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zai C/C++ suan fa she ji zhong shi yong ren yi wei kuan

2008-06-01 02:08:49 编辑來源:互联网 评论
 
 
 
本文为【在C/C++算法设计中使用任意位宽】的拼音翻译版
  kai fa ding dian (fixed-point) suan fa shi , tong chang xu yao zai she ji gong neng xing 、 shu zi jing du jian mo 、 ji yan zheng ( fang zhen ) su du zhi jian qu de yi ge ping heng 。 xian zai , yi zhong xin de shu ju lei ke shi ci guo cheng jian dan hua , you ci de dao geng jian dan jing que de jian mo jing du 、 geng hao de shu zi qiu jing 、 ji geng kuai de yan zheng zhou qi , er ANSI C/C++ zheng shi kai fa zhe zhong shu zi qiu jing suan fa de zui jia yu yan 。
  mou ci suan fa tian sheng jiu shi yong yu cao zuo zheng shu , huo na xie li xiang zhong de shi shu ( ru shu zi lv bo qi de xi shu ), ta men ye ke neng hui shi yong fu dian huo ding dian lei xing 。 yi ban er yan , zai suan fa kai fa de zao qi jie duan , hui jing chang yong dao C yu yan de float huo double fu dian lei xing , yin wei ta men ke ti gong yi ge fei chang da de dong tai shu ju fan wei , qie dui da duo shu cheng xu lai shuo dou shi shi yong de 。 jian tu 1:
在C/C++算法设计中使用任意位宽

  shi yong C nei zhi de float lei xing lai jian mo yi ge FIR lv bo qi
  suan fa ke jin xing shu zi qiu jing , yi bian shi yong ding dian suan shu lai jiang di zui zhong ying jian huo ruan jian shi xian de fu duo xing 。 zai ying jian fang mian , jiang zheng shu huo ding dian suan shu xian zhi wei zui xiao wei kuan , ke zai ben zhi shang man zu xing neng 、 kong jian 、 neng hao de xu yao ; jia ru shi xian zhong yong dao le DSP chu li qi , na me ba suan fa xian zhi wei zheng shu huo ding dian suan shu , jiu ke wei te ding cheng xu shi yong jin ke neng bian yi de chu li qi 。
  ding dian suan shu de jian mo ke tong guo C yu yan nei zhi de fu dian huo zheng shu lei xing lai wan cheng , zhe zuo de hua , xu yao xian shi bian ma bing shou xian yu C zhong fu dian shu ji zheng shu ke biao shi de zui da shu :64 wei zheng shu huo 53 wei yi shu ; zhe xie dou hui gei cao zuo shu de wei kuan dai lai geng duo de xian zhi , li ru ,2 ge 33 wei de shu xiang cheng , hui chao guo 64 wei C zheng shu ke biao shi de fan wei 。 tu 2 yan shi le yi ge FIR lv bo qi de li zi , dan temp bian liang xian zhi wei 15 wei de ding dian jing du , qi zhong 10 wei yong yu zheng shu wei 。 zai zhe ge shi xian zhong ,LSB de you bu wei bei she qi ( liang hua mo xing de jie duan ), er MSB de zuo bu wei ye bei she qi ( bao zhuang de yi chu mo xing ), ying gai yi shi dao , shi yong float( huo double) de mo xing zai jing du shang shi shou xian de , qie bu neng zai ci he cheng (synthesis)。 tong yang , you yu you qu zheng mo xing de yan ge wei jing du ding yi you xian , you you yu nei zhi fu dian lei xing de qu zheng jiang hui xian bei ying yong , suo yi dui chu fa zhe yang de cao zuo lai shuo , jiu fei chang nan shi xian le 。
在C/C++算法设计中使用任意位宽

