Differences

This shows you the differences between two versions of the page.

--- gibson:teaching:fall-2016:math753:hw1 [2016/09/14 05:41]
gibson
+++ gibson:teaching:fall-2016:math753:hw1 [2016/09/15 08:07] (current)
gibson
@@ Line 13: / Line 13: @@
 A PDF of the Julia notebook is available so you can view the assignment in a browser, without Julia.
 {{:gibson:teaching:fall-2016:math753:math753-hw1-floatingpoint.pdf|(HW1 viewable as PDF)}}
+====== update to HW1, 9/15/2016 ======
+**Due date: ** changed to Friday 9/16 at midnight.
+**Problem 4:** The syntax for inputting a 16-bit float is ''Float16(9.4)'', not ''9.0f0''. The latter produces a 32-bit float.
+**Problem 6:** This one's proving challenging for people. Some hints:
+How many of the 7s will survive when ''x = 4778 + 3.77777e-10'' is computed in 16 digits? Same for ''y''.
+Once you have those rounded numbers, how many significant digits will survive in the floating=point computations $x+y$, $x-y$, etc.? If you can't figure this out, go ahead and do the computations in 64 bits and see if you can explain the answers you get.
+If you want to compare the 64-bit calculations to something more accurate, use Julia's 256-bit ''BigFloat'' type. There are two ways to get a ''BigFloat''.
+<code>
+julia> BigFloat(9.4)
+.400000000000000355271367880050092935562133789062500000000000000000000000000000
+julia> big(9.4)
+.400000000000000355271367880050092935562133789062500000000000000000000000000000
+</code>
+Observe, however, that though we have 80 digits of precision in a ''BigFloat'', we've produced 9.4 accurate only to 16 digits. This is because you type 9.4, it's interpreted as a 64-bit float before it's handed off to the ''BigFloat'' type. To get an accurate 9.4, you can do this
+<code>
+julia> big(94.0)/big(10.0)^1
+.399999999999999999999999999999999999999999999999999999999999999999999999999945
+</code>

channelflow.org

User Tools

Site Tools

Differences

Page Tools