static double bsloww(double x,double dx, double orig,int n) {
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
double y,x1,x2,xx,r,t,res,cor,w[2];
#if 0
double a,da,xn;
union {int4 i[2]; double x;} v;
#endif
x1=(x+th2_36)-th2_36;
y = aa.x*x1*x1*x1;
r=x+y;
x2=(x-x1)+dx;
xx=x*x;
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
t=((x-r)+y)+t;
res=r+t;
cor = (r-res)+t;
cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
if (res == res + cor) return res;
else {
(x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24;
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
else return (n&1)?__mpcos1(orig):__mpsin1(orig);
}
}
void __docos(double x, double dx, double v[]) {
double y,yy,p,w[2];
if (x>0) {y=x; yy=dx;}
else {y=-x; yy=-dx;}
if (y<0.5*hp0.x) /* y< PI/4 */
{__dubcos(y,yy,w); v[0]=w[0]; v[1]=w[1];}
else if (y<1.5*hp0.x) { /* y< 3/4 * PI */
p=hp0.x-y; /* p = PI/2 - y */
yy=hp1.x-yy;
y=p+yy;
yy=(p-y)+yy;
if (y>0) {__dubsin(y,yy,w); v[0]=w[0]; v[1]=w[1];}
/* cos(x) = sin ( 90 - x ) */
else {__dubsin(-y,-yy,w); v[0]=-w[0]; v[1]=-w[1];
}
}
else { /* y>= 3/4 * PI */
p=2.0*hp0.x-y; /* p = PI- y */
yy=2.0*hp1.x-yy;
y=p+yy;
yy=(p-y)+yy;
__dubcos(y,yy,w);
v[0]=-w[0];
v[1]=-w[1];
}
}
static double
SECTION
sloww (double x, double dx, double orig)
{
double y, t, res, cor, w[2], a, da, xn;
mynumber v;
int4 n;
res = TAYLOR_SLOW (x, dx, cor);
if (cor > 0)
cor = 1.0005 * cor + fabs (orig) * 3.1e-30;
else
cor = 1.0005 * cor - fabs (orig) * 3.1e-30;
if (res == res + cor)
return res;
else
{
(x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
if (w[1] > 0)
cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-30;
else
cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-30;
if (w[0] == w[0] + cor)
return (x > 0) ? w[0] : -w[0];
else
{
t = (orig * hpinv + toint);
xn = t - toint;
v.x = t;
y = (orig - xn * mp1) - xn * mp2;
n = v.i[LOW_HALF] & 3;
da = xn * pp3;
t = y - da;
da = (y - t) - da;
y = xn * pp4;
a = t - y;
da = ((t - a) - y) + da;
if (n & 2)
{
a = -a;
da = -da;
}
(a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
if (w[1] > 0)
cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-40;
else
cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-40;
if (w[0] == w[0] + cor)
return (a > 0) ? w[0] : -w[0];
else
return __mpsin (orig, 0, true);
}
}
}
static double
SECTION
sloww1 (double x, double dx, double orig, int m)
{
mynumber u;
double w[2], y, cor, res;
u.x = big + x;
y = x - (u.x - big);
res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
if (res == res + cor)
return (m > 0) ? res : -res;
else
{
__dubsin (x, dx, w);
if (w[1] > 0)
cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
else
cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
if (w[0] == w[0] + cor)
return (m > 0) ? w[0] : -w[0];
else
return __mpsin (orig, 0, true);
}
}
static double
SECTION
bsloww1 (double x, double dx, double orig, int n)
{
mynumber u;
double w[2], y, cor, res;
y = fabs (x);
u.x = big + y;
y = y - (u.x - big);
dx = (x > 0) ? dx : -dx;
res = do_sin_slow (u, y, dx, 1.1e-24, &cor);
if (res == res + cor)
return (x > 0) ? res : -res;
else
{
__dubsin (fabs (x), dx, w);
if (w[1] > 0)
cor = 1.000000005 * w[1] + 1.1e-24;
else
cor = 1.000000005 * w[1] - 1.1e-24;
if (w[0] == w[0] + cor)
return (x > 0) ? w[0] : -w[0];
else
return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
}
}
static double bsloww1(double x, double dx, double orig,int n) {
mynumber u;
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
static const double t22 = 6291456.0;
int4 k;
y=ABS(x);
u.x=big.x+y;
y=y-(u.x-big.x);
dx=(x>0)?dx:-dx;
xx=y*y;
s = y*xx*(sn3 +xx*sn5);
c = xx*(cs2 +xx*(cs4 + xx*cs6));
k=u.i[LOW_HALF]<<2;
sn=sincos.x[k];
ssn=sincos.x[k+1];
cs=sincos.x[k+2];
