diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-96/e_j1l.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/e_j1l.c | 156 |
1 files changed, 21 insertions, 135 deletions
diff --git a/sysdeps/ieee754/ldbl-96/e_j1l.c b/sysdeps/ieee754/ldbl-96/e_j1l.c index 62a8ce0cb7..369fd830fe 100644 --- a/sysdeps/ieee754/ldbl-96/e_j1l.c +++ b/sysdeps/ieee754/ldbl-96/e_j1l.c @@ -11,9 +11,9 @@ /* Long double expansions are Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> - and are incorporated herein by permission of the author. The author + and are incorporated herein by permission of the author. The author reserves the right to distribute this material elsewhere under different - copying permissions. These modifications are distributed here under + copying permissions. These modifications are distributed here under the following terms: This library is free software; you can redistribute it and/or @@ -38,17 +38,17 @@ * for x in (0,2) * j1(x) = x/2 + x*z*R0/S0, where z = x*x; * for x in (2,inf) - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) * as follow: * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) * = 1/sqrt(2) * (sin(x) - cos(x)) * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) * = -1/sqrt(2) * (sin(x) + cos(x)) - * (To avoid cancellation, use + * (To avoid cancellation, use * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) + * to compute the worse one.) * * 3 Special cases * j1(nan)= nan @@ -66,25 +66,17 @@ * Note: For tiny x, 1/x dominate y1 and hence * y1(tiny) = -2/pi/tiny * 3. For x>=2. - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) * by method mentioned above. */ #include "math.h" #include "math_private.h" -#ifdef __STDC__ static long double pone (long double), qone (long double); -#else -static long double pone (), qone (); -#endif -#ifdef __STDC__ static const long double -#else -static long double -#endif huge = 1e4930L, one = 1.0L, invsqrtpi = 5.6418958354775628694807945156077258584405e-1L, @@ -110,21 +102,11 @@ R[5] = { /* 1.000000000000000000000000000000000000000E0L, */ }; -#ifdef __STDC__ static const long double zero = 0.0; -#else -static long double zero = 0.0; -#endif -#ifdef __STDC__ long double __ieee754_j1l (long double x) -#else -long double -__ieee754_j1l (x) - long double x; -#endif { long double z, c, r, s, ss, cc, u, v, y; int32_t ix; @@ -132,7 +114,7 @@ __ieee754_j1l (x) GET_LDOUBLE_WORDS (se, i0, i1, x); ix = se & 0x7fff; - if (ix >= 0x7fff) + if (__builtin_expect (ix >= 0x7fff, 0)) return one / x; y = fabsl (x); if (ix >= 0x4000) @@ -152,7 +134,7 @@ __ieee754_j1l (x) * 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 > 0x4080) + if (__builtin_expect (ix > 0x4080, 0)) z = (invsqrtpi * cc) / __ieee754_sqrtl (y); else { @@ -165,7 +147,7 @@ __ieee754_j1l (x) else return z; } - if (ix < 0x3fde) /* |x| < 2^-33 */ + if (__builtin_expect (ix < 0x3fde, 0)) /* |x| < 2^-33 */ { if (huge + x > one) return 0.5 * x; /* inexact if x!