simplify Sel lowering code

[libfirm] / ir / tv / IeeeCC754 / BasicOp / testsets / divide

!! This file contains precision and range independent test vectors for
!! the operation divide (/). The first character in each
!! test vector refers to the origin of the test vector
!!
!! 2:  Jerome Coonen Version <2>
!! 3:  Jerome Coonen Version <3>
!!      @Phdthesis{
!!              author = {Coonen, J.T.},
!!              title  = {Contributions to a proposed standard for binary
!!                 floating-point arithmetic},
!!              school = {University of California, Berkeley},
!!              year   = {1984}}
!!
!! H:  precision independent encoding of UCB/<H>ough test vector
!!      @Unpublished{
!!             author = {David G. Hough and others},
!!             title  = {{UCBTEST}, a suite of programs for testing certain
!!                difficult cases of {IEEE} 754 floating-point arithmetic},
!!             year   = {1988},
!!             note   = {Restricted public domain software from
!!                http://netlib.bell-labs.com/netlib/fp/index.html}}
!!
!! A:  Verdonk-Cuyt-Verschaeren (University of <A>ntwerp)
!!      @Article{
!!             author  = {Verdonk, B. and Cuyt, A. and Verschaeren, D.},
!!             title   = {A precision- and range-independent tool for testing
!!                       floating-point arithmetic {I}: basic operations,
!!                       square root and remainder},
!!             journal = {ACM TOMS},
!!             volume  = {27},
!!             number  = {1},
!!             pages   = {92-118},
!!             year    = {2001}}
!!             note  = {Under revision}}
!!
!! This file is part of the tool IeeeCC754 or IEEE 754 Compliance Checker.
!! It is a precision and range independent tool to test whether
!! an implementation of floating-point arithmetic (in hardware or
!! software) is compliant with the principles of the IEEE 754-854
!! floating-point standards. You can find out more about the testing
!! tool IeeeCC754 and the syntax and semantics of the test vectors
!! at
!!            http://win-www.uia.ac.be/u/cant/ieeecc754.html
!!
!! Last updated:
!!              $Date$
!!
!! Contact:
!!      Brigitte.Verdonk@ua.ac.be
!!      Department of Mathematics and Computer Science
!!      University of Antwerp (UIA)
!!      Universiteitsplein 1
!!      B2610 Antwerp, BELGIUM
!!
!! Medium size numbers
2/         ALL     1p15    1p5      OK    1p10
A/         ALL     -1p15    -1p5    OK    1p10
2/         ALL     1p15    -1p5     OK    -1p10
2/         ALL     -1p15   1p5      OK    -1p10
2/         ALL     1p120   1p20     OK    1p100
A/         ALL     -1p120   -1p20   OK    1p100
2/         ALL     -1p120  1p20     OK    -1p100
2/         ALL     1p120   -1p20    OK    -1p100
2/         ALL     1p63    1p23     OK    1p40
A/         ALL     -1p63    -1p23   OK    1p40
A/         ALL     -1p63    1p23    OK    -1p40
A/         ALL     1p63    -1p23    OK    -1p40
2/         ALL     1p47    1p13     OK      1p34
A/         ALL     -1p47    -1p13   OK    1p34
A/         ALL     -1p47    1p13    OK    -1p34
A/         ALL     1p47    -1p13    OK    -1p34
!! divisions by 10
A/      ALL     40      10      OK      4
A/      ALL     -40     -10     OK      4
A/      ALL     -40     10      OK      -4
A/      ALL     40      -10     OK      -4
2/         ALL     32760   10       OK    3276
2/         ALL     10000   10       OK    1000
2/         ALL     10000   100      OK    100
2/         ALL     10000   1000     OK    10

!! / 1
2/       ALL   1   1    OK   1
2/       ALL   -1  -1   OK   1
A/       ALL   1   -1   OK   -1
2/       ALL   -1   1   OK   -1
2/       ALL   2   1    OK   2
2/       ALL   -2   -1  OK   2
2/       ALL   -2   1   OK   -2
2/       ALL   2   -1   OK   -2
2/       ALL   Td1  1   OK   Td1
2/       ALL   Td1  -1  OK   -Td1
A/       ALL   0i1   1    OK   0i1
A/       ALL   -0i1   -1  OK   0i1
A/       ALL   -0i1   1   OK   -0i1
A/       ALL   0i1   -1   OK   -0i1
!! / 2
2/       ALL   Hm1       2       OK       Hm2
2/       ALL   Hm1       -2       OK   -Hm2
2/       ALL   -Hm1d1   2   OK   -Hm2d1
2/       ALL   Hm1d3   -2   OK   -Hm2d3
2/       ALL   Hd1       -2       OK   -Hm1d1
2/       ALL   8   2   OK   4
A/       ALL   -8   -2   OK   4
2/       ALL   -8   2   OK   -4
A/       ALL   8   -2   OK   -4
2/       ALL   Tp1       -2       OK   -T
2/       ALL   Tp1i3   -2   OK   -Ti3
2/       ALL   Tp1i1   -2   OK   -Ti1
2/       ALL     Tp1d2  2      OK       Td1
A/       ALL   0i(1)1   2   OK  0i(2)1
A/       ALL   -0i(1)1   -2   OK   0i(2)1
A/       ALL   -0i(1)1   2   OK   -0i(2)1
A/       ALL   0i(1)1   -2   OK   -0i(2)1
A/       ALL   0i2   2    OK   0i1
A/       ALL   -0i2   -2   OK   0i1
A/       ALL   -0i2   2   OK   -0i1
A/       ALL   0i2   -2   OK   -0i1
2/       ALL   Hd1       Hm1d1   OK       2
2/       ALL   -Hm1i1   Hm2i1   OK       -2
2/       ALL   Hm1i3   -Hm2i3   OK       -2
2/       ALL   Tp1       T       OK       2
2/       ALL   -Tp1i1   Ti1       OK   -2
2/       ALL   Tp1i1   Ti1       OK       2
2/       ALL   Tp1i3   -Ti3       OK   -2
2/       ALL   -Tp1i5   Ti5       OK   -2
A/       ALL   0i(1)1   0i(2)1   OK     2
A/       ALL   -0i(1)1   -0i(2)1   OK   2
A/       ALL   -0i(1)1   0i(2)1   OK    -2
A/       ALL   0i(1)1   -0i(2)1   OK    -2
A/       ALL   0i2      0i1     OK      2
A/       ALL   -0i2     -0i1    OK      2
A/       ALL   0i2      -0i1    OK      -2