  shi yong float jian mo ding dian xing wei
  dang xu duo suan fa dou neng yi kao ben di C shu ju lei xing de jing du lai bian xie shi , dui zhi chi ren yi chang du de zheng shu ji ding dian suan fa , da jia jiu hui bao you ji da de qi wang , er ying jian miao shu yu yan (HDL) ru VHDL, zou de ye shi tong yi tiao lu 。 sui zhe C/C++ yue lai yue duo di bei yong yu gao ji he cheng yu yan zheng gong ju (High-Level Synthesis and Verification tools), ye zheng shi le zhe zhong yu yan ben zhi shang you yi ge zu yi man zu dang qian ji wei lai cheng xu xu yao de shu ju lei xing ku 。 ren yi chang du lei xing de zhi chi , ye ke shi shu ju lei xing de xing wei you yi ge tong yi de ding yi , er tong yi de yu yi ze bi mian le ren gong shi xian shang de yi xie xian zhi 。
  suan fa C shu ju lei xing
  suan fa C shu ju lei xing shi yi zhong ji yu lei de C++ ku , qi shi xian le ren yi chang du de zheng shu ji ding dian lei xing , er zhe xie ke zi you fang wen de lei xing you yi xi lie hao chu , bao kuo tong yi ji liang hao ding yi de yu yi , huan you bi mei C/C++ nei zhi shu ju lei xing de yun xing shi su du , dui bi SystemC zhong xiang ying de lei xing , qi yun xing su du ye chao guo 10 bei yi shang 。 zhe xie shu ju lei xing neng yong yu ren he fu he C++ huo SystemC gui fan biao zhun de cheng xu zhong , bing yong you gao du ke he cheng de yu yi 。
  yu yi
  yu yi de tong yi xing yu yi zhi xing shi bi mian zai suan fa zhong , fa sheng gong neng xing cuo wu de yao hai , yi xia de li zi , ye shuo ming le zhe dian :
在C/C++算法设计中使用任意位宽

  zhong suo zhou zhi , bian liang ActLength de fan wei wei 1 zhi 255, wan yi bian yi qi de he cheng bu zhi dao qi fan wei , jiu bu neng jin xing xiang ying de you hua , ta de sheng ming jiu hui cong int bian wei geng yan ge de sc_uint<8> lei xing ; sui ran he cheng hui de dao geng hao de jie guo , dan she ji jiu fang zhen de bu zheng que le 。 zai jing guo yi fan tiao shi zhi hou , zhao dao le wen ti de yuan tou : zai bi jiao biao da shi k >= ActLength zhong , liang ge cao zuo shu bian cheng le yi ge signed int yu yi ge unsigned long long( wei 64 wei wu fu hao zheng shu , qi shi sc_uint lei xing de ji lei xing ) zhi jian de bi jiao 。 dui ci de jie shi shi :C/C++ zheng shu ti sheng gui ze zhi ding le zai jin xing bi jiao zhi qian , hui ba cao zuo shu int ti sheng wei yi ge unsigned long long, li ru , jia ru k de zhi wei -1, zai ti sheng wei unsigned long long zhi hou , ta hui bian cheng 2^64 – 1。
  xiang zhe yang yu yi zhong de wen ti yi ban hui fei chang nan yi cha jiao , qie shi yu wei kuan xiang guan de , li ru , ke neng you ren xiang kuo da mou ge xian you suan fa de wei kuan , zhi you kan dao jie guo shi , cai zhi dao shi xing bu tong de ; zhe ge wen ti ye ke neng shi yu te ding ping tai xiang guan de , li ru , dui 1 << 32( liang ge cao zuo shu dou shi int lei xing , jie guo ye shi int lei xing ) da jia qi wang fan hui 0, dan zai da duo shu ping tai ( huo bian yi qi ) shang , ta dou hui fan hui 1( mei you yi wei , zhi yin wei di er ge cao zuo shu jiao di de wu wei bei ji suan jin lai le ); dang di yi ge cao zuo shu shi yi ge 64 wei zheng shu shi , ping tai yi kao xing hui biao xian de geng jia ming xian ji pin fan 。 zhu yao de wen ti shi C/C++ biao zhun mei you zhi ding zai 32 wei zheng shu qing kuang xia yi wei zhi ( di er ge cao zuo shu ) chao chu 0 zhi 31 fan wei 、 huo zai 64 wei zheng shu qing kuang xia yi wei zhi chao chu 0 zhi 63 fan wei shi de xing wei 。 bu xing de shi , xiang sc_int、sc_uint zhe yang de shu ju lei xing ye bu neng wei yong hu bi mian zhe lei ping tai yi kao xing de wen ti 。
  suan fa C shu ju lei xing bei she ji yong yu ti gong tong yi qie yi zhi de yu yi , yin ci , ta men shi ke cai ce de , li ru , dui you fu hao shu hun yong yi ge wu fu hao cao zuo shu reng hui chan sheng qi wang de jie guo ; zhe xie lei xing de chang du bu shou xian zhi , suo yi jiu bu cun zai suo wei de jing du wen ti 。 suo you de cao zuo —— bao kuo yi wei he chu fa —— dou you wan zheng qie yi zhi xing de ding yi , hun he bu tong de lei xing ye neng de dao qi wang de jie guo , ru , dang x wei yi ge C nei zhi lei xing , er y shi yi ge suan fa C lei xing shi , biao da shi x+y he y+x yun neng fan hui xiang tong de jie guo 。
  yun xing shi jian
  wo men de mu de shi wei le zai zhi chi ren yi chang du lei xing ji bi mian yong hu peng dao qian shu yu yi wen ti de qian ti xia , de dao shi yong nei zhi lei xing ( wei kuan bu chao guo 64 wei ) shou gong C/C++ bian ma you hua guo de yun xing shi jian 。 suan fa C lei xing shi wei kuai su zhi xing ji yi yu he cheng de yu yi er she ji ji shi xian de , suo you cao zuo de wei kuan you C++ bian yi qi jing tai que ding , zhe jiu bi mian le dong tai nei cun fen pei , jian shao le yun xing shi jian , ye shi de yu yi geng jia yi yu he cheng 。 ling wai , shi xian ye wei su du jin xing le you hua , yin ci ke neng hui tiao yong geng duo de zhuan yong ji gao xiao dai ma , chong fen li yong le dang jin bian yi qi de you hua te xing 。
在C/C++算法设计中使用任意位宽

