{"id":77,"date":"2007-04-21T09:33:16","date_gmt":"2007-04-21T13:33:16","guid":{"rendered":"http:\/\/jameslao.wordpress.com\/2007\/04\/21\/damn-numerical-error-in-fortran"},"modified":"2007-04-21T09:33:16","modified_gmt":"2007-04-21T13:33:16","slug":"damn-numerical-error-in-fortran","status":"publish","type":"post","link":"https:\/\/www.jlao.net\/en\/technology\/77\/","title":{"rendered":"damn numerical error in Fortran"},"content":{"rendered":"
\n
(reference to https:\/\/www.cemtach.com\/reference\/software\/toyFDTD\/fpu.html<\/a> )<\/div>\n
if we run the following simple code:<\/div>\n
\n\n\n\n
F90:<\/p>\n

program foo
\nreal*8 :: a = 0
\ninteger :: n
\ndo n=0,100,1
\nprint*,a
\na = a + 0.01
\nend do
\nend program foo<\/td>\n

C:<\/p>\n

#include <stdio.h>
\nvoid main(void)
\n{
\ndouble a = 0;
\nint n;
\nfor(n=0; n<=100; n++)
\n{
\nprintf(” %.10f n”,a);
\na += 0.01;
\n}
\n}<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

we may find different outputs from different compilers:<\/div>\n
\n\n\n\n\n
Intel Fortran<\/td>\ng95<\/td>\nGcc<\/td>\n<\/tr>\n
0.909999979659915
\n0.919999979436398
\n0.929999979212880
\n0.939999978989363
\n0.949999978765845
\n0.959999978542328
\n0.969999978318810
\n0.979999978095293
\n0.989999977871776
\n0.999999977648258<\/td>\n		0.909999979659915
\n0.9199999794363976
\n0.9299999792128801
\n0.9399999789893627
\n0.9499999787658453
\n0.9599999785423279
\n0.9699999783188105
\n0.979999978095293
\n0.9899999778717756
\n0.9999999776482582<\/td>\n		0.9100000000
\n0.9200000000
\n0.9300000000
\n0.9400000000
\n0.9500000000
\n0.9600000000
\n0.9700000000
\n0.9800000000
\n0.9900000000
\n1.0000000000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
if we change that +0.01 to +0.01d0, it will improve the accuracy but still unsatisfactory<\/div>\n
\n\n\n\n\n
Ifort real*16<\/td>\nIfort real*8<\/td>\nG95 real*8<\/td>\n<\/tr>\n
0.910000000000000018943180357666733
\n0.920000000000000019151347174783950 0.930000000000000019359513991901167 0.940000000000000019567680809018384 0.950000000000000019775847626135601 0.960000000000000019984014443252818 0.970000000000000020192181260370035 0.980000000000000020400348077487251 0.990000000000000020608514894604468 1.00000000000000002081668171172169<\/td>\n		0.910000000000001
\n0.920000000000001
\n0.930000000000001
\n0.940000000000001
\n0.950000000000001
\n0.960000000000001
\n0.970000000000001
\n0.980000000000001
\n0.990000000000001
\n1.00000000000000<\/td>\n		0.9100000000000006
\n0.9200000000000006
\n0.9300000000000006
\n0.9400000000000006
\n0.9500000000000006
\n0.9600000000000006
\n0.9700000000000006
\n0.9800000000000006
\n0.9900000000000007
\n1.0000000000000007<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
so.. god bless fortran…<\/div>\n
<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

(reference to https:\/\/www.cemtach.com\/reference\/software\/toyFDTD\/fpu.html ) if we run the following simple code: F90: program foo real*8 :: a = 0 integer :: n do n=0,100,1 print*,a a = a + 0.01 end do end program foo C: #include <stdio.h> void main(void) { double a = 0; int n; for(n=0; n<=100; n++) { printf(” %.10f n”,a); a … Continue reading damn numerical error in Fortran<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-77","post","type-post","status-publish","format-standard","hentry","category-technology"],"_links":{"self":[{"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/posts\/77","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/comments?post=77"}],"version-history":[{"count":0,"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/posts\/77\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/media?parent=77"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/categories?post=77"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.jlao.net\/en\/wp-json\/wp\/v2\/tags?post=77"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}