A/       ALL   -0i2     0i1     OK      -2
!! * 2
A/      ALL     3       1m1     OK      6
A/      ALL     -3      -1m1    OK      6
A/      ALL     -3      1m1     OK      -6
A/      ALL     3       -1m1    OK      -6
2/          ALL     Td1   1m1   OK        Tp1d2
A/          ALL     -Td1   -1m1 OK        Tp1d2
A/          ALL     -Td1   1m1  OK        -Tp1d2
A/          ALL     Td1   -1m1  OK        -Tp1d2
2/          ALL     0i1   1m1   OK        0i2
A/          ALL     -0i1   -1m1 OK        0i2
2/          ALL     -0i1   1m1  OK        -0i2
A/          ALL     0i1   -1m1  OK        -0i2
A/      ALL     3       6       OK      1m1
A/      ALL     -3      -6      OK      1m1
A/      ALL     -3      6       OK      -1m1
A/      ALL     3       -6      OK      -1m1
A/          ALL     Td1   Tp1d2         OK      1m1
A/          ALL     -Td1  -Tp1d2        OK      1m1
A/          ALL     -Td1  Tp1d2         OK      -1m1
A/          ALL     Td1   -Tp1d2        OK      -1m1
2/          ALL     0i1   0i2   OK      1m1
A/          ALL     -0i1  0i2   OK      -1m1
A/          ALL     -0i1  -0i2  OK      1m1
A/          ALL     0i1   -0i2  OK      -1m1
!! * 2^k
A/      ALL     3       1m9     OK      3p9
A/      ALL     -3      -1m9    OK      3p9
A/      ALL     -3      1m9     OK      -3p9
A/      ALL     3       -1m9    OK      -3p9
2/          ALL     Td1   1m9   OK         Tp9d2
A/          ALL     -Td1   -1m9   OK       Tp9d2
A/          ALL     -Td1   1m9   OK         -Tp9d2
A/          ALL     Td1   -1m9   OK         -Tp9d2
2/          ALL     0i1   1m3   OK               0i8
A/          ALL     -0i1   -1m3   OK         0i8
A/          ALL     -0i1   1m3   OK         -0i8
A/          ALL     0i1   -1m3   OK         -0i8
A/      ALL     3       3p9     OK      1m9
A/      ALL     -3      3p9     OK      -1m9
A/      ALL     -3      -3p9    OK      1m9
A/      ALL     3       -3p9    OK      -1m9
A/          ALL     Td1   Tp9d2         OK      1m9
A/          ALL     -Td1  Tp9d2         OK      -1m9
A/          ALL     -Td1  -Tp9d2        OK      1m9
A/          ALL     Td1   -Tp9d2        OK      -1m9
A/          ALL     0i1   0i8   OK      1m3
A/          ALL     -0i1  0i8   OK      -1m3
A/          ALL     -0i1  -0i8  OK      1m3
A/          ALL     0i1   -0i8  OK      -1m3
!! / 3
2/       ALL   9   3     OK    3
2/       ALL   -9  -3    OK    3
A/       ALL   -9   3    OK   -3
A/       ALL   9   -3    OK   -3
A/       ALL   6   3   OK       2
2/       ALL   -6   -3   OK       2
A/       ALL   6   -3   OK       -2
A/       ALL   -6   3   OK       -2
!! /4
2/       ALL   Hd3       4       OK       Hm2d3
2/       ALL   Hd3       -4       OK   -Hm2d3
2/       ALL   -Hd3       4       OK   -Hm2d3
2/       ALL   -Hd3       -4   OK   Hm2d3
A/       ALL   0i(1)1   4   OK  0i(3)1
A/       ALL   -0i(1)1   -4   OK   0i(3)1
A/       ALL   -0i(1)1   4   OK   -0i(3)1
A/       ALL   0i(1)1   -4   OK   -0i(3)1
A/       ALL   0i4   4   OK     0i1
A/       ALL   -0i4   -4   OK   0i1
A/       ALL   -0i4   4   OK   -0i1
A/       ALL   0i4   -4   OK   -0i1
2/       ALL   Hd1       Hm2d1   OK       4
2/       ALL   -Hd1       Hm2d1   OK   -4
2/       ALL   Hd1       -Hm2d1   OK   -4
2/       ALL   -Hd1       -Hm2d1   OK   4
A/       ALL   0i(1)1   0i(3)1   OK     4
A/       ALL   -0i(1)1   -0i(3)1   OK   4
A/       ALL   -0i(1)1   0i(3)1   OK    -4
A/       ALL   0i(1)1   -0i(3)1   OK    -4
A/       ALL   0i4      0i1     OK      4
A/       ALL   -0i4     -0i1    OK      4
A/       ALL   0i4      -0i1    OK      -4
A/       ALL   -0i4     0i1     OK      -4

!! equal operands
2/       ALL   5   5    OK   1
A/       ALL   -5   -5  OK   1
A/       ALL   5   -5   OK   -1
A/       ALL  -5   5   OK   -1
A/       ALL   3   3   OK       1
A/       ALL   -3   -3   OK       1
A/       ALL   -3   3   OK       -1
2/       ALL   3   -3   OK       -1
A/       ALL   7   7   OK       1
A/       ALL   -7   -7   OK       1
A/       ALL   7   -7   OK       -1
2/       ALL   -7   7   OK       -1
A/       ALL   0i1   0i1    OK   1
A/       ALL   -0i1   -0i1  OK   1
A/       ALL   0i1   -0i1   OK   -1
A/       ALL  -0i1   0i1   OK   -1
2/       ALL     0i9   9    OK       0i1
2/       ALL     0i9  -9    OK      -0i1

!! special representations
!! zero versus zero
2/       ALL   0   0   i   Q
2/       ALL   -0   0   i   -Q
2/       ALL   0   -0   i   -Q
2/       ALL   -0   -0   i       Q
!! zero versus denormal
! 0 / denormalized -> 0.
2/       ALL   0   0i1   OK       0
2/       ALL   -0   0i3   OK   -0
2/       ALL   0   -0i2   OK   -0
2/       ALL   -0   -0i4   OK   0
2/       ALL   0   Td1   OK       0
2/       ALL   -0   Td1   OK   -0
2/       ALL   0   -Td1   OK   -0
2/       ALL   -0   -Td1   OK   0
! Denormalized * 0 -> Inf, DivBy0
2/       ALL   0i1       0       z       H
2/       ALL   -0i3       0       z       -H
2/       ALL   0i2       -0       z       -H
2/       ALL   -0i4       -0   z   H
2/       ALL   Td1       0       z       H
2/       ALL   -Td1       0       z       -H
2/       ALL   Td1       -0       z       -H
2/       ALL   -Td1       -0   z   H
!! zero versus normal
! 0 / small_integer -> 0.
2/       ALL   0   1   OK   0
2/       ALL   -0   2   OK       -0
2/       ALL   0   -3   OK       -0
2/       ALL   -0   -4   OK       0
2/       ALL   0   5   OK   0
2/       ALL   -0   6   OK       -0
2/       ALL   0   -7   OK       -0
2/       ALL   -0   -8   OK       0
! Small_int / 0 -> Inf with DivBy0.
