Print all significant digits in sprintf scientific notation

Question

When R converts a large number to a string in scientific notation, it includes all significant digits and no trailing zero's. Is it possible to accomplish this in C with sprintf?

> as.character(12345e11)
[1] "1.2345e+15"
> as.character(1234500000e6)
[1] "1.2345e+15"
> as.character(1234500001e6)
[1] "1.234500001e+15"

I tried sprintf(buf, "%g", val) but this seems to include 5 decimal digits at most. I also tried to set a higher precision with sprintf(buf, "%.18g", val) but this will include non significant digits and trailing zeros.

Is there a way to get the behavior of sprintf(buf, "%g", val) but increase the 5 digit limit?

Answer 1

Code could use "%.18e" or "%.18g", but the question is how large should "18" be? Is 18 the best value? The answer lies in DBL_DECIMAL_DIG.

DBL_DECIMAL_DIG is the minimum number of significant digits to print to insure the round-trip of double to string to the same exact double for all double.

Recommend using format specifier "%.*e".

Note that the "18" in "%.18e" is the number of significant digits after the decimal point. So "%.18e" prints 19 significant digits.

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Use printf("%a", x); which prints in a hexadecimal output.
For a decimal output:

#include <float.h>

//    sign + digit +  dp +       digits          + e + sign + expo + \0
char buf[1 + 1 +      1  + (DBL_DECIMAL_DIG - 1) + 1 + 1    + 5    + 1]; 
sprintf(buf, "%.*e", DBL_DECIMAL_DIG - 1, x);

Ref Printf width specificer to maintain precision of floating-point value

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A number like y = 1.0/3.0 using the typical double binary64 format would need to see about 53 decimal digits to see its exact value. But many of the trailing digits are not needed for a successful round-trip.

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Now we know the most digits to print, use the below to get rid of those pesky trailing 0 digits.

#include <float.h>
#include <math.h>
#include <stdio.h>
#include <string.h>

char *trim0(double x, char *buf) {
  sprintf(buf, "% .*e", DBL_DECIMAL_DIG - 1, x);
  if (isfinite(x)) {
    char *p = &buf[DBL_DECIMAL_DIG + 1];  // address of last significand digit
    char *t;
    for (t=p; *t == '0'; t--);
    memmove(t+1, p+1, strlen(p+1)+1);
  }
  return buf;
}

int main(void) {
  char buf[1 + 1 + 1 + (DBL_DECIMAL_DIG - 1) + 1 + 1 + 5 + 1];
  printf("%s\n", trim0(1.2, buf));
  printf("%s\n", trim0(1.0/7, buf));
  return 0;
}

Output

 1.2e+00
 1.4285714285714285e-01