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If there are multiple roots, only the root closest to ze"577 #"ro is returned."578 ) 0 0 64 29 1 #"\n"579 0 0 17 3 12 #";Termination"580 0 0 17 3 1 #" "581 0 0 17 3 9 #"Argument:"582 0 0 17 3 1 #" "583 0 0 17 3 3 #"The"584 0 0 17 3 1 #" "585 0 0 17 3 8 #"interval"586 0 0 17 3 1 #" "587 0 0 17 3 2 #"of"588 0 0 17 3 1 #" "589 0 0 17 3 18 #"find-root-discrete"590 0 0 17 3 1 #" "591 0 0 17 3 9 #"decreases"592 0 0 17 3 1 #" "593 0 0 17 3 2 #"by"594 0 0 17 3 5 #" half"595 0 0 17 3 1 #" "596 0 0 17 3 4 #"each"597 0 0 17 3 1 #" "598 0 0 17 3 4 #"time"599 0 0 17 3 1 #" "600 0 0 17 3 5 #"until"601 0 0 17 11 1 #" "602 0 0 17 3 3 #"the"603 0 0 17 3 1 #" "604 0 0 17 3 8 #"interval"605 0 0 17 3 1 #" "606 0 0 17 3 4 #"size"607 0 0 17 3 1 #" "608 0 0 17 3 2 #"is"609 0 0 17 3 1 #" "610 0 0 17 3 4 #"only"611 0 0 17 3 1 #" "612 0 0 17 3 2 #"1."613 0 0 17 3 2 #" "614 0 0 17 3 4 #"Once"615 0 0 17 3 1 #" "616 0 0 17 3 4 #"this"617 0 0 17 3 1 #" "618 0 0 17 3 6 #"occurs"619 0 0 17 3 1 #","620 0 0 17 3 1 #" "621 0 0 17 3 18 #"find-root-discrete"622 0 0 17 3 1 #" "623 0 0 17 3 6 #"either"624 0 0 17 3 1 #" "625 0 0 17 3 7 #"returns"626 0 0 17 3 1 #" "627 0 0 17 3 3 #"the"628 0 0 17 3 1 #" "629 0 0 17 3 4 #"left"630 0 0 17 3 1 #" "631 0 0 17 3 2 #"or"632 0 0 17 11 1 #" "633 0 0 17 3 3 #"the"634 0 0 17 3 1 #" "635 0 0 17 3 67636 #"right index as the root. Hence, find-root-discrete must terminate."637 0 0 64 29 1 #"\n"638 0 0 17 3 17 #";midpoint : Given"639 0 0 17 3 71640 (641 #" left and right, determine the midpoint rounded to the nearest integ"642 #"er."643 ) 0 0 64 29 1 #"\n"644 0 0 17 3 44 #";No assumption about a-table being monotonic"645 0 0 64 29 1 #"\n"646 0 0 64 29 1 #"\n"647 0 0 63 29 1 #"\n"648 0 0 22 3 1 #"("649 0 0 15 3 6 #"define"650 0 0 63 3 1 #" "651 0 0 22 3 1 #"("652 0 0 14 3 19 #"find-root-discrete2"653 0 0 63 3 1 #" "654 0 0 14 3 7 #"a-table"655 0 0 63 3 1 #" "656 0 0 14 3 4 #"left"657 0 0 63 3 1 #" "658 0 0 14 3 5 #"right"659 0 0 22 3 1 #")"660 0 0 63 29 1 #"\n"661 0 0 63 3 2 #" "662 0 0 22 3 1 #"("663 0 0 15 3 4 #"cond"664 0 0 63 29 1 #"\n"665 0 0 63 3 4 #" "666 0 0 22 3 2 #"[("667 0 0 14 3 1 #"="668 0 0 63 3 1 #" "669 0 0 22 3 1 #"("670 0 0 14 3 1 #"-"671 0 0 63 3 1 #" "672 0 0 14 3 5 #"right"673 0 0 63 3 1 #" "674 0 0 14 3 4 #"left"675 0 0 22 3 1 #")"676 0 0 63 3 1 #" "677 0 0 20 3 1 #"1"678 0 0 22 3 1 #")"679 0 0 63 3 1 #" "680 0 0 64 3 1 #" "681 0 0 63 29 1 #"\n"682 0 0 63 3 5 #" "683 