2/       ALL   1   0   z   H
2/       ALL   -2   0   z   -H
2/       ALL   3   -0   z   -H
2/       ALL   -4   -0   z       H
2/       ALL   5   0   z   H
2/       ALL   -6   0   z   -H
2/       ALL   7   -0   z   -H
2/       ALL   -8   -0   z       H
! 0 / huge -> 0.
2/       ALL   0   Hm1   OK       0
2/       ALL   -0   Hm2   OK   -0
2/       ALL   0   -Hm1   OK   -0
2/       ALL   -0   -Hm2   OK   0
2/       ALL   0   Hm1d1   OK   0
2/       ALL   -0   Hm2d1   OK   -0
2/       ALL   0   -Hm2d1   OK   -0
2/       ALL   -0   -Hm1d1       OK       0
! Huge / 0 -> Inf with DivBy0.
2/       ALL   Hm1       0       z       H
2/       ALL   -Hm2       0       z       -H
2/       ALL   Hm1       -0       z       -H
2/       ALL   -Hm2       -0   z   H
2/       ALL   Hm1d1   0   z   H
2/       ALL   -Hm2d1   0   z   -H
2/       ALL   Hm2d1   -0   z   -H
2/       ALL   -Hm1d1   -0       z       H
! 0 / tiny -> 0.
2/       ALL   0   T   OK   0
2/       ALL   -0   Tp1   OK   -0
2/       ALL   0   -Tp1   OK   -0
2/       ALL   -0   -T   OK       0
2/       ALL   0   Tp1d1   OK   0
2/       ALL   -0   Ti1   OK   -0
2/       ALL   0   -Ti1   OK   -0
2/       ALL   -0   -Tp1d1       OK       0
! Tiny / 0 -> Inf with DivBy0.
2/       ALL   T   0   z   H
2/       ALL   -Tp1       0       z       -H
2/       ALL   Tp1       -0       z       -H
2/       ALL   -T   -0   z       H
2/       ALL   Tp1d1   0   z   H
2/       ALL   -Ti1       0       z       -H
2/       ALL   Ti1       -0       z       -H
2/       ALL   -Tp1d1   -0       z       H
!! zero versus infinity
! Inf / 0 --> Inf with no problem.
2/       ALL   H   0   OK   H
2/       ALL   -H   0   OK       -H
2/       ALL   H   -0   OK       -H
2/       ALL   -H   -0   OK       H
! 0 / Inf --> 0 with no problem.
2/       ALL   0   H    OK      0
2/       ALL   -0   H   OK       -0
2/       ALL   0   -H   OK       -0
2/       ALL   -0   -H   OK       0
!! zero versus NaN
2/          ALL     Q       0       OK      Q
2/          ALL     Q       -0      OK      Q
2/          ALL     0       Q       OK      Q
2/          ALL     -0      Q       OK      Q
!2/          ALL     S       0       i       Q
!2/          ALL     S       -0      i       Q
!2/          ALL     0       S       i       Q
!2/          ALL     -0      S       i       Q
!! infinity versus infinity
2/       ALL   H   H   i   Q
2/       ALL   -H   H   i   -Q
2/       ALL   H   -H   i   -Q
2/       ALL   -H   -H   i       Q
!! infinity versus denormal
! Inf / denormalized -> Inf.
2/       ALL   H   0i1   OK       H
2/       ALL   -H   0i3   OK   -H
2/       ALL   H   -0i2   OK   -H
2/       ALL   -H   -0i4   OK   H
2/       ALL   H   Td1   OK       H
2/       ALL   -H   Td1   OK   -H
2/       ALL   H   -Td1   OK   -H
2/       ALL   -H   -Td1   OK   H
! Denorm / Inf -> 0.
2/       ALL   0i1       H       OK       0
2/       ALL   -0i3       H       OK   -0
2/       ALL   0i2       -H       OK   -0
2/       ALL   -0i4       -H   OK   0
2/       ALL   Td1       H       OK       0
2/       ALL   -Td1       H       OK   -0
2/       ALL   Td1       -H       OK   -0
2/       ALL   -Td1       -H   OK   0
!! infinity versus normal
! Inf / small_integer -> Inf.
2/       ALL   H   1   OK   H
2/       ALL   -H   2   OK       -H
2/       ALL   H   -3   OK       -H
2/       ALL   -H   -4   OK       H
2/       ALL   H   5   OK   H
2/       ALL   -H   6   OK       -H
2/       ALL   H   -7   OK       -H
2/       ALL   -H   -8   OK       H
! Small_int / Inf -> 0.
2/       ALL   1   H   OK   0
2/       ALL   -2   H   OK       -0
2/       ALL   3   -H   OK       -0
2/       ALL   -4   -H   OK       0
2/       ALL   5   H   OK   0
2/       ALL   -6   H   OK       -0
2/       ALL   7   -H   OK       -0
2/       ALL   -8   -H   OK       0
! Huge / Inf -> 0.
2/       ALL   Hm1       H       OK       0
2/       ALL   -Hm2       H       OK   -0
2/       ALL   Hm1       -H       OK   -0
2/       ALL   -Hm2       -H   OK   0
2/       ALL   Hm1d1   H   OK   0
2/       ALL   -Hm2d1   H   OK   -0
2/       ALL   Hd1       -H       OK   -0
2/       ALL   -Hd1       -H   OK   0
! Inf / huge -> Inf.
2/       ALL   H   Hm1   OK       H
2/       ALL   -H   Hm2   OK   -H
2/       ALL   H   -Hm1   OK   -H
2/       ALL   -H   -Hm2   OK   H
2/       ALL   H   Hm1d1   OK   H
2/       ALL   H   -Hm2d1   OK   -H
2/       ALL   H   -Hd1   OK   -H
2/       ALL   -H   -Hd1   OK   H
! Inf / tiny -> Inf.
2/       ALL   H   T   OK   H
2/       ALL   -H   Tp1   OK   -H
2/       ALL   H   -Tp1   OK   -H
2/       ALL   -H   -T   OK       H
2/       ALL   H   Tp1d1   OK   H
2/       ALL   -H   Ti1   OK   -H
2/       ALL   H   -Ti1   OK   -H
2/       ALL   -H   -Tp1d1       OK       H
! Tiny / Inf -> 0.
