double nextafter(double x, double y) { int hx,hy,ix,iy; unsigned lx,ly; hx = CYG_LIBM_HI(x); /* high word of x */ lx = CYG_LIBM_LO(x); /* low word of x */ hy = CYG_LIBM_HI(y); /* high word of y */ ly = CYG_LIBM_LO(y); /* low word of y */ ix = hx&0x7fffffff; /* |x| */ iy = hy&0x7fffffff; /* |y| */ if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ return x+y; if(x==y) return x; /* x=y, return x */ if((ix|lx)==0) { /* x == 0 */ CYG_LIBM_HI(x) = hy&0x80000000; /* return +-minsubnormal */ CYG_LIBM_LO(x) = 1; y = x*x; if(y==x) return y; else return x; /* raise underflow flag */ } if(hx>=0) { /* x > 0 */ if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x < y, x += ulp */ lx += 1; if(lx==0) hx += 1; } } else { /* x < 0 */ if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ if(lx==0) hx -= 1; lx -= 1; } else { /* x > y, x += ulp */ lx += 1; if(lx==0) hx += 1; } } hy = hx&0x7ff00000; if(hy>=0x7ff00000) return x+x; /* overflow */ if(hy<0x00100000) { /* underflow */ y = x*x; if(y!=x) { /* raise underflow flag */ CYG_LIBM_HI(y) = hx; CYG_LIBM_LO(y) = lx; return y; } } CYG_LIBM_HI(x) = hx; CYG_LIBM_LO(x) = lx; return x; }
double __ieee754_log10(double x) { double y,z; int i,k,hx; unsigned lx; hx = CYG_LIBM_HI(x); /* high word of x */ lx = CYG_LIBM_LO(x); /* low word of x */ k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ if (((hx&0x7fffffff)|lx)==0) return -two54/zero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ k -= 54; x *= two54; /* subnormal number, scale up x */ hx = CYG_LIBM_HI(x); /* high word of x */ } if (hx >= 0x7ff00000) return x+x; k += (hx>>20)-1023; i = ((unsigned)k&0x80000000)>>31; hx = (hx&0x000fffff)|((0x3ff-i)<<20); y = (double)(k+i); CYG_LIBM_HI(x) = hx; z = y*log10_2lo + ivln10*__ieee754_log(x); return z+y*log10_2hi; }
double __kernel_tan(double x, double y, int iy) { double z,r,v,w,s; int ix,hx; hx = CYG_LIBM_HI(x); /* high word of x */ ix = hx&0x7fffffff; /* high word of |x| */ if(ix<0x3e300000) /* x < 2**-28 */ {if((int)x==0) { /* generate inexact */ if(((ix|CYG_LIBM_LO(x))|(iy+1))==0) return one/fabs(x); else return (iy==1)? x: -one/x; } } if(ix>=0x3FE59428) { /* |x|>=0.6744 */ if(hx<0) {x = -x; y = -y;} z = pio4-x; w = pio4lo-y; x = z+w; y = 0.0; } z = x*x; w = z*z; /* Break x^5*(T[1]+x^2*T[2]+...) into * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) */ r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); s = z*x; r = y + z*(s*(r+v)+y); r += T[0]*s; w = x+r; if(ix>=0x3FE59428) { v = (double)iy; return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); }
double __ieee754_log(double x) { double hfsq,f,s,z,R,w,t1,t2,dk; int k,hx,i,j; unsigned lx; hx = CYG_LIBM_HI(x); /* high word of x */ lx = CYG_LIBM_LO(x); /* low word of x */ k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ if (((hx&0x7fffffff)|lx)==0) return -two54/zero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ k -= 54; x *= two54; /* subnormal number, scale up x */ hx = CYG_LIBM_HI(x); /* high word of x */ } if (hx >= 0x7ff00000) return x+x; k += (hx>>20)-1023; hx &= 0x000fffff; i = (hx+0x95f64)&0x100000; CYG_LIBM_HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ k += (i>>20); f = x-1.0; if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ if(f==zero) { if(k==0) return zero; else { dk=(double)k; return dk*ln2_hi+dk*ln2_lo; } } R = f*f*(0.5-0.33333333333333333*f); if(k==0) return f-R; else { dk=(double)k; return dk*ln2_hi-((R-dk*ln2_lo)-f); } } s = f/(2.0+f); dk = (double)k; z = s*s; i = hx-0x6147a; w = z*z; j = 0x6b851-hx; t1= w*(Lg2+w*(Lg4+w*Lg6)); t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); i |= j; R = t2+t1; if(i>0) { hfsq=0.5*f*f; if(k==0) return f-(hfsq-s*(hfsq+R)); else return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); } else { if(k==0) return f-s*(f-R); else return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); } }