0 0 22 3 1 #"("684 0 0 15 3 4 #"cond"685 0 0 63 29 1 #"\n"686 0 0 63 3 7 #" "687 0 0 22 3 2 #"[("688 0 0 14 3 2 #"<="689 0 0 63 3 1 #" "690 0 0 22 3 1 #"("691 0 0 14 3 3 #"abs"692 0 0 63 3 1 #" "693 0 0 22 3 1 #"("694 0 0 14 3 7 #"a-table"695 0 0 63 3 1 #" "696 0 0 14 3 4 #"left"697 0 0 22 3 2 #"))"698 0 0 63 29 1 #"\n"699 0 0 63 3 12 #" "700 0 0 22 3 1 #"("701 0 0 14 3 3 #"abs"702 0 0 63 3 1 #" "703 0 0 22 3 1 #"("704 0 0 14 3 7 #"a-table"705 0 0 63 3 1 #" "706 0 0 14 3 5 #"right"707 0 0 22 3 3 #")))"708 0 0 63 3 1 #" "709 0 0 14 3 4 #"left"710 0 0 22 3 1 #"]"711 0 0 63 29 1 #"\n"712 0 0 63 3 7 #" "713 0 0 22 3 1 #"["714 0 0 14 3 4 #"else"715 0 0 63 3 1 #" "716 0 0 14 3 5 #"right"717 0 0 22 3 3 #"])]"718 0 0 63 29 1 #"\n"719 0 0 63 3 4 #" "720 0 0 22 3 1 #"["721 0 0 14 3 4 #"else"722 0 0 63 3 1 #" "723 0 0 22 3 1 #"("724 0 0 15 3 5 #"local"725 0 0 63 3 1 #" "726 0 0 22 3 2 #"(("727 0 0 15 3 6 #"define"728 0 0 63 3 1 #" "729 0 0 14 3 8 #"midpoint"730 0 0 63 29 1 #"\n"731 0 0 63 3 20 #" "732 0 0 22 3 1 #"("733 0 0 14 3 5 #"round"734 0 0 63 3 1 #" "735 0 0 22 3 1 #"("736 0 0 14 3 1 #"+"737 0 0 63 3 1 #" "738 0 0 14 3 4 #"left"739 0 0 63 29 1 #"\n"740 0 0 63 3 30 #" "741 0 0 22 3 1 #"("742 0 0 14 3 1 #"/"743 0 0 63 3 1 #" "744 0 0 22 3 1 #"("745 0 0 14 3 1 #"-"746 0 0 63 3 1 #" "747 0 0 14 3 5 #"right"748 0 0 63 3 1 #" "749 0 0 14 3 4 #"left"750 0 0 22 3 1 #")"751 0 0 63 3 1 #" "752 0 0 20 3 1 #"2"753 0 0 22 3 4 #"))))"754 0 0 63 29 1 #"\n"755 0 0 63 3 18 #" "756 0 0 22 3 1 #"("757 0 0 15 3 6 #"define"758 0 0 63 3 1 #" "759 0 0 14 3 14 #"left-side-root"760 0 0 63 3 1 #" "761 0 0 22 3 1 #"("762 0 0 14 3 18 #"find-root-discrete"763 0 0 63 3 1 #" "764 0 0 14 3 7 #"a-table"765 0 0 63 3 1 #" "766 0 0 14 3 4 #"left"767 0 0 63 3 1 #" "768 0 0 14 3 8 #"midpoint"769 0 0 22 3 2 #"))"770 0 0 63 29 1 #"\n"771 0 0 63 3 18 #" "772 0 0 22 3 1 #"("773 0 0 15 3 6 #"define"774 0 0 63 3 1 #" "775 0 0 14 3 15 #"right-side-root"776 0 0 63 3 1 #" "777 0 0 22 3 1 #"("778 0 0 14 3 18 #"find-root-discrete"779 0 0 63 3 1 #" "780 0 0 14 3 7 #"a-table"781 0 0 63 3 1 #" "782 0 0 14 3 8 #"midpoint"783 0 0 63 3 1 #" "784 0 0 14 3 5 #"right"785 0 0 22 3 3 #")))"786 0 0 63 29 1 #"\n"787 0 0 63 3 12 #" "788 0 0 22 3 1 #"("789 0 0 15 3 4 #"cond"790 0 0 63 3 14 #" "791 0 0 63 29 1 #"\n"792 0 0 63 3 14 #" "793 0 0 22 3 2 #"[("794 0 0 14 3 2 #"<="795 0 0 63 3 1 #" "796 0 0 22 3 1 #"("797 0 0 14 3 3 #"abs"798 0 0 63 3 1 #" "799 0 0 22 3 1 #"("800 0 0 14 3 7 #"a-table"801 