double
SECTION
__sin (double x)
{
double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
xn2;
mynumber u, v;
int4 k, m, n;
double retval = 0;
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
u.x = x;
m = u.i[HIGH_HALF];
k = 0x7fffffff & m; /* no sign */
if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
{
math_check_force_underflow (x);
retval = x;
}
/*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
else if (k < 0x3fd00000)
{
xx = x * x;
/* Taylor series. */
t = POLYNOMIAL (xx) * (xx * x);
res = x + t;
cor = (x - res) + t;
retval = (res == res + 1.07 * cor) ? res : slow (x);
} /* else if (k < 0x3fd00000) */
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
else if (k < 0x3feb6000)
{
u.x = (m > 0) ? big + x : big - x;
y = (m > 0) ? x - (u.x - big) : x + (u.x - big);
xx = y * y;
s = y + y * xx * (sn3 + xx * sn5);
c = xx * (cs2 + xx * (cs4 + xx * cs6));
SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
if (m <= 0)
{
sn = -sn;
ssn = -ssn;
}
cor = (ssn + s * ccs - sn * c) + cs * s;
res = sn + cor;
cor = (sn - res) + cor;
retval = (res == res + 1.096 * cor) ? res : slow1 (x);
} /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
else if (k < 0x400368fd)
{
y = (m > 0) ? hp0 - x : hp0 + x;
if (y >= 0)
{
u.x = big + y;
y = (y - (u.x - big)) + hp1;
}
else
{
u.x = big - y;
y = (-hp1) - (y + (u.x - big));
}
res = do_cos (u, y, &cor);
retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
} /* else if (k < 0x400368fd) */
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
else if (k < 0x419921FB)
{
t = (x * hpinv + toint);
xn = t - toint;
v.x = t;
y = (x - xn * mp1) - xn * mp2;
n = v.i[LOW_HALF] & 3;
da = xn * mp3;
a = y - da;
da = (y - a) - da;
eps = fabs (x) * 1.2e-30;
switch (n)
{ /* quarter of unit circle */
case 0:
case 2:
xx = a * a;
if (n)
{
a = -a;
da = -da;
}
if (xx < 0.01588)
{
/* Taylor series. */
res = TAYLOR_SIN (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
retval = (res == res + cor) ? res : sloww (a, da, x);
}
else
{
if (a > 0)
m = 1;
else
{
m = 0;
a = -a;
da = -da;
}
u.x = big + a;
y = a - (u.x - big);
res = do_sin (u, y, da, &cor);
cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
retval = ((res == res + cor) ? ((m) ? res : -res)
: sloww1 (a, da, x, m));
}
break;
case 1:
case 3:
if (a < 0)
{
a = -a;
da = -da;
}
u.x = big + a;
y = a - (u.x - big) + da;
res = do_cos (u, y, &cor);
cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
retval = ((res == res + cor) ? ((n & 2) ? -res : res)
: sloww2 (a, da, x, n));
break;
}
} /* else if (k < 0x419921FB ) */
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
else if (k < 0x42F00000)
{
t = (x * hpinv + toint);
xn = t - toint;
v.x = t;
xn1 = (xn + 8.0e22) - 8.0e22;
xn2 = xn - xn1;
y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
n = v.i[LOW_HALF] & 3;
da = xn1 * pp3;
t = y - da;
da = (y - t) - da;
da = (da - xn2 * pp3) - xn * pp4;
a = t + da;
da = (t - a) + da;
eps = 1.0e-24;
switch (n)
{
case 0:
case 2:
xx = a * a;
if (n)
{
a = -a;
da = -da;
}
if (xx < 0.01588)
{
/* Taylor series. */
res = TAYLOR_SIN (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
retval = (res == res + cor) ? res : bsloww (a, da, x, n);
}
else
{
double t;
if (a > 0)
{
m = 1;
t = a;
db = da;
}
else
{
m = 0;
t = -a;
db = -da;
}
u.x = big + t;
y = t - (u.x - big);
res = do_sin (u, y, db, &cor);
cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
retval = ((res == res + cor) ? ((m) ? res : -res)
: bsloww1 (a, da, x, n));
}
break;
case 1:
case 3:
if (a < 0)
{
a = -a;
da = -da;
}
u.x = big + a;
y = a - (u.x - big) + da;
res = do_cos (u, y, &cor);
cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
retval = ((res == res + cor) ? ((n & 2) ? -res : res)
: bsloww2 (a, da, x, n));
break;
}
} /* else if (k < 0x42F00000 ) */
/* -----------------281474976710656 <|x| <2^1024----------------------------*/
else if (k < 0x7ff00000)
retval = reduce_and_compute (x, 0);
/*--------------------- |x| > 2^1024 ----------------------------------*/
else
{
if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
__set_errno (EDOM);
retval = x / x;
}
return retval;
}
double __sin(double x){
double xx,res,t,cor,y,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
#if 0
double w[2];
#endif
mynumber u,v;
int4 k,m,n;
#if 0
int4 nn;
#endif
u.x = x;
m = u.i[HIGH_HALF];
k = 0x7fffffff&m; /* no sign */
if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
return x;
/*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