=0 necessary */ @@ -176,16 +158,13 @@ __ieee754_j1l (x) r *= x; return (x * 0.5 + r / s); } +strong_alias (__ieee754_j1l, __j1l_finite) /* Y1(x) = 2/pi * (log(x) * j1(x) - 1/x) + x R(x^2) 0 <= x <= 2 Peak relative error 2.3e-23 */ -#ifdef __STDC__ static const long double U0[6] = { -#else -static long double U0[6] = { -#endif -5.908077186259914699178903164682444848615E10L, 1.546219327181478013495975514375773435962E10L, -6.438303331169223128870035584107053228235E8L, @@ -193,11 +172,7 @@ static long double U0[6] = { -6.138043997084355564619377183564196265471E4L, 1.418503228220927321096904291501161800215E2L, }; -#ifdef __STDC__ static const long double V0[5] = { -#else -static long double V0[5] = { -#endif 3.013447341682896694781964795373783679861E11L, 4.669546565705981649470005402243136124523E9L, 3.595056091631351184676890179233695857260E7L, @@ -207,14 +182,8 @@ static long double V0[5] = { }; -#ifdef __STDC__ long double __ieee754_y1l (long double x) -#else -long double -__ieee754_y1l (x) - long double x; -#endif { long double z, s, c, ss, cc, u, v; int32_t ix; @@ -223,11 +192,11 @@ __ieee754_y1l (x) GET_LDOUBLE_WORDS (se, i0, i1, x); ix = se & 0x7fff; /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if (se & 0x8000) + if (__builtin_expect (se & 0x8000, 0)) return zero / (zero * x); - if (ix >= 0x7fff) + if (__builtin_expect (ix >= 0x7fff, 0)) return one / (x + x * x); - if ((i0 | i1) == 0) + if (__builtin_expect ((i0 | i1) == 0, 0)) return -HUGE_VALL + x; /* -inf and overflow exception. */ if (ix >= 0x4000) { /* |x| >= 2.0 */ @@ -253,7 +222,7 @@ __ieee754_y1l (x) * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one. */ - if (ix > 0x4080) + if (__builtin_expect (ix > 0x4080, 0)) z = (invsqrtpi * ss) / __ieee754_sqrtl (x); else { @@ -263,7 +232,7 @@ __ieee754_y1l (x) } return z; } - if (ix <= 0x3fbe) + if (__builtin_expect (ix <= 0x3fbe, 0)) { /* x < 2**-65 */ return (-tpi / x); } @@ -273,12 +242,13 @@ __ieee754_y1l (x) return (x * (u / v) + tpi * (__ieee754_j1l (x) * __ieee754_logl (x) - one / x)); } +strong_alias (__ieee754_y1l, __y1l_finite) /* 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) + * pone(x) = 1 + (R/S) */ /* J1(x) cosX + Y1(x) sinX = sqrt( 2/(pi x)) P1(x) @@ -286,11 +256,7 @@ __ieee754_y1l (x) 8 <= x <= inf (0 <= z <= 0.125) Peak relative error 5.2e-22 */ -#ifdef __STDC__ static const long double pr8[7] = { -#else -static long double pr8[7] = { -#endif 8.402048819032978959298664869941375143163E-9L, 1.813743245316438056192649247507255996036E-6L, 1.260704554112906152344932388588243836276E-4L, @@ -299,11 +265,7 @@ static long double pr8[7] = { 1.131111483254318243139953003461511308672E-1L, 4.480715825681029711521286449131671880953E-2L, }; -#ifdef __STDC__ static const long double ps8[6] = { -#else -static long double ps8[6] = { -#endif 7.169748325574809484893888315707824924354E-8L, 1.556549720596672576431813934184403614817E-5L, 1.094540125521337139209062035774174565882E-3L, @@ -317,11 +279,7 @@ static long double ps8[6] = { P1(x) = 1 + z^2 R(z^2), z=1/x 4.54541015625 <= x <= 8 Peak relative error 7.7e-22 */ -#ifdef __STDC__ static const long double pr5[7] = { -#else -static long double pr5[7] = { -#endif 4.318486887948814529950980396300969247900E-7L, 4.715341880798817230333360497524173929315E-5L, 1.642719430496086618401091544113220340094E-3L, @@ -330,11 +288,7 @@ static long double pr5[7] = { 1.755576530055079253910829652698703791957E-1L, 3.218803858282095929559165965353784980613E-2L, }; -#ifdef __STDC__ static const long double ps5[6] = { -#else -static long double ps5[6] = { -#endif 3.685108812227721334719884358034713967557E-6L, 4.069102509511177498808856515005792027639E-4L, 1.449728676496155025507893322405597039816E-2L, @@ -348,11 +302,7 @@ static long double ps5[6] = { P1(x) = 1 + z^2 R(z^2), z=1/x 2.85711669921875 <= x <= 4.54541015625 Peak relative error 6.5e-21 */ -#ifdef __STDC__ static const long double pr3[7] = { -#else -static long