Related
guys, I'm making simple graph drawer and want to find beautiful values for horizontal lines.
For example, if I have value equals to 72089.601562, beautiful is 70000, or 75000. So, I think that beautifulNumber%5 = 0.
Have you any ideas?
How about this?
#import <math.h>
#import <stdio.h>
#define ROUNDING 5000
int beautify(float input)
{
// Cast to int, losing the decimal value.
int value = (int)input;
value = (value / ROUNDING) * ROUNDING;
if ((int)input % ROUNDING > ROUNDING / 2 )
{
value += ROUNDING;
}
return value;
}
int main()
{
printf("%d\n", beautify(70000.601562)); // 70000
printf("%d\n", beautify(72089.601562)); // 70000
printf("%d\n", beautify(76089.601562)); // 75000
printf("%d\n", beautify(79089.601562)); // 80000
printf("%d\n", beautify(70000.601562)); // 70000
return 0;
}
It depends whether you want a floor value, a ceiling value or just to round to the nearest 5000.
For a floor value:
int beautiful = (int)(floor(ugly / 5000.0) * 5000.0);
For a ceiling value:
int beautiful = (int)(ceil(ugly / 5000.0) * 5000.0);
For rounding:
int beautiful = (int)(round(ugly / 5000.0) * 5000.0);
For making graph lines, I'd probably find the minimum and maximum values you have to graph, start with a floor value for the minimum value and then add your desired interval until you have surpassed your maximum value.
For instance:
float minValue = 2.34;
float maxValue = 7.72;
int interval = 1;
NSMutableArray *horizLines = [NSMutableArray array];
int line = (int)(floor(minValue / interval) * interval);
[horizLines addObject:[NSNumber numberWithInt:line]];
do {
line = (int)(ceil(minValue / interval) * interval);
[horizLines addObject:[NSNumber numberWithInt:line]];
if (minValue >= maxValue) break;
minValue = minValue + interval;
}
Use as needed!
Well, it seems like you'd want it to scale based on the size of the number. If the range only goes to 10, then obviously rounding to the nearest 5,000 doesn't make sense. There's probably a really elegant way to code it using bit shifting but just something like this will do the trick:
float value = 72089.601562
int beautiful = 0;
// EDIT to support returning a float for small numbers:
if (value < 0.2) beautiful = int(value*100)/100.;
else if (value < 2.) beautiful = int(value*10)/10.;
// Anything bigger is easy:
else if (value < 20) beautiful = (int)value;
else if (value < 200) beautiful = (int)value/10;
else if (value < 2000) beautiful = (int)value/100;
else if (value < 20000) beautiful = (int)value/1000;
// etc
Sounds like what you want to do is round to 1 or perhaps 2 significant digits. Rounding to n significant digits is pretty easy:
double roundToNDigits(double x, int n) {
double basis = pow(10.0, floor(log10(x)) - (n-1));
return basis * round(x / basis);
}
This will give you roundToNDigits(74518.7, 1) == 70000.0 and roundToNDigits(7628.54, 1) == 8000.00
If you want to round to 1 or 2 digits (only 2 where the second digit is 5), you want something like:
double roundSpecial(double x) {
double basis = pow(10.0, floor(log10(x))) / 2.0;
return basis * round(x / basis);
}
This is a simple number series question, I have numbers in series like
2,4,8,16,32,64,128,256 these numbers are formed by 2,2(square),2(cube) and so on.
Now if I add 2+4+8 = 14. 14 will get only by the addition 2,4 and 8.
so i have 14in my hand now, By some logic i need to get the values which are helped to get 14
Example:
2+4+8 = 14
14(some logic) = 2,4,8.
This is an easy one:
2+4+8=14 ... 14+2=16
2+4+8+16=30 ... 30+2=32
2+4+8+16+32=62 ... 62+2=64
So you just need to add 2 to your sum, then calculate ld (binary logarithm), and then subtract 1. This gives you the number of elements of your sequence you need to add up.
e.g. in PHP:
$target=14;
$count=log($target+2)/log(2)-1;
echo $count;
gives 3, so you have to add the first 3 elements of your sequence to get 14.