else if (k < 0x3fd00000){
xx = x*x;
/*Taylor series */
t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x);
res = x+t;
cor = (x-res)+t;
return (res == res + 1.07*cor)? res : slow(x);
} /* else if (k < 0x3fd00000) */
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
else if (k < 0x3feb6000) {
u.x=(m>0)?big.x+x:big.x-x;
y=(m>0)?x-(u.x-big.x):x+(u.x-big.x);
xx=y*y;
s = y + y*xx*(sn3 +xx*sn5);
c = xx*(cs2 +xx*(cs4 + xx*cs6));
k=u.i[LOW_HALF]<<2;
sn=(m>0)?sincos.x[k]:-sincos.x[k];
ssn=(m>0)?sincos.x[k+1]:-sincos.x[k+1];
cs=sincos.x[k+2];
ccs=sincos.x[k+3];
cor=(ssn+s*ccs-sn*c)+cs*s;
res=sn+cor;
cor=(sn-res)+cor;
return (res==res+1.025*cor)? res : slow1(x);
} /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
else if (k < 0x400368fd ) {
y = (m>0)? hp0.x-x:hp0.x+x;
if (y>=0) {
u.x = big.x+y;
y = (y-(u.x-big.x))+hp1.x;
}
else {
u.x = big.x-y;
y = (-hp1.x) - (y+(u.x-big.x));
}
xx=y*y;
s = y + 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];
cor=(ccs-s*ssn-cs*c)-sn*s;
res=cs+cor;
cor=(cs-res)+cor;
return (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x);
} /* else if (k < 0x400368fd) */
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
else if (k < 0x419921FB ) {
t = (x*hpinv.x + toint.x);
xn = t - toint.x;
v.x = t;
y = (x - xn*mp1.x) - xn*mp2.x;
n =v.i[LOW_HALF]&3;
da = xn*mp3.x;
a=y-da;
da = (y-a)-da;
eps = ABS(x)*1.2e-30;
switch (n) { /* quarter of unit circle */
case 0:
case 2:
xx = a*a;
if (n) {a=-a;da=-da;}
if (xx < 0.01588) {
/*Taylor series */
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
res = a+t;
cor = (a-res)+t;
cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
return (res == res + cor)? res : sloww(a,da,x);
}
else {
if (a>0)
{m=1;t=a;db=da;}
else
{m=0;t=-a;db=-da;}
u.x=big.x+t;
y=t-(u.x-big.x);
xx=y*y;
s = y + (db+y*xx*(sn3 +xx*sn5));
c = y*db+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];
cor=(ssn+s*ccs-sn*c)+cs*s;
res=sn+cor;
cor=(sn-res)+cor;
cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
return (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x);
}
break;
case 1:
case 3:
if (a<0)
{a=-a;da=-da;}
u.x=big.x+a;
y=a-(u.x-big.x)+da;
xx=y*y;
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];
s = y + y*xx*(sn3 +xx*sn5);
c = xx*(cs2 +xx*(cs4 + xx*cs6));
cor=(ccs-s*ssn-cs*c)-sn*s;
res=cs+cor;
cor=(cs-res)+cor;
cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
return (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n);
break;
}
} /* else if (k < 0x419921FB ) */
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
else if (k < 0x42F00000 ) {
t = (x*hpinv.x + toint.x);
xn = t - toint.x;
v.x = t;
xn1 = (xn+8.0e22)-8.0e22;
xn2 = xn - xn1;
y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
n =v.i[LOW_HALF]&3;
da = xn1*pp3.x;
t=y-da;
da = (y-t)-da;
da = (da - xn2*pp3.x) -xn*pp4.x;
a = t+da;
da = (t-a)+da;
eps = 1.0e-24;
switch (n) {
case 0:
case 2:
xx = a*a;
if (n) {a=-a;da=-da;}
if (xx < 0.01588) {
/* Taylor series */
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
res = a+t;
cor = (a-res)+t;
cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
return (res == res + cor)? res : bsloww(a,da,x,n);
}
else {
if (a>0) {m=1;t=a;db=da;}
else {m=0;t=-a;db=-da;}
u.x=big.x+t;
y=t-(u.x-big.x);
xx=y*y;
s = y + (db+y*xx*(sn3 +xx*sn5));
c = y*db+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];
cor=(ssn+s*ccs-sn*c)+cs*s;
res=sn+cor;
cor=(sn-res)+cor;
cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
}
break;
case 1:
case 3:
if (a<0)
{a=-a;da=-da;}
u.x=big.x+a;
y=a-(u.x-big.x)+da;
xx=y*y;
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];
s = y + y*xx*(sn3 +xx*sn5);
c = xx*(cs2 +xx*(cs4 + xx*cs6));
cor=(ccs-s*ssn-cs*c)-sn*s;
res=cs+cor;
cor=(cs-res)+cor;
cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
return (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n);
break;
}
} /* else if (k < 0x42F00000 ) */
/* -----------------281474976710656 <|x| <2^1024----------------------------*/
else if (k < 0x7ff00000) {
n = __branred(x,&a,&da);
switch (n) {
case 0:
if (a*a < 0.01588) return bsloww(a,da,x,n);
else return bsloww1(a,da,x,n);
break;
case 2:
if (a*a < 0.01588) return bsloww(-a,-da,x,n);
else return bsloww1(-a,-da,x,n);
break;
case 1:
case 3:
return bsloww2(a,da,x,n);
break;
}
} /* else if (k < 0x7ff00000 ) */
/*--------------------- |x| > 2^1024 ----------------------------------*/
else return x / x;
return 0; /* unreachable */
}