  biao 1: gui ge hua wei ac_fixed de yun xing shi jian bi jiao
  biao 1 shi dang ding dian suan shu yong suan fa C ding dian lei xing ac_fixed lai jian mo shi , ge zhong bu tong de yun xing shi bi jiao ;float de shi xian zai tu 2 zhong ,sc_fixed_fast wei SystemC zhong jing du shou xian de ding dian shu ju lei xing ,sc_fixed wei ren yi jing du de ding dian lei xing 。 shi ji zhong dui FIR lv bo qi jin xing 10^8 ci tiao yong ,TRN/WRAP de yun xing shi jian wei 6.5 miao ,RND/SAT wei 29 miao 。 qi ta lei xing de yun xing shi jian ye neng cong zhe zhang biao zhong yi ci tui chu , ru sc_fixed TRN/WRAP jiang hua fei 6.5s × 227 = 1476s( jiang jin 25 fen zhong )。 zuo wei shen kao , tu 1 zhong de suan fa ( shi yong wu ding dian jian mo de float) hua fei shi jian wei 3.5s( bi qi shi yong ding dian jian mo de ac_fixed, man le jin liang bei )。
  shang shu de yun xing shi jian shu ju , yun you GCC 4.1.1 ce liang de lai , er zai zhi qian ban ben de GCC huo Visual C++ 2005 zhong de dao de shu ju da zhi jie jin 。
  ling wai , yun xing shi jian ye neng tong guo zheng xing shu ju lei xing huo wei cao zuo jin yi bu suo duan 。 biao 2 wei yi ge DCT suan fa de xiang ying jie guo , ta you yi ge mei ci du xie 2 wei de yi wei cao zuo de lai , yu ci dui bi de yun xing shi jian wei SystemC jing du shou xian de sc_int yu ren yi chang du de sc_bigint。
在C/C++算法设计中使用任意位宽

  biao 2: gui ge hua wei ac_int de yun xing shi jian bi jiao
  jie lun
  ji yu tong yong biao zhun ANSI C++, zhe zhong xin de zheng shu yu ding dian suan fa C lei xing da ying suan fa ji xi tong she ji zhe zhi ding ren yi wei kuan , cong er ti gong bi chuan tong shu ju lei xing gao 200 bei de fang zhen xiao lv 。 zhe xie xin shu ju lei xing ke cheng wei C-to-RTL she ji lian zhong fei chang you jia zhi de yi huan , ji zai zheng ge shi xian liu cheng zhong bao zheng le ren yi wei kuan de jing du 。【原文】【汉音对照
 
 
 
 
 
 
 
 
 