Check the following C# code:
x = 14; // In your case
indices = new List<int>();
for (var i = 31; i >= i; i--)
{
var pow = Math.Pow(2, i);
if x - pow >= 0)
{
indices.Add(pow);
x -= pow;
}
}
indices.Reverse();
assuming C:
unsigned int a = 14;
while( a>>=1)
{
printf("%d ", a+1);
}
if this is programming, something like this would suffice:
int myval = 14;
int maxval = 256;
string elements = "";
for (int i = 1; i <= maxval; i*=2)
{
if ((myval & i) != 0)
elements += "," + i.ToString();
}
Use congruency module 2-powers: 14 mod 2 = 0, 14 mod 4 = 2, 14 mod 8 = 6, 14 mod 16 = 14, 14 mod 32 = 14...
The differences of this sequence are the numbers you look for 2 - 0 = 2, 6 - 2 = 4, 14 - 6 = 8, 14 - 14 = 0, ...
It's called the p-adic representation and is formally a bit more difficult to explain, but I hope this gives you an idea for an algorithm.
Imagine a std:vector, say, with 100 things on it (0 to 99) currently. You are treating it as a loop. So the 105th item is index 4; forward 7 from index 98 is 5.
You want to delete N items after index position P.
So, delete 5 items after index 50; easy.
Or 5 items after index 99: as you delete 0 five times, or 4 through 0, noting that position at 99 will be erased from existence.
Worst, 5 items after index 97 - you have to deal with both modes of deletion.
What's the elegant and solid approach?
Here's a boring routine I wrote
-(void)knotRemovalHelper:(NSMutableArray*)original
after:(NSInteger)nn howManyToDelete:(NSInteger)desired
{
#define ORCO ((NSInteger)[original count])
static NSInteger kount, howManyUntilLoop, howManyExtraAferLoop;
if ( ... our array is NOT a loop ... )
// trivial, if messy...
{
for ( kount = 1; kount<=desired; ++kount )
{
if ( (nn+1) >= ORCO )
return;
[original removeObjectAtIndex:( nn+1 )];
}
return;
}
else // our array is a loop
// messy, confusing and inelegant. how to improve?
// here we go...
{
howManyUntilLoop = (ORCO-1) - nn;
if ( howManyUntilLoop > desired )
{
for ( kount = 1; kount<=desired; ++kount )
[original removeObjectAtIndex:( nn+1 )];
return;
}
howManyExtraAferLoop = desired - howManyUntilLoop;
for ( kount = 1; kount<=howManyUntilLoop; ++kount )
[original removeObjectAtIndex:( nn+1 )];
for ( kount = 1; kount<=howManyExtraAferLoop; ++kount )
[original removeObjectAtIndex:0];
return;
}
#undef ORCO
}
Update!
InVariant's second answer leads to the following excellent solution. "starting with" is much better than "starting after". So the routine now uses "start with". Invariant's second answer leads to this very simple solution...
N times do if P < currentsize remove P else remove 0
-(void)removeLoopilyFrom:(NSMutableArray*)ra
startingWithThisOne:(NSInteger)removeThisOneFirst
howManyToDelete:(NSInteger)countToDelete
{
// exception if removeThisOneFirst > ra highestIndex
// exception if countToDelete is > ra size
// so easy thanks to Invariant:
for ( do this countToDelete times )
{
if ( removeThisOneFirst < [ra count] )
[ra removeObjectAtIndex:removeThisOneFirst];
else
[ra removeObjectAtIndex:0];
}
}
Update!
Toolbox has pointed out the excellent idea of working to a new array - super KISS.
Here's an idea off the top of my head.
First, generate an array of integers representing the indices to remove. So "remove 5 from index 97" would generate [97,98,99,0,1]. This can be done with the application of a simple modulus operator.
Then, sort this array descending giving [99,98,97,1,0] and then remove the entries in that order.
Should work in all cases.
This solution seems to work, and it copies all remaining elements in the vector only once (to their final destination).
