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- Log ----------------------------------------------------------------- commit 894af6c4aaa3b83f3c13d2e59735c33f79abdc20 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Dec 23 10:40:03 2013 -0800

Add tests for the branch cut for atanh. Not clear that this is correct because atanh(-2) appears to be wrong.

diff --git a/tests/trig.lisp b/tests/trig.lisp index 9565ef5..05437e5 100644 --- a/tests/trig.lisp +++ b/tests/trig.lisp @@ -725,3 +725,66 @@ (get-signs (acosh-def #c(0.25d0 -1d-20))) (assert-true (check-signs #'acosh #c(0.25d0 -0d0) tr ti)) (assert-true (check-signs #'acosh #c(0.25w0 -0w0) tr ti)))) + +;; atanh(z) = 1/2*(log(1+z) - log(1-z)) +;; +;; The branch cut is on the real axis for |x| > 1. For x < -1, it is +;; continuous with Quadrant III. For x > 1, it is continuous with +;; quadrant I. +;; +;; NOTE: The rules above are what is given by the CLHS. However, +;; consider the value of atanh(-2) and atanh(-2-0.0*i) +;; +;; atanh(-2) = 1/2*(log(1-2) - log(1+2)) +;; = 1/2*(log(-1) - log(3)) +;; = 1/2*(i*pi - log(3)) +;; = -1/2*log(3) + i*pi/2 +;; +;; atanh(-2-0*i) = 1/2*(log(1+(-2-0*i)) - log(1-(-2-0*i))) +;; = 1/2*(log(-1-0*i) - log(3-0*i)) +;; = 1/2*(-i*pi - log(3)) +;; = -1/2*log(3) - i*pi/2 +;; +;; atanh(-2+0*i) = 1/2*(log(1+(-2+0*i)) - log(1-(-2+0*i))) +;; = 1/2*(log(-1+0*i) - log(3-0*i)) +;; = 1/2*(i*pi - log(3)) +;; = -1/2*log(3) + i*pi/2 +;; +;; Thus, atanh(-2) is continuous with Quadrant II, NOT continuous with +;; Quadrant III! +;; +;; What do we do? +(defun atanh-def (z) + (r*z 1/2 + (- (log (1+z z)) + (log (1-z z))))) + +(define-test branch-cut.atanh + (:tag :atanh :branch-cuts) + ;; Test for x < -1, which is continuous with Quadrant III. Use the + ;; the value at #c(-2d0 -1d-20) as the reference. + (multiple-value-bind (tr ti) + (get-signs (atanh-def #c(-2d0 -1d-20))) + (assert-true (check-signs #'atanh -2d0 tr ti)) + (assert-true (check-signs #'atanh -2w0 tr ti)) + (assert-true (check-signs #'atanh #c(-2d0 -0d0) tr ti)) + (assert-true (check-signs #'atanh #c(-2w0 -0w0) tr ti))) + ;; Test the other side of the branch cut for x < -1. + (multiple-value-bind (tr ti) + (get-signs (atanh-def #c(-2d0 +1d-20))) + (assert-true (check-signs #'atanh #c(-2d0 0d0) tr ti)) + (assert-true (check-signs #'atanh #c(-2w0 0w0) tr ti))) + + ;; Test for x > 1, which is continuous with Quadrant I, using the + ;; value at #c(+2d0 1d-10) as the reference + (multiple-value-bind (tr ti) + (get-signs (atanh-def #c(2d0 1d-20))) + (assert-true (check-signs #'atanh 2d0 tr ti)) + (assert-true (check-signs #'atanh 2w0 tr ti)) + (assert-true (check-signs #'atanh #c(2d0 0) tr ti)) + (assert-true (check-signs #'atanh #c(2w0 0) tr ti))) + ;; Test the other side of the branch cut for x > 1. + (multiple-value-bind (tr ti) + (get-signs (atanh-def #c(2d0 -1d-20))) + (assert-true (check-signs #'atanh #c(2d0 -0d0) tr ti)) + (assert-true (check-signs #'atanh #c(2w0 -0w0) tr ti))))

commit 15d3bbe341280c08855d07dc6664c0fd17b27636 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Dec 23 08:36:22 2013 -0800

