

Link: http://codepad.org/s28WBi5y raw code | output | fork ]



C , pasted on Jun 7:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 /* * qsqrt.c * * Created on: Jun 6, 2012 * Author: Lee */ #include <stdio.h> #include <math.h> #define SQRT2 1.4142135623730951 float qsqrt ( float x ){ // x = [0 eeeeeeeeeee mmmmmmmmmmmmmmmmmmmmmmm] int i = * ( int * ) & x ; int j = ((( i / 2 - 0x1fc00000 ) + 0x3f800000 ) & 0x3ff800000 ) + (( i & 0x7fffff ) / 5 * 2 ); float y = ( * ( float * ) & j ) * (( i - 0x3f800000 ) & ( 0x800000 ) ? SQRT2 : 1 ); // 2-3 sig figs of significance // two iterations of newton: y = y - (y^2 - x)/2y yields 2^-18 points of precision y = ( y + x / y ) / 2 ; // this yields 2^-8 points of precision return ( y + x / y ) / 2 ; } int main (){ int i = 1 ; for (; i < 1000 ; i ++ ){ float f = ( qsqrt ( i ) - sqrt ( i )) / ( sqrt ( i )); printf ( "%3d %10f %10f \t rel err: %10f

" , i , qsqrt ( i ), sqrt ( i ), f ); } return 0 ; }



Output: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 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526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1 1.000000 1.000000 rel err: 0.000000 2 1.414214 1.414214 rel err: 0.000000 3 1.732051 1.732051 rel err: 0.000000 4 2.000000 2.000000 rel err: 0.000000 5 2.236068 2.236068 rel err: 0.000000 6 2.449490 2.449490 rel err: 0.000000 7 2.645751 2.645751 rel err: 0.000000 8 2.828427 2.828427 rel err: 0.000000 9 3.000000 3.000000 rel err: 0.000000 10 3.162278 3.162278 rel err: 0.000000 11 3.316625 3.316625 rel err: 0.000000 12 3.464102 3.464102 rel err: 0.000000 13 3.605551 3.605551 rel err: 0.000000 14 3.741657 3.741657 rel err: 0.000000 15 3.872983 3.872983 rel err: 0.000000 16 4.000000 4.000000 rel err: 0.000000 17 4.123106 4.123106 rel err: 0.000000 18 4.242641 4.242641 rel err: 0.000000 19 4.358899 4.358899 rel err: 0.000000 20 4.472136 4.472136 rel err: 0.000000 21 4.582576 4.582576 rel err: 0.000000 22 4.690416 4.690416 rel err: 0.000000 23 4.795832 4.795832 rel err: 0.000000 24 4.898980 4.898979 rel err: 0.000000 25 5.000000 5.000000 rel err: 0.000000 26 5.099020 5.099020 rel err: 0.000000 27 5.196153 5.196152 rel err: 0.000000 28 5.291503 5.291503 rel err: 0.000000 29 5.385165 5.385165 rel err: 0.000000 30 5.477226 5.477226 rel err: 0.000000 31 5.567764 5.567764 rel err: 0.000000 32 5.656854 5.656854 rel err: 0.000000 33 5.744563 5.744563 rel err: 0.000000 34 5.830952 5.830952 rel err: 0.000000 35 5.916080 5.916080 rel err: 0.000000 36 6.000000 6.000000 rel err: 0.000000 37 6.082763 6.082763 rel err: 0.000000 38 6.164414 6.164414 rel err: 0.000000 39 6.244998 6.244998 rel err: 0.000000 40 6.324555 6.324555 rel err: 0.000000 41 6.403124 6.403124 rel err: 0.000000 42 6.480741 6.480741 rel err: 0.000000 43 6.557439 6.557439 rel err: 0.000000 44 6.633250 6.633250 rel err: 0.000000 45 6.708204 6.708204 rel err: 0.000000 46 6.782330 6.782330 rel err: 0.000000 47 6.855655 6.855655 rel err: 0.000000 48 6.928203 6.928203 rel err: 0.000000 49 7.000000 7.000000 rel err: 0.000000 50 7.071068 7.071068 rel err: 0.000000 51 7.141429 7.141428 rel err: 0.000000 52 7.211103 7.211103 rel err: 0.000000 53 7.280110 7.280110 rel err: 0.000000 54 7.348469 7.348469 rel err: 0.000000 55 7.416199 7.416198 rel err: 0.000000 56 7.483315 7.483315 rel err: 0.000000 57 7.549835 7.549834 rel err: 0.000000 58 7.615773 7.615773 rel err: 0.000000 59 7.681146 7.681146 rel err: 0.000000 60 7.745967 7.745967 rel err: 0.000000 61 7.810250 7.810250 rel err: 0.000000 62 7.874008 7.874008 rel err: 0.000000 63 7.937254 7.937254 rel err: 0.000000 64 8.000000 8.000000 rel err: 0.000000 65 8.062258 8.062258 rel err: 0.000000 66 8.124038 8.124038 rel err: 0.000000 67 8.185353 8.185353 rel err: 0.000000 68 8.246211 8.246211 rel err: 0.000000 69 8.306624 8.306624 