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file := "acos": // data file to be tested
f := arccos: // corresponding MuPAD function
// ------------------------ do not edit below this line -----------------------
// auxiliary function for file log10
log10 := proc(x)
begin
if testtype(x, Type::Numeric) then return (ln(x)/ln(10))
else return (procname (x))
end_if
end_proc:
log10 := funcenv(log10):
log10::type := "log10":
log10::print := "log10":
// auxiliary function for file mulpi
mulpi := proc(x)
begin
if testtype(x, Type::Numeric) then return (x * 884279719003555/2^48)
else return (procname (x))
end_if
end_proc:
mulpi := funcenv(mulpi):
mulpi::type := "mulpi":
mulpi::print := "mulpi":
// auxiliary function for file exp2
exp2 := proc(x)
begin
if testtype(x, Type::Numeric) then return(2^x)
else return (procname (x))
end_if
end_proc:
exp2 := funcenv(exp2):
exp2::type := "exp2":
exp2::print := "exp2":
// auxiliary function for file pow275
pow275 := proc(x)
begin
if testtype(x, Type::Numeric) then return(x^(11/4))
else return (procname (x))
end_if
end_proc:
pow275 := funcenv(pow275):
pow275::type := "pow275":
pow275::print := "pow275":
print (Unquoted, _concat ("Checking file ", file, " with MuPAD function ", f));
prec := 20: // default working precision
// tries to parse an unsigned integer x from l[i]
// return [FAIL, i] if an error occurred
// otherwise return [x, j] where j is the next position (after x)
scanf_uint := proc (l, i)
local x, c, n;
begin
n := length (l);
if i > n then return ([FAIL, i])
else
c := stringlib::contains ("0123456789", l[i], IndexList);
if c = [] then return ([FAIL, i]) end_if;
x := c[1] - 1;
i := i + 1;
while i <= n do
c := stringlib::contains ("0123456789", l[i], IndexList);
if c = [] then return ([x, i]) end_if;
x := 10*x + (c[1] - 1);
i := i + 1;
end_while;
return ([x, i]);
end_if
end_proc:
scanf_hex := proc (l, i)
local x, c, n, s, se, e;
begin
n := length (l);
if i > n then return ([FAIL, i]) end_if;
if l[i] = "-" then s := -1; i := i + 1 else s := 1 end_if;
// we need to read at least 0xd, thus l[i..i+2]
if i + 2 > n or l[i..i+1] <> "0x" then return ([FAIL, i]) end_if;
i := i + 2;
c := stringlib::contains ("0123456789ABCDEF", l[i], IndexList);
if c = [] then return ([FAIL, i]) end_if;
x := c[1] - 1;
i := i + 1;
while i <= n do
c := stringlib::contains ("0123456789ABCDEF", l[i], IndexList);
if c = [] then break end_if;
x := 16*x + (c[1] - 1);
i := i + 1;
end_while;
// now read p<exp> (if any)
if i <= n and l[i] = "p" then
i := i + 1;
if i > n then return ([FAIL, i]) end_if;
if l[i] = "-" then se := -1; i := i + 1 else se := 1 end_if;
e := scanf_uint (l, i);
if e[1] = FAIL then return (e) end_if;
i := e[2];
e := se * e[1];
else e := 0
end_if;
return ([s*x*2^e, i])
end_proc:
scanf_rnd := proc (l, i)
local n, r;
begin
n := length (l);
if i > n then return ([FAIL, i]) end_if;
r := l[i];
if contains (["n", "z", "u", "d"], r) = 0 then return ([FAIL, i])
else return ([r, i+1])
end_if
end_proc:
// return new i
skip_blanks := proc (l, i)
local n;
begin
n := length (l);
while i <= n and l[i] = " " do
i := i + 1;
end_while;
return (i)
end_proc:
// round z with mode r and precision p bits
Round := proc (z, r, p)
local e, s, m;
begin
if iszero(z) then return(0) end_if;
// first compute exponent
if z < 0 then s := -1; m := -z else s := 1; m := z end_if;
e := ceil (log(2, m));
m := m * 2 ^ (p - e);
if r = "n" then m := round (m)
elif r = "z" then m := floor (m)
elif r = "u" then m := ceil (s * m); s := 1
elif r = "d" then m := floor (s * m); s := 1
else error (_concat("unknown rounding mode: ", r))
end_if;
return (s * m * 2^(e-p))
end_proc:
foo := fopen (file, Read, Text):
l := ftextinput (foo):
checked := 0: // number of checked lines
maxprec := 0: // maximal precision used
while type(l) <> DOM_NULL do
if l[1] <> "#" then
i := 1; // current index in l
xprec := scanf_uint (l, i);
i := xprec[2];
xprec := xprec[1];
if xprec = FAIL then
error ("cannot read input precision")
end_if;
i := skip_blanks (l, i);
yprec := scanf_uint (l, i);
i := yprec[2];
yprec := yprec[1];
if yprec = FAIL then
error ("cannot read output precision")
end_if;
i := skip_blanks (l, i);
rnd := scanf_rnd (l, i);
i := rnd[2];
rnd := rnd[1];
if rnd = FAIL then
error ("cannot read rounding mode")
end_if;
i := skip_blanks (l, i);
x := scanf_hex (l, i);
i := x[2];
x := x[1];
if x = FAIL then
error ("cannot read input number")
end_if;
i := skip_blanks (l, i);
y := scanf_hex (l, i);
i := y[2];
y := y[1];
if y = FAIL then
error ("cannot read output number")
end_if;
DIGITS := prec;
exact := bool(type(f(x)) <> type(f(xxx)));
repeat
if exact then z := f(x)...f(x) else z := f(x...x) end_if;
z1 := Round (op(z, 1), rnd, yprec);
z2 := Round (op(z, 2), rnd, yprec);
if z1 = z2 then break end_if;
DIGITS := DIGITS + iquo (DIGITS, 2);
until z1 = z2 end_repeat;
if DIGITS > maxprec then maxprec := DIGITS end_if;
if y <> z1 then
print (Unquoted, _concat ("x=", x));
print (Unquoted, _concat ("file contains ", y));
print (Unquoted, _concat ("MuPAD claims ", z1));
error (_concat("wrong data line: ", l))
end_if;
checked := checked + 1;
end_if;
l := ftextinput (foo); // read next line
end_while;
print (Unquoted, _concat ("checked lines: ", checked));
print (Unquoted, _concat ("maximal precision: ", maxprec));
print (Unquoted, _concat ("total time: ", time ()));
fclose (foo);
quit;
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