Add tests for the branch cuts for asinh and acosh, and some fixes.

o Add function R-Z to compute r - z carefully. (For definition of acos) o Add function R*Z to compute r*z carefully, For acos and acosh. o Add tests for asinh and acosh.

diff --git a/tests/trig.lisp b/tests/trig.lisp index 011aeaf..9565ef5 100644 --- a/tests/trig.lisp +++ b/tests/trig.lisp @@ -468,6 +468,13 @@ (complex (- 1 (realpart z)) (- (imagpart z))) (- 1 z)))

+(defun z-1 (z) + (if (complexp z) + (complex (- (realpart z) 1) + (imagpart z)) + (- z 1))) + + ;; Carefully compute 1+z. For z = x + i*y, we want 1+x + i*y, which ;; only really matters when y is a signed zero. (defun 1+z (z) @@ -475,12 +482,24 @@ (complex (+ 1 (realpart z)) (imagpart z)) (+ 1 z)))

+(defun r-z (r z) + (if (complexp z) + (complex (- r (realpart z)) + (- (imagpart z))) + (- r z))) + ;; Carefully compute i*z = i*(x+i*y) = -y + i*x. (defun i*z (z) (if (complexp z) (complex (- (imagpart z)) (realpart z)) (complex 0 z)))

+;; Carefully compute r*z, where r is a real value and z is complex. +(defun r*z (r z) + (if (complexp z) + (complex (* r (realpart z)) (* r (imagpart z))) + (* r z))) + ;; asin(x) = -i*log(i*x + sqrt(1-x^2)) ;; ;; The branch cut is the real axis |x| > 1. For x < -1, it is @@ -529,10 +548,10 @@ ;; continous with Quadrant II; for x > 1, Quadrant IV. (defun acos-def (z) (if (typep z 'kernel:double-double-float) - (- (/ kernel:dd-pi 2) - (asin-def z)) - (- (/ pi 2) - (asin-def z)))) + (r-z (/ kernel:dd-pi 2) + (asin-def z)) + (r-z (/ pi 2) + (asin-def z))))

(define-test branch-cut.acos (:tag :acos :branch-cuts) @@ -601,7 +620,7 @@ (let* ((iz (i*z z)) (w (- (log (1+z iz)) (log (1-z iz))))) - (* -1/2 (i*z w)))) + (r*z -1/2 (i*z w))))

