#! /bin/bash

tempfile=$$.tmp
errfile=$$.2.tmp

function tryit(){
  good_stat=$1
  cliffer > $tempfile 2> $errfile
  status=$?
  if ! test "_$status" = "_$good_stat" ; then
    cat $errfile
    exit $status
  fi
}

didsome=0;
function checkit(){
  test="$1"
  cat > ref$tempfile
  if ! diff -q ref$tempfile $tempfile > /dev/null; then
    echo ""
    echo "Ooops test $test failed."
    echo "Hint:"
    echo "  :; diff ref$tempfile $tempfile"
    exit 3;
  fi
  printf "OK %2d... " $test
  rm $tempfile ref$tempfile $errfile
  if ((++didsome >= 5)) ; then
    echo "";
    didsome=0
  fi
}

#############
# Compound rotation:  two 90 degree rotations
# makes a 120 degree rotation about the 1,1,1 diagonal:
<<EoF tryit 0
 1 0 0  90 deg vrml dup @v dup @m
[0 0 1] -90° VRML rev mul dup @v @m
EoF

<<EoF checkit 1
    1.00000 0.00000 0.00000 1.57080 =  90.0000°
      [  1.00000  0.00000  0.00000 ]
      [  0.00000  0.00000 -1.00000 ]
      [  0.00000  1.00000  0.00000 ]
    0.57735 0.57735 0.57735 2.09440 = 120.0000°
      [  0.00000  0.00000  1.00000 ]
      [  1.00000  0.00000  0.00000 ]
      [  0.00000  1.00000  0.00000 ]
EoF


#############
#  Multiply two vectors to create a bivector,
# then use that to crank a vector:
<<EoF tryit 0
[ 1 0 0 ] [ 1 1 0 ] mul normalize [ 0 1 0 ] crank @
EoF

<<EoF checkit 2
    [-1, 0, 0]
EoF

############
# Calculate the angle between two vectors:
<<EoF tryit 0
[ -1 0 0 ] [ 1 1 0 ] mul normalize rangle @a
EoF

<<EoF checkit 3
    2.35619 = 135.0000°
EoF

############
# Powers:
# Exponentiate a quaternion.  Find rotor that rotates only half as much:
<<EoF tryit 0
[ 0 0 1 ] [ 1 0 0 ] mul 2 mul dup rangle @a .5 pow
1 setbasis dup rangle @a dup @ @x
EoF

<<EoF checkit 4
    1.57080 =  90.0000°
    0.78540 =  45.0000°
    1 + [0, 1, 0]§
    1
    0x + 0y + 0z
    0xy - 1xz + 0yz
    0xyz
EoF

############
# Take the 4th root using pow and sqrt, then take the
# fourth power using direct multiplication of quaternions:
<<EoF tryit 0
[ 1 0 0 ] [ 0 1 0 ] mul dup @v
  .5 pow sqrt dup @v dup mul dup mul @v
EoF

<<EoF checkit 5
    0.00000 0.00000 1.00000 3.14159 = 180.0000°
    0.00000 0.00000 1.00000 0.78540 =  45.0000°
    0.00000 0.00000 1.00000 3.14159 = 180.0000°
EoF

############
# Test the "reverse" operator:
<<EoF tryit 0
[ 1 0 0 ] [ 1 1 0 ] cmul dup @ rev @
EoF

<<EoF checkit 6
    1 + [0, 0, 1]§
    1 + [0, 0, -1]§
EoF

############
# Test the "hodge" operator:
<<EoF tryit 0
[ 1 0 0 ] [ 1 1 0 ] cmul dup @ hodge dup @ § @
EoF

<<EoF checkit 7
    1 + [0, 0, 1]§
    [0, 0, 1] + 1§
    1 + [0, 0, 1]§
EoF

############
# Wring out the mul and cmul operators:
<<EoF tryit 0
[ 1 0 0 ] [ 0 1 0 ]  mul @
[ 1 0 0 ] [ 0 1 0 ] cmul @
[ 0 1 0 ] [ 0 0 1 ]  mul @
[ 0 1 0 ] [ 0 0 1 ] cmul @
[ 0 0 1 ] [ 1 0 0 ]  mul @
[ 0 0 1 ] [ 1 0 0 ] cmul @
EoF

<<EoF checkit 8
    [0, 0, 1]§
    [0, 0, 1]§
    [1, 0, 0]§
    [1, 0, 0]§
    [0, 1, 0]§
    [0, 1, 0]§
EoF

############
# Mild test of dot, wedge, and mul operators:
<<EoF tryit 0
[ 1 0 0 ]  [ 1 1 0 ] · @        # unicode dot
[ 1 -1 0 ] [ 1 1 0 ] ⋅ @        # another unicode dot
[ 1 0 0 ]  [ 1 1 0 ] ⋀ @        # unicode wedge
[ 1 0 0 ]  [ 1 1 0 ] mul @
[ 1 0 0 ]  [ 9 1 0 ] wedge [ 3 2 1 ] wedge @
EoF

