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+ proper (i.e. not broken) implementation of arctan() for the 8087 and 80287

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git-svn-id: trunk@26226 -
This commit is contained in:
nickysn 2013-12-12 23:46:51 +00:00
parent 179586f589
commit a7b4953795
2 changed files with 105 additions and 7 deletions
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9
compiler/x86/nx86inl.pas
View File

@ -103,6 +103,15 @@ implementation
function tx86inlinenode.first_arctan_real : tnode;
begin
{$ifdef i8086}
{ FPATAN's range is limited to (0 <= value < 1) on the 8087 and 80287,
so we need to use the RTL helper on these FPUs }
if current_settings.cputype < cpu_386 then
begin
result := inherited;
exit;
end;
{$endif i8086}
if (tfloatdef(pbestrealtype^).floattype=s80real) then
begin
expectloc:=LOC_FPUREGISTER;

103
rtl/i8086/math.inc
View File

@ -75,13 +75,6 @@
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_ARCTAN}
function fpc_arctan_real(d : ValReal) : ValReal;compilerproc;
begin
{ Function is handled internal in the compiler }
runerror(207);
result:=0;
end;
{$define FPC_SYSTEM_HAS_LN}
function fpc_ln_real(d : ValReal) : ValReal;compilerproc;
begin
@ -90,6 +83,102 @@
result:=0;
end;
const
{ the exact binary representation of pi (as generated by the fldpi instruction),
and then divided by 2 and 4. I've tested the following FPUs and they produce
the exact same values:
i8087
Pentium III (Coppermine)
Athlon 64 (K8)
}
Extended_PIO2: array [0..4] of word=($C235,$2168,$DAA2,$C90F,$3FFF); { pi/2 }
Extended_PIO4: array [0..4] of word=($C235,$2168,$DAA2,$C90F,$3FFE); { pi/4 }
{$define FPC_SYSTEM_HAS_ARCTAN}
function fpc_arctan_real(d : ValReal) : ValReal;assembler;compilerproc;
var
sw: word;
asm
{ the fpatan instruction on the 8087 and 80287 has the following restrictions:
0 <= ST(1) < ST(0) < +inf
which makes it useful only for calculating arctan in the range:
0 <= d < 1
so in order to cover the full range, we use the following properties of arctan:
arctan(1) = pi/4
arctan(-d) = -arctan(d)
arctan(d) = pi/2 - arctan(1/d), if d>0
}
fld tbyte [d]
ftst
fstsw sw
mov ah, [sw + 1]
sahf
jb @@negative
{ d >= 0 }
fld1 // 1 d
fcom
fstsw sw
mov ah, [sw + 1]
sahf
jb @@greater_than_one
jz @@equal_to_one
{ 0 <= d < 1 }
fpatan
jmp @@done
@@greater_than_one:
{ d > 1 }
fdivr st(1), st // 1 1/d
fpatan // arctan(1/d)
fld tbyte [Extended_PIO2] // pi/2 arctan(1/d)
fsubrp st(1), st // pi/2-arctan(1/d)
jmp @@done
@@equal_to_one:
{ d = 1, return pi/4 }
fstp st
fstp st
fld tbyte [Extended_PIO4]
jmp @@done
@@negative:
{ d < 0; -d > 0 }
fchs // -d
fld1 // 1 -d
fcom
fstsw sw
mov ah, [sw + 1]
sahf
jb @@less_than_minus_one
jz @@equal_to_minus_one
{ -1 < d < 0; 0 < -d < 1 }
fpatan // arctan(-d)
fchs // -arctan(-d)
jmp @@done
@@equal_to_minus_one:
{ d = -1, return -pi/4 }
fstp st
fstp st
fld tbyte [Extended_PIO4]
fchs
jmp @@done
@@less_than_minus_one:
{ d < -1; -d > 1 }
fdivr st(1), st // 1 -1/d
fpatan // arctan(-1/d)
fld tbyte [Extended_PIO2] // pi/2 arctan(-1/d)
fsubp st(1), st // arctan(-1/d)-pi/2
@@done:
end;
{$define FPC_SYSTEM_HAS_EXP}
function fpc_exp_real(d : ValReal) : ValReal;assembler;compilerproc;
var