Assume kNumElements, kStartIndex, and kNumToRemove are defined as const size_t values.
vector<int> my_vec(kNumElements);
for (size_t i = 0; i < my_vec.size(); ++i) {
my_vec[i] = i;
}
for (size_t i = 0, cur = 0; i < my_vec.size(); ++i) {
// What is the "distance" from the current index to the start, taking
// into account the wrapping behavior?
size_t distance = (i + kNumElements - kStartIndex) % kNumElements;
// If it's not one of the ones to remove, then we keep it by copying it
// into its proper place.
if (distance >= kNumToRemove) {
my_vec[cur++] = my_vec[i];
}
}
my_vec.resize(kNumElements - kNumToRemove);
There's nothing wrong with two loop solutions as long as they're readable and don't do anything redundant. I don't know Objective-C syntax, but here's the pseudocode approach I'd take:
endIdx = after + howManyToDelete
if (Len <= after + howManyToDelete) //will have a second loop
firstloop = Len - after; //handle end in the first loop, beginning in second
else
firstpass = howManyToDelete; //the first loop will get them all
for (kount = 0; kount < firstpass; kount++)
remove after+1
for ( ; kount < howManyToDelete; kount++) //if firstpass < howManyToDelete, clean up leftovers
remove 0
This solution doesn't use mod, does the limit calculation outside the loop, and touches the relevant samples once each. The second for loop won't execute if all the samples were handled in the first loop.
The common way to do this in DSP is with a circular buffer. This is just a fixed length buffer with two associated counters:
//make sure BUFSIZE is a power of 2 for quick mod trick
#define BUFSIZE 1024
int CircBuf[BUFSIZE];
int InCtr, OutCtr;
void PutData(int *Buf, int count) {
int srcCtr;
int destCtr = InCtr & (BUFSIZE - 1); // if BUFSIZE is a power of 2, equivalent to and faster than destCtr = InCtr % BUFSIZE
for (srcCtr = 0; (srcCtr < count) && (destCtr < BUFSIZE); srcCtr++, destCtr++)
CircBuf[destCtr] = Buf[srcCtr];
for (destCtr = 0; srcCtr < count; srcCtr++, destCtr++)
CircBuf[destCtr] = Buf[srcCtr];
InCtr += count;
}
void GetData(int *Buf, int count) {
int srcCtr = OutCtr & (BUFSIZE - 1);
int destCtr = 0;
for (destCtr = 0; (srcCtr < BUFSIZE) && (destCtr < count); srcCtr++, destCtr++)
Buf[destCtr] = CircBuf[srcCtr];
for (srcCtr = 0; srcCtr < count; srcCtr++, destCtr++)
Buf[destCtr] = CircBuf[srcCtr];
OutCtr += count;
}
int BufferOverflow() {
return ((InCtr - OutCtr) > BUFSIZE);
}
This is pretty lightweight, but effective. And aside from the ctr = BigCtr & (SIZE-1) stuff, I'd argue it's highly readable. The only reason for the & trick is in old DSP environments, mod was an expensive operation so for something that ran often, like every time a buffer was ready for processing, you'd find ways to remove stuff like that. And if you were doing FFT's, your buffers were probably a power of 2 anyway.
These days, of course, you have 1 GHz processors and magically resizing arrays. You kids get off my lawn.
