float
__asinhf(float x)
{
float w;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(__builtin_expect(ix< 0x38000000, 0)) { /* |x|<2**-14 */
math_check_force_underflow (x);
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(__builtin_expect(ix>0x47000000, 0)) { /* |x| > 2**14 */
if(ix>=0x7f800000) return x+x; /* x is inf or NaN */
w = __ieee754_logf(fabsf(x))+ln2;
} else {
float xa = fabsf(x);
if (ix>0x40000000) { /* 2**14 > |x| > 2.0 */
w = __ieee754_logf(2.0f*xa+one/(__ieee754_sqrtf(xa*xa+one)+xa));
} else { /* 2.0 > |x| > 2**-14 */
float t = xa*xa;
w =__log1pf(xa+t/(one+__ieee754_sqrtf(one+t)));
}
}
return __copysignf(w, x);
}
float
__ieee754_y1f(float x)
{
float z, s,c,ss,cc,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(__builtin_expect(ix>=0x7f800000, 0)) return one/(x+x*x);
if(__builtin_expect(ix==0, 0))
return -HUGE_VALF+x; /* -inf and overflow exception. */
if(__builtin_expect(hx<0, 0)) return zero/(zero*x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
SET_RESTORE_ROUNDF (FE_TONEAREST);
__sincosf (x, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) { /* make sure x+x not overflow */
z = __cosf(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_sqrtf(x);
else {
u = ponef(x); v = qonef(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
}
return z;
}
if(__builtin_expect(ix<=0x33000000, 0)) { /* x < 2**-25 */
z = -tpi / x;
if (__isinff (z))
__set_errno (ERANGE);
return z;
}
z = x*x;
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]))));
return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
}
float
__ieee754_y0f(float x)
{
float z, s,c,ss,cc,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */
if(ix>=0x7f800000) return one/(x+x*x);
if(ix==0) return -HUGE_VALF+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.
*/
__sincosf (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<0x7f000000) { /* make sure x+x not overflow */
z = -__cosf(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<=0x32000000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_logf(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
}
float
sqrtf(float x) /* wrapper sqrtf */
{
#ifdef _IEEE_LIBM
return __ieee754_sqrtf(x);
#else
float z;
z = __ieee754_sqrtf(x);
if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z;
if(x<(float)0.0) {
/* sqrtf(negative) */
return (float)__kernel_standard((double)x,(double)x,126);
} else
return z;
#endif
}
/* wrapper sqrtf */
float
__sqrtf (float x)
{
if (__builtin_expect (isless (x, 0.0f), 0) && _LIB_VERSION != _IEEE_)
return __kernel_standard_f (x, x, 126); /* sqrt(negative) */
return __ieee754_sqrtf (x);
}
float
__ieee754_j0f(float x)
{
float z, s,c,ss,cc,r,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return one/(x*x);
x = fabsf(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincosf (x, &s, &c);
ss = s-c;
cc = s+c;
if(ix<0x7f000000) { /* make sure x+x not overflow */
z = -__cosf(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_sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<0x39000000) { /* |x| < 2**-13 */
math_force_eval(huge+x); /* raise inexact if x != 0 */
if(ix<0x32000000) return one; /* |x|<2**-27 */
else return one - (float)0.25*x*x;
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3F800000) { /* |x| < 1.00 */
return one + z*((float)-0.25+(r/s));
} else {
u = (float)0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
//------------------------------------------------------------------------------
float Cmath::__ieee754_acoshf( float x )
{
static const float one = 1.0;
static const float ln2 = 6.9314718246e-01; // 0x3f317218
float t;
Cmp_signed__int32 hx;
get_float_word( hx, x );
if( hx < 0x3f800000 )