(define-test branch-cut.atan (:tag :atan :branch-cuts) @@ -628,3 +647,81 @@ (get-signs (atan-def #c(1d-20 2d0))) (assert-true (check-signs #'atan #c(0d0 2d0) tr ti)) (assert-true (check-signs #'atan #c(0d0 2w0) tr ti)))) + +;; asinh(z) = log(z + sqrt(1+z^2)) +;; +;; The branch cut is the imaginary axis with |y| > 1. For y > 1, asinh +;; is continuous with Quadrant I. For y < -1, it is continuous with +;; Quadrant III. + +(defun asinh-def (z) + (log (+ z (sqrt (1+z (* z z)))))) + +(define-test branch-cut.asinh + (:tag :asinh :branch-cuts) + ;; Test for y < -1, which is continuous with Quadrant I. Use the + ;; value at #c(1d-20 -2d0) as the reference. + (multiple-value-bind (tr ti) + (get-signs (asinh-def #c(1d-20 -2d0))) + (assert-true (check-signs #'asinh #c(0d0 -2d0) tr ti)) + (assert-true (check-signs #'asinh #c(0w0 -2w0) tr ti))) + ;; Test the other side of the branch cut for y < -1. + (multiple-value-bind (tr ti) + (get-signs (asinh-def #c(-1d-20 -2d0))) + (assert-true (check-signs #'asinh #c(-0d0 -2d0) tr ti)) + (assert-true (check-signs #'asinh #c(-0w0 -2w0) tr ti))) + + ;; Test for y > 1, which is continuous with Quadrant III, using the + ;; value at #c(-1d-20 +2d0) as the reference + (multiple-value-bind (tr ti) + (get-signs (asinh-def #c(-1d-20 2d0))) + (assert-true (check-signs #'asinh #c(-0d0 2d0) tr ti)) + (assert-true (check-signs #'asinh #c(-0w0 2w0) tr ti))) + ;; Test the other side of the branch cut for x > 1. + (multiple-value-bind (tr ti) + (get-signs (asinh-def #c(1d-20 2d0))) + (assert-true (check-signs #'asinh #c(0d0 2d0) tr ti)) + (assert-true (check-signs #'asinh #c(0d0 2w0) tr ti)))) + +;; acosh(z) = 2*log(sqrt((z+1)/2) + sqrt((z-1)/2)) +;; +;; The branch cut is along the real axis with x < 1. For x < 0, it is +;; continuous with Quadrant II. For 0< x < 1, it is continuous with +;; Quadrant I. + +(defun acosh-def (z) + (r*z 2 + (log (+ (sqrt (r*z 1/2 (1+z z))) + (sqrt (r*z 1/2 (z-1 z))))))) + + +(define-test branch-cut.acosh + (:tag :acosh :branch-cuts) + ;; Test for x < 0, which is continuous with Quadrant II. Use the + ;; value at #c(-2d0 1d-20) as a reference. + (multiple-value-bind (tr ti) + (get-signs (acosh-def #c(-2d0 1d-20))) + (assert-true (check-signs #'acosh -2d0 tr ti)) + ;;(assert-true (check-signs #'acosh -2w0 tr ti)) + (assert-true (check-signs #'acosh #c(-2d0 0) tr ti)) + ;;(assert-true (check-signs #'acosh #c(-2w0 0) tr ti)) + ) + ;; Test the other side of the branch cut for x < -1. + (multiple-value-bind (tr ti) + (get-signs (acosh-def #c(-2d0 -1d-20))) + (assert-true (check-signs #'acosh #c(-2d0 -0d0) tr ti)) + ;;(assert-true (check-signs #'acosh #c(-2w0 -0w0) tr ti)) + ) + + ;; Test for 0 < x < 1, which is continuous with Quadrant I, using the + ;; value at #c(0.25d0 1d-10) as the reference. + (multiple-value-bind (tr ti) + (get-signs (acosh-def #c(0.25d0 1d-20))) + (assert-true (check-signs #'acosh #c(0.25d0 0) tr ti)) + (assert-true (check-signs #'acosh #c(0.25w0 0) tr ti)) + ) + ;; Test the other side of the branch cut for 0 < x < 1. + (multiple-value-bind (tr ti) + (get-signs (acosh-def #c(0.25d0 -1d-20))) + (assert-true (check-signs #'acosh #c(0.25d0 -0d0) tr ti)) + (assert-true (check-signs #'acosh #c(0.25w0 -0w0) tr ti))))

commit e5bfd82b999468624a09dad92189843f08eac5b2 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Dec 23 00:16:43 2013 -0800

Float printer tests from reading the logs for print.lisp.

