Re: output rounding bug in vasnprintf %e format implementation

[Bruno Haible]

Ben Pfaff wrote:
> By adding a printf
> around here, I can see that floorlog10 chooses an exponent of 3.

The floorlog10 function was intended to return a result with at most 10^-7
error. There was a bug here too (I confused log and log2.) This fixes it.


2008-04-19  Bruno Haible  <address@hidden>

        * lib/vasnprintf.c (floorlog10l, floorlog10): Reduce maximum error
        from 0.0058 to less than 10^-7.

*** lib/vasnprintf.c.orig       2008-04-19 17:51:44.000000000 +0200
--- lib/vasnprintf.c    2008-04-19 17:45:19.000000000 +0200
***************
*** 1301,1309 ****
      }
    /* Now 0.95 <= z <= 1.01.  */
    z = 1 - z;
!   /* log(1-z) = - z - z^2/2 - z^3/3 - z^4/4 - ...
       Four terms are enough to get an approximation with error < 10^-7.  */
!   l -= z * (1.0 + z * (0.5 + z * ((1.0 / 3) + z * 0.25)));
    /* Finally multiply with log(2)/log(10), yields an approximation for
       log10(x).  */
    l *= 0.30102999566398119523;
--- 1301,1309 ----
      }
    /* Now 0.95 <= z <= 1.01.  */
    z = 1 - z;
!   /* log2(1-z) = 1/log(2) * (- z - z^2/2 - z^3/3 - z^4/4 - ...)
       Four terms are enough to get an approximation with error < 10^-7.  */
!   l -= 1.4426950408889634074 * z * (1.0 + z * (0.5 + z * ((1.0 / 3) + z * 
0.25)));
    /* Finally multiply with log(2)/log(10), yields an approximation for
       log10(x).  */
    l *= 0.30102999566398119523;
***************
*** 1392,1400 ****
      }
    /* Now 0.95 <= z <= 1.01.  */
    z = 1 - z;
!   /* log(1-z) = - z - z^2/2 - z^3/3 - z^4/4 - ...
       Four terms are enough to get an approximation with error < 10^-7.  */
!   l -= z * (1.0 + z * (0.5 + z * ((1.0 / 3) + z * 0.25)));
    /* Finally multiply with log(2)/log(10), yields an approximation for
       log10(x).  */
    l *= 0.30102999566398119523;
--- 1392,1400 ----
      }
    /* Now 0.95 <= z <= 1.01.  */
    z = 1 - z;
!   /* log2(1-z) = 1/log(2) * (- z - z^2/2 - z^3/3 - z^4/4 - ...)
       Four terms are enough to get an approximation with error < 10^-7.  */
!   l -= 1.4426950408889634074 * z * (1.0 + z * (0.5 + z * ((1.0 / 3) + z * 
0.25)));
    /* Finally multiply with log(2)/log(10), yields an approximation for
       log10(x).  */
    l *= 0.30102999566398119523;