Another method:
N times do {remove entry at index P mod max(ArraySize, P)}
Example:
N=5, P=97, ArraySize=100
1: max(100, 97)=100 so remove at 97%100 = 97
2: max(99, 97)=99 so remove at 97%99 = 97 // array size is now 99
3: max(98, 97)=98 so remove at 97%98 = 97
4: max(97, 97)=97 so remove at 97%97 = 0
5: max(96, 97)=97 so remove at 97%97 = 0
I don't program iphone for know, so I image std::vector, it's quite easy, simple and elegant enough:
#include <iostream>
using std::cout;
#include <vector>
using std::vector;
#include <cassert> //no need for using, assert is macro
template<typename T>
void eraseCircularVector(vector<T> & vec, size_t position, size_t count)
{
assert(count <= vec.size());
if (count > 0)
{
position %= vec.size(); //normalize position
size_t positionEnd = (position + count) % vec.size();
if (positionEnd < position)
{
vec.erase(vec.begin() + position, vec.end());
vec.erase(vec.begin(), vec.begin() + positionEnd);
}
else
vec.erase(vec.begin() + position, vec.begin() + positionEnd);
}
}
int main()
{
vector<int> values;
for (int i = 0; i < 10; ++i)
values.push_back(i);
cout << "Values: ";
for (vector<int>::const_iterator cit = values.begin(); cit != values.end(); cit++)
cout << *cit << ' ';
cout << '\n';
eraseCircularVector(values, 5, 1); //remains 9: 0,1,2,3,4,6,7,8,9
eraseCircularVector(values, 16, 5); //remains 4: 3,4,6,7
cout << "Values: ";
for (vector<int>::const_iterator cit = values.begin(); cit != values.end(); cit++)
cout << *cit << ' ';
cout << '\n';
return 0;
}
However, you might consider:
creating new loop_vector class, if you use this kind of functionality enough
using list if you perform many deletions (or few deletions (not from end, that's simple pop_back) but large array)
If your container (NSMutableArray or whatever) is not list, but vector (i.e. resizable array), you most definitely don't want to delete items one by one, but whole range (e.g. std::vector's erase(begin, end)!
Edit: reacting to comment, to fully realize what must be done by vector, if you erase element other than the last one: it must copy all values after that element (e.g. 1000 items in array, you erase first, 999x copying (moving) of item, that is very costly).
Example:
#include <iostream>
#include <vector>
#include <ctime>
using namespace std;
int main()
{
clock_t start, end;
vector<int> vec;
const int items = 64 * 1024;
cout << "using " << items << " items in vector\n";
for (size_t i = 0; i < items; ++i) vec.push_back(i);
start = clock();
while (!vec.empty()) vec.erase(vec.begin());
end = clock();
cout << "Inefficient method took: "
<< (end - start) * 1.0 / CLOCKS_PER_SEC << " ms\n";
for (size_t i = 0; i < items; ++i) vec.push_back(i);
start = clock();
vec.erase(vec.begin(), vec.end());
end = clock();
cout << "Efficient method took: "
<< (end - start) * 1.0 / CLOCKS_PER_SEC << " ms\n";
return 0;
}
Produces output:
using 65536 items in vector
Inefficient method took: 1.705 ms
Efficient method took: 0 ms
Note it's very easy to get inefficient, look e.g. have at http://www.cplusplus.com/reference/stl/vector/erase/
I want to check if a floating point value is "nearly" a multiple of 32. E.g. 64.1 is "nearly" divisible by 32, and so is 63.9.
Right now I'm doing this:
#define NEARLY_DIVISIBLE 0.1f
float offset = fmodf( val, 32.0f ) ;
if( offset < NEARLY_DIVISIBLE )
{
// its near from above
}
// if it was 63.9, then the remainder would be large, so add some then and check again
else if( fmodf( val + 2*NEARLY_DIVISIBLE, 32.0f ) < NEARLY_DIVISIBLE )
{
// its near from below
}
Got a better way to do this?
well, you could cut out the second fmodf by just subtracting 32 one more time to get the mod from below.
if( offset < NEARLY_DIVISIBLE )
{
// it's near from above
}
else if( offset-32.0f>-1*NEARLY_DIVISIBLE)
{
// it's near from below
}
In a standard-compliant C implementation, one would use the remainder function instead of fmod:
#define NEARLY_DIVISIBLE 0.1f
float offset = remainderf(val, 32.0f);
if (fabsf(offset) < NEARLY_DIVISIBLE) {
// Stuff
}
If one is on a non-compliant platform (MSVC++, for example), then remainder isn't available, sadly. I think that fastmultiplication's answer is quite reasonable in that case.
