Torture tests: what do they mean?

[Paul Dale]

(05-14-2014 05:35 AM)DavidM Wrote:  I wonder how much more interesting Pauli's table would be with \(\pi\)/2 as the target of the TAN function?

Assuming the 34S calculates accurately this close to the pole:

Code:

digits  pi/2                             tan(col #2)    rounded(pi)/2          tan (col #4)
   8    1.5707963                           37320540    1.5707964                 -13660250
   9    1.57079633                        -312002417    1.57079632                147169274
  10    1.570796327                      -4875590038    1.570796327             -4875590038
  11    1.5707963268                   -195948537910
  12    1.57079632679                   204222536562    1.57079632680         -195948537906
  13    1.570796326795                -9672978957157
  14    1.5707963267949             -295790719553270
  15    1.57079632679490            -295790719553274
  16    1.570796326794897          -2626266436731868    1.570796326794896  1614905391523416
  17    1.5707963267948966         51998506188720271
  18    1.57079632679489662     -1300934329906107200
  19    1.570796326794896619     4322984121858095330
  20    1.5707963267948966192   31926755792808630288

The second column is round(pi/2). The fourth is round(round(pi)/2) but only where it is different.

The difference for fifteen digits from the above is that 1.57079632679489 isn't correctly rounded


As Deiter wrote, we're really in a steep part of the tan function here.


- Pauli