float 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 */ if (ix >= 0x7f800000) return 1.0f/(x+x*x); if (ix == 0) return -1.0f/0.0f; if (hx < 0) return 0.0f/0.0f; 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 = sinf(x); c = cosf(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 < 0x7f000000) { /* make sure x+x not overflow */ z = -cosf(x+x); if (s*c < 0.0f) cc = z/ss; else ss = z/cc; } if (ix > 0x80000000) z = (invsqrtpi*ss)/sqrtf(x); else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); } return z; } if (ix <= 0x32000000) { /* x < 2**-27 */ return u00 + tpi*logf(x); } z = x*x; u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); v = 1.0f+z*(v01+z*(v02+z*(v03+z*v04))); return u/v + tpi*(j0f(x)*logf(x)); }
float 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 1.0f/(x*x); x = fabsf(x); if (ix >= 0x40000000) { /* |x| >= 2.0 */ s = sinf(x); c = cosf(x); ss = s-c; cc = s+c; if (ix < 0x7f000000) { /* make sure x+x does not overflow */ z = -cosf(x+x); if (s*c < 0.0f) 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 > 0x80000000) z = (invsqrtpi*cc)/sqrtf(x); else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); } return z; } if (ix < 0x39000000) { /* |x| < 2**-13 */ /* raise inexact if x != 0 */ if (huge+x > 1.0f) { if (ix < 0x32000000) /* |x| < 2**-27 */ return 1.0f; return 1.0f - 0.25f*x*x; } } z = x*x; r = z*(R02+z*(R03+z*(R04+z*R05))); s = 1.0f+z*(S01+z*(S02+z*(S03+z*S04))); if(ix < 0x3F800000) { /* |x| < 1.00 */ return 1.0f + z*(-0.25f + (r/s)); } else { u = 0.5f*x; return (1.0f+u)*(1.0f-u) + z*(r/s); } }
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; if(ix>=0x7f800000) return vone/(x+x*x); if(ix==0) return -one/vzero; if(hx<0) return vzero/vzero; 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 = sinf(x); c = cosf(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<0x7f000000) { /* make sure x+x not overflow */ z = -cosf(x+x); if ((s*c)<zero) cc = z/ss; else ss = z/cc; } if(ix>0x58000000) z = (invsqrtpi*ss)/sqrtf(x); /* |x|>2**49 */ else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); } return z; } if(ix<=0x39000000) { /* x < 2**-13 */ 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 __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 __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 */ s = sinf(x); c = cosf(x); 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) */ #ifdef DEAD_CODE if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x); else #endif { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); } return z; } if(ix<0x39000000) { /* |x| < 2**-13 */ if(huge+x>one) { /* 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 __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 */ s = sinf(x); c = cosf(x); ss = s-c; cc = s+c; if(ix<0x7f000000) { /* Make sure x+x does 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>0x58000000) z = (invsqrtpi*cc)/sqrtf(x); /* |x|>2**49 */ else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); } return z; } if(ix<0x3b000000) { /* |x| < 2**-9 */ if(huge+x>one) { /* raise inexact if x != 0 */ if(ix<0x39800000) return one; /* |x|<2**-12 */ else return one - x*x/4; } } 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*((r/s)-qrtr); } else { u = x/2; return((one+u)*(one-u)+z*(r/s)); } }