2/       ALL   T   H   OK   0
2/       ALL   -Tp1       H       OK   -0
2/       ALL   Tp1       -H       OK   -0
2/       ALL   -T   -H   OK       0
2/       ALL   Tp1d1   H   OK   0
2/       ALL   -Ti1       H       OK   -0
2/       ALL   Ti1       -H       OK   -0
2/       ALL   -Tp1d1   -H       OK       0
!! infinity versus NaN
2/          ALL     Q       H      OK      Q
2/          ALL     Q       -H     OK      Q
2/          ALL     H      Q       OK      Q
2/          ALL     -H     Q       OK      Q
!2/          ALL     S       H      i       Q
!2/          ALL     S       -H     i       Q
!2/          ALL     H      S       i       Q
!2/          ALL     -H     S       i       Q
!! NaN versus NaN
2/          ALL     Q       Q       OK      Q
!2/          ALL     Q       S       i       Q
!2/          ALL     S       Q       i       Q
!2/          ALL     S       S       i       Q
!! NaN versus denormal
2/          ALL     Td1  Q               OK              Q
2/          ALL     -Td1 Q               OK              Q
2/          ALL     Q       Td1  OK              Q
2/          ALL     Q       -Td1 OK              Q
2/          ALL     Q       0i1   OK      Q
2/          ALL     Q       -0i1  OK      Q
2/          ALL     0i1   Q               OK      Q
2/          ALL     -0i1  Q               OK      Q
!2/          ALL     Td1  S               i               Q
!2/          ALL     -Td1 S               i               Q
!2/          ALL     S       Td1  i               Q
!2/          ALL     S       -Td1 i               Q
!2/          ALL     S       0i1   i               Q
!2/          ALL     S       -0i1  i               Q
!2/          ALL     0i1   S               i               Q
!2/          ALL     -0i1  S               i               Q
!! NaN versus normal
2/          ALL     Q       1       OK      Q
2/          ALL     Q       -1      OK      Q
2/          ALL     1       Q       OK      Q
2/          ALL     -1      Q       OK      Q
2/          ALL     Q       Hd1  OK              Q
2/          ALL     Q       -Hd1 OK              Q
2/          ALL     Hd1  Q               OK              Q
2/          ALL     -Hd1 Q               OK              Q
!2/          ALL     S       1       i       Q
!2/          ALL     S       -1      i       Q
!2/          ALL     1       S       i       Q
!2/          ALL     -1      S       i       Q
!2/          ALL     S       Hd1  i               Q
!2/          ALL     S       -Hd1 i               Q
!2/          ALL     Hd1  S               i               Q
!2/          ALL     -Hd1 S               i               Q

!! exceptions
!! invalid and divide by zero, see special representations
!! inexact, overflow
!! exp. Z >= U
2/          =>      Hm1          1m1    xo          H
2/          0<      Hm1          1m1    xo          Hd1
2/          =>      -Hm1         -1m1   xo          H
2/          0<      -Hm1         -1m1   xo          Hd1
2/          =<      Hm1          -1m1   xo          -H
2/          =<      -Hm1         1m1    xo          -H
2/          0>      Hm1          -1m1   xo          -Hd1
2/          0>      -Hm1         1m1    xo          -Hd1
2/          =>      Hm9          Tp9    xo      H
2/          0<      Hm9          Tp9    xo      Hd1
2/          =>      Hd1         0i1     xo          H
2/          0<      Hd1         0i1     xo          Hd1
2/          =>      Hm1          Td1    xo          H
2/          0<      Hm1          Td1    xo          Hd1
2/          =>      Hd1         1d1     xo          H
2/          0<      Hd1         1d1     xo          Hd1
!! Result = Max. normal, round or sticky bit <> 0
!! This combination is not possible
!! inexact, underflow
!! X - Y <= -B-t
!! Z = 0.0...0, round bit = 0
A/      =0<     T       2pt     xu      0
A/      >       T       2pt     xu      0i1
A/      =0<     -T      -2pt    xu      0
A/      >       -T      -2pt    xu      0i1
A/      =0>     T       -2pt    xu      -0
A/      <       T       -2pt    xu      -0i1
A/      =0>     -T      2pt     xu      -0
A/      <       -T      2pt     xu      -0i1
!! denormal
A/      =0<     0i1     4       xu      0
A/      >       0i1     4       xu      0i1
A/      =0<     -0i1    -4      xu      0
A/      >       -0i1    -4      xu      0i1
A/      =0>     0i1     -4      xu      -0
A/      <       0i1     -4      xu      -0i1
A/      =0>     -0i1    4       xu      -0
A/      <       -0i1    4       xu      -0i1
! Tiny / huge -> underflow.
2/          =<0     0i1   Hd1  xu          0
2/          >       0i1   Hd1  xu          0i1
2/          =<0     -0i1  -Hd1  xu          0
2/          >       -0i1  -Hd1  xu          0i1
2/          =0>     0i1   -Hd1 xu          -0
2/          <       0i1   -Hd1 xu          -0i1
2/          =0>     -0i1   Hd1 xu          -0
2/          <       -0i1   Hd1 xu          -0i1
!! X - Y = -B-t+1, round bit = 1, sticky bit = 1
A/      0<      Tp1d1   1pt     xu      0
A/      =>      Tp1d1   1pt     xu      0i1
A/      0<      -Tp1d1  -1pt    xu      0
A/      =>      -Tp1d1  -1pt    xu      0i1
A/      0>      -Tp1d1  1pt     xu      -0
A/      =<      -Tp1d1  1pt     xu      -0i1
A/      0>      Tp1d1   -1pt    xu      -0
A/      =<      Tp1d1   -1pt    xu      -0i1
!! denormal
A/      0<      Td1     1ptm1   xu      0
A/      =>      Td1     1ptm1   xu      0i1
A/      0<      -Td1    -1ptm1  xu      0
A/      =>      -Td1    -1ptm1  xu      0i1
A/      0>      -Td1    1ptm1   xu      -0
A/      =<      -Td1    1ptm1   xu      -0i1
A/      0>      Td1     -1ptm1  xu      -0
A/      =<      Td1     -1ptm1  xu      -0i1
!! X - Y = -B-t+1, round bit = 1, sticky bits = 0
A/      0<      3mB     1pt     xu      0
A/      =>      3mB     1pt     xu      0i1
A/      0<      -3mB    -1pt    xu      0
A/      =>      -3mB    -1pt    xu      0i1
A/      0>      -3mB    1pt     xu      -0
A/      =<      -3mB    1pt     xu      -0i1
A/      0>      3mB     -1pt    xu      -0
A/      =<      3mB     -1pt    xu      -0i1
!! denormal
A/      0<      0i3     4       xu      0
A/      =>      0i3     4       xu      0i1
A/      0<      -0i3    -4      xu      0
A/      =>      -0i3    -4      xu      0i1
A/      0>      -0i3    4       xu      -0
A/      =<      -0i3    4       xu      -0i1
A/      0>      0i3     -4      xu      -0
A/      =<      0i3     -4      xu      -0i1
!! X - Y = -B-t+1, round bit = 1, sticky bits = 1
