The HP67 stores PI\/4 in ROM subroutine 05043 with 13 digit precision. It multiplies that by 4 (“c + c -> c[w]” twice) to get 3.1415926535900 and then rounds that to 3.141592654.
\nIt works like this:
\n<\/p>\n
\r\nHP67 Logging started.\r\n\r\n(00167 - 00213 wait loop)\r\n[h]\r\n...\r\n\r\n(00167 - 00213 wait loop)\r\n[PI]\r\n00214 display off\r\n00215 b exchange c[w]\r\n00216 CRC 400\r\n00217 keys to a\r\n...\r\n00252 delayed rom 01\r\n00253 a -> rom address\r\n00537 if n\/c go to 0427\r\n00427 ...\r\n00435 if n\/c go to 0542\r\n00542 ...\r\n00544 if n\/c go to 0436\r\n00436 ...\r\n00442 jsb 01205 ; clear s 4,6-8,10,13\r\n00443 ...\r\n00446 if n\/c go to 06021\r\n06021 ...\r\n06027 a -> rom address \r\n06004 if n\/c go to 06046\r\n06046 ...\r\n06051 a -> rom address \r\n07110 if n\/c go to 07172\r\n07172 ...\r\n07173 delayed rom 012 \r\n07174 jsb 05043\r\n.05043 p <- 12 \r\n.05044 0 -> c[w] \r\n.05045 load constant 7 \r\n.05046 load constant 8 \r\n.05047 load constant 5 \r\n.05050 load constant 3 \r\n.05051 load constant 9 \r\n.05052 load constant 8 \r\n.05053 load constant 1 \r\n.05054 load constant 6 \r\n.05055 load constant 3 \r\n.05056 load constant 3 \r\n.05057 load constant 9 \r\n.05060 load constant 7 \r\n.05061 load constant 5 ; C=07853981633975\r\n.05062 p <- 12 \r\n.05063 return \r\n07175 c + c -> c[w] ; C=15707963267950\r\n07176 c + c -> c[w] ; C=31415926535900\r\n07177 shift right c[w] ; C=03141592653590\r\n07200 c + 1 -> c[m] ; C=03141592654590\r\n07201 0 -> c[x] ; C=03141592654000\r\n07202 if n\/c go to 07372\r\n07372 delayed rom 00 \r\n07373 if n\/c go to 0103\r\n00103 ...\r\n00110 then go to 0114\r\n00114 ...\r\n00115 if n\/c go to 0124\r\n00124 ...\r\n00156 jsb 02007 ; A=03140000000000\r\n00157 delayed rom 02\r\n00160 jsb 01162 ; A=3014fffffff100 B=03000000000022\r\n00161 hi im woodstock\r\n00162 display off\r\n00163 display toggle ; \"3.14\"\r\n00164 0 -> s 15\r\n00165 if 1 = s 15\r\n00166 then go to 0164\r\n\r\n(00167 - 00213 wait loop)\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"The HP67 stores PI\/4 in ROM subroutine 05043 with 13 digit precision. It multiplies that by 4 (“c + c -> c[w]” twice) to get 3.1415926535900 and then rounds that to 3.141592654. It works like this:<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[16,5,3],"tags":[33,32],"_links":{"self":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/1208"}],"collection":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/comments?post=1208"}],"version-history":[{"count":7,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/1208\/revisions"}],"predecessor-version":[{"id":1351,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/posts\/1208\/revisions\/1351"}],"wp:attachment":[{"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/media?parent=1208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/categories?post=1208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sydneysmith.com\/wordpress\/wp-json\/wp\/v2\/tags?post=1208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}