int isnan(double x) { int hx,lx; hx = (CYG_LIBM_HI(x)&0x7fffffff); lx = CYG_LIBM_LO(x); hx |= (unsigned)(lx|(-lx))>>31; hx = 0x7ff00000 - hx; return ((unsigned)(hx))>>31; }
double cbrt(double x) { int hx; double r,s,t=0.0,w; unsigned sign; hx = CYG_LIBM_HI(x); /* high word of x */ sign=hx&0x80000000; /* sign= sign(x) */ hx ^=sign; if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ if((hx|CYG_LIBM_LO(x))==0) return(x); /* cbrt(0) is itself */ CYG_LIBM_HI(x) = hx; /* x <- |x| */ /* rough cbrt to 5 bits */ if(hx<0x00100000) /* subnormal number */ {CYG_LIBM_HI(t)=0x43500000; /* set t= 2**54 */ t*=x; CYG_LIBM_HI(t)=CYG_LIBM_HI(t)/3+B2; } else CYG_LIBM_HI(t)=hx/3+B1; /* new cbrt to 23 bits, may be implemented in single precision */ r=t*t/x; s=C+r*t; t*=G+F/(s+E+D/s); /* chopped to 20 bits and make it larger than cbrt(x) */ CYG_LIBM_LO(t)=0; CYG_LIBM_HI(t)+=0x00000001; /* one step newton iteration to 53 bits with error less than 0.667 ulps */ s=t*t; /* t*t is exact */ r=x/s; w=t+t; r=(r-t)/(w+r); /* r-s is exact */ t=t+t*r; /* retore the sign bit */ CYG_LIBM_HI(t) |= sign; return(t); }
double __ieee754_asin(double x) { double t,w,p,q,c,r,s; int hx,ix; hx = CYG_LIBM_HI(x); ix = hx&0x7fffffff; if(ix>= 0x3ff00000) { /* |x|>= 1 */ if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==0) /* asin(1)=+-pi/2 with inexact */ return x*pio2_hi+x*pio2_lo; return (x-x)/(x-x); /* asin(|x|>1) is NaN */ } else if (ix<0x3fe00000) { /* |x|<0.5 */ if(ix<0x3e400000) { /* 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-fabs(x); t = w*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 = sqrt(t); if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ w = p/q; t = pio2_hi-(2.0*(s+s*w)-pio2_lo); } else { w = s; CYG_LIBM_LO(w) = 0; c = (t-w*w)/(s+w); r = p/q; p = 2.0*s*r-(pio2_lo-2.0*c); q = pio4_hi-2.0*w; t = pio4_hi-(p-q); } if(hx>0) return t; else return -t; }
double logb(double x) { int lx,ix; ix = (CYG_LIBM_HI(x))&0x7fffffff; /* high |x| */ lx = CYG_LIBM_LO(x); /* low x */ if((ix|lx)==0) return -1.0/fabs(x); if(ix>=0x7ff00000) return x*x; if((ix>>=20)==0) /* IEEE 754 logb */ return -1022.0; else return (double) (ix-1023);
double __ieee754_acos(double x) { double z,p,q,r,w,s,c,df; int hx,ix; hx = CYG_LIBM_HI(x); ix = hx&0x7fffffff; if(ix>=0x3ff00000) { /* |x| >= 1 */ if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==0) { /* |x|==1 */ if(hx>0) return 0.0; /* acos(1) = 0 */ else return pi+2.0*pio2_lo; /* acos(-1)= pi */ } return (x-x)/(x-x); /* acos(|x|>1) is NaN */ } if(ix<0x3fe00000) { /* |x| < 0.5 */ if(ix<=0x3c600000) 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)*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 = sqrt(z); r = p/q; w = r*s-pio2_lo; return pi - 2.0*(s+w); } else { /* x > 0.5 */ z = (one-x)*0.5; s = sqrt(z); df = s; CYG_LIBM_LO(df) = 0; 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 2.0*(df+w); } }
