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