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fix compute-maceps arguments

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This commit is contained in:
Elizabeth Hunt 2023-09-27 09:38:55 -06:00
parent 58c73fd511
commit 5e85a662d2
Signed by: simponic
GPG Key ID: 52B3774857EB24B1
3 changed files with 101 additions and 16 deletions
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14
cl/src/approx/maceps.lisp
View File

@ -1,13 +1,11 @@
(in-package :lizfcm.approx)
(defun compute-maceps (val f)
(let* ((h val)
(a val)
(err val))
(defun compute-maceps (f a init)
(let ((h init)
(err init))
(loop while (> err 0)
do
(progn
(setf h (/ h 2)
err (abs (- (funcall f (+ a h))
(funcall f a)))))
(setf h (/ h 2)
err (abs (- (funcall f (+ a h))
(funcall f a))))
collect (list a h err))))

10
cl/tests/maceps.lisp
View File

@ -13,10 +13,12 @@
(test maceps
:description "double precision provides precision about (mac eps of single precision) squared"
(let* ((maceps-computation-double (compute-maceps 1.0d0
(lambda (x) x)))
(maceps-computation-single (compute-maceps 1.0
(lambda (x) x)))
(let* ((maceps-computation-double (compute-maceps (lambda (x) x)
1.0d0
1.0d0))
(maceps-computation-single (compute-maceps (lambda (x) x)
1.0
1.0))
(last-double-h (cadar (last maceps-computation-double)))
(last-single-h (cadar (last maceps-computation-single))))
(is (within-range-p