double __ieee754_y0(double x) { double z, s,c,ss,cc,u,v; int hx,ix,lx; hx = CYG_LIBM_HI(x); ix = 0x7fffffff&hx; lx = CYG_LIBM_LO(x); /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ if(ix>=0x7ff00000) return one/(x+x*x); if((ix|lx)==0) return -one/zero; if(hx<0) return zero/zero; 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. */ s = sin(x); c = cos(x); 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)/sqrt(x); else { u = pzero(x); v = qzero(x); z = invsqrtpi*(u*ss+v*cc)/sqrt(x); } return z; } if(ix<=0x3e400000) { /* x < 2**-27 */ return(u00 + tpi*__ieee754_log(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_j0(x)*__ieee754_log(x))); }
double frexp(double x, int *eptr) { int hx, ix, lx; hx = CYG_LIBM_HI(x); ix = 0x7fffffff&hx; lx = CYG_LIBM_LO(x); *eptr = 0; if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ if (ix<0x00100000) { /* subnormal */ x *= two54; hx = CYG_LIBM_HI(x); ix = hx&0x7fffffff; *eptr = -54; } *eptr += (ix>>20)-1022; hx = (hx&0x800fffff)|0x3fe00000; CYG_LIBM_HI(x) = hx; return x; }
double __ieee754_acosh(double x) { double t; int hx; hx = CYG_LIBM_HI(x); if(hx<0x3ff00000) { /* x < 1 */ return (x-x)/(x-x); } else if(hx >=0x41b00000) { /* x > 2**28 */ if(hx >=0x7ff00000) { /* x is inf of NaN */ return x+x; } else return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ } else if(((hx-0x3ff00000)|CYG_LIBM_LO(x))==0) { return 0.0; /* acosh(1) = 0 */ } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ t=x*x; return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); } else { /* 1<x<2 */ t = x-one; return log1p(t+sqrt(2.0*t+t*t)); } }
double __ieee754_sinh(double x) { double t,w,h; int ix,jx; unsigned lx; /* High word of |x|. */ jx = CYG_LIBM_HI(x); ix = jx&0x7fffffff; /* x is INF or NaN */ if(ix>=0x7ff00000) return x+x; h = 0.5; if (jx<0) h = -h; /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ if (ix < 0x40360000) { /* |x|<22 */ if (ix<0x3e300000) /* |x|<2**-28 */ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ t = expm1(fabs(x)); if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); return h*(t+t/(t+one)); } /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ lx = CYG_LIBM_LO(x); if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) { w = __ieee754_exp(0.5*fabs(x)); t = h*w; return t*w; } /* |x| > overflowthresold, sinh(x) overflow */ return x*shuge; }
double __ieee754_hypot(double x, double y) { double a=x,b=y,t1,t2,y1,y2,w; int j,k,ha,hb; ha = CYG_LIBM_HI(x)&0x7fffffff; /* high word of x */ hb = CYG_LIBM_HI(y)&0x7fffffff; /* high word of y */ if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} CYG_LIBM_HI(a) = ha; /* a <- |a| */ CYG_LIBM_HI(b) = hb; /* b <- |b| */ if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ k=0; if(ha > 0x5f300000) { /* a>2**500 */ if(ha >= 0x7ff00000) { /* Inf or NaN */ w = a+b; /* for sNaN */ if(((ha&0xfffff)|CYG_LIBM_LO(a))==0) w = a; if(((hb^0x7ff00000)|CYG_LIBM_LO(b))==0) w = b; return w; } /* scale a and b by 2**-600 */ ha -= 0x25800000; hb -= 0x25800000; k += 600; CYG_LIBM_HI(a) = ha; CYG_LIBM_HI(b) = hb; } if(hb < 0x20b00000) { /* b < 2**-500 */ if(hb <= 0x000fffff) { /* subnormal b or 0 */ if((hb|(CYG_LIBM_LO(b)))==0) return a; t1=0; CYG_LIBM_HI(t1) = 0x7fd00000; /* t1=2^1022 */ b *= t1; a *= t1; k -= 1022; } else { /* scale a and b by 2^600 */ ha += 0x25800000; /* a *= 2^600 */ hb += 0x25800000; /* b *= 2^600 */ k -= 600; CYG_LIBM_HI(a) = ha; CYG_LIBM_HI(b) = hb; } } /* medium size a and b */ w = a-b; if (w>b) { t1 = 0; CYG_LIBM_HI(t1) = ha; t2 = a-t1; w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); } else { a = a+a; y1 = 0; CYG_LIBM_HI(y1) = hb; y2 = b - y1; t1 = 0; CYG_LIBM_HI(t1) = ha+0x00100000; t2 = a - t1; w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); } if(k!=0) { t1 = 1.0; CYG_LIBM_HI(t1) += (k<<20); return t1*w; } else return w; }