rel err: 0.000000 70 8.366600 8.366600 rel err: 0.000000 71 8.426150 8.426150 rel err: 0.000000 72 8.485281 8.485281 rel err: 0.000000 73 8.544004 8.544004 rel err: 0.000000 74 8.602325 8.602325 rel err: 0.000000 75 8.660254 8.660254 rel err: 0.000000 76 8.717798 8.717798 rel err: 0.000000 77 8.774964 8.774964 rel err: 0.000000 78 8.831761 8.831761 rel err: 0.000000 79 8.888194 8.888194 rel err: 0.000000 80 8.944272 8.944272 rel err: 0.000000 81 9.000000 9.000000 rel err: 0.000000 82 9.055385 9.055385 rel err: 0.000000 83 9.110434 9.110434 rel err: 0.000000 84 9.165152 9.165151 rel err: 0.000000 85 9.219545 9.219544 rel err: 0.000000 86 9.273619 9.273618 rel err: 0.000000 87 9.327379 9.327379 rel err: 0.000000 88 9.380832 9.380832 rel err: 0.000000 89 9.433981 9.433981 rel err: 0.000000 90 9.486833 9.486833 rel err: 0.000000 91 9.539392 9.539392 rel err: 0.000000 92 9.591663 9.591663 rel err: 0.000000 93 9.643651 9.643651 rel err: 0.000000 94 9.695360 9.695360 rel err: 0.000000 95 9.746795 9.746794 rel err: 0.000000 96 9.797959 9.797959 rel err: 0.000000 97 9.848858 9.848858 rel err: 0.000000 98 9.899495 9.899495 rel err: 0.000000 99 9.949875 9.949874 rel err: 0.000000 100 10.000000 10.000000 rel err: 0.000000 101 10.049876 10.049876 rel err: 0.000000 102 10.099505 10.099505 rel err: 0.000000 103 10.148892 10.148892 rel err: 0.000000 104 10.198039 10.198039 rel err: 0.000000 105 10.246951 10.246951 rel err: 0.000000 106 10.295630 10.295630 rel err: 0.000000 107 10.344081 10.344080 rel err: 0.000000 108 10.392305 10.392305 rel err: 0.000000 109 10.440307 10.440307 rel err: 0.000000 110 10.488089 10.488088 rel err: 0.000000 111 10.535654 10.535654 rel err: 0.000000 112 10.583005 10.583005 rel err: 0.000000 113 10.630146 10.630146 rel err: 0.000000 114 10.677078 10.677078 rel err: 0.000000 115 10.723805 10.723805 rel err: 0.000000 116 10.770330 10.770330 rel err: 0.000000 117 10.816654 10.816654 rel err: 0.000000 118 10.862781 10.862780 rel err: 0.000000 119 10.908712 10.908712 rel err: 0.000000 120 10.954451 10.954451 rel err: 0.000000 121 11.000000 11.000000 rel err: 0.000000 122 11.045361 11.045361 rel err: 0.000000 123 11.090537 11.090537 rel err: 0.000000 124 11.135529 11.135529 rel err: 0.000000 125 11.180340 11.180340 rel err: 0.000000 126 11.224972 11.224972 rel err: 0.000000 127 11.269428 11.269428 rel err: 0.000000 128 11.313708 11.313708 rel err: 0.000000 129 11.357817 11.357817 rel err: 0.000000 130 11.401754 11.401754 rel err: 0.000000 131 11.445523 11.445523 rel err: 0.000000 132 11.489125 11.489125 rel err: 0.000000 133 11.532563 11.532563 rel err: 0.000000 134 11.575837 11.575837 rel err: 0.000000 135 11.618950 11.618950 rel err: 0.000000 136 11.661904 11.661904 rel err: 0.000000 137 11.704700 11.704700 rel err: 0.000000 138 11.747340 11.747340 rel err: 0.000000 139 11.789826 11.789826 rel err: 0.000000 140 11.832160 11.832160 rel err: 0.000000 141 11.874342 11.874342 rel err: 0.000000 142 11.916375 11.916375 rel err: 0.000000 143 11.958261 11.958261 rel err: 0.000000 144 12.000000 12.000000 rel err: 0.000000 145 12.041595 12.041595 rel err: 0.000000 146 12.083046 12.083046 rel err: 0.000000 147 12.124356 12.124356 rel err: 0.000000 148 12.165525 12.165525 rel err: 0.000000 149 12.206556 12.206556 rel err: 0.000000 150 12.247449 12.247449 rel err: 0.000000 151 12.288206 12.288206 rel err: 0.000000 152 12.328828 12.328828 rel err: 0.000000 153 12.369317 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13.304135 13.304135 rel err: 0.000000 178 13.341664 13.341664 rel err: 0.000000 179 13.379088 13.379088 rel err: 0.000000 180 13.416408 13.416408 rel err: 0.000000 181 13.453624 13.453624 rel err: 0.000000 182 13.490738 13.490738 rel err: 0.000000 183 13.527750 13.527749 rel err: 0.000000 184 13.564660 