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* replaced all HandleError() calls to appropriate float_raise() calls

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* added overflow handling for fpc_exp_real
* removed arbitrary tabbing by spaces, improving readability somewhat

git-svn-id: trunk@6061 -
This commit is contained in:
tom_at_work 2007-01-18 22:10:32 +00:00
parent 30db0a17db
commit e501fab034
1 changed files with 67 additions and 69 deletions
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136
rtl/inc/genmath.inc
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@ -1,8 +1,8 @@
{
This file is part of the Free Pascal run time library.
Copyright (c) 1999-2001 by Several contributors
Copyright (c) 1999-2007 by Several contributors
Generic mathemtical routines (on type real)
Generic mathematical routines (on type real)
See the file COPYING.FPC, included in this distribution,
for details about the copyright.
@ -610,8 +610,10 @@ invalid:
begin
if( d <= 0.0 ) then
begin
if d < 0.0 then
d:=0/0;
if d < 0.0 then begin
float_raise(float_flag_invalid);
d := 0/0;
end;
result := 0.0;
end
else
@ -668,55 +670,55 @@ invalid:
* Method
* 1. Argument reduction:
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
* Given x, find r and integer k such that
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2.
*
* Here r will be represented as r = hi-lo for better
* accuracy.
* accuracy.
*
* 2. Approximation of exp(r) by a special rational function on
* the interval [0,0.34658]:
* Write
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
* the interval [0,0.34658]:
* Write
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
* We use a special Reme algorithm on [0,0.34658] to generate
* a polynomial of degree 5 to approximate R. The maximum error
* of this polynomial approximation is bounded by 2**-59. In
* other words,
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
* (where z=r*r, and the values of P1 to P5 are listed below)
* and
* | 5 | -59
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
* | |
* The computation of exp(r) thus becomes
* 2*r
* exp(r) = 1 + -------
* R - r
* r*R1(r)
* = 1 + r + ----------- (for better accuracy)
* 2 - R1(r)
* where
* 2 4 10
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
* a polynomial of degree 5 to approximate R. The maximum error
* of this polynomial approximation is bounded by 2**-59. In
* other words,
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
* (where z=r*r, and the values of P1 to P5 are listed below)
* and
* | 5 | -59
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
* | |
* The computation of exp(r) thus becomes
* 2*r
* exp(r) = 1 + -------
* R - r
* r*R1(r)
* = 1 + r + ----------- (for better accuracy)
* 2 - R1(r)
* where
2 4 10
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
*
* 3. Scale back to obtain exp(x):
* From step 1, we have
* exp(x) = 2^k * exp(r)
* From step 1, we have
* exp(x) = 2^k * exp(r)
*
* Special cases:
* exp(INF) is INF, exp(NaN) is NaN;
* exp(-INF) is 0, and
* for finite argument, only exp(0)=1 is exact.
* exp(INF) is INF, exp(NaN) is NaN;
* exp(-INF) is 0, and
* for finite argument, only exp(0)=1 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then exp(x) overflow
* if x < -7.45133219101941108420e+02 then exp(x) underflow
* For IEEE double
* if x > 7.09782712893383973096e+02 then exp(x) overflow
* if x < -7.45133219101941108420e+02 then exp(x) underflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
@ -744,9 +746,9 @@ invalid:
P4 = -1.65339022054652515390e-06; { 0xBEBBBD41, 0xC5D26BF1 }
P5 = 4.13813679705723846039e-08; { 0x3E663769, 0x72BEA4D0 }
var
c,hi,lo,t,y : double;
k,xsb : longint;
hx,hy,lx : dword;
c,hi,lo,t,y : double;
k,xsb : longint;
hx,hy,lx : dword;
begin
hi:=0.0;
lo:=0.0;
@ -768,27 +770,23 @@ invalid:
end
else
begin
if xsb=0 then
if xsb=0 then begin
float_raise(float_flag_overflow);
result:=d
else
end else
result:=0.0; { exp(+-inf)=begininf,0end }
exit;
end;
end;
if d > o_threshold then
begin
float_raise(float_flag_overflow); { overflow }
result:=huge*huge;
exit;
end;
if d < u_threshold then
begin
float_raise(float_flag_underflow); { underflow }
result:=twom1000*twom1000;
exit;
end;
if d > o_threshold then begin
float_raise(float_flag_overflow); { overflow }
exit;
end;
if d < u_threshold then begin
float_raise(float_flag_underflow); { underflow }
exit;
end;
end;
{ argument reduction }
if hx > $3fd62e42 then
begin { if |d| > 0.5 ln2 }
@ -800,10 +798,10 @@ invalid:
end
else
begin
k := round(invln2*d+halF[xsb]);
t := k;
hi := d - t*ln2HI[0]; { t*ln2HI is exact here }
lo := t*ln2LO[0];
k := round(invln2*d+halF[xsb]);
t := k;
hi := d - t*ln2HI[0]; { t*ln2HI is exact here }
lo := t*ln2LO[0];
end;
d := hi - lo;
end
@ -815,18 +813,18 @@ invalid:
exit;
end;
end
else
else
k := 0;
{ d is now in primary range }
t:=d*d;
c:=d - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if k=0 then
t:=d*d;
c:=d - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if k=0 then
begin
result:=one-((d*c)/(c-2.0)-d);
exit;
end
else
else
y := one-((lo-(d*c)/(2.0-c))-hi);
if k >= -1021 then
@ -837,9 +835,9 @@ invalid:
end
else
begin
hy:=float64(y).high;
hy:=float64(y).high;
float64(y).high:=longint(hy)+((k+1000) shl 20); { add k to y's exponent }
result:=y*twom1000;
result:=y*twom1000;
end;
end;
@ -885,11 +883,11 @@ invalid:
px, qx, xx : Real;
begin
if( d > MAXLOG) then
HandleError(205)
float_raise(float_flag_overflow)
else
if( d < MINLOG ) then
begin
HandleError(205);
float_raise(float_flag_underflow);
end
else
begin