A/      0<      5mBm1   1pt     xu      0
A/      =>      5mBm1   1pt     xu      0i1
A/      0<      -5mBm1  -1pt    xu      0
A/      =>      -5mBm1  -1pt    xu      0i1
A/      0>      -5mBm1  1pt     xu      -0
A/      =<      -5mBm1  1pt     xu      -0i1
A/      0>      5mBm1   -1pt    xu      -0
A/      =<      5mBm1   -1pt    xu      -0i1
!! denormal
A/      0<      0i5     8       xu      0
A/      =>      0i5     8       xu      0i1
A/      0<      -0i5    -8      xu      0
A/      =>      -0i5    -8      xu      0i1
A/      0>      -0i5    8       xu      -0
A/      =<      -0i5    8       xu      -0i1
A/      0>      0i5     -8      xu      -0
A/      =<      0i5     -8      xu      -0i1
!! X - Y = -B-t+1, round bit = 1, sticky bit = 0, round to even
A/      =0<     T       1pt     xu      0
A/      >       T       1pt     xu      0i1
A/      =0<     -T      -1pt    xu      0
A/      >       -T      -1pt    xu      0i1
A/      =0>     -T      1pt     xu      -0
A/      <       -T      1pt     xu      -0i1
A/      =0>     T       -1pt    xu      -0
A/      <       T       -1pt    xu      -0i1
!! denormal
2/      =0<     0i1     2       xu      0
2/      >       0i1     2       xu      0i1
2/      =0<     -0i1    -2      xu      0
2/      >       -0i1    -2      xu      0i1
2/      =0>     -0i1    2       xu      -0
2/      <       -0i1    2       xu      -0i1
2/      =0>     0i1     -2      xu      -0
2/      <       0i1     -2      xu      -0i1
!! X - Y = -B-t+2, round bit = 1, sticky bit = 0, round to even
A/      0<      Tp1i(1)1        1pt     xu      0i1
A/      =>      Tp1i(1)1        1pt     xu      0i2
A/      0<      -Tp1i(1)1       -1pt    xu      0i1
A/      =>      -Tp1i(1)1       -1pt    xu      0i2
A/      0>      -Tp1i(1)1       1pt     xu      -0i1
A/      =<      -Tp1i(1)1       1pt     xu      -0i2
A/      0>      Tp1i(1)1        -1pt    xu      -0i1
A/      =<      Tp1i(1)1        -1pt    xu      -0i2
!! denormal
A/      0<      0i3     2       xu      0i1
A/      =>      0i3     2       xu      0i2
A/      0<      -0i3    -2      xu      0i1
A/      =>      -0i3    -2      xu      0i2
A/      0>      -0i3    2       xu      -0i1
A/      =<      -0i3    2       xu      -0i2
A/      0>      0i3     -2      xu      -0i1
A/      =<      0i3     -2      xu      -0i2
!! exp. Z = -B + denormalization loss => inexactness
A/      =0<     Tp1d3   2       xu      Td2
A/      >       Tp1d3   2       xu      Td1
A/      =0<     -Tp1d3  -2      xu      Td2
A/      >       -Tp1d3  -2      xu      Td1
A/      =0>     -Tp1d3  2       xu      -Td2
A/      <       -Tp1d3  2       xu      -Td1
A/      =0>     Tp1d3   -2      xu      -Td2
A/      <       Tp1d3   -2      xu      -Td1
A/      0<=     Ti(3)7i3       1p2i(1)1    xu  0i(4)5
A/      >       Ti(3)7i3       1p2i(1)1    xu  0i(4)5i1
A/      0<      Ti(3)7i3       1pti(1)1    xu  0
A/      >=      Ti(3)7i3       1pti(1)1    xu  0i1
!! denormal
A/      0<      Td1     2       xu      0i(1)1d1
A/      =>      Td1     2       xu      0i(1)1
A/      0<      -Td1    -2      xu      0i(1)1d1
A/      =>      -Td1    -2      xu      0i(1)1
A/      0>      -Td1    2       xu      -0i(1)1d1
A/      =<      -Td1    2       xu      -0i(1)1
A/      0>      Td1     -2      xu      -0i(1)1d1
A/      =<      Td1     -2      xu      -0i(1)1
!! exp. Z = -B + inexactness, no denormalization loss
2/      =0<     T       1i1     xv      Td1
2/      >       T       1i1     xu      T
A/      =0<     -T      -1i1    xv      Td1
A/      >       -T      -1i1    xu      T
2/      =0>     -T      1i1     xv      -Td1
2/      <       -T      1i1     xu      -T
A/      =0>     T       -1i1    xv      -Td1
A/      <       T       -1i1    xu      -T
2/          <=0     Ti1     1i2     xv      Td1
2/          >       Ti1     1i2     xu      T
2/          <=0     Ti2     1i6     xv      Td4
!! denormal
2/      =0<     Td1     1i1     xv      Td2
A/      >       Td1     1i1     xu      Td1
A/      =0<     -Td1    -1i1    xv      Td2
A/      >       -Td1    -1i1    xu      Td1
A/      =0>     -Td1    1i1     xv      -Td2
A/      <       -Td1    1i1     xu      -Td1
A/      =0>     Td1     -1i1    xv      -Td2
A/      <       Td1     -1i1    xu      -Td1
2/          >=      Td2     1d2     xv      Td1
2/          >=      Td9     1d2     xv      Td8
2/          <=      -Td8    1d2     xv      -Td7
2/          <=0     Td1     1i2     xv      Td3
2/          >       Td1     1i2     xu      Td2
!! exp. Z = -B + tininess after rounding
A/          >       Ti(1)1d1     3m1     xu      T
A/          =       Ti(1)1d1     3m1     xu      Td1
A/          0<      Ti(1)1d1     3m1     xv      Td1
A/          <       -Ti(1)1d1    3m1     xu      -T
A/          =       -Ti(1)1d1    3m1     xu      -Td1
A/          0>      -Ti(1)1d1    3m1     xv      -Td1
A/          =>       1d1         Hm2     xu      T
A/          <0       1d1         Hm2     xu      Td1
A/          =<       -1d1        Hm2     xu      -T
A/          >0       -1d1        Hm2     xu      -Td1
!! tininess before and after rounding
!! as though the exponent range were unbounded
2/      0<      Tp1d1   2       xu      Td1
2/      =>      Tp1d1   2       xu      T
A/      0<      -Tp1d1  -2      xu      Td1
A/      =>      -Tp1d1  -2      xu      T
A/      0>      -Tp1d1  2       xu      -Td1
A/      =<      -Tp1d1  2       xu      -T
2/      0>      Tp1d1   -2      xu      -Td1
A/      =<      Tp1d1   -2      xu      -T
!! inexact, see rounding properties below

!! exact rounding
!! round bit = 0, sticky bit = 1 => inexact, round down
! Tricky divides based on power series expansions
! 1 / (1 + Nulp+) --> 1 - (2Nulp-) + tiny.
2/       =0<     1       1i1   x   1d2
2/       >       1       1i1   x   1d1
2/       =0<     -1      -1i1   x   1d2
2/       >       -1      -1i1   x   1d1
2/       =0>     -1       1i1   x   -1d2
2/       <       -1       1i1   x   -1d1
2/       =0>     1      -1i1   x   -1d2
2/       <       1      -1i1   x   -1d1
2/       =0<     1       1i2   x   1d4
2/       >       1       1i2   x   1d3
2/       =       1       1i3   x   1d6
2/       0       1       1i3   x   1d6
2/       <       1       1i3   x   1d6
2/       >       1       1i3   x   1d5
2/       =       1       1i4   x   1d8
2/       0       1       1i4   x   1d8
2/       <       1       1i4   x   1d8
2/       >       1       1i4   x   1d7
! 1 / (1 - Nu-) --> 1 + (Q/2 u+) + tiny.