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   kai fa ding dian (fixed-point) suan fa shi , tong chang xu yao zai she ji gong neng xing 、 shu zi jing du jian mo 、 ji yan zheng ( fang zhen ) su du zhi jian qu de yi ge ping heng 。 xian zai , yi zhong xin de shu ju lei ke shi ci guo cheng jian dan hua , you ci de dao geng jian dan jing que de jian mo jing du 、 geng hao de shu zi qiu jing 、 ji geng kuai de yan zheng zhou qi , er ANSI C/C++ zheng shi kai fa zhe zhong shu zi qiu jing suan fa de zui jia yu yan 。    mou ci suan fa tian sheng jiu shi yong yu cao zuo zheng shu , huo na xie li xiang zhong de shi shu ( ru shu zi lv bo qi de xi shu ), ta men ye ke neng hui shi yong fu dian huo ding dian lei xing 。 yi ban er yan , zai suan fa kai fa de zao qi jie duan , hui jing chang yong dao C yu yan de float huo double fu dian lei xing , yin wei ta men ke ti gong yi ge fei chang da de dong tai shu ju fan wei , qie dui da duo shu cheng xu lai shuo dou shi shi yong de 。 jian tu 1:   [url=http://www.wangchao.net.cn/bbs/pydetail_1785429.html][img]http://image.wangchao.net.cn/it/1323423394823.jpg[/img][/url]    shi yong C nei zhi de float lei xing lai jian mo yi ge FIR lv bo qi    suan fa ke jin xing shu zi qiu jing , yi bian shi yong ding dian suan shu lai jiang di zui zhong ying jian huo ruan jian shi xian de fu duo xing 。 zai ying jian fang mian , jiang zheng shu huo ding dian suan shu xian zhi wei zui xiao wei kuan , ke zai ben zhi shang man zu xing neng 、 kong jian 、 neng hao de xu yao ; jia ru shi xian zhong yong dao le DSP chu li qi , na me ba suan fa xian zhi wei zheng shu huo ding dian suan shu , jiu ke wei te ding cheng xu shi yong jin ke neng bian yi de chu li qi 。    ding dian suan shu de jian mo ke tong guo C yu yan nei zhi de fu dian huo zheng shu lei xing lai wan cheng , zhe zuo de hua , xu yao xian shi bian ma bing shou xian yu C zhong fu dian shu ji zheng shu ke biao shi de zui da shu :64 wei zheng shu huo 53 wei yi shu ; zhe xie dou hui gei cao zuo shu de wei kuan dai lai geng duo de xian zhi , li ru ,2 ge 33 wei de shu xiang cheng , hui chao guo 64 wei C zheng shu ke biao shi de fan wei 。 tu 2 yan shi le yi ge FIR lv bo qi de li zi , dan temp bian liang xian zhi wei 15 wei de ding dian jing du , qi zhong 10 wei yong yu zheng shu wei 。 zai zhe ge shi xian zhong ,LSB de you bu wei bei she qi ( liang hua mo xing de jie duan ), er MSB de zuo bu wei ye bei she qi ( bao zhuang de yi chu mo xing ), ying gai yi shi dao , shi yong float( huo double) de mo xing zai jing du shang shi shou xian de , qie bu neng zai ci he cheng (synthesis)。 tong yang , you yu you qu zheng mo xing de yan ge wei jing du ding yi you xian , you you yu nei zhi fu dian lei xing de qu zheng jiang hui xian bei ying yong , suo yi dui chu fa zhe yang de cao zuo lai shuo , jiu fei chang nan shi xian le 。 [url=http://www.wangchao.net.cn/bbs/pydetail_1785429.html][img]http://image.wangchao.net.cn/it/1323423410028.jpg[/img][/url]    shi yong float jian mo ding dian xing wei    dang xu duo suan fa dou neng yi kao ben di C shu ju lei xing de jing du lai bian xie shi , dui zhi chi ren yi chang du de zheng shu ji ding dian suan fa , da jia jiu hui bao you ji da de qi wang , er ying jian miao shu yu yan (HDL) ru VHDL, zou de ye shi tong yi tiao lu 。 