double cos(double x)
{
double y[2],z=0.0;
int32_t n, ix;
GET_HIGH_WORD(ix, x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) {
if (ix < 0x3e46a09e) /* if x < 2**-27 * sqrt(2) */
/* raise inexact if x != 0 */
if ((int)x == 0)
return 1.0;
return __cos(x, z);
}
/* cos(Inf or NaN) is NaN */
if (ix >= 0x7ff00000)
return x-x;
/* argument reduction needed */
n = __rem_pio2(x, y);
switch (n&3) {
case 0: return __cos(y[0], y[1]);
case 1: return -__sin(y[0], y[1], 1);
case 2: return -__cos(y[0], y[1]);
default:
return __sin(y[0], y[1], 1);
}
}
double sin(double x)
{
double y[2];
uint32_t ix;
unsigned n;
/* High word of x. */
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
if (ix <= 0x3fe921fb) {
if (ix < 0x3e500000) { /* |x| < 2**-26 */
/* raise inexact if x != 0 and underflow if subnormal*/
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __sin(x, 0.0, 0);
}
/* sin(Inf or NaN) is NaN */
if (ix >= 0x7ff00000)
return x - x;
/* argument reduction needed */
n = __rem_pio2(x, y);
switch (n&3) {
case 0: return __sin(y[0], y[1], 1);
case 1: return __cos(y[0], y[1]);
case 2: return -__sin(y[0], y[1], 1);
default:
return -__cos(y[0], y[1]);
}
}
/*
* complex(kind=8) raised to a real(kind=8) = _CTOR
*
* x = a+b*i
*
* if ((x == 0+0*i) && (y == 0)) then return(NAN)
* if (x == 0+0*i) then return(0+0*i)
* if (y == 0) then return(1+0*i)
*/
void
_CTOR(c_complex_t *ret_val,
c_complex_t x,
_f_real8 *r)
{
_f_real8 __atan2(_f_real8 x, _f_real8 y);
_f_real8 __cos(_f_real8 x);
_f_real8 __exp(_f_real8 x);
_f_real8 __log(_f_real8 x);
_f_real8 __sin(_f_real8 x);
_f_real8 _CABS(c_complex_t z);
_f_real8 y = *r;
_f_real8 one;
_f_real8 two;
if (x.real == (_f_real8) 0.0 && x.imag == (_f_real8) 0.0) {
if (y == (_f_real8) 0.0) {
ret_val->real = _SGL_NaN;
ret_val->imag = _SGL_NaN;
}
else {
ret_val->real = (_f_real8) 0.0;
ret_val->imag = (_f_real8) 0.0;
}
return;
}
one = y * __atan2(x.imag, x.real);
two = y * __log(_CABS(x));
ret_val->real = __exp(two) * __cos(one);
ret_val->imag = __exp(two) * __sin(one);
}
static double sinpi(double x)
{
int n;
/* argument reduction: x = |x| mod 2 */
/* spurious inexact when x is odd int */
x = x * 0.5;
x = 2 * (x - floor(x));
/* reduce x into [-.25,.25] */
n = 4 * x;
n = (n + 1) / 2;
x -= n * 0.5;
x *= pi;
switch (n) {
default: /* case 4 */
case 0:
return __sin(x, 0, 0);
case 1:
return __cos(x, 0);
case 2:
return __sin(-x, 0, 0);
case 3:
return -__cos(x, 0);
}
}
void sincos(double x, double *sin, double *cos)
{
double y[2], s, c;
uint32_t ix;
unsigned n;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
if (ix <= 0x3fe921fb) {
/* if |x| < 2**-27 * sqrt(2) */
if (ix < 0x3e46a09e) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
*sin = x;
*cos = 1.0;
return;
}
*sin = __sin(x, 0.0, 0);
*cos = __cos(x, 0.0);
return;
}
/* sincos(Inf or NaN) is NaN */
if (ix >= 0x7ff00000) {
*sin = *cos = x - x;
return;
}
/* argument reduction needed */
n = __rem_pio2(x, y);
s = __sin(y[0], y[1], 1);
c = __cos(y[0], y[1]);
switch (n&3) {
case 0:
*sin = s;
*cos = c;
break;
case 1:
*sin = c;
*cos = -s;
break;
case 2:
*sin = -s;
*cos = -c;
break;
case 3:
default:
*sin = -c;
*cos = s;
break;
}
}
/*
* CSIN - complex(kind=8) - pass by value
*
* Semantics: sin(z) = sin(a)*cosh(b) + cos(a)*sinh(b)*i
* (where z = a + b*i)
*/
void
_CSIN(c_complex_t *ret_val,
c_complex_t z)
{
_f_real8 __cos(_f_real8 x);
_f_real8 __cosh(_f_real8 x);
_f_real8 __sin(_f_real8 x);