2/       =       1       1d2   x   1i1
2/       0       1       1d2   x   1i1
2/       <       1       1d2   x   1i1
2/       >       1       1d2   x   1i2
2/       =       1       1d4   x   1i2
2/       0       1       1d4   x   1i2
2/       <       1       1d4   x   1i2
2/       >       1       1d4   x   1i3
2/       =       1       1d8   x   1i4
2/       0       1       1d8   x   1i4
2/       <       1       1d8   x   1i4
2/       >       1       1d8   x   1i5
! (1 + Mulp+) / (1 + Qulp+) -->
! Case M < Q: (1 + 2Mulp-) * (1 - 2Qulp- + (2Qulp-)^2 - tiny) -->
! 1 - 2(Q-M)ulp- + 4(QQ-MQ)(ulp-)^2 + tiny -->
! 1 - 2(Q-M)ulp- + tiny.
! M + Q = 3.
2/       =       1i1   1i2       x       1d2
2/       0       1i1   1i2       x       1d2
2/       <       1i1   1i2       x       1d2
2/       >       1i1   1i2       x       1d1
! M + Q = 4.
2/       =       1i1   1i3       x       1d4
2/       0       1i1   1i3       x       1d4
2/       <       1i1   1i3       x       1d4
2/       >       1i1   1i3       x       1d3
! M + Q = 5.
2/       =       1i2   1i3       x       1d2
2/       0       1i2   1i3       x       1d2
2/       <       1i2   1i3       x       1d2
2/       >       1i2   1i3       x       1d1
! M + Q = 11.
2/       =       1i4   1i7       x       1d6
2/       0       1i4   1i7       x       1d6
2/       <       1i4   1i7       x       1d6
2/       >       1i4   1i7       x       1d5
! M + Q = 14.
2/       =       1i6   1i8       x       1d4
2/       0       1i6   1i8       x       1d4
2/       <       1i6   1i8       x       1d4
2/       >       1i6   1i8       x       1d3
! (1 - Mulp-) / (1 - Qulp-) -->
! Case M < Q: (1 - (M/2)ulp+) * (1 + (Q/2)ulp+ + ((Q/2)ulp+)^2 + tiny) -->
! 1 + ((Q-M)/2)ulp+ + (QQ-MQ)/4(ulp+)^2 + tiny -->
! 1 + (Q-M)/2ulp+ + tiny.
! M + Q = 4.
2/       =       1d1   1d3       x       1i1
2/       0       1d1   1d3       x       1i1
2/       <       1d1   1d3       x       1i1
2/       >       1d1   1d3       x       1i2
! M + Q = 6.
2/       =       1d2   1d4       x       1i1
2/       0       1d2   1d4       x       1i1
2/       <       1d2   1d4       x       1i1
2/       >       1d2   1d4       x       1i2
! M + Q = 8.
2/       =       1d1   1d7       x       1i3
2/       0       1d1   1d7       x       1i3
2/       <       1d1   1d7       x       1i3
2/       >       1d1   1d7       x       1i4
! M + Q = 10.
2/       =       1d3   1d7       x       1i2
2/       0       1d3   1d7       x       1i2
2/       <       1d3   1d7       x       1i2
2/       >       1d3   1d7       x       1i3
! M + Q = 12.
2/       =       1d5   1d7       x       1i1
2/       0       1d5   1d7       x       1i1
2/       <       1d5   1d7       x       1i1
2/       >       1d5   1d7       x       1i2
! (1 + Mulp+) / (1 - Qulp-) -->
! (1 + Mulp+) * (1 + (Q/2)ulp+ + ((Q/2)ulp+)^2 + tiny) -->
! 1 + (M + Q/2)ulp+ + tiny.
! M + Q = 3.
2/       =       1i1   1d2       x       1i2
2/       0       1i1   1d2       x       1i2
2/       <       1i1   1d2       x       1i2
2/       >       1i1   1d2       x       1i3
! M + Q = 4.
2/       =       1i2   1d2       x       1i3
2/       0       1i2   1d2       x       1i3
2/       <       1i2   1d2       x       1i3
2/       >       1i2   1d2       x       1i4
! M + Q = 5.
2/       =       1i3   1d2       x       1i4
2/       0       1i3   1d2       x       1i4
2/       <       1i3   1d2       x       1i4
2/       >       1i3   1d2       x       1i5
! M + Q = 6.
2/       =       1i2   1d4       x       1i4
2/       0       1i2   1d4       x       1i4
2/       <       1i2   1d4       x       1i4
2/       >       1i2   1d4       x       1i5
2/       =       1i4   1d2       x       1i5
2/       0       1i4   1d2       x       1i5
2/       <       1i4   1d2       x       1i5
2/       >       1i4   1d2       x       1i6
! (1 - Mulp-) / (1 + Qulp+) -->
! (1 - Mulp-) * (1 - 2Qulp- + (2Qulp-)^2 - tiny) -->
! 1 - (M + 2Q)ulp- + tiny.
! M + Q = 2.
2/       =       1d1   1i1       x       1d3
2/       0       1d1   1i1       x       1d3
2/       <       1d1   1i1       x       1d3
2/       >       1d1   1i1       x       1d2
! M + Q = 3.
2/       =       1d2   1i1       x       1d4
2/       0       1d2   1i1       x       1d4
2/       <       1d2   1i1       x       1d4
2/       >       1d2   1i1       x       1d3
2/       =       1d1   1i2       x       1d5
2/       0       1d1   1i2       x       1d5
2/       <       1d1   1i2       x       1d5
2/       >       1d1   1i2       x       1d4
! M + Q = 4.
2/       =       1d3   1i1       x       1d5
2/       0       1d3   1i1       x       1d5
2/       <       1d3   1i1       x       1d5
2/       >       1d3   1i1       x       1d4
2/       =       1d1   1i3       x       1d7
2/       0       1d1   1i3       x       1d7
2/       <       1d1   1i3       x       1d7
2/       >       1d1   1i3       x       1d6
2/       =       1d2   1i2       x       1d6
2/       0       1d2   1i2       x       1d6
2/       <       1d2   1i2       x       1d6
2/       >       1d2   1i2       x       1d5
! M + Q = 5.
