c_cpp/etc/calc/jump.c

   1 /*
   2  * jump - trivial prime jump table
   3  *
   4  * Copyright (C) 1999  Landon Curt Noll
   5  *
   6  * Calc is open software; you can redistribute it and/or modify it under
   7  * the terms of the version 2.1 of the GNU Lesser General Public License
   8  * as published by the Free Software Foundation.
   9  *
  10  * Calc is distributed in the hope that it will be useful, but WITHOUT
  11  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  12  * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
  13  * Public License for more details.
  14  *
  15  * A copy of version 2.1 of the GNU Lesser General Public License is
  16  * distributed with calc under the filename COPYING-LGPL.  You should have
  17  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  18  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  19  *
  20  * @(#) $Revision: 30.1 $
  21  * @(#) $Id: jump.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
  22  * @(#) $Source: /usr/local/src/bin/calc/RCS/jump.c,v $
  23  *
  24  * Under source code control:   1994/06/29 04:03:54
  25  * File existed as early as:    1994
  26  *
  27  * chongo <was here> /\oo/\     http://www.isthe.com/chongo/
  28  * Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
  29  */
  30
  31 /*
  32  * If x is divisible by a trivial prime (2,3,5,7,11), then:
  33  *
  34  *              x + jmpindx[ (x>>1)%JMPMOD ]
  35  *
  36  * is the value of the smallest value > x that is not divisible by a
  37  * trivial prime.  JMPMOD is the product of the odd trivial primes.
  38  *
  39  * This table is useful for skipping values that are obviously not prime
  40  * by skipping values that are a multiple of trivial prime.
  41  *
  42  * If x is not divisible by a trivial prime, then:
  43  *
  44  *              x + jmp[ -jmpindx[(x>>1)%JMPMOD] ]
  45  *
  46  * is the value of the smallest value > x that is not divisible by a
  47  * trivial prime.
  48  *
  49  * Instead of testing successive odd values, this system allows us to
  50  * skip odd values divisible by trivial primes.  This is process on the
  51  * average reduces the values we need to test by a factor of at least 2.4.
  52  */
  53
  54
  55 #include "jump.h"
  56
  57 /*
  58  * jmpindx - how to find the next value not divisible by a trivial prime
  59  *
  60  * If jmpindx[y] > 0 (y = x mod JMPMOD*2), then it refers to an 'x' that
  61  * is divisible by a trivial prime and jmpindx[y] is the offset to the next
  62  * value that is not divisible.
  63  *
  64  * If jmpindx[y] <= 0, then 'x' is not divisible by a trivial prime and
  65  * the negative of jmpindx[y] is the index into the jmp[] table.  We use
  66  * successive values from jmp[] (wrapping around to the beginning when
  67  * we move off the end of jmp[]) to move to higher and higher values
  68  * that are not divisible by trivial primes.
  69  */
  70 CONST short jmpindx[JMPMOD] = {
  71     0, 10, 8, 6, 4, 2, -1, 2, -2, -3, 2, -4, 4, 2, -5, -6, 4, 2, -7, 2, -8, -9,
  72     2, -10, 4, 2, -11, 4, 2, -12, -13, 4, 2, -14, 2, -15, -16, 4, 2, -17, 2,
  73     -18, 4, 2, -19, 6, 4, 2, -20, 2, -21, -22, 2, -23, -24, 2, -25, 12, 10,
  74     8, 6, 4, 2, -26, 2, -27, 4, 2, -28, -29, 8, 6, 4, 2, -30, -31, 4, 2, -32,
  75     4, 2, -33, 2, -34, -35, 2, -36, 4, 2, -37, -38, 8, 6, 4, 2, -39, -40, 2,
  76     -41, -42, 10, 8, 6, 4, 2, -43, 8, 6, 4, 2, -44, -45, 2, -46, -47, 2, -48,
