|
|
@@ -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);
|
|
|
-
|
|
|
- { tan( 3*pi/8 ) }
|
|
|
- T3P8 = 2.41421356237309504880;
|
|
|
- { tan( pi/8 ) }
|
|
|
- TP8 = 0.41421356237309504880;
|
|
|
-
|
|
|
- var y,z : Real;
|
|
|
- Sign : Integer;
|
|
|
+ {
|
|
|
+ This code was translated from uclibc code, the original code
|
|
|
+ had the following copyright notice:
|
|
|
+
|
|
|
+ *
|
|
|
+ * ====================================================
|
|
|
+ * 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.
|
|
|
+ * ====================================================
|
|
|
+ *}
|
|
|
+
|
|
|
+ {********************************************************************}
|
|
|
+ { 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 );
|
|
|
+ if (ix < $3e200000) then { |x| < 2^-29 }
|
|
|
+ begin
|
|
|
+ if (huge+d>one) then exit(d); { raise inexact }
|
|
|
+ end;
|
|
|
+ id := -1;
|
|
|
end
|
|
|
- else if( d > TP8 ) then
|
|
|
+ else
|
|
|
begin
|
|
|
- y := PIO4;
|
|
|
- d := (d-1.0)/(d+1.0);
|
|
|
- end
|
|
|
+ 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 < $40038000) then { |x| < 2.4375 }
|
|
|
+ begin
|
|
|
+ id := 2; d := (d-1.5)/(one+1.5*d);
|
|
|
+ end
|
|
|
+ else { 2.4375 <= |x| < 2^66 }
|
|
|
+ begin
|
|
|
+ id := 3; d := -1.0/d;
|
|
|
+ end;
|
|
|
+ end;
|
|
|
+ end;
|
|
|
+ { end of argument reduction }
|
|
|
+ z := d*d;
|
|
|
+ w := z*z;
|
|
|
+ { break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly }
|
|
|
+ s1 := z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
|
|
+ s2 := w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
|
|
+ if (id<0) then
|
|
|
+ result := d - d*(s1+s2)
|
|
|
else
|
|
|
- y := 0.0;
|
|
|
-
|
|
|
- { rational form in x**2 }
|
|
|
-
|
|
|
- z := d * d;
|
|
|
- y := y + ( polevl( z, P, 3 ) / p1evl( z, Q, 4 ) ) * z * d + d;
|
|
|
-
|
|
|
- if( sign < 0 ) then
|
|
|
- y := -y;
|
|
|
- result := y;
|
|
|
+ begin
|
|
|
+ z := atanhi[id] - ((d*(s1+s2) - atanlo[id]) - d);
|
|
|
+ if hx<0 then
|
|
|
+ result := -z
|
|
|
+ else
|
|
|
+ result := z;
|
|
|
+ end;
|
|
|
end;
|
|
|
{$endif}
|
|
|
|
sergei