錛岃屼笖瀹屾垚鍦板姝ゅ嚭鑹詫紝浠ヨ嚧浜嶪EEE緇勭粐鍐沖畾閲囩敤涓涓潪甯告帴榪慘CS鐨勬柟妗堜綔涓篒EEE鐨勬爣鍑嗘誕鐐規牸寮忋傜洰鍓嶏紝鍑犱箮鎵鏈夎綆楁満閮芥敮鎸佽鏍囧噯錛屽ぇ澶ф敼鍠勪簡縐戝搴旂敤紼嬪簭鐨勫彲縐繪鎬с?br>
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銆銆浠庤〃闈笂鐪嬶紝嫻偣鏁頒篃鏄竴涓?鍜?鏋勬垚鐨勪綅搴忓垪(bit sequence)錛屽茍涓嶆槸涓夊ご鍏噦鐨勬墿錛屾洿涓嶄細鍜漢銆傜劧鑰孖EEE鏍囧噯浠庨昏緫涓婄敤涓夊厓緇剓S,E,M}琛ㄧず涓涓暟N,濡備笅鍥炬墍紺猴細
銆銆N鐨勫疄闄呭糿鐢變笅鍒楀紡瀛愯〃紺猴細
鍏朵腑錛?br>銆銆鈽?n,s,e,m鍒嗗埆涓篘,S,E,M瀵瑰簲鐨勫疄闄呮暟鍊?鑰孨,S,E,M浠呬粎鏄竴涓蹭簩榪涘埗浣嶃?br>銆銆鈽?S(sign)琛ㄧずN鐨勭鍙蜂綅銆傚搴斿約婊¤凍錛歯>0鏃訛紝s=0; n<0鏃訛紝s=1銆?br>銆銆鈽?E(exponent)琛ㄧずN鐨勬寚鏁頒綅錛屼綅浜嶴鍜孧涔嬮棿鐨勮嫢騫蹭綅銆傚搴斿糴鍊間篃鍙鍙礋銆?br>銆銆鈽?M(mantissa)琛ㄧずN鐨勫熬鏁頒綅錛屾伆濂斤紝瀹冧綅浜嶯鏈熬銆侻涔熷彨鏈夋晥鏁板瓧浣嶏紙sinificand錛夈佺郴鏁頒綅錛坈oefficient錛? 鐢氳嚦琚О浣?#8220;灝忔暟”銆?br>
涓夈佹誕鐐規暟鏍煎紡
銆銆IEEE鏍囧噯754瑙勫畾浜嗕笁縐嶆誕鐐規暟鏍煎紡錛氬崟綺懼害銆佸弻綺懼害銆佹墿灞曠簿搴︺傚墠涓よ呮濂藉搴?span class=t_tag onclick=tagshow(event) href="tag.php?name=C%E8%AF%AD%E8%A8%80">C璇█閲屽ご鐨刦loat銆乨ouble鎴栬匜ORTRAN閲屽ご鐨剅eal銆乨ouble綺懼害綾誨瀷銆傞檺浜庣瘒騫咃紝鏈枃浠呬粙緇嶅崟綺懼害銆佸弻綺懼害嫻偣鏍煎紡銆?br>銆銆鈽?鍗曠簿搴?N鍏?2浣嶏紝鍏朵腑S鍗?浣嶏紝E鍗?浣嶏紝M鍗?3浣嶃?img id=img_0.34765354359280337 alt="" src="http://www.cublog.cn/u/20985/photo/060622140125.png" width=430 height=157>
銆銆鈽?鍙岀簿搴?N鍏?4浣嶏紝鍏朵腑S鍗?浣嶏紝E鍗?1浣嶏紝M鍗?2浣嶃?br>
鍊煎緱娉ㄦ剰鐨勬槸錛孧铏界劧鏄?3浣嶆垨鑰?2浣嶏紝浣嗗畠浠彧鏄〃紺哄皬鏁扮偣涔嬪悗鐨勪簩榪涘埗浣嶆暟錛屼篃灝辨槸璇達紝鍋囧畾M涓?#8220;010110011...”,鍦ㄤ簩榪涘埗鏁板間笂鍏跺疄鏄?#8220;.010110011...”銆傝屼簨瀹炰笂錛屾爣鍑嗚瀹氬皬鏁扮偣宸﹁竟榪樻湁涓涓殣鍚綅錛岃繖涓殣鍚綅閫氬父錛屽摝涓嶏紝搴旇璇寸粷澶у鏁版儏鍐典笅鏄?錛岄偅浠涔堟儏鍐典笅鏄?鍛紵絳旀鏄疦瀵瑰簲鐨刵闈炲父灝忕殑鏃跺欙紝姣斿灝忎簬2^(-126)(32浣嶅崟綺懼害嫻偣鏁?銆備笉瑕佸洶鎯戞庝箞璁＄畻鍑烘潵鐨勶紝鐪嬪埌鍚庨潰浣犲氨浼氭槑鐧姐傛諱箣錛岄殣鍚綅綆楁槸璧氭潵浜嗕竴浣嶇簿搴?浜庢槸M瀵瑰簲鐨刴鏈鍚庣粨鏋滃彲鑳芥槸"m=1.010110011...”鎴栬?#8220;m=0.010110011...”