0 0 63 3 1 #" "802 0 0 14 3 14 #"left-side-root"803 0 0 22 3 2 #"))"804 0 0 63 29 1 #"\n"805 0 0 63 3 19 #" "806 0 0 22 3 1 #"("807 0 0 14 3 3 #"abs"808 0 0 63 3 1 #" "809 0 0 22 3 1 #"("810 0 0 14 3 7 #"a-table"811 0 0 63 3 1 #" "812 0 0 14 3 15 #"right-side-root"813 0 0 22 3 3 #")))"814 0 0 63 3 1 #" "815 0 0 14 3 14 #"left-side-root"816 0 0 22 3 1 #"]"817 0 0 63 29 1 #"\n"818 0 0 63 3 14 #" "819 0 0 22 3 1 #"["820 0 0 14 3 4 #"else"821 0 0 63 3 1 #" "822 0 0 14 3 15 #"right-side-root"823 0 0 22 3 6 #"]))]))"824 0 0 63 29 1 #"\n"825 0 0 63 29 1 #"\n"826 0 0 77 29 1 #"\n"827 0 0 77 29 1 #"\n"828 0 0 17 3 44 #";find-root-discrete : (N -> number) N N -> N"829 0 0 77 29 1 #"\n"830 0 0 17 3 6 #";Given"831 0 0 17 3 1 #" "832 0 0 17 3 7 #"a-table"833 0 0 17 3 1 #","834 0 0 17 3 1 #" "835 0 0 17 3 4 #"left"836 0 0 17 3 1 #","837 0 0 17 3 1 #" "838 0 0 17 3 3 #"and"839 0 0 17 3 1 #" "840 0 0 17 3 5 #"right"841 0 0 17 3 1 #","842 0 0 17 3 1 #" "843 0 0 17 3 4 #"find"844 0 0 17 3 1 #" "845 0 0 17 3 1 #"a"846 0 0 17 3 1 #" "847 0 0 17 3 5 #"root "848 0 0 17 3 2 #"of"849 0 0 17 3 1 #" "850 0 0 17 3 3 #"the"851 0 0 17 3 1 #" "852 0 0 17 3 5 #"table"853 0 0 17 3 1 #" "854 0 0 17 3 5 #"using"855 0 0 17 3 1 #" "856 0 0 17 3 6 #"binary"857 0 0 17 3 7 #" search"858 0 0 17 3 1 #" "859 0 0 17 3 10 #"generative"860 0 0 17 11 1 #" "861 0 0 17 3 83862 (863 #"recursion. If there are multiple roots, only the root closest to ze"864 #"ro is returned."865 ) 0 0 77 29 1 #"\n"866 0 0 17 3 12 #";Termination"867 0 0 17 3 1 #" "868 0 0 17 3 9 #"Argument:"869 0 0 17 3 1 #" "870 0 0 17 3 3 #"The"871 0 0 17 3 1 #" "872 0 0 17 3 8 #"interval"873 0 0 17 3 1 #" "874 0 0 17 3 2 #"of"875 0 0 17 3 1 #" "876 0 0 17 3 18 #"find-root-discrete"877 0 0 17 3 1 #" "878 0 0 17 3 9 #"decreases"879 0 0 17 3 1 #" "880 0 0 17 3 2 #"by"881 0 0 17 3 5 #" half"882 0 0 17 3 1 #" "883 0 0 17 3 4 #"each"884 0 0 17 3 1 #" "885 0 0 17 3 4 #"time"886 0 0 17 3 1 #" "887 0 0 17 3 5 #"until"888 0 0 17 11 1 #" "889 0 0 17 3 3 #"the"890 0 0 17 3 1 #" "891 0 0 17 3 8 #"interval"892 0 0 17 3 1 #" "893 0 0 17 3 4 #"size"894 0 0 17 3 1 #" "895 0 0 17 3 2 #"is"896 0 0 17 3 1 #" "897 0 0 17 3 4 #"only"898 0 0 17 3 1 #" "899 0 0 17 3 2 #"1."900 0 0 17 3 2 #" "901 0 0 17 3 4 #"Once"902 0 0 17 3 1 #" "903 0 0 17 3 4 #"this"904 0 0 17 3 1 #" "905 0 0 17 3 6 #"occurs"906 0 0 17 3 1 #","907 0 0 17 3 1 #" "908 0 0 17 3 18 #"find-root-discrete"909 0 0 17 3 1 #" "910 0 0 17 3 6 #"either"911 0 0 17 3 1 #" "912 