You mention that you have to test near-divisibility with 32. The following theory ought to hold true for near-divisibility testing against powers of two:
#define THRESHOLD 0.11
int nearly_divisible(float f) {
// printf(" %f\n", (a - (float)((long) a)));
register long l1, l2;
l1 = (long) (f + THRESHOLD);
l2 = (long) f;
return !(l1 & 31) && (l2 & 31 ? 1 : f - (float) l2 <= THRESHOLD);
}
What we're doing is coercing the float, and float + THRESHOLD to long.
f (long) f (long) (f + THRESHOLD)
63.9 63 64
64 64 64
64.1 64 64
Now we test if (long) f is divisible with 32. Just check the lower five bits, if they are all set to zero, the number is divisible by 32. This leads to a series of false positives: 64.2 to 64.8, when converted to long, are also 64, and would pass the first test. So, we check if the difference between their truncated form and f is less than or equal to THRESHOLD.
This, too, has a problem: f - (float) l2 <= THRESHOLD would hold true for 64 and 64.1, but not for 63.9. So, we add an exception for numbers less than 64 (which, when incremented by THRESHOLD and subsequently coerced to long -- note that the test under discussion has to be inclusive with the first test -- is divisible by 32), by specifying that the lower 5 bits are not zero. This will hold true for 63 (1000000 - 1 == 1 11111).
A combination of these three tests would indicate whether the number is divisible by 32 or not. I hope this is clear, please forgive my weird English.
I just tested the extensibility to other powers of three -- the following program prints numbers between 383.5 and 388.4 that are divisible by 128.
#include <stdio.h>
#define THRESHOLD 0.11
int main(void) {
int nearly_divisible(float);
int i;
float f = 383.5;
for (i=0; i<50; i++) {
printf("%6.1f %s\n", f, (nearly_divisible(f) ? "true" : "false"));
f += 0.1;
}
return 0;
}
int nearly_divisible(float f) {
// printf(" %f\n", (a - (float)((long) a)));
register long l1, l2;
l1 = (long) (f + THRESHOLD);
l2 = (long) f;
return !(l1 & 127) && (l2 & 127 ? 1 : f - (float) l2 <= THRESHOLD);
}
Seems to work well so far!
I think it's right:
bool nearlyDivisible(float num,float div){
float f = num % div;
if(f>div/2.0f){
f=f-div;
}
f=f>0?f:0.0f-f;
return f<0.1f;
}
For what I gather you want to detect if a number is nearly divisible by other, right?
I'd do something like this:
#define NEARLY_DIVISIBLE 0.1f
bool IsNearlyDivisible(float n1, float n2)
{
float remainder = (fmodf(n1, n2) / n2);
remainder = remainder < 0f ? -remainder : remainder;
remainder = remainder > 0.5f ? 1 - remainder : remainder;
return (remainder <= NEARLY_DIVISIBLE);
}
Why wouldn't you just divide by 32, then round and take the difference between the rounded number and the actual result?
Something like (forgive the untested/pseudo code, no time to lookup):
#define NEARLY_DIVISIBLE 0.1f
float result = val / 32.0f;
float nearest_int = nearbyintf(result);
float difference = abs(result - nearest_int);
if( difference < NEARLY_DIVISIBLE )
{
// It's nearly divisible
}
If you still wanted to do checks from above and below, you could remove the abs, and check to see if the difference is >0 or <0.
This is without uing the fmodf twice.
int main(void)
{
#define NEARLY_DIVISIBLE 0.1f
#define DIVISOR 32.0f
#define ARRAY_SIZE 4
double test_var1[ARRAY_SIZE] = {63.9,64.1,65,63.8};
int i = 54;
double rest;
for(i=0;i<ARRAY_SIZE;i++)
{
rest = fmod(test_var1[i] ,DIVISOR);
if(rest < NEARLY_DIVISIBLE)
{
printf("Number %f max %f larger than a factor of the divisor:%f\n",test_var1[i],NEARLY_DIVISIBLE,DIVISOR);
}
else if( -(rest-DIVISOR) < NEARLY_DIVISIBLE)
{
printf("Number %f max %f less than a factor of the divisor:%f\n",test_var1[i],NEARLY_DIVISIBLE,DIVISOR);
}
}
return 0;
}
Say I have a large number (integer or float) like 12345 and I want it to look like 12,345.
How would I accomplish that?
