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--- gibson:teaching:fall-2016:math753:hw1 [2016/09/13 07:53]
gibson
+++ gibson:teaching:fall-2016:math753:hw1 [2016/09/15 08:07] (current)
gibson
@@ Line 7: / Line 7: @@
   * Work through the HW1 Julia notebook. Provide answers to the questions by filling in the cells with verbal answers or Julia code as appropriate (following [[:gibson:teaching:fall-2016:math753:notebook-workflow | these instructions]]).
   * Clean up or remove any mistakes you made along the way so that the notebook is polished and easy to read.
-  * Convert the HW1 Julia notebook file to something that Canvas can handle, either compressing it with
+  * Convert the HW1 Julia notebook file to something that Canvas can handle, either compressing it with [[https://en.wikipedia.org/wiki/Zip_(file_format) | zip]] (using something like [[http://www.7-zip.org/|7-zip]] (free) or [[http://www.winzip.com/win/en/index.htm | winzip]] (%%$$%%)), or by simply change the ''.ipynb'' file extention to ''.txt''.
-[[https://en.wikipedia.org/wiki/Zip_(file_format) | zip]] (using something like [[http://www.7-zip.org/|7-zip] (free) or [[http://www.winzip.com/win/en/index.htm | winzip]] ($$)), or by simply change the ''.ipynb'' file extention to ''.txt''.
   * Upload your ''.zip'' or ''.txt'' HW1 Julia notebook file to the Math 753 Canvas website.
+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 ======
-A PDF of the Julia notebook is available so you can view the assignment in a browser, without Julia.
+**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.
-{{:gibson:teaching:fall-2016:math753:math753-hw1-floatingpoint.pdf|(HW1 viewable as PDF)}}
+**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>

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