e_j1.c

eCos/RedBoot for勤研ARM AnywhereII(4510) 含全部源代码

                    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(ix<=0x3c900000) {    /* x < 2**-54 */
            return(-tpi/x);
        } 
        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_j1(x)*__ieee754_log(x)-one/x));
}

/* For x >= 8, the asymptotic expansions of pone is
 *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
 * We approximate pone by
 *      pone(x) = 1 + (R/S)
 * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
 *        S = 1 + ps0*s^2 + ... + ps4*s^10
 * and
 *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
 */

static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
  1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
  4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
  3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
  7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
};
static const double ps8[5] = {
  1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
  3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
  3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
  9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
  3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
};

static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
  1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
  6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
  1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
  5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
  5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
};
static const double ps5[5] = {
  5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
  9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
  5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
  7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
  1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
};

static const double pr3[6] = {
  3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
  1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
  3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
  3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
  9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
  4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
};
static const double ps3[5] = {
  3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
  3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
  1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
  8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
  1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
};

static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
  1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
  2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
  1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
  1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
  5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
};
static const double ps2[5] = {
  2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
  1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
  2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
  1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
  8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
};

        static double pone(double x)
{
        const double *p,*q;
        double z,r,s;
        int ix;
        ix = 0x7fffffff&CYG_LIBM_HI(x);
        if(ix>=0x40200000)     {p = pr8; q= ps8;}
        else if(ix>=0x40122E8B){p = pr5; q= ps5;}
        else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
        else                   {p = pr2; q= ps2;} /* if(ix>=0x40000000) */
        z = one/(x*x);
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
        return one+ r/s;
}
                

/* For x >= 8, the asymptotic expansions of qone is
 *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
 * We approximate pone by
 *      qone(x) = s*(0.375 + (R/S))
 * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
 *        S = 1 + qs1*s^2 + ... + qs6*s^12
 * and
 *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
 */

static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
};
static const double qs8[6] = {
  1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
  7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
  1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
  7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
  6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
};

static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
};
static const double qs5[6] = {
  8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
  1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
  1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
  4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
  2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
};

static const double qr3[6] = {
 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
};
static const double qs3[6] = {
  4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
  6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
  3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
  5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
  1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
};

static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
};
static const double qs2[6] = {
  2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
  2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
  7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
  7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
  1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
};

        static double qone(double x)
{
        const double *p,*q;
        double  s,r,z;
        int ix;
        ix = 0x7fffffff&CYG_LIBM_HI(x);
        if(ix>=0x40200000)     {p = qr8; q= qs8;}
        else if(ix>=0x40122E8B){p = qr5; q= qs5;}
        else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
        else                   {p = qr2; q= qs2;} /* if(ix>=0x40000000) */
        z = one/(x*x);
        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
        return (.375 + r/s)/x;
}

#endif // ifdef CYGPKG_LIBM     

// EOF e_j1.c