93
homeworks/hw-2.org
View File

@ -12,13 +12,41 @@ Computing $\epsilon_{\text{mac}}$ for single precision numbers
(load "../cl/lizfcm.asd")
(ql:quickload :lizfcm)
(let ((domain-values (lizfcm.approx:compute-maceps 1.0
(lambda (x) x))))
(let ((domain-values (lizfcm.approx:compute-maceps (lambda (x) x)
1.0
1.0)))
(lizfcm.utils:table (:headers '("a" "h" "err")
:domain-order (a h err)
:domain-values domain-values)))
#+END_SRC
#+RESULTS:
| a | h | err |
| 1.0 | 0.5 | 0.5 |
| 1.0 | 0.25 | 0.25 |
| 1.0 | 0.125 | 0.125 |
| 1.0 | 0.0625 | 0.0625 |
| 1.0 | 0.03125 | 0.03125 |
| 1.0 | 0.015625 | 0.015625 |
| 1.0 | 0.0078125 | 0.0078125 |
| 1.0 | 0.00390625 | 0.00390625 |
| 1.0 | 0.001953125 | 0.001953125 |
| 1.0 | 0.0009765625 | 0.0009765625 |
| 1.0 | 0.00048828125 | 0.00048828125 |
| 1.0 | 0.00024414063 | 0.00024414063 |
| 1.0 | 0.00012207031 | 0.00012207031 |
| 1.0 | 6.1035156e-05 | 6.1035156e-05 |
| 1.0 | 3.0517578e-05 | 3.0517578e-05 |
| 1.0 | 1.5258789e-05 | 1.5258789e-05 |
| 1.0 | 7.6293945e-06 | 7.6293945e-06 |
| 1.0 | 3.8146973e-06 | 3.8146973e-06 |
| 1.0 | 1.9073486e-06 | 1.9073486e-06 |
| 1.0 | 9.536743e-07 | 9.536743e-07 |
| 1.0 | 4.7683716e-07 | 4.7683716e-07 |
| 1.0 | 2.3841858e-07 | 2.3841858e-07 |
| 1.0 | 1.1920929e-07 | 1.1920929e-07 |
| 1.0 | 5.9604645e-08 | 0.0 |
(with many rows truncated)
| a | h | err |
@ -39,13 +67,70 @@ $\epsilon_{\text{mac}}$ \approx 5.9604 \cdot 10^{-8}
Computing $\epsilon_{\text{mac}}$ for double precision numbers:
#+BEGIN_SRC lisp :session t :results table
(let ((domain-values (lizfcm.approx:compute-maceps 1.0d0
(lambda (x) x))))
(let ((domain-values (lizfcm.approx:compute-maceps (lambda (x) x)
1.0d0
1.0d0)))
(lizfcm.utils:table (:headers '("a" "h" "err")
:domain-order (a h err)
:domain-values domain-values)))
#+END_SRC
#+RESULTS:
| a | h | err |
| 1.0d0 | 0.5d0 | 0.5d0 |
| 1.0d0 | 0.25d0 | 0.25d0 |
| 1.0d0 | 0.125d0 | 0.125d0 |
| 1.0d0 | 0.0625d0 | 0.0625d0 |
| 1.0d0 | 0.03125d0 | 0.03125d0 |
| 1.0d0 | 0.015625d0 | 0.015625d0 |
| 1.0d0 | 0.0078125d0 | 0.0078125d0 |
| 1.0d0 | 0.00390625d0 | 0.00390625d0 |
| 1.0d0 | 0.001953125d0 | 0.001953125d0 |
| 1.0d0 | 9.765625d-4 | 9.765625d-4 |
| 1.0d0 | 4.8828125d-4 | 4.8828125d-4 |
| 1.0d0 | 2.44140625d-4 | 2.44140625d-4 |
| 1.0d0 | 1.220703125d-4 | 1.220703125d-4 |
| 1.0d0 | 6.103515625d-5 | 6.103515625d-5 |
| 1.0d0 | 3.0517578125d-5 | 3.0517578125d-5 |
| 1.0d0 | 1.52587890625d-5 | 1.52587890625d-5 |
| 1.0d0 | 7.62939453125d-6 | 7.62939453125d-6 |
| 1.0d0 | 3.814697265625d-6 | 3.814697265625d-6 |
| 1.0d0 | 1.9073486328125d-6 | 1.9073486328125d-6 |
| 1.0d0 | 9.5367431640625d-7 | 9.5367431640625d-7 |
| 1.0d0 | 4.76837158203125d-7 | 4.76837158203125d-7 |
| 1.0d0 | 2.384185791015625d-7 | 2.384185791015625d-7 |
| 1.0d0 | 1.1920928955078125d-7 | 1.1920928955078125d-7 |
| 1.0d0 | 5.960464477539063d-8 | 5.960464477539063d-8 |
| 1.0d0 | 2.9802322387695313d-8 | 2.9802322387695313d-8 |
| 1.0d0 | 1.4901161193847656d-8 | 1.4901161193847656d-8 |
| 1.0d0 | 7.450580596923828d-9 | 7.450580596923828d-9 |
| 1.0d0 | 3.725290298461914d-9 | 3.725290298461914d-9 |
| 1.0d0 | 1.862645149230957d-9 | 1.862645149230957d-9 |
| 1.0d0 | 9.313225746154785d-10 | 9.313225746154785d-10 |
| 1.0d0 | 4.656612873077393d-10 | 4.656612873077393d-10 |
| 1.0d0 | 2.3283064365386963d-10 | 2.3283064365386963d-10 |
| 1.0d0 | 1.1641532182693481d-10 | 1.1641532182693481d-10 |
| 1.0d0 | 5.820766091346741d-11 | 5.820766091346741d-11 |
| 1.0d0 | 2.9103830456733704d-11 | 2.9103830456733704d-11 |
| 1.0d0 | 1.4551915228366852d-11 | 1.4551915228366852d-11 |
| 1.0d0 | 7.275957614183426d-12 | 7.275957614183426d-12 |
| 1.0d0 | 3.637978807091713d-12 | 3.637978807091713d-12 |
| 1.0d0 | 1.8189894035458565d-12 | 1.8189894035458565d-12 |
| 1.0d0 | 9.094947017729282d-13 | 9.094947017729282d-13 |
| 1.0d0 | 4.547473508864641d-13 | 4.547473508864641d-13 |
| 1.0d0 | 2.2737367544323206d-13 | 2.2737367544323206d-13 |
| 1.0d0 | 1.1368683772161603d-13 | 1.1368683772161603d-13 |
| 1.0d0 | 5.684341886080802d-14 | 5.684341886080802d-14 |
| 1.0d0 | 2.842170943040401d-14 | 2.842170943040401d-14 |
| 1.0d0 | 1.4210854715202004d-14 | 1.4210854715202004d-14 |
| 1.0d0 | 7.105427357601002d-15 | 7.105427357601002d-15 |
| 1.0d0 | 3.552713678800501d-15 | 3.552713678800501d-15 |
| 1.0d0 | 1.7763568394002505d-15 | 1.7763568394002505d-15 |
| 1.0d0 | 8.881784197001252d-16 | 8.881784197001252d-16 |
| 1.0d0 | 4.440892098500626d-16 | 4.440892098500626d-16 |
| 1.0d0 | 2.220446049250313d-16 | 2.220446049250313d-16 |
| 1.0d0 | 1.1102230246251565d-16 | 0.0d0 |
(with many rows truncated)
| a | h | err |
| 1.0d0 | 0.5d0 | 0.5d0 |