ccs=sincos.x[k+3];
y1 = (y+t22)-t22;
y2 = (y - y1)+dx;
c1 = (cs+t22)-t22;
c2=(cs-c1)+ccs;
cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
y=sn+c1*y1;
cor = cor+((sn-y)+c1*y1);
res=y+cor;
cor=(y-res)+cor;
cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
if (res == res + cor) return (x>0)?res:-res;
else {
__dubsin(ABS(x),dx,w);
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24;
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
else return (n&1)?__mpcos1(orig):__mpsin1(orig);
}
}
static double slow1(double x) {
mynumber u;
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
static const double t22 = 6291456.0;
int4 k;
y=ABS(x);
u.x=big.x+y;
y=y-(u.x-big.x);
xx=y*y;
s = y*xx*(sn3 +xx*sn5);
c = xx*(cs2 +xx*(cs4 + xx*cs6));
k=u.i[LOW_HALF]<<2;
sn=sincos.x[k]; /* Data */
ssn=sincos.x[k+1]; /* from */
cs=sincos.x[k+2]; /* tables */
ccs=sincos.x[k+3]; /* sincos.tbl */
y1 = (y+t22)-t22;
y2 = y - y1;
c1 = (cs+t22)-t22;
c2=(cs-c1)+ccs;
cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c;
y=sn+c1*y1;
cor = cor+((sn-y)+c1*y1);
res=y+cor;
cor=(y-res)+cor;
if (res == res+1.0005*cor) return (x>0)?res:-res;
else {
__dubsin(ABS(x),0,w);
if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
}
}
static double csloww(double x,double dx, double orig) {
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
union {int4 i[2]; double x;} v;
int4 n;
x1=(x+th2_36)-th2_36;
y = aa.x*x1*x1*x1;
r=x+y;
x2=(x-x1)+dx;
xx=x*x;
/* Taylor series */
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
t=((x-r)+y)+t;
res=r+t;
cor = (r-res)+t;
cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
if (res == res + cor) return res;
else {
(x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
else {
t = (orig*hpinv.x + toint.x);
xn = t - toint.x;
v.x = t;
y = (orig - xn*mp1.x) - xn*mp2.x;
n =v.i[LOW_HALF]&3;
da = xn*pp3.x;
t=y-da;
da = (y-t)-da;
y = xn*pp4.x;
a = t - y;
da = ((t-a)-y)+da;
if (n==1) {a=-a; da=-da;}
(a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
else return __mpcos1(orig);
}
}
}
static double
SECTION
bsloww (double x, double dx, double orig, int n)
{
double res, cor, w[2];
res = TAYLOR_SLOW (x, dx, cor);
cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
if (res == res + cor)
return res;
else
{
(x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
if (w[1] > 0)
cor = 1.000000001 * w[1] + 1.1e-24;
else
cor = 1.000000001 * w[1] - 1.1e-24;
if (w[0] == w[0] + cor)
return (x > 0) ? w[0] : -w[0];
else
return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
}
}
static double
SECTION
slow (double x)
{
double res, cor, w[2];
res = TAYLOR_SLOW (x, 0, cor);
if (res == res + 1.0007 * cor)
return res;
else
{
__dubsin (fabs (x), 0, w);
if (w[0] == w[0] + 1.000000001 * w[1])
return (x > 0) ? w[0] : -w[0];
else
return (x > 0) ? __mpsin (x, 0, false) : -__mpsin (-x, 0, false);
}
}
static double slow(double x) {
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
double y,x1,x2,xx,r,t,res,cor,w[2];
x1=(x+th2_36)-th2_36;
y = aa.x*x1*x1*x1;
r=x+y;
x2=x-x1;
xx=x*x;
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2;
t=((x-r)+y)+t;
res=r+t;
cor = (r-res)+t;
if (res == res + 1.0007*cor) return res;
else {
__dubsin(ABS(x),0,w);
if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0];
else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
}
}
static double
SECTION
slow1 (double x)
{
mynumber u;
double w[2], y, cor, res;
y = fabs (x);
u.x = big + y;
y = y - (u.x - big);
res = do_sin_slow (u, y, 0, 0, &cor);
if (res == res + cor)
return (x > 0) ? res : -res;
else
{
__dubsin (fabs (x), 0, w);
if (w[0] == w[0] + 1.000000005 * w[1])
return (x > 0) ? w[0] : -w[0];
else
return (x > 0) ? __mpsin (x, 0, false) : -__mpsin (-x, 0, false);
}
}