0 0 17 3 7 #"returns"913 0 0 17 3 1 #" "914 0 0 17 3 3 #"the"915 0 0 17 3 1 #" "916 0 0 17 3 4 #"left"917 0 0 17 3 1 #" "918 0 0 17 3 2 #"or"919 0 0 17 11 1 #" "920 0 0 17 3 71921 (922 #"the right index as the root. Hence, find-root-discrete must termina"923 #"te."924 ) 0 0 77 29 1 #"\n"925 0 0 17 3 88926 (927 #";midpoint : Given left and right, determine the midpoint rounded to "928 #"the nearest integer."929 ) 0 0 77 29 1 #"\n"930 0 0 17 3 70931 (932 #";ASSUMPTION : a-table is monotonic increasing or monotonic decreasin"933 #"g."934 ) 0 0 77 29 1 #"\n"935 0 0 77 29 1 #"\n"936 0 0 22 3 1 #"("937 0 0 15 3 6 #"define"938 0 0 77 3 1 #" "939 0 0 22 3 1 #"("940 0 0 14 3 18 #"find-root-discrete"941 0 0 77 3 1 #" "942 0 0 14 3 7 #"a-table"943 0 0 77 3 1 #" "944 0 0 14 3 4 #"left"945 0 0 77 3 1 #" "946 0 0 14 3 5 #"right"947 0 0 22 3 1 #")"948 0 0 77 29 1 #"\n"949 0 0 77 3 2 #" "950 0 0 22 3 1 #"("951 0 0 15 3 5 #"local"952 0 0 77 3 1 #" "953 0 0 22 3 2 #"(("954 0 0 15 3 6 #"define"955 0 0 77 3 1 #" "956 0 0 14 3 8 #"midpoint"957 0 0 77 29 1 #"\n"958 0 0 77 3 12 #" "959 0 0 22 3 1 #"("960 0 0 14 3 5 #"round"961 0 0 77 3 1 #" "962 0 0 22 3 1 #"("963 0 0 14 3 1 #"+"964 0 0 77 3 1 #" "965 0 0 14 3 4 #"left"966 0 0 77 29 1 #"\n"967 0 0 77 3 22 #" "968 0 0 22 3 1 #"("969 0 0 14 3 1 #"/"970 0 0 77 3 1 #" "971 0 0 22 3 1 #"("972 0 0 14 3 1 #"-"973 0 0 77 3 1 #" "974 0 0 14 3 5 #"right"975 0 0 77 3 1 #" "976 0 0 14 3 4 #"left"977 0 0 22 3 1 #")"978 0 0 77 3 1 #" "979 0 0 20 3 1 #"2"980 0 0 22 3 5 #")))))"981 0 0 77 29 1 #"\n"982 0 0 77 3 4 #" "983 0 0 22 3 1 #"("984 0 0 15 3 4 #"cond"985 0 0 77 29 1 #"\n"986 0 0 77 3 6 #" "987 0 0 22 3 2 #"[("988 0 0 14 3 1 #"="989 0 0 77 3 1 #" "990 0 0 22 3 1 #"("991 0 0 14 3 1 #"-"992 0 0 77 3 1 #" "993 0 0 14 3 5 #"right"994 0 0 77 3 1 #" "995 0 0 14 3 4 #"left"996 0 0 22 3 1 #")"997 0 0 77 3 1 #" "998 0 0 20 3 1 #"1"999 0 0 22 3 1 #")"1000 0 0 77 3 1 #" "1001 0 0 77 29 1 #"\n"1002 0 0 77 3 7 #" "1003 0 0 22 3 1 #"("1004 0 0 15 3 4 #"cond"1005 0 0 77 29 1 #"\n"1006 0 0 77 3 9 #" "1007 0 0 22 3 2 #"[("1008 0 0 14 3 2 #"<="1009 0 0 77 3 1 #" "1010 0 0 22 3 1 #"("1011 0 0 14 3 3 #"abs"1012 0 0 77 3 1 #" "1013 0 0 22 3 1 #"("1014 0 0 14 3 7 #"a-table"1015 0 0 77 3 1 #" "1016 0 0 14 3 4 #"left"1017 0 0 22 3 2 #"))"1018 0 0 77 29 1 #"\n"1019 0 0 77 3 14 #" "1020 0 0 22 3 1 #"("1021 0 0 14 3 3 #"abs"1022 0 0 77 3 1 #" "1023 0 0 22 3 1 #"("1024 0 0 14 3 7 #"a-table"1025 0 0 77 3 1 #" "1026 0 0 14 3 5 #"right"1027 0 0 