_f_real8 __sinh(_f_real8 x);
ret_val->real = __sin(z.real) * __cosh(z.imag);
ret_val->imag = __cos(z.real) * __sinh(z.imag);
}
void
_CHCOS( h_complex_t *ret_val,
h_complex_t z )
{
_f_real8 __cos(_f_real8 x);
_f_real8 __cosh(_f_real8 x);
_f_real8 __sin(_f_real8 x);
_f_real8 __sinh(_f_real8 x);
_f_real8 real = (_f_real8) z.real;
_f_real8 imag = (_f_real8) z.imag;
ret_val->real = (_f_real4) (__cos(real) * __cosh(imag));
ret_val->imag = (_f_real4) (- (__sin(real) * __sinh(imag)));
}
void
_CHEXP(h_complex_t *ret_val,
h_complex_t z )
{
_f_real8 __exp(_f_real8 x);
_f_real8 __cos(_f_real8 x);
_f_real8 __sin(_f_real8 x);
_f_real8 real = (_f_real8) z.real;
_f_real8 imag = (_f_real8) z.imag;
_f_real8 realtmp = __exp(real);
ret_val->real = (_f_real4) (realtmp * __cos(imag));
ret_val->imag = (_f_real4) (realtmp * __sin(imag));
}
static ALvoid EchoUpdate(ALeffectState *effect, ALCcontext *Context, const ALeffect *Effect)
{
ALechoState *state = (ALechoState*)effect;
ALuint frequency = Context->Device->Frequency;
ALfp lrpan, cw, a, g;
state->Tap[0].delay = (ALuint)ALfp2int((ALfpMult(Effect->Echo.Delay, int2ALfp(frequency)) + int2ALfp(1)));
state->Tap[1].delay = (ALuint)ALfp2int(ALfpMult(Effect->Echo.LRDelay, int2ALfp(frequency)));
state->Tap[1].delay += state->Tap[0].delay;
lrpan = (ALfpMult(Effect->Echo.Spread, float2ALfp(0.5f)) + float2ALfp(0.5f));
state->GainL = aluSqrt( lrpan);
state->GainR = aluSqrt((int2ALfp(1)-lrpan));
state->FeedGain = Effect->Echo.Feedback;
cw = __cos(ALfpDiv(float2ALfp(2.0*M_PI * LOWPASSFREQCUTOFF), int2ALfp(frequency)));
g = (int2ALfp(1) - Effect->Echo.Damping);
a = int2ALfp(0);
if(g < float2ALfp(0.9999f)) { /* 1-epsilon */
// a = (1 - g*cw - aluSqrt(2*g*(1-cw) - g*g*(1 - cw*cw))) / (1 - g);
a = ALfpDiv((int2ALfp(1) - ALfpMult(g,cw) - aluSqrt((ALfpMult(ALfpMult(int2ALfp(2),g),(int2ALfp(1)-cw)) -
ALfpMult(ALfpMult(g,g),(int2ALfp(1) - ALfpMult(cw,cw)))))),
(int2ALfp(1) - g));
}
state->iirFilter.coeff = a;
}
static double sin_pi(double x)
{
double y,z;
int n,ix;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
if (ix < 0x3fd00000)
return __sin(pi*x, 0.0, 0);
y = -x; /* negative x is assumed */
/*
* argument reduction, make sure inexact flag not raised if input
* is an integer
*/
z = floor(y);
if (z != y) { /* inexact anyway */
y *= 0.5;
y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */
n = (int)(y*4.0);
} else {
if (ix >= 0x43400000) {
y = 0.0; /* y must be even */
n = 0;
} else {
if (ix < 0x43300000)
z = y + two52; /* exact */
GET_LOW_WORD(n, z);
n &= 1;
y = n;
n <<= 2;
}
}
switch (n) {
case 0: y = __sin(pi*y, 0.0, 0); break;
case 1:
case 2: y = __cos(pi*(0.5-y), 0.0); break;
case 3:
case 4: y = __sin(pi*(1.0-y), 0.0, 0); break;
case 5:
case 6: y = -__cos(pi*(y-1.5), 0.0); break;
default: y = __sin(pi*(y-2.0), 0.0, 0); break;
}
return -y;
}
void
__sincos (double x, double *sinx, double *cosx)
{
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
*sinx = __sin (x);
*cosx = __cos (x);
}
double
__ieee754_y1(double x)
{
double z, s,c,ss,cc,u,v,u1,u2,v1,v2,v3,z2,z4;
int32_t hx,ix,lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(__builtin_expect(ix>=0x7ff00000, 0)) return one/(x+x*x);
if(__builtin_expect((ix|lx)==0, 0))
return -HUGE_VAL+x; /* -inf and overflow exception. */;
if(__builtin_expect(hx<0, 0)) return zero/(zero*x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincos (x, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = __cos(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
