0af62b015a
ordinary numbers and the LogEst representation. FossilOrigin-Name: 5252aeb61988e511dcf8d527fa81e51a5c9385f9
142 lines
3.6 KiB
C
142 lines
3.6 KiB
C
/*
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** 2013-06-10
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**
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** The author disclaims copyright to this source code. In place of
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** a legal notice, here is a blessing:
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**
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** May you do good and not evil.
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** May you find forgiveness for yourself and forgive others.
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** May you share freely, never taking more than you give.
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**
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*************************************************************************
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** This file contains a simple command-line utility for converting from
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** integers and LogEst values and back again and for doing simple
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** arithmetic operations (multiple and add) on LogEst values.
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**
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** Usage:
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**
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** ./LogEst ARGS
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**
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** Arguments:
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**
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** 'x' Multiple the top two elements of the stack
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** '+' Add the top two elements of the stack
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** NUM Convert NUM from integer to LogEst and push onto the stack
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** ^NUM Interpret NUM as a LogEst and push onto stack.
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**
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** Examples:
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**
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** To convert 123 from LogEst to integer:
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**
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** ./LogEst ^123
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**
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** To convert 123456 from integer to LogEst:
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**
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** ./LogEst 123456
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**
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <ctype.h>
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#include <assert.h>
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#include <string.h>
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#include "sqlite3.h"
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typedef short int LogEst; /* 10 times log2() */
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LogEst logEstMultiply(LogEst a, LogEst b){ return a+b; }
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LogEst logEstAdd(LogEst a, LogEst b){
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static const unsigned char x[] = {
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10, 10, /* 0,1 */
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9, 9, /* 2,3 */
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8, 8, /* 4,5 */
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7, 7, 7, /* 6,7,8 */
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6, 6, 6, /* 9,10,11 */
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5, 5, 5, /* 12-14 */
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4, 4, 4, 4, /* 15-18 */
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3, 3, 3, 3, 3, 3, /* 19-24 */
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2, 2, 2, 2, 2, 2, 2, /* 25-31 */
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};
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if( a<b ){ LogEst t = a; a = b; b = t; }
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if( a>b+49 ) return a;
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if( a>b+31 ) return a+1;
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return a+x[a-b];
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}
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LogEst logEstFromInteger(sqlite3_uint64 x){
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static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
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LogEst y = 40;
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if( x<8 ){
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if( x<2 ) return 0;
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while( x<8 ){ y -= 10; x <<= 1; }
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}else{
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while( x>255 ){ y += 40; x >>= 4; }
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while( x>15 ){ y += 10; x >>= 1; }
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}
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return a[x&7] + y - 10;
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}
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static sqlite3_uint64 logEstToInt(LogEst x){
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sqlite3_uint64 n;
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if( x<10 ) return 1;
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n = x%10;
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x /= 10;
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if( n>=5 ) n -= 2;
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else if( n>=1 ) n -= 1;
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if( x>=3 ) return (n+8)<<(x-3);
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return (n+8)>>(3-x);
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}
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static LogEst logEstFromDouble(double x){
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sqlite3_uint64 a;
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LogEst e;
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assert( sizeof(x)==8 && sizeof(a)==8 );
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if( x<=0.0 ) return -32768;
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if( x<1.0 ) return -logEstFromDouble(1/x);
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if( x<1024.0 ) return logEstFromInteger((sqlite3_uint64)(1024.0*x)) - 100;
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if( x<=2000000000.0 ) return logEstFromInteger((sqlite3_uint64)x);
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memcpy(&a, &x, 8);
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e = (a>>52) - 1022;
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return e*10;
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}
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int isFloat(const char *z){
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while( z[0] ){
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if( z[0]=='.' || z[0]=='E' || z[0]=='e' ) return 1;
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z++;
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}
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return 0;
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}
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int main(int argc, char **argv){
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int i;
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int n = 0;
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LogEst a[100];
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for(i=1; i<argc; i++){
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const char *z = argv[i];
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if( z[0]=='+' ){
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if( n>=2 ){
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a[n-2] = logEstAdd(a[n-2],a[n-1]);
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n--;
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}
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}else if( z[0]=='x' ){
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if( n>=2 ){
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a[n-2] = logEstMultiply(a[n-2],a[n-1]);
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n--;
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}
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}else if( z[0]=='^' ){
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a[n++] = atoi(z+1);
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}else if( isFloat(z) ){
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a[n++] = logEstFromDouble(atof(z));
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}else{
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a[n++] = logEstFromInteger(atoi(z));
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}
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}
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for(i=n-1; i>=0; i--){
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if( a[i]<0 ){
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printf("%d (%f)\n", a[i], 1.0/(double)logEstToInt(-a[i]));
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}else{
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sqlite3_uint64 x = logEstToInt(a[i]+100)*100/1024;
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printf("%d (%lld.%02lld)\n", a[i], x/100, x%100);
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}
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}
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return 0;
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}
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