;-*- Mode: Lisp -*- ;;;; Author: Marius Gerbershagen ;;;; Created: Wed Feb 6 19:35:53 2019 ;;;; Contains: Tests of the ~e format directive ;;; Equivalent to PRIN1 for (abs x) outside of the range [10^-3,10^7), ;;; apart from the sign of the exponent, which is always printed. (deftest format.e.1 (let ((*print-readably* nil) (fn (formatter "~e"))) (loop for i = (random 4) for type = (elt #(short-float single-float double-float long-float) i) for min-value = (elt (vector least-positive-short-float least-positive-single-float least-positive-double-float least-positive-long-float) i) for max-value = (elt (vector most-positive-short-float most-positive-single-float most-positive-double-float most-positive-long-float) i) for x = (expt (coerce 10 type) (if (= (random 2) 0) (- -3 (random (- -3 (log min-value 10)))) (+ 7 (random (- (log max-value 10) 7))))) for s1 = (let ((*read-default-float-format* type)) (format nil "~e" x)) for s2 = (let* ((*read-default-float-format* type) (s (prin1-to-string x)) (exp-pos (1+ (position #\e s :test #'char-equal)))) (if (> x 1) (concatenate 'string (subseq s 0 exp-pos) "+" (subseq s exp-pos)) s)) for s3 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) repeat 1000 when (and (or (< x 1/1000) (>= x 10000000)) (or (not (string= s1 s2)) (not (string= s1 s3)))) collect (list x s1 s2 s3))) nil) (deftest format.e.2 (let ((*print-readably* nil) (fn (formatter "~e"))) (loop for i = (random 4) for type = (elt #(short-float single-float double-float long-float) i) for min-value = (elt (vector least-negative-short-float least-negative-single-float least-negative-double-float least-negative-long-float) i) for max-value = (elt (vector most-negative-short-float most-negative-single-float most-negative-double-float most-negative-long-float) i) for x = (- (expt (coerce 10 type) (if (= (random 2) 0) (- -3 (random (- -3 (log (abs min-value) 10)))) (+ 7 (random (- (log (abs max-value) 10) 7)))))) for s1 = (let ((*read-default-float-format* type)) (format nil "~e" x)) for s2 = (let* ((*read-default-float-format* type) (s (prin1-to-string x)) (exp-pos (1+ (position #\e s :test #'char-equal)))) (if (< x -1) (concatenate 'string (subseq s 0 exp-pos) "+" (subseq s exp-pos)) s)) for s3 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) repeat 1000 when (and (or (> x -1/1000) (<= x -10000000)) (or (not (string= s1 s2)) (not (string= s1 s3)))) collect (list x s1 s2 s3))) nil) ;;; "If the parameter d is omitted, [...] a value is chosen for d in ;;; such a way that as many digits as possible may be printed subject ;;; to [...] the constraint that no trailing zero digits may appear in ;;; the fraction, except that if the fraction to be printed is zero ;;; then a single zero digit should appear after the decimal point." (deftest format.e.3 (let ((fn (formatter "~6e"))) (loop for x in '(0 0.0s0 0.0f0 0.0d0 0.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~6e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "0.0e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.4 (let ((fn (formatter "~5e"))) (loop for x in '(1 1.0s0 1.0f0 1.0d0 1.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~5e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "1.e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.5 (let ((fn (formatter "~4e"))) (loop for x in '(1 1.0s0 1.0f0 1.0d0 1.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~4e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "1.e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.6 (let ((fn (formatter "~6e"))) (loop for x in '(1 1.0s0 1.0f0 1.0d0 1.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~6e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "1.0e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.7 (let ((fn (formatter "~6@e"))) (loop for x in '(1 1.0s0 1.0f0 1.0d0 1.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~6@e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "+1.e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.8 (let ((fn (formatter "~5@e"))) (loop for x in '(1 1.0s0 1.0f0 1.0d0 1.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~5@e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "+1.e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.9 (let ((fn (formatter "~6e"))) (loop for x in '(1 1.0s0 1.0f0 1.0d0 1.