Joe7M
commented
2 years ago I had a look to the source code of SmallBASIC. It is not a problem of round() as mentioned above, but a problem of the function bestfta_p(...) in fmt.c, which is used to convert a floating point number to a string for printing it to the screen.
It seems, that the function bestfta_p(...) is at the edge of precision. Sometime in line 167 of fmt.c fpart = fround(frac(x), FMT_RND) * FMT_xRND; the rounding error occurs.
One possible solution could be, to remove bestfta_p(...) and just replace it by sprintf(dest,"%.14G", x);. sprintfwill take care of the correct conversion. I made the following table to show what happens with bestfta_p(...)and what is the output of sprintf
INPUT bestfta_p(...) sprintf(dest,"%.14G", x);
0.00000000000001: 10E-15 1E-14
0.0000000000001: 10E-14 1E-13
0.000000000001: 10E-13 1E-12
0.00000000001: 10E-12 1E-11
0.0000000001: 1E-10 1E-10
0.000000001: 1E-9 1E-09
0.00000001: 0.00000001 1E-08
0.0000001: 0.0000001 1E-07
0.000001: 0.000001 1E-06
0.00001: 0.00001 1E-05
0.0001: 0.0001 0.0001
0.001: 0.001 0.001
0.01: 0.01 0.01
0.1: 0.1 0.1
1: 1 1
10: 10 10
100: 100 100
1000: 1000 1000
10000: 10000 10000
100000: 100000 100000
1000000: 1000000 1000000
10000000: 10000000 10000000
100000000: 100000000 100000000
1000000000: 1000000000 1000000000
10000000000: 10000000000 10000000000
100000000000: 100000000000 100000000000
1000000000000: 1000000000000 1000000000000
10000000000000: 10000000000000 10000000000000
100000000000000: 100000000000000 1E+14
1000000000000000: 1E+15 1E+15
1e10000: INF INF
0.20361889339983: 0.20361889339983 0.20361889339983
72.20361889339983: 72.20361889339983 72.2036188934
1072.20361889339983: 10072.20361889340165 10072.203618893
round(0.20361889339983,3): 0.204 0.204
round(72.20361889339983,3): 72.20399999999999 72.204
round(10072.20361889339983,3): 10072.20399999999972 10072.204
0.204: 0.204 0.204
72.204: 72.20399999999999 72.204for example fmt.c line 216 an following:
/*
* best float to string (user)
*/
void bestfta(var_num_t x, char *dest) {
sprintf(dest,"%.14G", x);
}
/*
* float to string (user, E mode)
*/
void expfta(var_num_t x, char *dest) {
sprintf(dest,"%.E", x);
}
see: https://www.syntaxbomb.com/smallbasic/rounding-numbers/
The Round() command should be straightforward, but sometimes the program seems to round then add or subtract 0.00000000001 to the number, any idea why? I compiled this to illustrate. I seem to be getting the same problem with external files. An alternative to round is using an expression like INT(100*number)/100, but it does the same.
FOR n=1 TO 100 a=100*RND PRINT a, ROUND(a,3) next n