<<EoF checkit 9
    1
    0
    [0, 0, 1]§
    1 + [0, 0, 1]§
    1§
EoF

############
# test unbave, add, and @x operators
<<EoF tryit 0
4 unbave 3 unbave add 2 unbave add 2 add @x
EoF

<<EoF checkit 10
    2
    0a + 1b + 1c + 1d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    0abc + 0abd + 0acd + 0bcd
    0abcd
EoF

############
# Test stuff in four dimensions; useful as a check on
# http://www.av8n.com/physics/clifford-intro.htm#eq-example-pieces
<<EoF tryit 0
1 unbave 2 unbave wedge dup @x
2 unbave 3 unbave add 4 unbave 1 unbave add wedge dup @x
mul @x
EoF

<<EoF checkit 11
    0
    0a + 0b
    1ab
    0
    0a + 0b + 0c + 0d
    -1ab - 1ac + 0ad + 0bc + 1bd + 1cd
    0abc + 0abd + 0acd + 0bcd
    0abcd
    1
    0a + 0b + 0c + 0d
    0ab + 0ac + 1ad + 1bc + 0bd + 0cd
    0abc + 0abd + 0acd + 0bcd
    1abcd
EoF

############
# test reverse in 4 dimensions
<<EoF tryit 0
1 unbave 2 unbave wedge
2 unbave 3 unbave add 4 unbave 1 unbave add wedge mul
2 unbave 1 add mul
rev dup @x rev @x
EoF

<<EoF checkit 12
    1
    0a + 1b - 1c + 0d
    0ab + 0ac - 1ad - 1bc + 0bd + 0cd
    0abc + 1abd - 1acd + 0bcd
    1abcd
    1
    0a + 1b - 1c + 0d
    0ab + 0ac + 1ad + 1bc + 0bd + 0cd
    0abc - 1abd + 1acd + 0bcd
    1abcd
EoF

############
# test hodge in 4 dimensions
<<EoF tryit 0
2 1 unbave add 2 unbave 2 mul add 4 unbave 4 mul add
dup dup @x hodge dup @x § dup @x sub @x
EoF

<<EoF checkit 13
    2
    1a + 2b + 0c + 4d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    0abc + 0abd + 0acd + 0bcd
    0abcd
    0
    0a + 0b + 0c + 0d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    4abc + 0abd + 2acd - 1bcd
    2abcd
    2
    -1a - 2b + 0c - 4d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    0abc + 0abd + 0acd + 0bcd
    0abcd
    0
    2a + 4b + 0c + 8d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    0abc + 0abd + 0acd + 0bcd
    0abcd
EoF

############
# test gradesel and div
<<EoF tryit 0
2 1 unbave add 2 unbave 2 mul add 4 unbave 4 mul add
 § 1 add 3 unbave 3 mul add 10 div dup @x 3 gradesel @x
EoF

<<EoF checkit 14
    0.1
    0a + 0b + 0.3c + 0d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    0.4abc + 0abd + 0.2acd - 0.1bcd
    0.2abcd
    0
    0a + 0b + 0c + 0d
    0ab + 0ac + 0ad + 0bc + 0bd + 0cd
    0.4abc + 0abd + 0.2acd - 0.1bcd
    0abcd
EoF

############
# test unpack and clif
<<EoF tryit 0
[ 7 [ 6 5 4 ] add § -.01 [ 1 2 3 ] add add unpack ] dump
clif dump [ exch unpack ] dump
EoF

cp $tempfile /tmp/foo

<<EoF checkit 15
 0: VECTOR  D=8 :    [-0.01, 1, 2, 3, 4, -5, 6, 7]
 0: CLIF    D=3 :    -0.01 + [1, 2, 3] + [6, 5, 4]§ + 7§
 0: VECTOR  D=8 :    [-0.01, 1, 2, 3, 4, -5, 6, 7]
EoF

############
# test dimset ... promotion and demotion
<<EoF tryit 0
11 3 dimset § dump pop
[ 1 2 3 ] § dump 2 dimset dump
EoF

<<EoF checkit 16
 0: CLIF    D=3 :    11§
 0: CLIF    D=3 :    [1, 2, 3]§
 0: CLIF    D=2 :    3§
EoF

############
# test math library functions
<<EoF tryit 0
1 asin π 2 div sub @     # unicode pi
1.1 acosh asinh atanh pop
2 exp sqrt ln @
1 0 atan2 sin @
0 sinh tanh cosh @
EoF

<<EoF checkit 17
    0
    1
    1
    1
EoF

if ((didsome++ > 0)) ; then
  echo "";
fi

echo All OK!
exit