2/       =       1d4   1i1       x       1d6
2/       0       1d4   1i1       x       1d6
2/       <       1d4   1i1       x       1d6
2/       >       1d4   1i1       x       1d5
2/       =       1d1   1i4       x       1d9
2/       0       1d1   1i4       x       1d9
2/       <       1d1   1i4       x       1d9
2/       >       1d1   1i4       x       1d8
2/       =       1d3   1i2       x       1d7
2/       0       1d3   1i2       x       1d7
2/       <       1d3   1i2       x       1d7
2/       >       1d3   1i2       x       1d6
2/       =       1d2   1i3       x       1d8
2/       0       1d2   1i3       x       1d8
2/       <       1d2   1i3       x       1d8
2/       >       1d2   1i3       x       1d7
! A few tricky cases.
A/      =0<     -1d4    -1i1    x       1d6
A/      >       -1d4    -1i1    x       1d5
A/      =0>     -1d4    1i1     x       -1d6
A/      <       -1d4    1i1     x       -1d5
A/      =0>     1d4     -1i1    x       -1d6
A/      <       1d4     -1i1    x       -1d5
!! 3ff7ffff ffffffff 3feffff fffffffe 3ff80000 00000000
H/      0<      3m1d1   1d2     x       3m1
H/      =>      3m1d1   1d2     x       3m1i1
A/      0<      -3m1d1  -1d2    x       3m1
A/      =>      -3m1d1  -1d2    x       3m1i1
A/      0>      -3m1d1  1d2     x       -3m1
A/      =<      -3m1d1  1d2     x       -3m1i1
A/      0>      3m1d1   -1d2    x       -3m1
A/      =<      3m1d1   -1d2    x       -3m1i1
!! denormal
A/      =0<     0i(1)1  Ti1     x       1m1d2
A/      >       0i(1)1  Ti1     x       1m1d1
A/      =0<     -0i(1)1 -Ti1    x       1m1d2
A/      >       -0i(1)1 -Ti1    x       1m1d1
A/      =0>     -0i(1)1 Ti1     x       -1m1d2
A/      <       -0i(1)1 Ti1     x       -1m1d1
A/      =0>     0i(1)1  -Ti1    x       -1m1d2
A/      <       0i(1)1  -Ti1    x       -1m1d1
!! round bit = 0, sticky bit = 10 => inexact, round down
!! This combination is not possible
!! round bit = 0, sticky bit = 1 => inexact, round down
A/      =0<     3i2     1i1     x       3
A/      >       3i2     1i1     x       3i1
A/      =0<     -3i2    -1i1    x       3
A/      >       -3i2    -1i1    x       3i1
A/      =0>     3i2     -1i1    x       -3
A/      <       3i2     -1i1    x       -3i1
A/      =0>     -3i2    1i1     x       -3
A/      <       -3i2    1i1     x       -3i1
!! denormal
A/      =0<     0i(2)3i1        Ti1     x       3m2
A/      >       0i(2)3i1        Ti1     x       3m2i1
A/      =0<     -0i(2)3i1       -Ti1    x       3m2
A/      >       -0i(2)3i1       -Ti1    x       3m2i1
A/      =0>     0i(2)3i1        -Ti1    x       -3m2
A/      <       0i(2)3i1        -Ti1    x       -3m2i1
A/      =0>     -0i(2)3i1       Ti1     x       -3m2
A/      <       -0i(2)3i1       Ti1     x       -3m2i1
!! round bit = 1, sticky bit = 0 => inexact, round up
!! This combination is not possible
!! round bit = 1, sticky bit = 1 => inexact, round up
! 1 / (1 - Qu-) --> 1 + (Q/2 u+) + tiny.
2/       =       1       1d3   x   1i2
2/       0       1       1d3   x   1i1
2/       <       1       1d3   x   1i1
2/       >       1       1d3   x   1i2
2/       =       1       1d5   x   1i3
2/       0       1       1d5   x   1i2
2/       <       1       1d5   x   1i2
2/       >       1       1d5   x   1i3
2/       =       1       1d9   x   1i5
2/       0       1       1d9   x   1i4
2/       <       1       1d9   x   1i4
2/       >       1       1d9   x   1i5
! 1 / (1 - Qu-) --> 1 + (Q/2 u+) + tiny.
2/       =>       1       1d1   x   1i1
2/       0<       1       1d1   x   1
2/       =>       -1      -1d1   x   1i1
2/       0<       -1      -1d1   x   1
2/       =<       -1      1d1   x   -1i1
2/       0>       -1      1d1   x   -1
2/       =<       1      -1d1   x   -1i1
2/       0>       1      -1d1   x   -1
! (1 - Mulp-) / (1 - Qulp-) -->
! Case M < Q: (1 - (M/2)ulp+) * (1 + (Q/2)ulp+ + ((Q/2)ulp+)^2 + tiny) -->
! 1 + ((Q-M)/2)ulp+ + (QQ-MQ)/4(ulp+)^2 + tiny -->
! 1 + (Q-M)/2ulp+ + tiny.
! M + Q = 3.
2/       =       1d1   1d2       x       1i1
2/       0       1d1   1d2       x       1
2/       <       1d1   1d2       x       1
2/       >       1d1   1d2       x       1i1
! M + Q = 5.
2/       =       1d2   1d3       x       1i1
2/       0       1d2   1d3       x       1
2/       <       1d2   1d3       x       1
2/       >       1d2   1d3       x       1i1
2/       =       1d1   1d4       x       1i2
2/       0       1d1   1d4       x       1i1
2/       <       1d1   1d4       x       1i1
2/       >       1d1   1d4       x       1i2
! M + Q = 7.
2/       =       1d3   1d4       x       1i1
2/       0       1d3   1d4       x       1
2/       <       1d3   1d4       x       1
2/       >       1d3   1d4       x       1i1
! M + Q = 9.
2/       =       1d2   1d7       x       1i3
2/       0       1d2   1d7       x       1i2
2/       <       1d2   1d7       x       1i2
2/       >       1d2   1d7       x       1i3
! M + Q = 11.
2/       =       1d4   1d7       x       1i2
2/       0       1d4   1d7       x       1i1
2/       <       1d4   1d7       x       1i1
2/       >       1d4   1d7       x       1i2
! M + Q = 13.
2/       =       1d6   1d7       x       1i1
2/       0       1d6   1d7       x       1
2/       <       1d6   1d7       x       1
2/       >       1d6   1d7       x       1i1
! (1 + Mulp+) / (1 - Qulp-) -->
! (1 + Mulp+) * (1 + (Q/2)ulp+ + ((Q/2)ulp+)^2 + tiny) -->
! 1 + (M + Q/2)ulp+ + tiny.
! M + Q = 2.
2/       =       1i1   1d1       x       1i2
2/       0       1i1   1d1       x       1i1
2/       <       1i1   1d1       x       1i1
2/       >       1i1   1d1       x       1i2
! M + Q = 3.
2/       =       1i2   1d1       x       1i3
2/       0       1i2   1d1       x       1i2
2/       <       1i2   1d1       x       1i2
2/       >       1i2   1d1       x       1i3
! M + Q = 4.
