diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_j0.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_j0.c | 374 |
1 files changed, 213 insertions, 161 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_j0.c b/sysdeps/ieee754/dbl-64/e_j0.c index ca54275..d165e80 100644 --- a/sysdeps/ieee754/dbl-64/e_j0.c +++ b/sysdeps/ieee754/dbl-64/e_j0.c @@ -11,7 +11,7 @@ */ /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, for performance improvement on pipelined processors. -*/ + */ /* __ieee754_j0(x), __ieee754_y0(x) * Bessel function of the first and second kinds of order zero. @@ -61,144 +61,166 @@ #include <math.h> #include <math_private.h> -static double pzero(double), qzero(double); +static double pzero (double), qzero (double); static const double -huge = 1e300, -one = 1.0, -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0, 2.00] */ -R[] = {0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ - -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ - 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ - -4.61832688532103189199e-09}, /* 0xBE33D5E7, 0x73D63FCE */ -S[] = {0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ - 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ - 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ - 1.16614003333790000205e-09}; /* 0x3E1408BC, 0xF4745D8F */ + huge = 1e300, + one = 1.0, + invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ + tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +/* R0/S0 on [0, 2.00] */ + R[] = { 0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ + -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ + 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ + -4.61832688532103189199e-09 }, /* 0xBE33D5E7, 0x73D63FCE */ + S[] = { 0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ + 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ + 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ + 1.16614003333790000205e-09 }; /* 0x3E1408BC, 0xF4745D8F */ static const double zero = 0.0; double -__ieee754_j0(double x) +__ieee754_j0 (double x) { - double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4; - int32_t hx,ix; + 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; + 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; } - z = x*x; - 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]; - 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)); + /* + * 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; + 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]; + 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)); + } } strong_alias (__ieee754_j0, __j0_finite) static const double -U[] = {-7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ - 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ - -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ - 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ - -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ - 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ - -3.98205194132103398453e-11}, /* 0xBDC5E43D, 0x693FB3C8 */ -V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ - 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ - 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ - 4.41110311332675467403e-10}; /* 0x3DFE5018, 0x3BD6D9EF */ +U[] = { -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ + 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ + -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ + 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ + -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ + 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ + -3.98205194132103398453e-11 }, /* 0xBDC5E43D, 0x693FB3C8 */ +V[] = { 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ + 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ + 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ + 4.41110311332675467403e-10 }; /* 0x3DFE5018, 0x3BD6D9EF */ double -__ieee754_y0(double x) +__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; + 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; + 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<=0x3e400000) { /* x < 2**-27 */ - return(U[0] + tpi*__ieee754_log(x)); + 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); } - z = x*x; - 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]; - return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); + return z; + } + if (ix <= 0x3e400000) /* x < 2**-27 */ + { + return (U[0] + tpi * __ieee754_log (x)); + } + z = x * x; + 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]; + return (u / v + tpi * (__ieee754_j0 (x) * __ieee754_log (x))); } strong_alias (__ieee754_y0, __y0_finite) @@ -276,28 +298,43 @@ static const double pS2[5] = { }; static double -pzero(double x) +pzero (double x) { - const double *p,*q; - double z,r,s,z2,z4,r1,r2,r3,s1,s2,s3; - int32_t ix; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; - if (ix>=0x41b00000) {return one;} - else if(ix>=0x40200000){p = pR8; q= pS8;} - else if(ix>=0x40122E8B){p = pR5; q= pS5;} - else if(ix>=0x4006DB6D){p = pR3; q= pS3;} - else if(ix>=0x40000000){p = pR2; q= pS2;} - z = one/(x*x); - r1 = p[0]+z*p[1]; z2=z*z; - r2 = p[2]+z*p[3]; z4=z2*z2; - r3 = p[4]+z*p[5]; - r = r1 + z2*r2 + z4*r3; - s1 = one+z*q[0]; - s2 = q[1]+z*q[2]; - s3 = q[3]+z*q[4]; - s = s1 + z2*s2 + z4*s3; - return one+ r/s; + const double *p, *q; + double z, r, s, z2, z4, r1, r2, r3, s1, s2, s3; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + if (ix >= 0x41b00000) + { + return one; + } + else if (ix >= 0x40200000) + { + p = pR8; q = pS8; + } + else if (ix >= 0x40122E8B) + { + p = pR5; q = pS5; + } + else if (ix >= 0x4006DB6D) + { + p = pR3; q = pS3; + } + else if (ix >= 0x40000000) + { + p = pR2; q = pS2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3; + return one + r / s; } @@ -379,26 +416,41 @@ static const double qS2[6] = { }; static double -qzero(double x) +qzero (double x) { - const double *p,*q; - double s,r,z,z2,z4,z6,r1,r2,r3,s1,s2,s3; - int32_t ix; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; - if (ix>=0x41b00000) {return -.125/x;} - else if(ix>=0x40200000){p = qR8; q= qS8;} - else if(ix>=0x40122E8B){p = qR5; q= qS5;} - else if(ix>=0x4006DB6D){p = qR3; q= qS3;} - else if(ix>=0x40000000){p = qR2; q= qS2;} - z = one/(x*x); - r1 = p[0]+z*p[1]; z2=z*z; - r2 = p[2]+z*p[3]; z4=z2*z2; - r3 = p[4]+z*p[5]; z6=z4*z2; - r= r1 + z2*r2 + z4*r3; - s1 = one+z*q[0]; - s2 = q[1]+z*q[2]; - s3 = q[3]+z*q[4]; - s = s1 + z2*s2 + z4*s3 +z6*q[5]; - return (-.125 + r/s)/x; + const double *p, *q; + double s, r, z, z2, z4, z6, r1, r2, r3, s1, s2, s3; + int32_t ix; + GET_HIGH_WORD (ix, x); + ix &= 0x7fffffff; + if (ix >= 0x41b00000) + { + return -.125 / x; + } + else if (ix >= 0x40200000) + { + p = qR8; q = qS8; + } + else if (ix >= 0x40122E8B) + { + p = qR5; q = qS5; + } + else if (ix >= 0x4006DB6D) + { + p = qR3; q = qS3; + } + else if (ix >= 0x40000000) + { + p = qR2; q = qS2; + } + z = one / (x * x); + r1 = p[0] + z * p[1]; z2 = z * z; + r2 = p[2] + z * p[3]; z4 = z2 * z2; + r3 = p[4] + z * p[5]; z6 = z4 * z2; + r = r1 + z2 * r2 + z4 * r3; + s1 = one + z * q[0]; + s2 = q[1] + z * q[2]; + s3 = q[3] + z * q[4]; + s = s1 + z2 * s2 + z4 * s3 + z6 * q[5]; + return (-.125 + r / s) / x; } |