}
return z;
}
if(__builtin_expect(ix<=0x3c900000, 0)) { /* x < 2**-54 */
return(-tpi/x);
}
z = x*x;
#ifdef DO_NOT_USE_THIS
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
#else
u1 = U0[0]+z*U0[1];z2=z*z;
u2 = U0[2]+z*U0[3];z4=z2*z2;
u = u1 + z2*u2 + z4*U0[4];
v1 = one+z*V0[0];
v2 = V0[1]+z*V0[2];
v3 = V0[3]+z*V0[4];
v = v1 + z2*v2 + z4*v3;
#endif
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}
double
__ieee754_j0(double x)
{
double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4;
int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/(x*x);
x = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincos (x, &s, &c);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -__cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x);
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
math_force_eval(huge+x); /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return one - 0.25*x*x;
}
z = x*x;
#ifdef DO_NOT_USE_THIS
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
#else
r1 = z*R[2]; z2=z*z;
r2 = R[3]+z*R[4]; z4=z2*z2;
r = r1 + z2*r2 + z4*R[5];
s1 = one+z*S[1];
s2 = S[2]+z*S[3];
s = s1 + z2*s2 + z4*S[4];
#endif
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return one + z*(-0.25+(r/s));
} else {
u = 0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
double
__ieee754_j1(double x)
{
double z, s,c,ss,cc,r,u,v,y,r1,r2,s1,s2,s3,z2,z4;
int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(__builtin_expect(ix>=0x7ff00000, 0)) return one/x;
y = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincos (y, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure y+y not overflow */
z = __cos(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
else {
u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
}
if(hx<0) return -z;
else return z;
}
if(__builtin_expect(ix<0x3e400000, 0)) { /* |x|<2**-27 */
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
#ifdef DO_NOT_USE_THIS
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
#else
r1 = z*R[0]; z2=z*z;
r2 = R[1]+z*R[2]; z4=z2*z2;
r = r1 + z2*r2 + z4*R[3];
r *= x;
s1 = one+z*S[1];
s2 = S[2]+z*S[3];
s3 = S[4]+z*S[5];
s = s1 + z2*s2 + z4*s3;
#endif
return(x*0.5+r/s);
}
void
__sincos (double x, double *sinx, double *cosx)
{
int32_t ix;
/* High word of x. */
GET_HIGH_WORD (ix, x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix >= 0x7ff00000)
{
/* sin(Inf or NaN) is NaN */
*sinx = *cosx = x - x;
}
else
{
*sinx = __sin (x);
*cosx = __cos (x);
}
}
double
__ieee754_gamma_r (double x, int *signgamp)
{
int32_t hx;
u_int32_t lx;
EXTRACT_WORDS (hx, lx, x);
if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__builtin_expect (hx < 0, 0)
&& (u_int32_t) hx < 0xfff00000 && __rint (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (x >= 172.0)
{
/* Overflow. */
*signgamp = 0;
return DBL_MAX * DBL_MAX;
}
else if (x > 0.0)
{
*signgamp = 0;
int exp2_adj;
double ret = gamma_positive (x, &exp2_adj);
return __scalbn (ret, exp2_adj);
}
else if (x >= -DBL_EPSILON / 4.0)
{
*signgamp = 0;
return 1.0 / x;
}
else
{
double tx = __trunc (x);
*signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1;
if (x <= -184.0)
/* Underflow. */
return DBL_MIN * DBL_MIN;
double frac = tx - x;
if (frac > 0.5)
frac = 1.0 - frac;
double sinpix = (frac <= 0.25
? __sin (M_PI * frac)
: __cos (M_PI * (0.5 - frac)));
int exp2_adj;
