numerical methods - error bound in function approximation algorithm -


suppose have set of floating point number "m" bit mantissa , "e" bits exponent. suppose more on want approximate function "f".

from theory know "range reduced function" used , such function derive global function value.

for example let x = (sx,ex,mx) (sign exp , mantissa) then... log2(x) = ex + log2(1.mx) range reduced function "log2(1.mx)".

i have implemented @ present reciprocal, square root, log2 , exp2, i've started work trigonometric functions. wandering if given global error bound (ulp error especially) possible derive error bound range reduced function, there study kind of problem? speaking of log2(x) (as example) lke able say...

"ok want log2(x) k ulp error, achieve given our floating point system need approximate log2(1.mx) p ulp error"

remember said know working floating point number, format generic, classic f32, example e=10, m = 8 end on.

i can't find reference shows such kind of study. reference have (i.e. muller book) doesn't treat topic in way looking kind of paper or similar. know reference?

i'm trying derive such bound myself not easy...

there description of current practice, along proposed improvement , error analysis, @ https://hal.inria.fr/ensl-00086904/document. description of current practice appears consistent overview @ https://docs.oracle.com/cd/e37069_01/html/e39019/z4000ac119729.html, consistent memory of talked problem being mod pi range reduction of trigonometric functions.

i think ieee floating point big step forwards because standardized things @ time when there variety of computer architectures, lowering risks of porting code between them, accuracy requirements implied may have been overkill: many problems constraint on accuracy of output accuracy of input data, not accuracy of calculation of intermediate values.


Comments

Post a Comment

Popular posts from this blog

c# - Validate object ID from GET to POST -

i have method allows user access comment have made on site. have post method lets them update comment. my normal solution send entire comment model through, let them update it, update on database when post back. involve sending commentid through in hiddenfor , can manipulated. how can verify commentid sent in get method same i'm getting in post , not able alter comment wish? how can verify commentid sent in method same i'm getting in post? basically have validate following things in post - user logged-in user. authenticated users post comments. commentid in post , should valid commentid , should present in database. userid associated logged-in user should same userid associated comment . comment should contain userid column, can check @ time of update. to make sure update happens comment has been sent in get - hold commentid in session , in post action compare commentid value in session .
Read more

node.js - Custom Model Validator SailsJS -

when using custom model validator checks record within model. return within spread doesn't seem end control flow. //post.js model /** * custom validator **/ types: { isuservalid: function(user_id) { var promise = require('bluebird'); promise.all([ user.findone({id: user_id}) ]) .spread(function(user) { console.log(user); if (user === null || user === undefined) { console.log('failed'); return false; }else{ console.log('passed'); return true; } }); } }, my response standard validation failed response. { "error": "e_validation", "status": 400, "summary": "1 attribute invalid", "model": "post", "invalidattributes": { "owner": [ { "rule": "isuservalid", ...
Read more

php - Find a regex to take part of Email -

i have following emails need extract part from: bestellnummer xxx: 1 von xxx, 1er pack ------------- anfang der nachricht ------------- foo bar baz foo bar baz // <<<<< need text here ------------- ende der nachricht ------------- ------------- anfang der nachricht ------------- foo bar baz foo bar baz ------------- ende der nachricht ------------- there 0 unlimited occurences of ------------- anfang der nachricht ------------- ------------- ende der nachricht ------------- and i'm able extract first part regex: $re = "/------------- .*? -------------.?(.*?).?------------- .*? -------------/s"; but, i'm quite new on learning regex, i'm pretty sure there must better regex extract part (foo bar baz foo bar baz) of text between ------------- anfang der nachricht ------------- ------------- ende der nachricht ------------- as can in different languages, i'm using .? to match between hyphens. i...
Read more