  77     4, 2, -49, -50, 4, 2, -51, 2, -52, 4, 2, -53, 4, 2, -54, 4, 2, -55, -56,
  78     4, 2, -57, 2, -58, -59, 4, 2, -60, 2, -61, 4, 2, -62, 6, 4, 2, -63, 2,
  79     -64, -65, 2, -66, 4, 2, -67, 6, 4, 2, -68, 4, 2, -69, 8, 6, 4, 2, -70,
  80     -71, 2, -72, 4, 2, -73, -74, 4, 2, -75, 4, 2, -76, 2, -77, -78, 2, -79,
  81     4, 2, -80, -81, 4, 2, -82, 2, -83, -84, 4, 2, -85, 8, 6, 4, 2, -86, -87,
  82     8, 6, 4, 2, -88, -89, 2, -90, -91, 2, -92, 4, 2, -93, 6, 4, 2, -94, 2,
  83     -95, -96, 2, -97, 10, 8, 6, 4, 2, -98, -99, 4, 2, -100, 2, -101, -102, 4,
  84     2, -103, 2, -104, 4, 2, -105, 10, 8, 6, 4, 2, -106, -107, 2, -108, -109,
  85     2, -110, 6, 4, 2, -111, 4, 2, -112, 2, -113, 4, 2, -114, -115, 2, -116,
  86     4, 2, -117, -118, 4, 2, -119, 8, 6, 4, 2, -120, -121, 2, -122, 4, 2, -123,
  87     -124, 4, 2, -125, 2, -126, -127, 2, -128, -129, 8, 6, 4, 2, -130, -131,
  88     8, 6, 4, 2, -132, -133, 2, -134, 4, 2, -135, 4, 2, -136, -137, 4, 2, -138,
  89     4, 2, -139, 2, -140, 4, 2, -141, 4, 2, -142, -143, 4, 2, -144, 2, -145,
  90     -146, 4, 2, -147, 2, -148, 4, 2, -149, 6, 4, 2, -150, 2, -151, -152, 4,
  91     2, -153, 2, -154, 6, 4, 2, -155, 4, 2, -156, 2, -157, 4, 2, -158, -159,
  92     2, -160, 4, 2, -161, 6, 4, 2, -162, 4, 2, -163, 2, -164, -165, 8, 6, 4,
  93     2, -166, -167, 4, 2, -168, 2, -169, -170, 2, -171, -172, 8, 6, 4, 2, -173,
  94     -174, 8, 6, 4, 2, -175, -176, 2, -177, -178, 2, -179, 6, 4, 2, -180, 4,
  95     2, -181, 2, -182, -183, 2, -184, 4, 2, -185, 4, 2, -186, -187, 4, 2, -188,
  96     2, -189, 6, 4, 2, -190, 2, -191, 4, 2, -192, 6, 4, 2, -193, 2, -194, -195,
  97     2, -196, -197, 2, -198, 6, 4, 2, -199, 4, 2, -200, 2, -201, 4, 2, -202,
  98     4, 2, -203, 4, 2, -204, -205, 4, 2, -206, 4, 2, -207, 2, -208, -209, 2,
  99     -210, 4, 2, -211, -212, 4, 2, -213, 2, -214, -215, 2, -216, -217, 8, 6,
 100     4, 2, -218, -219, 8, 6, 4, 2, -220, -221, 4, 2, -222, 2, -223, 4, 2, -224,
 101     -225, 4, 2, -226, 2, -227, -228, 2, -229, 4, 2, -230, 4, 2, -231, 6, 4,
 102     2, -232, 2, -233, -234, 4, 2, -235, 8, 6, 4, 2, -236, 6, 4, 2, -237, 2,
 103     -238, -239, 2, -240, -241, 2, -242, 6, 4, 2, -243, 8, 6, 4, 2, -244, 4,
 104     2, -245, -246, 2, -247, 6, 4, 2, -248, 4, 2, -249, 4, 2, -250, 2, -251,
 105     -252, 2, -253, 4, 2, -254, -255, 4, 2, -256, 2, -257, 4, 2, -258, -259,
 106     8, 6, 4, 2, -260, -261, 8, 6, 4, 2, -262, -263, 2, -264, -265, 2, -266,
 107     4, 2, -267, -268, 4, 2, -269, 2, -270, -271, 2, -272, 4, 2, -273, 4, 2,
 108     -274, -275, 4, 2, -276, 4, 2, -277, 4, 2, -278, 2, -279, 4, 2, -280, 6,
 109     4, 2, -281, 2, -282, -283, 2, -284, -285, 2, -286, 6, 4, 2, -287, 4, 2,
 110     -288, 2, -289, 6, 4, 2, -290, 2, -291, 4, 2, -292, -293, 4, 2, -294, 4,
 111     2, -295, 2, -296, -297, 2, -298, 4, 2, -299, 6, 4, 2, -300, 2, -301, -302,
 112     2, -303, -304, 8, 6, 4, 2, -305, -306, 8, 6, 4, 2, -307, -308, 2, -309,
 113     -310, 2, -311, 4, 2, -312, -313, 8, 6, 4, 2, -314, -315, 2, -316, 4, 2,
 114     -317, 6, 4, 2, -318, 4, 2, -319, 2, -320, -321, 4, 2, -322, 2, -323, 4,
 115     2, -324, 6, 4, 2, -325, 2, -326, 4, 2, -327, -328, 2, -329, 6, 4, 2, -330,
 116     4, 2, -331, 2, -332, 4, 2, -333, -334, 2, -335, 4, 2, -336, -337, 4, 2,
 117     -338, 4, 2, -339, 2, -340, 4, 2, -341, 4, 2, -342, -343, 4, 2, -344, 4,
 118     2, -345, 2, -346, -347, 8, 6, 4, 2, -348, -349, 8, 6, 4, 2, -350, -351,
 119     2, -352, -353, 2, -354, 4, 2, -355, -356, 4, 2, -357, 2, -358, -359, 8,
