{"id":1185,"date":"2023-02-18T11:10:45","date_gmt":"2023-02-18T03:10:45","guid":{"rendered":"https:\/\/www.aqwu.net\/wp\/?p=1185"},"modified":"2023-02-18T11:20:22","modified_gmt":"2023-02-18T03:20:22","slug":"%e7%a5%9e%e5%a5%87%e7%9a%84%e6%95%b0%e5%ad%973%ef%bc%9a%e5%88%a9%e7%94%a8%e9%98%b6%e4%b9%98%e5%80%92%e6%95%b0%e4%b9%8b%e5%92%8c%e6%9d%a5%e6%b1%82%e5%b8%b8%e6%95%b0e%e5%80%bc","status":"publish","type":"post","link":"https:\/\/www.aqwu.net\/wp\/?p=1185","title":{"rendered":"\u795e\u5947\u7684\u6570\u5b573\uff1a\u5229\u7528\u9636\u4e58\u5012\u6570\u4e4b\u548c\u6765\u6c42\u5e38\u6570e\u503c"},"content":{"rendered":"\n

e\uff0c\u4f5c\u4e3a\u6570\u5b66\u5e38\u6570\uff0c\u662f\u81ea\u7136\u5bf9\u6570\u51fd\u6570\u7684\u5e95\u6570\uff0c\u4ea6\u79f0\u81ea\u7136\u5e38\u6570\u3001\u81ea\u7136\u5e95\u6570\uff0c\u6216\u662f\u6b27\u62c9\u6570\uff08Euler’s number\uff09\uff0c\u4ee5\u745e\u58eb\u6570\u5b66\u5bb6\u6b27\u62c9\u547d\u540d\uff1b\u8fd8\u6709\u4e2a\u8f83\u5c11\u89c1\u7684\u540d\u5b57\u7eb3\u76ae\u5c14\u5e38\u6570\uff0c\u7528\u6765\u7eaa\u5ff5\u82cf\u683c\u5170\u6570\u5b66\u5bb6\u7ea6\u7ff0\u00b7\u7eb3\u76ae\u5c14\u5f15\u8fdb\u5bf9\u6570\u3002\u5b83\u662f\u4e00\u4e2a\u65e0\u9650\u4e0d\u5faa\u73af\u5c0f\u6570\uff0c\u6570\u503c\u7ea6\u662f\uff08\u5c0f\u6570\u70b9\u540e20\u4f4d\uff0cOEIS\u200aA001113\uff09\uff1ae = 2.71828182845904523536 \u22ef<\/p>\n\n\n\n

\u4e0b\u9762\u662f\u5176\u4e2d\u7684\u4e00\u4e2a\u5b9a\u4e49\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u6211\u4eec\u76f4\u63a5\u4e0a\u4ee3\u7801, \u8ba1\u7b97 e \u503c\u3002<\/p>\n\n\n\n

#include <iostream>\n#include <mpir.h>\n#include <mpirxx.h>\n\nusing namespace std;\n\nvoid main()\n{\n    \/\/ e = 1\/0! + 1\/1! + 1\/2! + 1\/3! + 1\/4! + ...\n    mpf_class D;\n    mpf_class E;\n    mpf_class F;\n\n    mpz_class I;\n    mpz_class N;\n\n    mp_bitcnt_t prec;\n    mp_exp_t exp;\n    char* Val;\n\n    prec = 100;\n\n    mpf_set_prec(D.get_mpf_t(), prec);\n    mpf_set_prec(E.get_mpf_t(), prec);\n    mpf_set_prec(F.get_mpf_t(), prec);\n    \n    E = 1;\n    F = 1;\n    N = \"25\";\n\n    for (I = 1; I <= N; I++)\n    {\n        F *= I;\n        \n        D = 1 \/ F;\n        E += D;\n\n        exp = 0;\n        Val = mpf_get_str(NULL, &exp, 10, 0, E.get_mpf_t());\n        cout << I << \",\" << \"e:\" << Val << \",exp:\" << exp << endl;\n        free(Val);\n    }\n}\n<\/code><\/pre>\n\n\n\n
\u8ba1\u7b97\u7684\u7ed3\u679c\u662f<\/p>\n\n\n\n
1,e:2,exp:1\n2,e:25,exp:1\n3,e:2666666666666666666666666666666666666665,exp:1\n4,e:2708333333333333333333333333333333333329,exp:1\n5,e:2716666666666666666666666666666666666662,exp:1\n6,e:271805555555555555555555555555555555555,exp:1\n7,e:2718253968253968253968253968253968253963,exp:1\n8,e:2718278769841269841269841269841269841264,exp:1\n9,e:2718281525573192239858906525573192239851,exp:1\n10,e:2718281801146384479717813051146384479707,exp:1\n11,e:2718281826198492865159531826198492865147,exp:1\n12,e:2718281828286168563946341724119501897265,exp:1\n13,e:2718281828446759002314557870113425668964,exp:1\n14,e:271828182845822974791228759482727736694,exp:1\n15,e:2718281828458994464285469576474867480137,exp:1\n16,e:271828182845904225905879345032784186221,exp:1\n17,e:2718281828459045070516047795848605061153,exp:1\n18,e:2718281828459045226708117481710869683316,exp:1\n19,e:2718281828459045234928752728335199400269,exp:1\n20,e:2718281828459045235339784490666415886116,exp:1\n21,e:2718281828459045235359357431729807147345,exp:1\n22,e:2718281828459045235360247110869052204673,exp:1\n23,e:2718281828459045235360285792570758511511,exp:1\n24,e:2718281828459045235360287404308329607628,exp:1\n25,e:2718281828459045235360287468777832451471,exp:1\n<\/code><\/pre>\n\n\n\n
\u4e0a\u9762\u7684exp \u8868\u793a\u5c0f\u6570\u70b9\u7684\u4f4d\u7f6e\uff0c1\u4f4d\uff0c\u8ba1\u7b97\u7684\u7ed3\u679c\u4e3a2.xxxx.<\/p>\n\n\n\n
\u53ef\u4ee5\u4fee\u6539N\u548cprec\u7684\u503c,\u6765\u83b7\u53d6\u66f4\u5927\u7684\u7cbe\u5ea6\u503c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
e\uff0c\u4f5c\u4e3a\u6570\u5b66\u5e38\u6570\uff0c\u662f\u81ea\u7136\u5bf9\u6570\u51fd\u6570\u7684\u5e95\u6570\uff0c\u4ea6\u79f0\u81ea\u7136\u5e38\u6570\u3001\u81ea\u7136\u5e95\u6570\uff0c\u6216\u662f\u6b27\u62c9\u6570\uff08Euler’s num […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[122,43],"tags":[123,301],"class_list":["post-1185","post","type-post","status-publish","format-standard","hentry","category-mpir","category-infoarticle","tag-mpir","tag-301"],"views":1702,"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1185","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1185"}],"version-history":[{"count":5,"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1185\/revisions"}],"predecessor-version":[{"id":1193,"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1185\/revisions\/1193"}],"wp:attachment":[{"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aqwu.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}