CFraction Library : Code for handling fraction strings
Classes | |
| class | CFraction |
| CFraction - Code for handling fraction strings. More... | |
Defines | |
| #define | FRACTION_MAX_PRECISION 10.0e-15 |
| Significant digits. | |
Functions | |
| double | Fracatof (const char *pszNum) |
| Convert string that may include a fraction to floating point (double). | |
| char * | Fracftoa (double f, char *pszBuffer, double AllowedError=FRACTION_MAX_PRECISION) |
| Convert double to a string that includes the whole part, space, and the fraction (numerator/denominator). | |
| char * | Fracftoa (double f, char *pszBuffer, int MaxDen) |
| Convert double to a string that includes the whole part, space, and the fraction (numerator/denominator). | |
| char * | DoubleToStockString (double f, char *pszBuffer, int MaxDen=256) |
| Returns 6.4f unless denominator is less than or equal to MaxDen and in 2,4,8,16,32,64,128,256. | |
| char * | ForceDoubleToStockString (double f, char *pszBuffer, int MaxDen=256) |
| Returns closest fraction string with a denominator less than or equal to MaxDen and in 2,4,8,16,32,64,128,256. | |
| double | FracParts (double f, __int64 &Whole, __int64 &Num, __int64 &Den, double AllowedError=FRACTION_MAX_PRECISION) |
| Convert a double to its fractional parts. | |
| double | FracParts (double f, __int64 &Whole, __int64 &Num, __int64 &Den, int MaxDen) |
| Convert a double to its fractional parts. | |
| double | FracPartsStock (double f, __int64 &Whole, __int64 &Num, __int64 &Den, int MaxDen) |
| Convert a double to its fractional parts. | |
Fraction Algorithm
The formula for converting a decimal fraction to a string fraction is based on reciprocals.Any fractional part can be represented as 1/(I1 + 1/(I2 + 1/(I3 + 1/In... where I1 is the integer part of the reciprocal of the fraction and I2 is the integer part of the reciprocal minus I1... etc.
To determine the integer numerator and denominator, the expression can be reduced. It turns out that the numerator is simpler to calculate than the denominator, so the denominator can simply be determined by dividing the numerator by the original decimal.
Reduction of 1/(I1 + 1/(I2 + 1/(I3 + 1/In... -
1 I term:
1
-- Numerator N1 = 1
I1
2 I terms:
1 I2
----- Multiply by I2 = -----------
I1 + 1 to reduce -- (I1*I2) + 1
-- I2
I2
Numerator N2 = I2
3 I terms
1 1 (I2*I3) + 1
----- = ------- = ---------------------
I1 + 1 I1 + I3 I1*((I2*I3) + 1) + I3
------ -----------
I2 + 1 (I2*I3) + 1
--
I3
Numerator N3 = N2*I3 + N1
4 I terms
1 1 1 I2*((I3*I4) + 1) + I4
------ -------- = ---------------- = -----------------------------------------
I1 + 1 I1 + 1 I1 + ((I3*I4) + 1) I1*(I2*((I3*I4) + 1) + I4) + ((I3*I4) + 1)
---- = ------- ---------------------
I2 + 1 I2 + I4 I2*((I3*I4) + 1) + I4
------- -----------
I3 + 1 (I3*I4) + 1
--
I4
Numerator N4 = I4*(I3*I2 + 1) + I2 = N3*I4 + N2
5 I terms
1 1 1 1
------ ------ ------ --------------
I1 + 1 I1 + 1 I1 + 1 I1 + (I3*((I4*I5) + 1) + I5)
------ = ------ = ---------------- -----------------------
I2 + 1 I2 + 1 I2 + (I4*I5) + 1 I2*(I3*((I4*I5) + 1) + I5) + (I4*I5) + 1
------- ------- ---------------------
I3 + 1 I3 + I5 I3*((I4*I5) + 1) + I5
------- ------------
I4 + 1 (I4*I5) + 1
--
I5
= I2*(I3*((I4*I5) + 1) + I5) + (I4*I5) + 1
----------------------------------------------------------------------
I1*(I2*(I3*((I4*I5) + 1) + I5) + (I4*I5) + 1) + (I3*((I4*I5) + 1) + I5)
Numerator N5 = I5*(I4*(I3*I2 + 1) + I2) + I3*I2 + 1 = N4*I5 + N3
So, the numerator is fairly simple to calcualte based on two previous numerators.
N1 = 1 N2 = I2 Nn = In*N[n-2] + N[n-3]
And since N1 = 1 and original saved numerator can be 0, the last equation can be used for all numerators except the first: N1 = 1 Nn = In*N[n-1] + N[n-2] where N[0] = 0;
So, this is fairly simple.
Define Documentation
| #define FRACTION_MAX_PRECISION 10.0e-15 |
Significant digits.
Function Documentation
| char* DoubleToStockString | ( | double | f, | |
| char * | pszBuffer, | |||
| int | MaxDen = 256 | |||
| ) |
Returns 6.4f unless denominator is less than or equal to MaxDen and in 2,4,8,16,32,64,128,256.
| char* ForceDoubleToStockString | ( | double | f, | |
| char * | pszBuffer, | |||
| int | MaxDen = 256 | |||
| ) |
Returns closest fraction string with a denominator less than or equal to MaxDen and in 2,4,8,16,32,64,128,256.
| double Fracatof | ( | const char * | pszNum | ) |
Convert string that may include a fraction to floating point (double).
- Parameters:
-
pszNum todo
- Returns:
- double
| char* Fracftoa | ( | double | f, | |
| char * | pszBuffer, | |||
| int | MaxDen | |||
| ) |
Convert double to a string that includes the whole part, space, and the fraction (numerator/denominator).
Limits the denominator to MaxDen
| char* Fracftoa | ( | double | f, | |
| char * | pszBuffer, | |||
| double | AllowedError = FRACTION_MAX_PRECISION | |||
| ) |
Convert double to a string that includes the whole part, space, and the fraction (numerator/denominator).
If you want to get a Num and Den for a fractional part less than the default AllowedError, pass an allowed error less than the fractional part. Otherwise the default should be fine.
| double FracParts | ( | double | f, | |
| __int64 & | Whole, | |||
| __int64 & | Num, | |||
| __int64 & | Den, | |||
| int | MaxDen | |||
| ) |
Convert a double to its fractional parts.
Returns Error difference. Limits the denominator to MaxDen
| double FracParts | ( | double | f, | |
| __int64 & | Whole, | |||
| __int64 & | Num, | |||
| __int64 & | Den, | |||
| double | AllowedError = FRACTION_MAX_PRECISION | |||
| ) |
Convert a double to its fractional parts.
Returns Error difference. If you want to get a Num and Den for a fractional part less than the default AllowedError, pass an allowed error less than the fractional part. Otherwise the default should be fine.
| double FracPartsStock | ( | double | f, | |
| __int64 & | Whole, | |||
| __int64 & | Num, | |||
| __int64 & | Den, | |||
| int | MaxDen | |||
| ) |
Convert a double to its fractional parts.
Returns Error difference. Limits the denominator to MaxDen and always returns Den as 2,4,8,16,32,64,128,256