sui zhe C/C++ yue lai yue duo di bei yong yu gao ji he cheng yu yan zheng gong ju (High-Level Synthesis and Verification tools), ye zheng shi le zhe zhong yu yan ben zhi shang you yi ge zu yi man zu dang qian ji wei lai cheng xu xu yao de shu ju lei xing ku 。 ren yi chang du lei xing de zhi chi , ye ke shi shu ju lei xing de xing wei you yi ge tong yi de ding yi , er tong yi de yu yi ze bi mian le ren gong shi xian shang de yi xie xian zhi 。    suan fa C shu ju lei xing    suan fa C shu ju lei xing shi yi zhong ji yu lei de C++ ku , qi shi xian le ren yi chang du de zheng shu ji ding dian lei xing , er zhe xie ke zi you fang wen de lei xing you yi xi lie hao chu , bao kuo tong yi ji liang hao ding yi de yu yi , huan you bi mei C/C++ nei zhi shu ju lei xing de yun xing shi su du , dui bi SystemC zhong xiang ying de lei xing , qi yun xing su du ye chao guo 10 bei yi shang 。 zhe xie shu ju lei xing neng yong yu ren he fu he C++ huo SystemC gui fan biao zhun de cheng xu zhong , bing yong you gao du ke he cheng de yu yi 。    yu yi    yu yi de tong yi xing yu yi zhi xing shi bi mian zai suan fa zhong , fa sheng gong neng xing cuo wu de yao hai , yi xia de li zi , ye shuo ming le zhe dian : [url=http://www.wangchao.net.cn/bbs/pydetail_1785429.html][img]http://image.wangchao.net.cn/it/1323423410226.gif[/img][/url]    zhong suo zhou zhi , bian liang ActLength de fan wei wei 1 zhi 255, wan yi bian yi qi de he cheng bu zhi dao qi fan wei , jiu bu neng jin xing xiang ying de you hua , ta de sheng ming jiu hui cong int bian wei geng yan ge de sc_uint<8> lei xing ; sui ran he cheng hui de dao geng hao de jie guo , dan she ji jiu fang zhen de bu zheng que le 。 zai jing guo yi fan tiao shi zhi hou , zhao dao le wen ti de yuan tou : zai bi jiao biao da shi k >= ActLength zhong , liang ge cao zuo shu bian cheng le yi ge signed int yu yi ge unsigned long long( wei 64 wei wu fu hao zheng shu , qi shi sc_uint lei xing de ji lei xing ) zhi jian de bi jiao 。 dui ci de jie shi shi :C/C++ zheng shu ti sheng gui ze zhi ding le zai jin xing bi jiao zhi qian , hui ba cao zuo shu int ti sheng wei yi ge unsigned long long, li ru , jia ru k de zhi wei -1, zai ti sheng wei unsigned long long zhi hou , ta hui bian cheng 2^64 – 1。    xiang zhe yang yu yi zhong de wen ti yi ban hui fei chang nan yi cha jiao , qie shi yu wei kuan xiang guan de , li ru , ke neng you ren xiang kuo da mou ge xian you suan fa de wei kuan , zhi you kan dao jie guo shi , cai zhi dao shi xing bu tong de ; zhe ge wen ti ye ke neng shi yu te ding ping tai xiang guan de , li ru , dui 1 << 32( liang ge cao zuo shu dou shi int lei xing , jie guo ye shi int lei xing ) da jia qi wang fan hui 0, dan zai da duo shu ping tai ( huo bian yi qi ) shang , ta dou hui fan hui 1( mei you yi wei , zhi yin wei di er ge cao zuo shu jiao di de wu wei bei ji suan jin lai le ); dang di yi ge cao zuo shu shi yi ge 64 wei zheng shu shi , ping tai yi kao xing hui biao xian de geng jia ming xian ji pin fan 。 zhu yao de wen ti shi C/C++ biao zhun mei you zhi ding zai 32 wei zheng shu qing kuang xia yi wei zhi ( di er ge cao zuo shu ) chao chu 0 zhi 31 fan wei 、 huo zai 64 wei zheng shu qing kuang xia yi wei zhi chao chu 0 zhi 63 fan wei shi de xing wei 。 bu xing de shi , xiang sc_int、sc_uint zhe yang de shu ju lei xing ye bu neng wei yong hu bi mian zhe lei ping tai yi kao xing de wen ti 。    