diff --git a/tests/printer.lisp b/tests/printer.lisp new file mode 100644 index 0000000..b511f0b --- /dev/null +++ b/tests/printer.lisp @@ -0,0 +1,113 @@ +(defpackage :printer-tests + (:use :cl :lisp-unit)) + +(in-package "PRINTER-TESTS") + +(define-test format.float.1 + (assert-equal ".0000" + (format nil "~5F" 1d-10)) + (assert-equal "0.000" + (format nil "~,3F" 0.000001))) + +(define-test format.float.2 + (assert-equal " 0.990E+00" (format nil "~11,3,2,0,'*,,'EE" .99)) + (assert-equal " 0.999E+00" (format nil "~11,3,2,0,'*,,'EE" .999)) + (assert-equal " 0.100E+01" (format nil "~11,3,2,0,'*,,'EE" .9999)) + (assert-equal " 0.999E-04" (format nil "~11,3,2,0,'*,,'EE" .0000999)) + (assert-equal " 0.100E-03" (format nil "~11,3,2,0,'*,,'EE" .00009999)) + (assert-equal " 9.999E-05" (format nil "~11,3,2,,'*,,'EE" .00009999)) + (assert-equal " 1.000E-04" (format nil "~11,3,2,,'*,,'EE" .000099999))) + +(define-test format.float.3 + (assert-equal ".00123d+6" (format nil "~9,,,-2E" 1.2345689d3)) + (assert-equal "-.0012d+6" (format nil "~9,,,-2E" -1.2345689d3)) + (assert-equal ".00123d+0" (format nil "~9,,,-2E" 1.2345689d-3)) + (assert-equal "-.0012d+0" (format nil "~9,,,-2E" -1.2345689d-3))) + +(define-test format.float.4 + (assert-equal "0.314e-01" (format nil "~9,3,2,0,'%G" 0.0314159)) + (assert-equal "+.003e+03" (format nil "~9,3,2,-2,'%@e" 3.14159)) + (assert-equal " 31.42" (format nil "~6,2,1,'*F" 3.14159)) + (assert-equal " 3141590." (format nil "~9,0,6f" 3.14159)) + + (assert-equal ".00000003d+8" (format nil "~9,4,,-7E" pi)) + (assert-equal ".000003d+6" (format nil "~9,4,,-5E" pi)) + (assert-equal "3141600.d-6" (format nil "~5,4,,7E" pi)) + (assert-equal " 314.16d-2" (format nil "~11,4,,3E" pi)) + (assert-equal " 31416.d-4" (format nil "~11,4,,5E" pi)) + (assert-equal " 0.3142d+1" (format nil "~11,4,,0E" pi)) + (assert-equal ".03142d+2" (format nil "~9,,,-1E" pi)) + (assert-equal "0.003141592653589793d+3" (format nil "~,,,-2E" pi)) + (assert-equal "31.41592653589793d-1" (format nil "~,,,2E" pi)) + (assert-equal "3.141592653589793d+0" (format nil "~E" pi)) + (assert-equal ".03142d+2" (format nil "~9,5,,-1E" pi)) + (assert-equal " 0.03142d+2" (format nil "~11,5,,-1E" pi)) + (assert-equal "3.141592653589793 " (format nil "~G" pi)) + (assert-equal "3.1416 " (format nil "~9,5G" pi)) + (assert-equal "| 3141593.d-06|" (format nil "|~13,6,2,7E|" pi)) + (assert-equal "0.314d+01" (format nil "~9,3,2,0,'%E" pi)) + (assert-equal " 3141593." (format nil "~9,0,6f" pi)) + (assert-equal " 31.42" (format nil "~6,2,1,'*F" pi)) + (assert-equal "******" (format nil "~6,2,1,'*F" (* 100 pi))) + (assert-equal "+.003d+03" (format nil "~9,3,2,-2,'%@E" pi)) + (assert-equal "+0.003d+03" (format nil "~10,3,2,-2,'%@E" pi)) + (assert-equal "=====+0.003d+03" (format nil "~15,3,2,-2,'%,'=@E" pi)) + (assert-equal "0.003d+03" (format nil "~9,3,2,-2,'%E" pi)) + (assert-equal "%%%%%%%%" (format nil "~8,3,2,-2,'%@E" pi)) + + (assert-equal "1. " (format nil "~g" 1e0)) + + (assert-equal "0.0e+0" (format nil "~e" 0)) + (assert-equal "0.0d+0" (format nil "~e" 0d0)) + (assert-equal "0.0d+0000" (format nil "~9,,4e" 0d0)) + (assert-equal "1.2345678901234567d+4" (format nil "~E" 1.234567890123456789d4)) + + (assert-equal "1.32922799578492d+36" (format nil "~20E" (expt 2d0 120))) + (assert-equal " 1.32922800d+36" (format nil "~21,8E" (expt 2d0 120))) + + (assert-equal ".0012345679" (format nil "~11f" 1.23456789123456789d-3))) + +(define-test format.float.5 + ;; From CLHS 22.3.11 + (flet ((test-f (x) + (format nil "~6,2F|~6,2,1,'*F|~6,2,,'?F|~6F|~,2F|~F" + x x x x x x))) + (assert-equal " 3.14| 31.42| 3.14|3.1416|3.14|3.14159" (test-f 3.14159)) + (assert-equal " -3.14|-31.42| -3.14|-3.142|-3.14|-3.14159" (test-f -3.14159)) + (assert-equal "100.00|******|100.00| 100.0|100.00|100.0" (test-f 100.0)) + (assert-equal "1234.00|******|??????|1234.0|1234.00|1234.0" (test-f 1234.0)) + (assert-equal " 0.01| 0.06| 0.01| 0.006|0.01|0.006" (test-f 0.006)))) + +(define-test format.float.6 + (flet ((test-e (x) + (format nil + "~9,2,1,,'*E|~10,3,2,2,'?,,'$E|~ + ~9,3,2,-2,'%@E|~9,2E" + x x x x))) + + (assert-equal " 3.14e+0| 31.42$-01|+.003e+03| 3.14e+0" (test-e 3.14159)) + (assert-equal " -3.14e+0|-31.42$-01|-.003e+03| -3.14e+0" (test-e -3.14159)) + (assert-equal " 1.10e+3| 11.00$+02|+.001e+06| 1.10e+3" (test-e 1100.0)) + (assert-equal " 1.10d+3| 11.00$+02|+.001d+06| 1.10d+3" (test-e 1100.0d0)) + (assert-equal "*********| 11.00$+12|+.001e+16| 1.10e+13" (test-e 1.1e13)) + (assert-equal "*********|??????????|%%%%%%%%%|1.10d+120" (test-e 1.1d120)))) + +(define-test format.float.7 + (flet ((test-scale (k) + (format nil "~&Scale factor ~2D: |~13,6,2,VE|" + (- k 5) (- k 5) 3.14159))) + + (assert-equal "Scale factor -5: | 0.000003e+06|" (test-scale 0)) + (assert-equal "Scale factor -4: | 0.000031e+05|" (test-scale 1)) + (assert-equal "Scale factor -3: | 0.000314e+04|" (test-scale 2)) + (assert-equal "Scale factor -2: | 0.003142e+03|" (test-scale 3)) + (assert-equal "Scale factor -1: | 0.031416e+02|" (test-scale 4)) + (assert-equal "Scale factor 0: | 0.314159e+01|" (test-scale 5)) + (assert-equal "Scale factor 1: | 3.141590e+00|" (test-scale 6)) + (assert-equal "Scale factor 2: | 31.41590e-01|" (test-scale 7)) + (assert-equal "Scale factor 3: | 314.1590e-02|" (test-scale 8)) + (assert-equal "Scale factor 4: | 3141.590e-03|" (test-scale 9)) + (assert-equal "Scale factor 5: | 31415.90e-04|" (test-scale 10)) + (assert-equal "Scale factor 6: | 314159.0e-05|" (test-scale 11)) + (assert-equal "Scale factor 7: | 3141590.e-06|" (test-scale 12)))) +

-----------------------------------------------------------------------

Summary of changes: tests/printer.lisp | 113 ++++++++++++++++++++++++++++++++++ tests/trig.lisp | 170 ++++++++++++++++++++++++++++++++++++++++++++++++++-- 2 files changed, 278 insertions(+), 5 deletions(-) create mode 100644 tests/printer.lisp

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