{
// x < 1
return ( x - x ) / ( x - x );
}
else if( hx >= 0x4d800000 )
{
// x > 2**28
if( !uword_isfinite( hx ) )
{
// x is inf of NaN
return x + x;
}
else
{
return __ieee754_logf( x ) + ln2; // acosh(huge)=log(2x)
}
}
else if ( hx == 0x3f800000 )
{
return 0.0; // acosh(1) = 0
}
else if ( hx > 0x40000000 )
{
// 2**28 > x > 2
t = x * x;
return __ieee754_logf( (float)2.0 * x - one / ( x + __ieee754_sqrtf( t - one ) ) );
}
else
{
// 1<x<2
t = x - one;
return log1pf( t + __ieee754_sqrtf( (float)2.0 * t + t * t ) );
}
}
float
__ieee754_acosf(float x)
{
float z,p,q,r,w,s,c,df;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
} else if(ix>0x3f800000) { /* |x| >= 1 */
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3f000000) { /* |x| < 0.5 */
if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
z = x*x;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*(float)0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
s = __ieee754_sqrtf(z);
r = p/q;
w = r*s-pio2_lo;
return pi - (float)2.0*(s+w);
} else { /* x > 0.5 */
int32_t idf;
z = (one-x)*(float)0.5;
s = __ieee754_sqrtf(z);
df = s;
GET_FLOAT_WORD(idf,df);
SET_FLOAT_WORD(df,idf&0xfffff000);
c = (z-df*df)/(s+df);
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
w = r*s+c;
return (float)2.0*(df+w);
}
}
float
__ieee754_j1f(float x)
{
float z, s,c,ss,cc,r,u,v,y;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(__builtin_expect(ix>=0x7f800000, 0)) return one/x;
y = fabsf(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincosf (y, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) { /* make sure y+y not overflow */
z = __cosf(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_sqrtf(y);
else {
u = ponef(y); v = qonef(y);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
}
if(hx<0) return -z;
else return z;
}
if(__builtin_expect(ix<0x32000000, 0)) { /* |x|<2**-27 */
if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*(float)0.5+r/s);
}
float
asinhf(float x)
{
float t,w;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return x+x; /* x is inf or NaN */
if(ix< 0x31800000) { /* |x|<2**-28 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x4d800000) { /* |x| > 2**28 */
w = __ieee754_logf(fabsf(x))+ln2;
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
t = fabsf(x);
w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t)));
}
if(hx>0) return w; else return -w;
}
float
__ieee754_acoshf(float x)
{
float t;
int32_t hx;
GET_FLOAT_WORD(hx,x);
if(hx<0x3f800000) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x4d800000) { /* x > 2**28 */
if(hx >=0x7f800000) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */
} else if (hx==0x3f800000) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one)));
} else { /* 1<x<2 */
t = x-one;
return log1pf(t+__ieee754_sqrtf((float)2.0*t+t*t));
}
}
float
__ieee754_asinf(float x)
{
float t,w,p,q,c,r,s;
int32_t hx,ix;
t = 0;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) {
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
} else if(ix> 0x3f800000) { /* |x|>= 1 */
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3f000000) { /* |x|<0.5 */
if(ix<0x32000000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fabsf(x);
t = w*(float)0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = __ieee754_sqrtf(t);
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
} else {
int32_t iw;
w = s;
GET_FLOAT_WORD(iw,w);
SET_FLOAT_WORD(w,iw&0xfffff000);
c = (t-w*w)/(s+w);
r = p/q;
p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
q = pio4_hi-(float)2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}
float __ieee754_asinf(float x)
{
float t,w,p,q,c,r,s;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) {