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~6e" (- x))) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn (- x))) unless (and (string-equal s "-1.e+0") (string-equal s s2)) collect (list x s s2))) nil) ;;; d parameter (deftest format.e.10 (let ((fn (formatter "~7,2e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~7,2e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5.00e-1") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.11 (let ((fn (formatter "~6,2e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~6,2e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5.00e-1") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.12 (let ((fn (formatter "~7,2@e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~7,2@e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "+5.00e-1") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.13 (let ((fn (formatter "~,2e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5.00e-1") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.14 (let ((fn (formatter "~,2e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2e" (- x))) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn (- x))) unless (and (string-equal s "-5.00e-1") (string-equal s s2)) collect (list x s s2))) nil) ;;; e parameter (deftest format.e.15 (let ((fn (formatter "~,2,2e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,2e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5.00e-01") (string-equal s s2)) collect (list x s s2))) nil) ;;; k parameter (deftest format.e.16 (let ((fn (formatter "~,2,,-1e"))) (loop for x in '(5 5.0s0 5.0f0 5.0d0 5.0l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,,-1e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "0.05e+2") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.17 (let ((fn (formatter "~,2,,0e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,,0e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "0.50e+0") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.18 (let ((fn (formatter "~,2,,2e"))) (loop for x in '(1/20 0.05s0 0.05f0 0.05d0 0.05l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,,2e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "50.0e-3") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.19 (let ((fn (formatter "~,2,,3e"))) (loop for x in '(1/20 0.05s0 0.05f0 0.05d0 0.05l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,,3e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "500.e-4") (string-equal s s2)) collect (list x s s2))) nil) ;;; undefined behaviour: the format string is "~,2,,4E": d is 2 and k ;;; is 4, but k (4) is not strictly less than d+2 (4). #+(or) (deftest format.e.20 (let ((fn (formatter "~,2,,4e"))) (loop for x in '(1/20 0.05s0 0.05f0 0.05d0 0.05l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,,4e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5000.e-5") (string-equal s s2)) collect (list x s s2))) nil) ;;; overflow (deftest format.e.21 (let ((fn (formatter "~6,2,,,'*e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~6,2,,,'*e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "******") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.22 (let ((fn (formatter "~7,2,,,'*e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~7,2,,,'*e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5.00e-1") (string-equal s s2)) collect (list x s s2))) nil) ;;; padchar (deftest format.e.23 (let ((fn (formatter "~10,1,,,e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~10,1,,,e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s " 5.0e-1") (string-equal s s2)) collect (list x s s2))) nil) (deftest format.e.24 (let ((fn (formatter "~10,1,,,,'*e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~10,1,,,,'*e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "****5.0e-1") (string-equal s s2)) collect (list x s s2))) nil) ;;; exponentchar (deftest format.e.25 (let ((fn (formatter "~,2,,,,,'^e"))) (loop for x in '(1/2 0.5s0 0.5f0 0.5d0 0.5l0) for type in '(single-float short-float single-float double-float long-float) for s = (let ((*read-default-float-format* type)) (format nil "~,2,,,,,'^e" x)) for s2 = (let ((*read-default-float-format* type)) (formatter-call-to-string fn x)) unless (and (string-equal s "5.00^-1") (string-equal s s2)) collect (list x s s2))) nil) ;;; verify correct rounding (deftest format.e.26 (loop for i = (random 4) for type = (elt #(short-float single-float double-float long-float) i) for min-value = (elt (vector least-positive-short-float least-positive-single-float least-positive-double-float least-positive-long-float) i) for max-value = (elt (vector most-positive-short-float most-positive-single-float most-positive-double-float most-positive-long-float) i) ;; create a random float ... for x = (exp (+ (random (- (log max-value) (log min-value))) (log min-value))) ;; ... and check the correct rounding for as many significant ;; digits as the precision of the float allows for incorrect-roundings = (loop for d from 1 upto (floor (* (float-precision x) (log (float-radix x) 10))) for format-string = (format nil "~~,~d,,0e" d) for s1 = (let* ((*read-default-float-format* type) (s1 (format nil format-string x))) ;; e might be lowercase or uppercase (subseq s1 (1+ (position #\. s1)) (position #\e s1 :test #'char-equal))) with ret = nil do (multiple-value-bind (s2 s3) (round-ratio-to-n-digits (rational x) d) (unless (or (string-equal s1 s2) (and s3 (string-equal s1 s3))) (push (list x format-string (format nil format-string x) s1 s2 s3) ret))) finally (return ret)) repeat 20 if incorrect-roundings collect incorrect-roundings) nil)