/* Reduce range of X and compute sin of a + da. K is the amount by which to
rotate the quadrants. This allows us to use the same routine to compute cos
by simply rotating the quadrants by 1. */
static inline double
__always_inline
reduce_and_compute (double x, unsigned int k)
{
double retval = 0, a, da;
unsigned int n = __branred (x, &a, &da);
k = (n + k) % 4;
switch (k)
{
case 0:
if (a * a < 0.01588)
retval = bsloww (a, da, x, n);
else
retval = bsloww1 (a, da, x, n);
break;
case 2:
if (a * a < 0.01588)
retval = bsloww (-a, -da, x, n);
else
retval = bsloww1 (-a, -da, x, n);
break;
case 1:
case 3:
retval = bsloww2 (a, da, x, n);
break;
}
return retval;
}
/* Consolidated version of reduce_and_compute in s_sin.c that does range
reduction only once and computes sin and cos together. */
static inline void
__always_inline
reduce_and_compute_sincos (double x, double *sinx, double *cosx)
{
double a, da;
unsigned int n = __branred (x, &a, &da);
n = n & 3;
if (n == 1 || n == 2)
{
a = -a;
da = -da;
}
if (n & 1)
{
double *temp = cosx;
cosx = sinx;
sinx = temp;
}
if (a * a < 0.01588)
*sinx = bsloww (a, da, x, n);
else
*sinx = bsloww1 (a, da, x, n);
*cosx = bsloww2 (a, da, x, n);
}
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 */
}
double __cos(double x)
{
double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
mynumber u,v;
int4 k,m,n;
u.x = x;
m = u.i[HIGH_HALF];
k = 0x7fffffff&m;
if (k < 0x3e400000 ) return 1.0; /* |x|<2^-27 => cos(x)=1 */
else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */
y=ABS(x);
u.x = big.x+y;
y = 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)? res : cslow2(x);
} /* else if (k < 0x3feb6000) */
else if (k < 0x400368fd ) {/* 0.855469 <|x|<2.426265 */;
y=hp0.x-ABS(x);
a=y+hp1.x;
da=(y-a)+hp1.x;
xx=a*a;
if (xx < 0.01588) {
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+1.0e-31 : 1.02*cor -1.0e-31;
return (res == res + cor)? res : csloww(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+1.0e-31 : 1.035*cor-1.0e-31;
return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
}
} /* else if (k < 0x400368fd) */
else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */
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) {
case 1:
case 3:
xx = a*a;
if (n == 1) {a=-a;da=-da;}
if (xx < 0.01588) {
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 : csloww(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) : csloww1(a,da,x);
}
break;
case 0:
case 2:
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)?-res:res) : csloww2(a,da,x,n);
break;
}
} /* else if (k < 0x419921FB ) */
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 1:
case 3:
xx = a*a;
if (n==1) {a=-a;da=-da;}
if (xx < 0.01588) {
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 0:
case 2:
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)?-res:res) : bsloww2(a,da,x,n);
break;
}
} /* else if (k < 0x42F00000 ) */
else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */
n = __branred(x,&a,&da);
switch (n) {
case 1:
if (a*a < 0.01588) return bsloww(-a,-da,x,n);
else return bsloww1(-a,-da,x,n);
break;
case 3:
if (a*a < 0.01588) return bsloww(a,da,x,n);
else return bsloww1(a,da,x,n);
break;
case 0:
case 2:
return bsloww2(a,da,x,n);
break;
}
} /* else if (k < 0x7ff00000 ) */
else return x / x; /* |x| > 2^1024 */
return 0;
}