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
} else if(ix> 0x3f800000) { /* |x|>= 1 */
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3f000000) { /* |x|<0.5 */
if(ix<0x32000000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else {
t = x*x;
w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
return x+x*w;
}
}
/* 1> |x|>= 0.5 */
w = one-fabsf(x);
t = w*0.5f;
p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
s = __ieee754_sqrtf(t);
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
t = pio2_hi-(2.0f*(s+s*p)-pio2_lo);
} else {
int32_t iw;
w = s;
GET_FLOAT_WORD(iw,w);
SET_FLOAT_WORD(w,iw&0xfffff000);
c = (t-w*w)/(s+w);
r = p;
p = 2.0f*s*r-(pio2_lo-2.0f*c);
q = pio4_hi-2.0f*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}
__complex__ float
__csqrtf (__complex__ float x)
{
__complex__ float res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALF;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nanf ("") : 0;
__imag__ res = __copysignf (HUGE_VALF, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nanf ("") : __copysignf (0.0, __imag__ x));
}
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
}
}
else
{
if (__builtin_expect (icls == FP_ZERO, 0))
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysignf (__ieee754_sqrtf (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabsf (__ieee754_sqrtf (__real__ x));
__imag__ res = __copysignf (0.0, __imag__ x);
}
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
float r;
if (fabsf (__imag__ x) >= 2.0f * FLT_MIN)
r = __ieee754_sqrtf (0.5f * fabsf (__imag__ x));
else
r = 0.5f * __ieee754_sqrtf (2.0f * fabsf (__imag__ x));
__real__ res = r;
__imag__ res = __copysignf (r, __imag__ x);
}
else
{
float d, r, s;
int scale = 0;
if (fabsf (__real__ x) > FLT_MAX / 4.0f)
{
scale = 1;
__real__ x = __scalbnf (__real__ x, -2 * scale);
__imag__ x = __scalbnf (__imag__ x, -2 * scale);
}
else if (fabsf (__imag__ x) > FLT_MAX / 4.0f)
{
scale = 1;
if (fabsf (__real__ x) >= 4.0f * FLT_MIN)
__real__ x = __scalbnf (__real__ x, -2 * scale);
else
__real__ x = 0.0f;
__imag__ x = __scalbnf (__imag__ x, -2 * scale);
}
else if (fabsf (__real__ x) < FLT_MIN
&& fabsf (__imag__ x) < FLT_MIN)
{
scale = -(FLT_MANT_DIG / 2);
__real__ x = __scalbnf (__real__ x, -2 * scale);
__imag__ x = __scalbnf (__imag__ x, -2 * scale);
}
d = __ieee754_hypotf (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = __ieee754_sqrtf (0.5f * (d + __real__ x));
s = 0.5f * (__imag__ x / r);
}
else
{
s = __ieee754_sqrtf (0.5f * (d - __real__ x));
r = fabsf (0.5f * (__imag__ x / s));
}
if (scale)
{
r = __scalbnf (r, scale);
s = __scalbnf (s, scale);
}
__real__ res = r;
__imag__ res = __copysignf (s, __imag__ x);
}
}
return res;
}
__complex__ float
__cacoshf (__complex__ float x)
{
__complex__ float res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALF;
if (rcls == FP_NAN)
__imag__ res = __nanf ("");
else
__imag__ res = __copysignf ((rcls == FP_INFINITE
? (__real__ x < 0.0
? M_PI - M_PI_4 : M_PI_4)
: M_PI_2), __imag__ x);
}
else if (rcls == FP_INFINITE)
{
__real__ res = HUGE_VALF;
if (icls >= FP_ZERO)
__imag__ res = __copysignf (signbit (__real__ x) ? M_PI : 0.0,
__imag__ x);
else
__imag__ res = __nanf ("");
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
}
}
else if (rcls == FP_ZERO && icls == FP_ZERO)
{
__real__ res = 0.0;
__imag__ res = __copysignf (M_PI_2, __imag__ x);
}
else
{
#if 1
__complex__ float y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = __csqrtf (y);
if (__real__ x < 0.0)
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = __clogf (y);
#else
float re2 = __real__ x * __real__ x;
