On 2017-11-09 16:46:58 +0100, Vincent Lefevre wrote: > On 2017-11-09 10:01:45 +0100, Mason wrote: > > Basically, using "IEEE 754 double-precision binary floating-point format" > > 4.6 is approximated as D=4.5999999999999996447286321199499070644378662109375 > > ( https://en.wikipedia.org/wiki/Double-precision_floating-point_format ) > > > > Thus, it is obvious why floor(D*100) equals 459. > > No, this is not obvious. The multiplication by 100 introduces a > rounding error. Thus this doesn't prove that the rounded value > D*100 is strictly less than 460. For instance: #include <stdio.h> #include <math.h> int main (void) { double x = 1.7; printf ("%.30g\n", x); printf ("%.30g\n", 100 * x); printf ("%.30g\n", floor (100 * x)); return 0; } outputs: 1.69999999999999995559107901499 170 170 despite the fact that 1.7 is approximated by a value less than 1.7. -- Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <https://www.vinc17.net/> 100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/> Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)
