From 5e85a662d21081bc27adc1142759659cca59cd62 Mon Sep 17 00:00:00 2001
From: Elizabeth Hunt <elizabeth.hunt@simponic.xyz>
Date: Wed, 27 Sep 2023 09:38:55 -0600
Subject: [PATCH] fix compute-maceps arguments

---
 cl/src/approx/maceps.lisp | 14 +++---
 cl/tests/maceps.lisp      | 10 +++--
 homeworks/hw-2.org        | 93 +++++++++++++++++++++++++++++++++++++--
 3 files changed, 101 insertions(+), 16 deletions(-)

diff --git a/cl/src/approx/maceps.lisp b/cl/src/approx/maceps.lisp
index cd24482..ad234e8 100644
--- a/cl/src/approx/maceps.lisp
+++ b/cl/src/approx/maceps.lisp
@@ -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))))
diff --git a/cl/tests/maceps.lisp b/cl/tests/maceps.lisp
index 9d61772..cd5ced9 100644
--- a/cl/tests/maceps.lisp
+++ b/cl/tests/maceps.lisp
@@ -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
diff --git a/homeworks/hw-2.org b/homeworks/hw-2.org
index c570b65..90807b6 100644
--- a/homeworks/hw-2.org
+++ b/homeworks/hw-2.org
@@ -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 |