float im2 = __imag__ x * __imag__ x;
float sq = re2 - im2 - 1.0;
float ro = __ieee754_sqrtf (sq * sq + 4 * re2 * im2);
float a = __ieee754_sqrtf ((sq + ro) / 2.0);
float b = __ieee754_sqrtf ((-sq + ro) / 2.0);
__real__ res = 0.5 * __ieee754_logf (re2 + __real__ x * 2 * a
+ im2 + __imag__ x * 2 * b
+ ro);
__imag__ res = __ieee754_atan2f (__imag__ x + b, __real__ x + a);
#endif
/* We have to use the positive branch. */
if (__real__ res < 0.0)
res = -res;
}
return res;
}
__complex__ float
__csqrtf (__complex__ float x)
{
__complex__ float res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALF;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nanf ("") : 0;
__imag__ res = __copysignf (HUGE_VALF, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nanf ("") : __copysignf (0.0, __imag__ x));
}
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
}
}
else
{
if (icls == FP_ZERO)
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysignf (__ieee754_sqrtf (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabsf (__ieee754_sqrtf (__real__ x));
__imag__ res = __copysignf (0.0, __imag__ x);
}
}
else if (rcls == FP_ZERO)
{
float r = __ieee754_sqrtf (0.5 * fabsf (__imag__ x));
__real__ res = __copysignf (r, __imag__ x);
__imag__ res = r;
}
else
{
float d, r, s;
d = __ieee754_hypotf (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = __ieee754_sqrtf (0.5f * d + 0.5f * __real__ x);
s = (0.5f * __imag__ x) / r;
}
else
{
s = __ieee754_sqrtf (0.5f * d - 0.5f * __real__ x);
r = fabsf ((0.5f * __imag__ x) / s);
}
__real__ res = r;
__imag__ res = __copysignf (s, __imag__ x);
}
}
return res;
}
__complex__ float
__kernel_casinhf (__complex__ float x, int adj)
{
__complex__ float res;
float rx, ix;
__complex__ float y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsf (__real__ x);
ix = fabsf (__imag__ x);
if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
float t = __real__ y;
__real__ y = __copysignf (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogf (y);
__real__ res += (float) M_LN2;
}
else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
{
float s = __ieee754_hypotf (1.0f, rx);
__real__ res = __ieee754_logf (rx + s);
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
{
float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
__real__ res = __ieee754_logf (ix + s);
if (adj)
__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
else
__imag__ res = __ieee754_atan2f (s, rx);
}
else if (ix > 1.0f && ix < 1.5f && rx < 0.5f)
{
if (rx < FLT_EPSILON * FLT_EPSILON)
{
float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
float s = __ieee754_sqrtf (ix2m1);
__real__ res = __log1pf (2.0f * (ix2m1 + ix * s)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
else
__imag__ res = __ieee754_atan2f (s, rx);
}
else
{
float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
float rx2 = rx * rx;
float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
float d = __ieee754_sqrtf (ix2m1 * ix2m1 + f);
float dp = d + ix2m1;
float dm = f / dp;
float r1 = __ieee754_sqrtf ((dm + rx2) / 2.0f);
float r2 = rx * ix / r1;
__real__ res
= __log1pf (rx2 + dp + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
}
}
else if (ix == 1.0f && rx < 0.5f)
{
if (rx < FLT_EPSILON / 8.0f)
{
__real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx),
__copysignf (1.0f, __imag__ x));
else
__imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx));
}
else
{
float d = rx * __ieee754_sqrtf (4.0f + rx * rx);
float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f);
float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f);
__real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + s1,
__copysignf (1.0f + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1);
}