double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj));
return __scalbn (ret, -exp2_adj);
}
}
double
__ieee754_y0(double x)
{
double z, s,c,ss,cc,u,v,z2,z4,z6,u1,u2,u3,v1,v2;
int32_t hx,ix,lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */
if(hx<0) return zero/(zero*x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
__sincos (x, &s, &c);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -__cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return(U[0] + tpi*__ieee754_log(x));
}
z = x*x;
#ifdef DO_NOT_USE_THIS
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
#else
u1 = U[0]+z*U[1]; z2=z*z;
u2 = U[2]+z*U[3]; z4=z2*z2;
u3 = U[4]+z*U[5]; z6=z4*z2;
u = u1 + z2*u2 + z4*u3 + z6*U[6];
v1 = one+z*V[0];
v2 = V[1]+z*V[2];
v = v1 + z2*v2 + z4*V[3];
#endif
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
}
double
__ieee754_y1 (double x)
{
double z, s, c, ss, cc, u, v, u1, u2, v1, v2, v3, z2, z4;
int32_t hx, ix, lx;
EXTRACT_WORDS (hx, lx, x);
ix = 0x7fffffff & hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if (__glibc_unlikely (ix >= 0x7ff00000))
return one / (x + x * x);
if (__glibc_unlikely ((ix | lx) == 0))
return -1 / zero; /* -inf and divide by zero exception. */
/* -inf and overflow exception. */;
if (__glibc_unlikely (hx < 0))
return zero / (zero * x);
if (ix >= 0x40000000) /* |x| >= 2.0 */
{
__sincos (x, &s, &c);
ss = -s - c;
cc = s - c;
if (ix < 0x7fe00000) /* make sure x+x not overflow */
{
z = __cos (x + x);
if ((s * c) > zero)
cc = z / ss;
else
ss = z / cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if (ix > 0x48000000)
z = (invsqrtpi * ss) / sqrt (x);
else
{
u = pone (x); v = qone (x);
z = invsqrtpi * (u * ss + v * cc) / sqrt (x);
}
return z;
}
if (__glibc_unlikely (ix <= 0x3c900000)) /* x < 2**-54 */
{
z = -tpi / x;
if (isinf (z))
__set_errno (ERANGE);
return z;
}
z = x * x;
u1 = U0[0] + z * U0[1]; z2 = z * z;
u2 = U0[2] + z * U0[3]; z4 = z2 * z2;
u = u1 + z2 * u2 + z4 * U0[4];
v1 = one + z * V0[0];
v2 = V0[1] + z * V0[2];
v3 = V0[3] + z * V0[4];
v = v1 + z2 * v2 + z4 * v3;
return (x * (u / v) + tpi * (__ieee754_j1 (x) * __ieee754_log (x) - one / x));
}
double
__ieee754_j1 (double x)
{
double z, s, c, ss, cc, r, u, v, y, r1, r2, s1, s2, s3, z2, z4;
int32_t hx, ix;
GET_HIGH_WORD (hx, x);
ix = hx & 0x7fffffff;
if (__glibc_unlikely (ix >= 0x7ff00000))
return one / x;
y = fabs (x);
if (ix >= 0x40000000) /* |x| >= 2.0 */
{
__sincos (y, &s, &c);
ss = -s - c;
cc = s - c;
if (ix < 0x7fe00000) /* make sure y+y not overflow */
{
z = __cos (y + y);
if ((s * c) > zero)
cc = z / ss;
else
ss = z / cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if (ix > 0x48000000)
z = (invsqrtpi * cc) / sqrt (y);
else
{
u = pone (y); v = qone (y);
z = invsqrtpi * (u * cc - v * ss) / sqrt (y);
}
if (hx < 0)
return -z;
else
return z;
}
if (__glibc_unlikely (ix < 0x3e400000)) /* |x|<2**-27 */
{
if (huge + x > one) /* inexact if x!=0 necessary */
{
double ret = math_narrow_eval (0.5 * x);
math_check_force_underflow (ret);
if (ret == 0 && x != 0)
__set_errno (ERANGE);
return ret;
}
}
z = x * x;
r1 = z * R[0]; z2 = z * z;
r2 = R[1] + z * R[2]; z4 = z2 * z2;
r = r1 + z2 * r2 + z4 * R[3];
r *= x;
s1 = one + z * S[1];
s2 = S[2] + z * S[3];
s3 = S[4] + z * S[5];
s = s1 + z2 * s2 + z4 * s3;
return (x * 0.5 + r / s);
}
Err mathlib_cos(UInt16 refnum, double x, double *result) {
#pragma unused(refnum)
*result = __cos(x);
return mlErrNone;
}
