mirror of
https://gitlab.com/freepascal.org/fpc/source.git
synced 2025-04-16 10:19:30 +02:00
* Replaced fpc_arctan_real() implementation with one providing a better precision.
git-svn-id: trunk@25994 -
This commit is contained in:
sergei
parent
7516b87382
commit
d83fbd7602
@ -1273,75 +1273,156 @@ invalid:
|
||||
|
||||
{$ifndef FPC_SYSTEM_HAS_ARCTAN}
|
||||
function fpc_ArcTan_real(d:ValReal):ValReal;compilerproc;
|
||||
{*****************************************************************}
|
||||
{ Inverse circular tangent (arctangent) }
|
||||
{*****************************************************************}
|
||||
{ }
|
||||
{ SYNOPSIS: }
|
||||
{ }
|
||||
{ double x, y, atan(); }
|
||||
{ }
|
||||
{ y = atan( x ); }
|
||||
{ }
|
||||
{ DESCRIPTION: }
|
||||
{ }
|
||||
{ Returns radian angle between -pi/2 and +pi/2 whose tangent }
|
||||
{ is x. }
|
||||
{ }
|
||||
{ Range reduction is from four intervals into the interval }
|
||||
{ from zero to tan( pi/8 ). The approximant uses a rational }
|
||||
{ function of degree 3/4 of the form x + x**3 P(x)/Q(x). }
|
||||
{*****************************************************************}
|
||||
const P : TabCoef = (
|
||||
-8.40980878064499716001E-1,
|
||||
-8.83860837023772394279E0,
|
||||
-2.18476213081316705724E1,
|
||||
-1.48307050340438946993E1, 0, 0, 0);
|
||||
Q : TabCoef = (
|
||||
1.54974124675307267552E1,
|
||||
6.27906555762653017263E1,
|
||||
9.22381329856214406485E1,
|
||||
4.44921151021319438465E1, 0, 0, 0);
|
||||
{
|
||||
This code was translated from uclibc code, the original code
|
||||
had the following copyright notice:
|
||||
|
||||
{ tan( 3*pi/8 ) }
|
||||
T3P8 = 2.41421356237309504880;
|
||||
{ tan( pi/8 ) }
|
||||
TP8 = 0.41421356237309504880;
|
||||
*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*}
|
||||
|
||||
var y,z : Real;
|
||||
Sign : Integer;
|
||||
{********************************************************************}
|
||||
{ Inverse circular tangent (arctangent) }
|
||||
{********************************************************************}
|
||||
{ }
|
||||
{ SYNOPSIS: }
|
||||
{ }
|
||||
{ double x, y, atan(); }
|
||||
{ }
|
||||
{ y = atan( x ); }
|
||||
{ }
|
||||
{ DESCRIPTION: }
|
||||
{ }
|
||||
{ Returns radian angle between -pi/2 and +pi/2 whose tangent }
|
||||
{ is x. }
|
||||
{ }
|
||||
{ Method }
|
||||
{ 1. Reduce x to positive by atan(x) = -atan(-x). }
|
||||
{ 2. According to the integer k=4t+0.25 chopped, t=x, the argument }
|
||||
{ is further reduced to one of the following intervals and the }
|
||||
{ arctangent of t is evaluated by the corresponding formula: }
|
||||
{ }
|
||||
{ [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) }
|
||||
{ [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) }
|
||||
{ [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) }
|
||||
{ [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) }
|
||||
{ [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) }
|
||||
{********************************************************************}
|
||||
const
|
||||
atanhi: array [0..3] of double = (
|
||||
4.63647609000806093515e-01, { atan(0.5)hi 0x3FDDAC67, 0x0561BB4F }
|
||||
7.85398163397448278999e-01, { atan(1.0)hi 0x3FE921FB, 0x54442D18 }
|
||||
9.82793723247329054082e-01, { atan(1.5)hi 0x3FEF730B, 0xD281F69B }
|
||||
1.57079632679489655800e+00 { atan(inf)hi 0x3FF921FB, 0x54442D18 }
|
||||
);
|
||||
|
||||
atanlo: array [0..3] of double = (
|
||||
2.26987774529616870924e-17, { atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 }
|
||||
3.06161699786838301793e-17, { atan(1.0)lo 0x3C81A626, 0x33145C07 }
|
||||