}
else if (ix < 1.0f && rx < 0.5f)
{
if (ix >= FLT_EPSILON)
{
if (rx < FLT_EPSILON * FLT_EPSILON)
{
float onemix2 = (1.0f + ix) * (1.0f - ix);
float s = __ieee754_sqrtf (onemix2);
__real__ res = __log1pf (2.0f * rx / s) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
else
{
float onemix2 = (1.0f + ix) * (1.0f - ix);
float rx2 = rx * rx;
float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
float d = __ieee754_sqrtf (onemix2 * onemix2 + f);
float dp = d + onemix2;
float dm = f / dp;
float r1 = __ieee754_sqrtf ((dp + rx2) / 2.0f);
float r2 = rx * ix / r1;
__real__ res
= __log1pf (rx2 + dm + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + r1,
__copysignf (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
}
}
else
{
float s = __ieee754_hypotf (1.0f, rx);
__real__ res = __log1pf (2.0f * rx * (rx + s)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
if (__real__ res < FLT_MIN)
{
volatile float force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0f;
__imag__ y = 2.0f * rx * ix;
y = __csqrtf (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
float t = __real__ y;
__real__ y = __copysignf (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogf (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysignf (__real__ res, __real__ x);
__imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));
return res;
}
//------------------------------------------------------------------------------
float Cmath::__ieee754_hypotf( float x, float y )
{
float a = x, b = y, t1, t2, y1, y2, w;
Cmp_signed__int32 j, k, ha, hb;
get_float_word( ha, x );
ha &= 0x7fffffffL;
get_float_word( hb, y );
hb &= 0x7fffffffL;
if( hb > ha )
{
a = y;
b = x;
j = ha;
ha = hb;
hb = j;
}
else
{
a = x;
b = y;
}
set_float_word( a, ha ); // a <- |a|
set_float_word( b, hb ); // b <- |b|
if( ( ha - hb ) > 0xf000000L )
{
return a + b; // x/y > 2**30
}
k = 0;
if( ha > 0x58800000L )
{
// a>2**50
if( !uword_isfinite( ha ) )
{
// Inf or NaN
w = a + b; // for sNaN
if( uword_is_infinite( ha ) )
{
w = a;
}
if( uword_is_infinite( hb ) )
{
w = b;
}
return w;
}
// scale a and b by 2**-68
ha -= 0x22000000L;
hb -= 0x22000000L;
k += 68;
set_float_word( a, ha );
set_float_word( b, hb );
}
if( hb < 0x26800000L )
{
// b < 2**-50
if( uword_is_zero( hb ) )
{
return a;
}
else if( uword_is_subnormal( hb ) )
{
set_float_word( t1, 0x7e800000L ); // t1=2^126
b *= t1;
a *= t1;
k -= 126;
}
else
{
// scale a and b by 2^68
ha += 0x22000000; // a *= 2^68
hb += 0x22000000; // b *= 2^68
k -= 68;
set_float_word( a, ha );
set_float_word( b, hb );
}
}
// medium size a and b
w = a - b;
if( w > b )
{
set_float_word( t1, ha & 0xfffff000L );
t2 = a - t1;
w = __ieee754_sqrtf( t1 * t1 - ( b * (-b) - t2 * ( a + t1 ) ) );
}
else
{
a = a + a;
set_float_word( y1, hb & 0xfffff000L );
y2 = b - y1;
set_float_word( t1, ha + 0x00800000L );
t2 = a - t1;
w = __ieee754_sqrtf( t1 * y1 - ( w * (-w) - ( t1 * y2 + t2 * b ) ) );
}
if( k != 0 )
{
set_float_word( t1, 0x3f800000L + ( k << 23 ) );
return t1 * w;
}
else
{
return w;
}
}
float
__ieee754_hypotf(float x, float y)
{
float a=x,b=y,t1,t2,y1,y2,w;
int32_t j,k,ha,hb;
GET_FLOAT_WORD(ha,x);
ha &= 0x7fffffff;
GET_FLOAT_WORD(hb,y);
hb &= 0x7fffffff;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_FLOAT_WORD(a,ha); /* a <- |a| */
SET_FLOAT_WORD(b,hb); /* b <- |b| */
if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
k=0;
if(ha > 0x58800000) { /* a>2**50 */
if(ha >= 0x7f800000) { /* Inf or NaN */
w = a+b; /* for sNaN */
if(ha == 0x7f800000) w = a;
if(hb == 0x7f800000) w = b;
return w;
}
/* scale a and b by 2**-60 */
ha -= 0x5d800000; hb -= 0x5d800000; k += 60;