suan fa C shu ju lei xing bei she ji yong yu ti gong tong yi qie yi zhi de yu yi , yin ci , ta men shi ke cai ce de , li ru , dui you fu hao shu hun yong yi ge wu fu hao cao zuo shu reng hui chan sheng qi wang de jie guo ; zhe xie lei xing de chang du bu shou xian zhi , suo yi jiu bu cun zai suo wei de jing du wen ti 。 suo you de cao zuo —— bao kuo yi wei he chu fa —— dou you wan zheng qie yi zhi xing de ding yi , hun he bu tong de lei xing ye neng de dao qi wang de jie guo , ru , dang x wei yi ge C nei zhi lei xing , er y shi yi ge suan fa C lei xing shi , biao da shi x+y he y+x yun neng fan hui xiang tong de jie guo 。    yun xing shi jian    wo men de mu de shi wei le zai zhi chi ren yi chang du lei xing ji bi mian yong hu peng dao qian shu yu yi wen ti de qian ti xia , de dao shi yong nei zhi lei xing ( wei kuan bu chao guo 64 wei ) shou gong C/C++ bian ma you hua guo de yun xing shi jian 。 suan fa C lei xing shi wei kuai su zhi xing ji yi yu he cheng de yu yi er she ji ji shi xian de , suo you cao zuo de wei kuan you C++ bian yi qi jing tai que ding , zhe jiu bi mian le dong tai nei cun fen pei , jian shao le yun xing shi jian , ye shi de yu yi geng jia yi yu he cheng 。 ling wai , shi xian ye wei su du jin xing le you hua , yin ci ke neng hui tiao yong geng duo de zhuan yong ji gao xiao dai ma , chong fen li yong le dang jin bian yi qi de you hua te xing 。 [url=http://www.wangchao.net.cn/bbs/pydetail_1785429.html][img]http://image.wangchao.net.cn/it/1323423410262.gif[/img][/url]    biao 1: gui ge hua wei ac_fixed de yun xing shi jian bi jiao    biao 1 shi dang ding dian suan shu yong suan fa C ding dian lei xing ac_fixed lai jian mo shi , ge zhong bu tong de yun xing shi bi jiao ;float de shi xian zai tu 2 zhong ,sc_fixed_fast wei SystemC zhong jing du shou xian de ding dian shu ju lei xing ,sc_fixed wei ren yi jing du de ding dian lei xing 。 shi ji zhong dui FIR lv bo qi jin xing 10^8 ci tiao yong ,TRN/WRAP de yun xing shi jian wei 6.5 miao ,RND/SAT wei 29 miao 。 qi ta lei xing de yun xing shi jian ye neng cong zhe zhang biao zhong yi ci tui chu , ru sc_fixed TRN/WRAP jiang hua fei 6.5s × 227 = 1476s( jiang jin 25 fen zhong )。 zuo wei shen kao , tu 1 zhong de suan fa ( shi yong wu ding dian jian mo de float) hua fei shi jian wei 3.5s( bi qi shi yong ding dian jian mo de ac_fixed, man le jin liang bei )。    shang shu de yun xing shi jian shu ju , yun you GCC 4.1.1 ce liang de lai , er zai zhi qian ban ben de GCC huo Visual C++ 2005 zhong de dao de shu ju da zhi jie jin 。    ling wai , yun xing shi jian ye neng tong guo zheng xing shu ju lei xing huo wei cao zuo jin yi bu suo duan 。 biao 2 wei yi ge DCT suan fa de xiang ying jie guo , ta you yi ge mei ci du xie 2 wei de yi wei cao zuo de lai , yu ci dui bi de yun xing shi jian wei SystemC jing du shou xian de sc_int yu ren yi chang du de sc_bigint。   [url=http://www.wangchao.net.cn/bbs/pydetail_1785429.html][img]http://image.wangchao.net.cn/it/1323423410291.gif[/img][/url]    biao 2: gui ge hua wei ac_int de yun xing shi jian bi jiao    jie lun    ji yu tong yong biao zhun ANSI C++, zhe zhong xin de zheng shu yu ding dian suan fa C lei xing da ying suan fa ji xi tong she ji zhe zhi ding ren yi wei kuan , cong er ti gong bi chuan tong shu ju lei xing gao 200 bei de fang zhen xiao lv 。 zhe xie xin shu ju lei xing ke cheng wei C-to-RTL she ji lian zhong fei chang you jia zhi de yi huan , ji zai zheng ge shi xian liu cheng zhong bao zheng le ren yi wei kuan de jing du 。
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