1.39033110312309984516e-17, { atan(1.5)lo 0x3C700788, 0x7AF0CBBD }
|
||||
6.12323399573676603587e-17 { atan(inf)lo 0x3C91A626, 0x33145C07 }
|
||||
);
|
||||
|
||||
aT: array[0..10] of double = (
|
||||
3.33333333333329318027e-01, { 0x3FD55555, 0x5555550D }
|
||||
-1.99999999998764832476e-01, { 0xBFC99999, 0x9998EBC4 }
|
||||
1.42857142725034663711e-01, { 0x3FC24924, 0x920083FF }
|
||||
-1.11111104054623557880e-01, { 0xBFBC71C6, 0xFE231671 }
|
||||
9.09088713343650656196e-02, { 0x3FB745CD, 0xC54C206E }
|
||||
-7.69187620504482999495e-02, { 0xBFB3B0F2, 0xAF749A6D }
|
||||
6.66107313738753120669e-02, { 0x3FB10D66, 0xA0D03D51 }
|
||||
-5.83357013379057348645e-02, { 0xBFADDE2D, 0x52DEFD9A }
|
||||
4.97687799461593236017e-02, { 0x3FA97B4B, 0x24760DEB }
|
||||
-3.65315727442169155270e-02, { 0xBFA2B444, 0x2C6A6C2F }
|
||||
1.62858201153657823623e-02 { 0x3F90AD3A, 0xE322DA11 }
|
||||
);
|
||||
|
||||
one: double = 1.0;
|
||||
huge: double = 1.0e300;
|
||||
|
||||
var
|
||||
w,s1,s2,z: double;
|
||||
ix,hx,id: longint;
|
||||
low: longword;
|
||||
begin
|
||||
{ make argument positive and save the sign }
|
||||
sign := 1;
|
||||
if( d < 0.0 ) then
|
||||
{$ifdef FPC_DOUBLE_HILO_SWAPPED}
|
||||
hx:=float64(d).low;
|
||||
{$else}
|
||||
hx:=float64(d).high;
|
||||
{$endif FPC_DOUBLE_HILO_SWAPPED}
|
||||
ix := hx and $7fffffff;
|
||||
if (ix>=$44100000) then { if |x| >= 2^66 }
|
||||
begin
|
||||
sign := -1;
|
||||
d := -d;
|
||||
end;
|
||||
{$ifdef FPC_DOUBLE_HILO_SWAPPED}
|
||||
low:=float64(d).high;
|
||||
{$else}
|
||||
low:=float64(d).low;
|
||||
{$endif FPC_DOUBLE_HILO_SWAPPED}
|
||||
|
||||
{ range reduction }
|
||||
if( d > T3P8 ) then
|
||||
if (ix > $7ff00000) or ((ix = $7ff00000) and (low<>0)) then
|
||||
exit(d+d); { NaN }
|
||||
if (hx>0) then
|
||||
exit(atanhi[3]+atanlo[3])
|
||||
else
|
||||
exit(-atanhi[3]-atanlo[3]);
|
||||
end;
|
||||
if (ix < $3fdc0000) then { |x| < 0.4375 }
|
||||
begin
|
||||
y := PIO2;
|
||||
d := -( 1.0/d );
|
||||
end
|
||||
else if( d > TP8 ) then
|
||||
begin
|
||||
y := PIO4;
|
||||
d := (d-1.0)/(d+1.0);
|
||||
if (ix < $3e200000) then { |x| < 2^-29 }
|
||||
begin
|
||||
if (huge+d>one) then exit(d); { raise inexact }
|
||||
end;
|
||||
id := -1;
|
||||
end
|
||||
else
|
||||
y := 0.0;
|
||||
|
||||
{ rational form in x**2 }
|
||||
|
||||
z := d * d;
|
||||
y := y + ( polevl( z, P, 3 ) / p1evl( z, Q, 4 ) ) * z * d + d;
|
||||
|
||||
if( sign < 0 ) then
|
||||
y := -y;
|
||||
result := y;
|
||||
begin
|
||||
d := abs(d);
|
||||
if (ix < $3ff30000) then { |x| < 1.1875 }
|
||||
begin
|
||||
if (ix < $3fe60000) then { 7/16 <=|x|<11/16 }
|
||||
begin
|
||||
id := 0; d := (2.0*d-one)/(2.0+d);
|
||||
end
|
||||
else { 11/16<=|x|< 19/16 }
|
||||
begin
|
||||
id := 1; d := (d-one)/(d+one);
|
||||
end
|
||||
end
|
||||
else
|
||||
begin
|
||||
if (ix < $40038000) then { |x| < 2.4375 }
|
||||
begin
|
||||
id := 2; d := (d-1.5)/(one+1.5*d);
|
||||
end
|
||||
else { 2.4375 <= |x| < 2^66 }
|
||||
begin
|
||||
id := 3; d := -1.0/d;
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
{ end of argument reduction }
|
||||
z := d*d;
|
||||
w := z*z;
|
||||
{ break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly }
|
||||
s1 := z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||||
s2 := w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||||
if (id<0) then
|
||||
result := d - d*(s1+s2)
|
||||
else
|
||||
begin
|
||||
z := atanhi[id] - ((d*(s1+s2) - atanlo[id]) - d);
|
||||
if hx<0 then
|
||||
result := -z
|
||||
else
|
||||
result := z;
|
||||
end;
|
||||
end;
|
||||
{$endif}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user