2/       =       1i1   1d3       x       1i3
2/       0       1i1   1d3       x       1i2
2/       <       1i1   1d3       x       1i2
2/       >       1i1   1d3       x       1i3
2/       =       1i3   1d1       x       1i4
2/       0       1i3   1d1       x       1i3
2/       <       1i3   1d1       x       1i3
2/       >       1i3   1d1       x       1i4
! M + Q = 5.
2/       =       1i2   1d3       x       1i4
2/       0       1i2   1d3       x       1i3
2/       <       1i2   1d3       x       1i3
2/       >       1i2   1d3       x       1i4
! M + Q = 6.
2/       =       1i3   1d3       x       1i5
2/       0       1i3   1d3       x       1i4
2/       <       1i3   1d3       x       1i4
2/       >       1i3   1d3       x       1i5
2/       =       1i1   1d5       x       1i4
2/       0       1i1   1d5       x       1i3
2/       <       1i1   1d5       x       1i3
2/       >       1i1   1d5       x       1i4
2/       =       1i5   1d1       x       1i6
2/       0       1i5   1d1       x       1i5
2/       <       1i5   1d1       x       1i5
2/       >       1i5   1d1       x       1i6
!! denormal
A/      =>      0i(1)1  Tp1d1   x       1m2i1
A/      0<      0i(1)1  Tp1d1   x       1m2
A/      =>      -0i(1)1 -Tp1d1  x       1m2i1
A/      0<      -0i(1)1 -Tp1d1  x       1m2
A/      =<      -0i(1)1 Tp1d1   x       -1m2i1
A/      0>      -0i(1)1 Tp1d1   x       -1m2
A/      =<      0i(1)1  -Tp1d1  x       -1m2i1
A/      0>      0i(1)1  -Tp1d1  x       -1m2
!! 3ff80000 00000001 3ff00000 00000001 3ff7ffff ffffffff
H/      =>      3m1i1   1i1     x       3m1
H/      0<      3m1i1   1i1     x       3m1d1
A/      =>      -3m1i1  -1i1    x       3m1
A/      0<      -3m1i1  -1i1    x       3m1d1
A/      =<      -3m1i1  1i1     x       -3m1
A/      0>      -3m1i1  1i1     x       -3m1d1
A/      =<      3m1i1   -1i1    x       -3m1
A/      0>      3m1i1   -1i1    x       -3m1d1
!! round bit = 1, sticky bit = 1 => inexact, round up
! (1 + Mu+) / (1 + Qu+) -->
! Case M > Q: (1 + Mu+) * (1 - Qu+ + (Qu+)^2 - tiny) -->
! 1 + (M-Q)u+ - (MQ-QQ)(u+)^2 + tiny -->
! 1 + (M-Q)u+ - tiny.
! M + Q = 3.
2/       =>       1i2   1i1       x       1i1
2/       0<       1i2   1i1       x       1
2/       =>       -1i2   -1i1      x       1i1
2/       0<       -1i2   -1i1      x       1
2/       =<       -1i2   1i1       x       -1i1
2/       0>       -1i2   1i1       x       -1
2/       =<       1i2   -1i1       x       -1i1
2/       0>       1i2   -1i1       x       -1
! M + Q = 4.
2/       =       1i3   1i1       x       1i2
2/       0       1i3   1i1       x       1i1
2/       <       1i3   1i1       x       1i1
2/       >       1i3   1i1       x       1i2
! M + Q = 5.
2/       =       1i4   1i1       x       1i3
2/       0       1i4   1i1       x       1i2
2/       <       1i4   1i1       x       1i2
2/       >       1i4   1i1       x       1i3
! M + Q = 9.
2/       =       1i7   1i2       x       1i5
2/       0       1i7   1i2       x       1i4
2/       <       1i7   1i2       x       1i4
2/       >       1i7   1i2       x       1i5
! Q = 17.
2/       =       1i9   1i8       x       1i1
2/       0       1i9   1i8       x       1
2/       <       1i9   1i8       x       1
2/       >       1i9   1i8       x       1i1
! (1 - Mulp-) / (1 - Qulp-) -->
! Case M > Q: (1 - Mulp-) * (1 + Qulp- + (Qulp-)^2 + tiny) -->
! 1 - (M-Q)ulp- - (MQ-QQ)(ulp-)^2 + tiny -->
! 1 - (M-Q)ulp- - tiny.
! M + Q = 3.
2/       =       1d2   1d1       x       1d1
2/       0       1d2   1d1       x       1d2
2/       <       1d2   1d1       x       1d2
2/       >       1d2   1d1       x       1d1
! M + Q = 4.
2/       =       1d3   1d1       x       1d2
2/       0       1d3   1d1       x       1d3
2/       <       1d3   1d1       x       1d3
2/       >       1d3   1d1       x       1d2
! M + Q = 5.
2/       =       1d3   1d2       x       1d1
2/       0       1d3   1d2       x       1d2
2/       <       1d3   1d2       x       1d2
2/       >       1d3   1d2       x       1d1
2/       =       1d4   1d1       x       1d3
2/       0       1d4   1d1       x       1d4
2/       <       1d4   1d1       x       1d4
2/       >       1d4   1d1       x       1d3
! M + Q = 6.
2/       =       1d4   1d2       x       1d2
2/       0       1d4   1d2       x       1d3
2/       <       1d4   1d2       x       1d3
2/       >       1d4   1d2       x       1d2
! M + Q = 7.
2/       =       1d4   1d3       x       1d1
2/       0       1d4   1d3       x       1d2
2/       <       1d4   1d3       x       1d2
2/       >       1d4   1d3       x       1d1
! M + Q = 11.
2/       =       1d8   1d3       x       1d5
2/       0       1d8   1d3       x       1d6
2/       <       1d8   1d3       x       1d6
2/       >       1d8   1d3       x       1d5
2/       =       1d9   1d2       x       1d7
2/       0       1d9   1d2       x       1d8
2/       <       1d9   1d2       x       1d8
2/       >       1d9   1d2       x       1d7
! M + Q = 12.
2/       =       1d8   1d4       x       1d4
2/       0       1d8   1d4       x       1d5
2/       <       1d8   1d4       x       1d5
2/       >       1d8   1d4       x       1d4
! M + Q = 14.
2/       =       1d9   1d5       x       1d4
2/       0       1d9   1d5       x       1d5
2/       <       1d9   1d5       x       1d5
2/       >       1d9   1d5       x       1d4
!! denormal
A/      =>      Td2     Tp1d1   x       1m1d3
A/      0<      Td2     Tp1d1   x       1m1d4
A/      =>      -Td2    -Tp1d1  x       1m1d3
A/      0<      -Td2    -Tp1d1  x       1m1d4
A/      =<      -Td2    Tp1d1   x       -1m1d3
A/      0>      -Td2    Tp1d1   x       -1m1d4
A/      =<      Td2     -Tp1d1  x       -1m1d3
A/      0>      Td2     -Tp1d1  x       -1m1d4