I'm trying to do this for an iPhone app, so something in Objective-C or C would be nice.
Here is the answer.
NSNumber* number = [NSNumber numberWithDouble:10000000];
NSNumberFormatter *numberFormatter = [[NSNumberFormatter alloc] init];
[numberFormatter setNumberStyle:kCFNumberFormatterDecimalStyle];
[numberFormatter setGroupingSeparator:#","];
NSString* commaString = [numberFormatter stringForObjectValue:number];
[numberFormatter release];
NSLog(#"%# -> %#", number, commaString);
Try using an NSNumberFormatter.
This should allow you to handle this correctly on an iPhone. Make sure you use the 10.4+ style, though. From that page:
"iPhone OS: The v10.0 compatibility mode is not available on iPhone OS—only the 10.4 mode is available."
At least on Mac OS X, you can just use the "'" string formatter with printf(3).
$ man 3 printf
`'' Decimal conversions (d, u, or i) or the integral portion
of a floating point conversion (f or F) should be
grouped and separated by thousands using the non-mone-
tary separator returned by localeconv(3).
as in printf("%'6d",1000000);
Cleaner C code
// write integer value in ASCII into buf of size bufSize, inserting commas at tousands
// character string in buf is terminated by 0.
// return length of character string or bufSize+1 if buf is too small.
size_t int2str( char *buf, size_t bufSize, int val )
{
char *p;
size_t len, neg;
// handle easy case of value 0 first
if( val == 0 )
{
a[0] = '0';
a[1] = '\0';
return 1;
}
// extract sign of value and set val to absolute value
if( val < 0 )
{
val = -val;
neg = 1;
}
else
neg = 0;
// initialize encoding
p = buf + bufSize;
*--p = '\0';
len = 1;
// while the buffer is not yet full
while( len < bufSize )
{
// put front next digit
*--p = '0' + val % 10;
val /= 10;
++len;
// if the value has become 0 we are done
if( val == 0 )
break;
// increment length and if it's a multiple of 3 put front a comma
if( (len % 3) == 0 )
*--p = ',';
}
// if buffer is too small return bufSize +1
if( len == bufSize && (val > 0 || neg == 1) )
return bufSize + 1;
// add negative sign if required
if( neg == 1 )
{
*--p = '-';
++len;
}
// move string to front of buffer if required
if( p != buf )
while( *buf++ = *p++ );
// return encoded string length not including \0
return len-1;
}
I did this for an iPhone game recently. I was using the built-in LCD font, which is a monospaced font. I formatted the numbers, ignoring the commas, then stuck the commas in afterward. (The way calculators do it, where the comma is not considered a character.)
Check out the screenshots at RetroJuJu. Sorry--they aren't full-sized screenshots so you'll have to squint!
Hope that helps you (it's in C) :
char* intToFormat(int a)
{
int nb = 0;
int i = 1;
char* res;
res = (char*)malloc(12*sizeof(char));
// Should be enough to get you in the billions. Get it higher if you need
// to use bigger numbers.
while(a > 0)
{
if( nb > 3 && nb%3 == 0)
res[nb++] = ',';
// Get the code for the '0' char and add it the position of the
// number to add (ex: '0' + 5 = '5')
res[nb] = '0' + a%10;
nb++;
a /= 10;
}
reverse(&res);
return res;
}
There might be a few errors I didn't see (I'm blind when it comes to this...)
It's like an enhanced iToA so maybe it's not the best solution.
Use recursion, Luke:
#include <stdio.h>
#include <stdlib.h>
static int sprint64u( char* buffer, unsigned __int64 x) {
unsigned __int64 quot = x / 1000;
int chars_written;
if ( quot != 0) {
chars_written = sprint64u( buffer, quot);
chars_written += sprintf( buffer + chars_written, ".%03u", ( unsigned int)( x % 1000));
}
else {
chars_written = sprintf( buffer, "%u", ( unsigned int)( x % 1000));
}
return chars_written;
}
int main( void) {
char buffer[ 32];
sprint64u( buffer, 0x100000000ULL);
puts( buffer);
return EXIT_SUCCESS;
}