13.564660 rel err: 0.000000 185 13.601471 13.601471 rel err: 0.000000 186 13.638182 13.638182 rel err: 0.000000 187 13.674795 13.674794 rel err: 0.000000 188 13.711309 13.711309 rel err: 0.000000 189 13.747727 13.747727 rel err: 0.000000 190 13.784049 13.784049 rel err: 0.000000 191 13.820275 13.820275 rel err: 0.000000 192 13.856407 13.856406 rel err: 0.000000 193 13.892444 13.892444 rel err: 0.000000 194 13.928389 13.928388 rel err: 0.000000 195 13.964240 13.964240 rel err: 0.000000 196 14.000000 14.000000 rel err: 0.000000 197 14.035669 14.035669 rel err: 0.000000 198 14.071248 14.071247 rel err: 0.000000 199 14.106736 14.106736 rel err: 0.000000 200 14.142136 14.142136 rel err: 0.000000 201 14.177447 14.177447 rel err: 0.000000 202 14.212671 14.212670 rel err: 0.000000 203 14.247807 14.247807 rel err: 0.000000 204 14.282857 14.282857 rel err: 0.000000 205 14.317821 14.317821 rel err: 0.000000 206 14.352700 14.352700 rel err: 0.000000 207 14.387495 14.387495 rel err: 0.000000 208 14.422205 14.422205 rel err: 0.000000 209 14.456833 14.456832 rel err: 0.000000 210 14.491377 14.491377 rel err: 0.000000 211 14.525839 14.525839 rel err: 0.000000 212 14.560220 14.560220 rel err: 0.000000 213 14.594520 14.594520 rel err: 0.000000 214 14.628739 14.628739 rel err: 0.000000 215 14.662879 14.662878 rel err: 0.000000 216 14.696939 14.696938 rel err: 0.000000 217 14.730920 14.730920 rel err: 0.000000 218 14.764823 14.764823 rel err: 0.000000 219 14.798649 14.798649 rel err: 0.000000 220 14.832397 14.832397 rel err: 0.000000 221 14.866069 14.866069 rel err: 0.000000 222 14.899665 14.899664 rel err: 0.000000 223 14.933185 14.933185 rel err: 0.000000 224 14.966630 14.966630 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15.748016 rel err: 0.000000 249 15.779734 15.779734 rel err: 0.000000 250 15.811388 15.811388 rel err: 0.000000 251 15.842980 15.842980 rel err: 0.000000 252 15.874508 15.874508 rel err: 0.000000 253 15.905974 15.905974 rel err: 0.000000 254 15.937377 15.937377 rel err: 0.000000 255 15.968719 15.968719 rel err: 0.000000 256 16.000000 16.000000 rel err: 0.000000 257 16.031220 16.031220 rel err: 0.000000 258 16.062378 16.062378 rel err: 0.000000 259 16.093477 16.093477 rel err: 0.000000 260 16.124515 16.124515 rel err: 0.000000 261 16.155494 16.155494 rel err: 0.000000 262 16.186414 16.186414 rel err: 0.000000 263 16.217275 16.217275 rel err: 0.000000 264 16.248077 16.248077 rel err: 0.000000 265 16.278821 16.278821 rel err: 0.000000 266 16.309506 16.309506 rel err: 0.000000 267 16.340135 16.340135 rel err: 0.000000 268 16.370706 16.370706 rel err: 0.000000 269 16.401219 16.401219 rel err: 0.000000 270 16.431677 16.431677 rel err: 0.000000 271 16.462078 16.462078 rel err: 0.000000 272 16.492423 16.492423 rel err: 0.000000 273 16.522712 16.522712 rel err: 0.000000 274 16.552945 16.552945 rel err: 0.000000 275 16.583124 16.583124 rel err: 0.000000 276 16.613248 16.613248 rel err: 0.000000 277 16.643317 16.643317 rel err: 0.000000 278 16.673332 16.673332 rel err: 0.000000 279 16.703293 16.703293 rel err: 0.000000 280 16.733201 16.733201 rel err: 0.000000 281 16.763055 16.763055 rel err: 0.000000 282 16.792856 16.792856 rel err: 0.000000 283 16.822604 16.822604 rel err: 0.000000 284 16.852300 16.852300 rel err: 0.000000 285 16.881943 16.881943 rel err: 0.000000 286 16.911535 16.911535 rel err: 0.000000 287 16.941074 16.941074 rel err: 0.000000 288 16.970563 16.970563 rel err: 0.000000 289 17.000000 17.000000 rel err: 0.000000 290 17.029386 17.029386 rel err: 0.000000 291 17.058722 17.058722 rel err: 0.000000 292 17.088008 17.088007 rel err: 0.000000 293 17.117243 17.117243 rel err: 0.000000 294 17.146428 17.146428 rel err: 0.000000 295 17.175564 17.175564 rel err: 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