SET_FLOAT_WORD(a,ha);
SET_FLOAT_WORD(b,hb);
}
if(hb < 0x26800000) { /* b < 2**-50 */
if(hb <= 0x007fffff) { /* subnormal b or 0 */
if(hb==0) return a;
SET_FLOAT_WORD(t1,0x3f000000); /* t1=2^126 */
b *= t1;
a *= t1;
k -= 126;
} else { /* scale a and b by 2^60 */
ha += 0x5d800000; /* a *= 2^60 */
hb += 0x5d800000; /* b *= 2^60 */
k -= 60;
SET_FLOAT_WORD(a,ha);
SET_FLOAT_WORD(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
SET_FLOAT_WORD(t1,ha&0xfffff000);
t2 = a-t1;
w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
SET_FLOAT_WORD(y1,hb&0xfffff000);
y2 = b - y1;
SET_FLOAT_WORD(t1,ha+0x00800000);
t2 = a - t1;
w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
SET_FLOAT_WORD(t1,0x3f800000+(k<<23));
return t1*w;
} else return w;
}
OLM_DLLEXPORT float
__ieee754_hypotf(float x, float y)
{
float a,b,t1,t2,y1,y2,w;
int32_t j,k,ha,hb;
GET_FLOAT_WORD(ha,x);
ha &= 0x7fffffff;
GET_FLOAT_WORD(hb,y);
hb &= 0x7fffffff;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
a = fabsf(a);
b = fabsf(b);
if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
k=0;
if(ha > 0x58800000) { /* a>2**50 */
if(ha >= 0x7f800000) { /* Inf or NaN */
/* Use original arg order iff result is NaN; quieten sNaNs. */
w = fabsf(x+0.0F)-fabsf(y+0.0F);
if(ha == 0x7f800000) w = a;
if(hb == 0x7f800000) w = b;
return w;
}
/* scale a and b by 2**-68 */
ha -= 0x22000000; hb -= 0x22000000; k += 68;
SET_FLOAT_WORD(a,ha);
SET_FLOAT_WORD(b,hb);
}
if(hb < 0x26800000) { /* b < 2**-50 */
if(hb <= 0x007fffff) { /* subnormal b or 0 */
if(hb==0) return a;
SET_FLOAT_WORD(t1,0x7e800000); /* t1=2^126 */
b *= t1;
a *= t1;
k -= 126;
} else { /* scale a and b by 2^68 */
ha += 0x22000000; /* a *= 2^68 */
hb += 0x22000000; /* b *= 2^68 */
k -= 68;
SET_FLOAT_WORD(a,ha);
SET_FLOAT_WORD(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
SET_FLOAT_WORD(t1,ha&0xfffff000);
t2 = a-t1;
w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
SET_FLOAT_WORD(y1,hb&0xfffff000);
y2 = b - y1;
SET_FLOAT_WORD(t1,(ha+0x00800000)&0xfffff000);
t2 = a - t1;
w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
SET_FLOAT_WORD(t1,0x3f800000+(k<<23));
return t1*w;
} else return w;
}
static float
gammaf_positive (float x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5f)
{
*exp2_adj = 0;
return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5f)
{
*exp2_adj = 0;
return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));
}
else if (x < 2.5f)
{
*exp2_adj = 0;
float x_adj = x - 1;
return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))
* x_adj);
}
else
{
float eps = 0;
float x_eps = 0;
float x_adj = x;
float prod = 1;
if (x < 4.0f)
{
/* Adjust into the range for applying Stirling's
approximation. */
float n = __ceilf (4.0f - x);
x_adj = math_narrow_eval (x + n);
x_eps = (x - (x_adj - n));
prod = __gamma_productf (x_adj - n, x_eps, n, &eps);
}
/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
starting by computing pow (X_ADJ, X_ADJ) with a power of 2
factored out. */
float exp_adj = -eps;
float x_adj_int = __roundf (x_adj);
float x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
if (x_adj_mant < (float) M_SQRT1_2)
{
x_adj_log2--;
x_adj_mant *= 2.0f;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
float ret = (__ieee754_powf (x_adj_mant, x_adj)
* __ieee754_exp2f (x_adj_log2 * x_adj_frac)
* __ieee754_expf (-x_adj)
* __ieee754_sqrtf (2 * (float) M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logf (x_adj);
float bsum = gamma_coeff[NCOEFF - 1];
float x_adj2 = x_adj * x_adj;
for (size_t i = 1; i <= NCOEFF - 1; i++)
bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
exp_adj += bsum / x_adj;
return ret + ret * __expm1f (exp_adj);
}
}