 120     6, 4, 2, -360, 4, 2, -361, -362, 4, 2, -363, 2, -364, -365, 4, 2, -366,
 121     2, -367, 4, 2, -368, 6, 4, 2, -369, 2, -370, -371, 2, -372, -373, 10, 8,
 122     6, 4, 2, -374, 4, 2, -375, 2, -376, 4, 2, -377, -378, 2, -379, 4, 2, -380,
 123     -381, 10, 8, 6, 4, 2, -382, 2, -383, -384, 2, -385, 6, 4, 2, -386, 4,
 124     2, -387, 2, -388, -389, 2, -390, -391, 8, 6, 4, 2, -392, -393, 8, 6, 4,
 125     2, -394, 4, 2, -395, -396, 2, -397, 4, 2, -398, -399, 4, 2, -400, 2, -401,
 126     -402, 2, -403, 4, 2, -404, 4, 2, -405, -406, 4, 2, -407, 2, -408, -409,
 127     8, 6, 4, 2, -410, 4, 2, -411, 6, 4, 2, -412, 4, 2, -413, 2, -414, -415,
 128     2, -416, 6, 4, 2, -417, 4, 2, -418, 2, -419, 4, 2, -420, -421, 2, -422,
 129     4, 2, -423, -424, 4, 2, -425, 4, 2, -426, 4, 2, -427, 2, -428, 4, 2, -429,
 130     -430, 4, 2, -431, 2, -432, -433, 2, -434, -435, 8, 6, 4, 2, -436, 10, 8,
 131     6, 4, 2, -437, -438, 2, -439, -440, 8, 6, 4, 2, -441, -442, 4, 2, -443,
 132     2, -444, -445, 2, -446, 4, 2, -447, 4, 2, -448, -449, 8, 6, 4, 2, -450,
 133     -451, 4, 2, -452, 2, -453, 12, 10, 8, 6, 4, 2, -454, 2, -455, -456, 2,
 134     -457, -458, 2, -459, 6, 4, 2, -460, 4, 2, -461, 2, -462, 4, 2, -463, -464,
 135     2, -465, 4, 2, -466, -467, 4, 2, -468, 4, 2, -469, 2, -470, -471, 2, -472,
 136     4, 2, -473, -474, 4, 2, -475, 2, -476, -477, 2, -478, 10, 8, 6, 4, 2, -479
 137 };
 138
 139 /*
 140  * jmp - intervals between successive integers not divisible by trivial primes
 141  */
 142 CONST unsigned char jmp[JMPSIZE] = {
 143     12, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4,
 144     2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 2, 4, 6, 2, 10, 2, 4, 2, 12, 10, 2,
 145     4, 2, 4, 6, 2, 6, 4, 6, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 6, 8, 6,
 146     10, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 6, 10, 2, 10, 2, 4, 2, 4,
 147     6, 8, 4, 2, 4, 12, 2, 6, 4, 2, 6, 4, 6, 12, 2, 4, 2, 4, 8, 6, 4, 6, 2,
 148     4, 6, 2, 6, 10, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2, 10, 2, 4, 6, 6, 2, 6,
 149     6, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 6, 4, 8, 6, 4, 6, 2, 4, 6, 8,
 150     6, 4, 2, 10, 2, 6, 4, 2, 4, 2, 10, 2, 10, 2, 4, 2, 4, 8, 6, 4, 2, 4, 6,
 151     6, 2, 6, 4, 8, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 6, 6, 6, 2, 6, 6, 4, 2,
 152     4, 6, 2, 6, 4, 2, 4, 2, 10, 2, 10, 2, 6, 4, 6, 2, 6, 4, 2, 4, 6, 6, 8,
 153     4, 2, 6, 10, 8, 4, 2, 4, 2, 4, 8, 10, 6, 2, 4, 8, 6, 6, 4, 2, 4, 6, 2,
 154     6, 4, 6, 2, 10, 2, 10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 6, 6,
 155     4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 8, 4, 6, 2, 6, 6, 4, 2, 4, 6, 8, 4, 2,
 156     4, 2, 10, 2, 10, 2, 4, 2, 4, 6, 2, 10, 2, 4, 6, 8, 6, 4, 2, 6, 4, 6, 8,
 157     4, 6, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 6, 6, 2, 6, 6, 4, 2, 10, 2,
 158     10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 10, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4,
 159     2, 12, 6, 4, 6, 2, 4, 6, 2, 12, 4, 2, 4, 8, 6, 4, 2, 4, 2, 10, 2, 10, 6,
 160     2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 10, 6, 8, 6, 4, 2, 4, 8, 6,
 161     4, 6, 2, 4, 6, 2, 6, 6, 6, 4, 6, 2, 6, 4, 2, 4, 2, 10, 12, 2, 4, 2, 10,
 162     2, 6, 4, 2, 4, 6, 6, 2, 10, 2, 6, 4, 14, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2,
 163     4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 12, 2
 164 };
 165 CONST unsigned char *CONST lastjmp = (jmp+JMPSIZE-1);