22 3 3 #")))"1028 0 0 77 3 1 #" "1029 0 0 14 3 4 #"left"1030 0 0 22 3 1 #"]"1031 0 0 77 29 1 #"\n"1032 0 0 77 3 9 #" "1033 0 0 22 3 1 #"["1034 0 0 14 3 4 #"else"1035 0 0 77 3 1 #" "1036 0 0 14 3 5 #"right"1037 0 0 22 3 3 #"])]"1038 0 0 77 29 1 #"\n"1039 0 0 77 3 6 #" "1040 0 0 22 3 2 #"[("1041 0 0 14 3 2 #"or"1042 0 0 77 3 1 #" "1043 0 0 22 3 1 #"("1044 0 0 14 3 2 #"<="1045 0 0 77 3 1 #" "1046 0 0 22 3 1 #"("1047 0 0 14 3 7 #"a-table"1048 0 0 77 3 1 #" "1049 0 0 14 3 4 #"left"1050 0 0 22 3 1 #")"1051 0 0 77 3 1 #" "1052 0 0 20 3 1 #"0"1053 0 0 77 3 1 #" "1054 0 0 22 3 1 #"("1055 0 0 14 3 7 #"a-table"1056 0 0 77 3 1 #" "1057 0 0 14 3 8 #"midpoint"1058 0 0 22 3 2 #"))"1059 0 0 77 29 1 #"\n"1060 0 0 77 3 11 #" "1061 0 0 22 3 1 #"("1062 0 0 14 3 2 #"<="1063 0 0 77 3 1 #" "1064 0 0 22 3 1 #"("1065 0 0 14 3 7 #"a-table"1066 0 0 77 3 1 #" "1067 0 0 14 3 8 #"midpoint"1068 0 0 22 3 1 #")"1069 0 0 77 3 1 #" "1070 0 0 20 3 1 #"0"1071 0 0 77 3 1 #" "1072 0 0 22 3 1 #"("1073 0 0 14 3 7 #"a-table"1074 0 0 77 3 1 #" "1075 0 0 14 3 4 #"left"1076 0 0 22 3 3 #")))"1077 0 0 77 3 1 #" "1078 0 0 22 3 1 #"("1079 0 0 14 3 18 #"find-root-discrete"1080 0 0 64 3 1 #" "1081 0 0 14 3 7 #"a-table"1082 0 0 64 3 1 #" "1083 0 0 14 3 4 #"left"1084 0 0 64 11 1 #" "1085 0 0 14 3 8 #"midpoint"1086 0 0 22 3 2 #")]"1087 0 0 77 29 1 #"\n"1088 0 0 77 3 6 #" "1089 0 0 22 3 1 #"["1090 0 0 14 3 4 #"else"1091 0 0 77 3 1 #" "1092 0 0 22 3 1 #"("1093 0 0 14 3 18 #"find-root-discrete"1094 0 0 64 3 1 #" "1095 0 0 14 3 7 #"a-table"1096 0 0 64 3 1 #" "1097 0 0 14 3 8 #"midpoint"1098 0 0 64 3 1 #" "1099 0 0 14 3 5 #"right"1100 0 0 22 3 5 #")])))"1101 0 0 64 29 1 #"\n"1102 0 0 64 29 1 #"\n"1103 0 0 22 3 1 #"("1104 0 0 14 3 4 #"time"1105 0 0 64 3 1 #" "1106 0 0 22 3 1 #"("1107 0 0 14 3 16 #"find-root-linear"1108 0 0 64 3 1 #" "1109 0 0 14 3 1 #"t"1110 0 0 64 3 1 #" "1111 0 0 20 3 5 #"30000"1112 0 0 22 3 2 #"))"1113 0 0 64 29 1 #"\n"1114 0 0 22 3 1 #"("1115 0 0 14 3 4 #"time"1116 0 0 63 3 1 #" "1117 0 0 22 3 1 #"("1118 0 0 14 3 19 #"find-root-discrete2"1119 0 0 63 3 1 #" "1120 0 0 14 3 1 #"t"1121 0 0 63 3 1 #" "1122 0 0 20 3 1 #"0"1123 0 0 63 3 1 #" "1124 0 0 20 3 5 #"30000"1125 0 0 22 3 2 #"))"1126 0 0 64 29 1 #"\n"1127 0 0 22 3 1 #"("1128 0 0 14 3 4 #"time"1129 0 0 64 3 1 #" "1130 0 0 22 3 1 #"("1131 0 0 14 3 18 #"find-root-discrete"1132 0 0 64 3 1 #" "1133 0 0 14 3 1 #"t"1134 0 0 64 3 1 #" "1135 0 0 20 3 1 #"0"1136 0 0 64 3 1 #" "1137 0 0 20 3 5 #"30000"1138 0 0 22 3 2 #"))"1139 0 0