鍥涖佽綆梕銆乵
銆銆棣栧厛灝嗘彁鍒頒護鍒濆鑰?/span>澶寸柤鐨?#8220;瑙勬牸鍖?normalized)”銆?#8220;闈炶鏍煎寲(denormalized)”銆傚櫌錛屽叾瀹炲茍娌℃湁榪欎箞闅劇殑錛岃窡鎴戞潵錛佹帉鎻″畠浠ュ悗浣犱細鍙戠幇涓鍒囬兘寰堜紭闆?鏇寸編濡欑殑鏄紝瑙勬牸鍖栥侀潪瑙勬牸鍖栨湰韜殑姒傚康鍑犱箮涓嶆庝箞閲嶈銆傝鐗㈣榪欏彞璇濓細瑙勬牸鍖栦笌鍚﹀叏鐪嬫寚鏁癊錛?/font>
銆銆涓嬮潰鍒嗕笁縐嶆儏鍐佃璁篍錛屽茍鍒嗗埆璁＄畻e鍜宮:
銆銆
銆銆1銆佽鏍煎寲錛氬綋E鐨勪簩榪涘埗浣嶄笉鍏ㄤ負0,涔熶笉鍏ㄤ負1鏃訛紝N涓鴻鏍煎寲褰㈠紡銆?/font>姝ゆ椂e琚В閲婁負琛ㄧず鍋忕疆錛坆iased錛夊艦寮忕殑鏁存暟,e鍊艱綆楀叕寮忓涓嬪浘鎵紺猴細
銆銆
銆銆2銆侀潪瑙勬牸鍖栵細褰揈鐨勪簩榪涘埗浣嶅叏閮ㄤ負0鏃訛紝N涓洪潪瑙勬牸鍖栧艦寮忋?/font>姝ゆ椂e錛宮鐨勮綆楅兘闈炲父綆鍗曘?br>
銆銆3銆佺壒孌婃暟鍊鹼細 褰揈鐨勪簩榪涘埗浣嶅叏涓?鏃朵負鐗規畩鏁板箋?/font>姝ゆ椂錛岃嫢M鐨勪簩榪涘埗浣嶅叏涓?錛屽垯n琛ㄧず鏃犵┓澶э紝鑻涓?鍒欎負璐熸棤絀峰ぇ錛岃嫢S涓?鍒欎負姝ｆ棤絀峰ぇ; 鑻鐨勪簩榪涘埗浣嶄笉鍏ㄤ負0鏃訛紝琛ㄧずNaN(Not a Number)錛岃〃紺鴻繖涓嶆槸涓涓悎娉曞疄鏁版垨鏃犵┓錛屾垨鑰呰鏁版湭緇忓垵濮嬪寲銆?br>銆銆
浜斻佽寖渚?/font>
銆銆浠旂粏鐮旇絎洓鐐瑰悗錛屽啀鍥炲繂涓涓?font color=#0000ff>鏂囩珷寮澶磋綆梟鐨勫叕寮?/font>錛屼綘搴旇鍐欏嚭涓涓誕鐐圭紪鐮佺殑瀹為檯鍊糿浜嗗惂錛熻繕涓嶈兘鍚楋紵涓嶆ワ紝鎴戝厛緇欎綘紺鴻寖涓涓嬨傛垜浠亣瀹歂鏄竴涓?浣嶆誕鐐規暟錛屽叾涓紝S鍗?浣嶏紝E鍗?浣嶏紝M鍗?浣嶃備笅闈㈣繖寮犺〃緗楀垪浜哊鍙兘鐨勬鏁板艦寮忥紝涔熷寘鍚簡e銆乵絳夊鹼紝璇蜂綘瀵圭収鐫榪欏紶琛紝閲嶆俯涓涓嬬鍥涚偣錛屼綘浼氭參鎱㈡槑鐧界殑銆傝瀹炲湪鐨勶紝榪欏紶琛ㄨ姳浜嗘垜涓嶅皯鍔熷か鍛?騫稿ソTeX鐢昏〃鏍艱繕綆楃渷浜嬶紒銆
銆銆
銆銆鈽?鐪?N 鍒楋紝浠庝笂鍒頒笅錛屼簩榪涘埗浣嶈〃紺烘槸鍧囧寑閫掑鐨勶紝涓斿閲忛兘鏄竴涓渶灝忎簩榪涘埗浣嶃傝繖涓嶆槸鍋剁劧錛屾鏄閥濡欒璁＄殑緇撴灉銆傝瀵熸渶澶х殑闈炶鏍兼暟錛屽彂鐜版伆濂藉氨鏄疢鍏ㄤ負1, E鍏ㄤ負0鐨勬儏鍐點備簬鏄垜浠眰鍑烘渶澶х殑闈炶鏍兼暟涓猴細
銆銆鈽?鐪?m 鍒楋紝瑙勬牸鍖栨暟閮芥槸 1+ x 鐨勫艦寮忥紝榪欎釜1姝ｆ槸闅愬惈浣?; 鑰岄潪瑙勬牸鍖栨暟闅愬惈浣嶄負0, 鎵浠ユ病鏈?"1+" 銆?br>銆銆鈽?鐪?n 鍒楋紝闈炶鏍煎寲鏁頒粠涓婂埌涓嬬殑澧為噺閮芥槸 1/512,涓旇繃娓″埌瑙勬牸鍖栨暟鏃訛紝澧為噺鏄鉤婊戠殑錛屼緷鏃ф槸1/512銆傝繖姝ｆ槸闈炶鏍煎寲鏁頒腑e絳変簬(1-bias)鑰屼笉鏄?-bias)鐨勭紭鏁咃紝涔熸槸宸у璁捐鐨勭粨鏋溿傚啀緇х畫寰涓嬬湅錛屽彂鐜板閲忓奸愭笎澧炲ぇ銆傚彲瑙侊紝嫻偣鏁扮殑鍙栧艱寖鍥翠笉鏄潎鍖鐨勩?br>銆銆
鍏佸疄鎴?/font>
銆銆鎴戜滑鐢ㄤ竴灝忔姹囩紪鏉ユ祴璇曚竴涓嬶紝嫻偣鏁板湪鍐呭瓨涓槸濡備綍琛ㄧず鐨勩傛祴璇?span class=t_tag onclick=tagshow(event) href="tag.php?name=%E7%8E%AF%E5%A2%83">鐜錛?GentooLinux2006.0/GNU assembler version 2.16.1/GNU gdb 6.4/AMD XP1600+銆?濡備笅鎵紺?br>浠ｇ爜:
~/coding/assemble $ gdb float
GNU gdb 6.4
Copyright 2005 Free Software Foundation, Inc.
GDB is free software, covered by the GNU General Public License, and you are
welcome to change it and/or distribute copies of it under certain conditions.
Type "show copying" to see the conditions.
There is absolutely no warranty for GDB. Type "show warranty" for details.
This GDB was configured as "i686-pc-linux-gnu"...Using host libthread_db library "/lib/libthread_db.so.1".
(gdb) list
1 .section .data
2 f1:
3 .float 5
4 f2:
5 .float 0.1
6 .section .text
7 .global _start
8 _start:
9 nop
10
(gdb) x/f &f1
0x80490a4 <f1>: 5
(gdb) x/xw &f1
0x80490a4 <f1>: 0x40a00000
(gdb) x/f &f2
0x80490a8 <f2>: 0.100000001
(gdb) x/xw &f2
0x80490a8 <f2>: 0x3dcccccd
(gdb)
銆銆浠庝笂闈㈢殑gdb鍛戒護緇撴灉鍙互鐪嬪嚭錛屾誕鐐規暟5琚〃紺轟負 0x40a00000錛屼簩榪涘埗褰㈠紡涓? 0100 0000 1010 0000 ... 0000 0000)銆傜孩鑹叉暟瀛椾負E錛屽彲浠ョ湅鍑簗E|=129>0, 鍒檈=129-bias=129-127=2 錛?钃濊壊鏁板瓧涓篗,涓攟E|>0錛岃鏄庢槸瑙勬牸鍖栨暟錛屽垯m=|1.M|=|1.01000..000|=1.25 ; 鐢眓鐨勮綆楀叕寮忓彲浠ユ眰寰?n=(-1)^0 *1.25 * 2^2 = 5錛?緇撴灉琚?span class=t_tag onclick=tagshow(event) href="tag.php?name=%E9%AA%8C%E8%AF%81">楠岃瘉浜嗐?
銆銆鍚屾牱錛屼綘涔熷彲浠ラ獙璇佷竴涓嬪崄榪涘埗嫻偣鏁?.1鐨勪簩榪涘埗褰㈠紡鏄惁姝ｇ‘錛屼綘浼氬彂鐜幫紝0.1涓嶈兘琛ㄧず涓烘湁闄愪釜浜岃繘鍒朵綅錛屽洜姝ゅ湪鍐呭瓨涓殑琛ㄧず鏄垗鍏?rounding)浠ュ悗鐨勭粨鏋滐紝鍗?0x3dcccccd, 鍗佽繘鍒朵負0.100000001錛?璇樊0.000000001鐢辨浜х敓浜嗐?br>
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