double pr3[7] = { -#endif 1.265251153957366716825382654273326407972E-5L, 8.031057269201324914127680782288352574567E-4L, 1.581648121115028333661412169396282881035E-2L, @@ -361,11 +311,7 @@ static long double pr3[7] = { 2.559223765418386621748404398017602935764E-1L, 2.277136933287817911091370397134882441046E-2L, }; -#ifdef __STDC__ static const long double ps3[6] = { -#else -static long double ps3[6] = { -#endif 1.079681071833391818661952793568345057548E-4L, 6.986017817100477138417481463810841529026E-3L, 1.429403701146942509913198539100230540503E-1L, @@ -379,11 +325,7 @@ static long double ps3[6] = { P1(x) = 1 + z^2 R(z^2), z=1/x 2 <= x <= 2.85711669921875 Peak relative error 3.5e-21 */ -#ifdef __STDC__ static const long double pr2[7] = { -#else -static long double pr2[7] = { -#endif 2.795623248568412225239401141338714516445E-4L, 1.092578168441856711925254839815430061135E-2L, 1.278024620468953761154963591853679640560E-1L, @@ -392,11 +334,7 @@ static long double pr2[7] = { 3.544176317308370086415403567097130611468E-1L, 1.604142674802373041247957048801599740644E-2L, }; -#ifdef __STDC__ static const long double ps2[6] = { -#else -static long double ps2[6] = { -#endif 2.385605161555183386205027000675875235980E-3L, 9.616778294482695283928617708206967248579E-2L, 1.195215570959693572089824415393951258510E0L, @@ -407,20 +345,10 @@ static long double ps2[6] = { }; -#ifdef __STDC__ static long double pone (long double x) -#else -static long double -pone (x) - long double x; -#endif { -#ifdef __STDC__ const long double *p, *q; -#else - long double *p, *q; -#endif long double z, r, s; int32_t ix; u_int32_t se, i0, i1; @@ -462,7 +390,7 @@ pone (x) /* 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)) + * qone(x) = s*(0.375 + (R/S)) */ /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), @@ -470,11 +398,7 @@ pone (x) 8 <= x <= inf Peak relative error 8.3e-22 */ -#ifdef __STDC__ static const long double qr8[7] = { -#else -static long double qr8[7] = { -#endif -5.691925079044209246015366919809404457380E-10L, -1.632587664706999307871963065396218379137E-7L, -1.577424682764651970003637263552027114600E-5L, @@ -483,11 +407,7 @@ static long double qr8[7] = { -6.854943629378084419631926076882330494217E-2L, -1.055448290469180032312893377152490183203E-1L, }; -#ifdef __STDC__ static const long double qs8[7] = { -#else -static long double qs8[7] = { -#endif 5.550982172325019811119223916998393907513E-9L, 1.607188366646736068460131091130644192244E-6L, 1.580792530091386496626494138334505893599E-4L, @@ -502,11 +422,7 @@ static long double qs8[7] = { Q1(x) = z(.375 + z^2 R(z^2)), z=1/x 4.54541015625 <= x <= 8 Peak relative error 4.1e-22 */ -#ifdef __STDC__ static const long double qr5[7] = { -#else -static long double qr5[7] = { -#endif -6.719134139179190546324213696633564965983E-8L, -9.467871458774950479909851595678622044140E-6L, -4.429341875348286176950914275723051452838E-4L, @@ -515,11 +431,7 @@ static long double qr5[7] = { -1.964432669771684034858848142418228214855E-1L, -1.333896496989238600119596538299938520726E-1L, }; -#ifdef __STDC__ static const long double qs5[7] = { -#else -static long double qs5[7] = { -#endif 6.552755584474634766937589285426911075101E-7L, 9.410814032118155978663509073200494000589E-5L, 4.561677087286518359461609153655021253238E-3L, @@ -534,11 +446,7 @@ static long double qs5[7] = { Q1(x) = z(.375 + z^2 R(z^2)), z=1/x 2.85711669921875 <= x <= 4.54541015625 Peak relative error 2.2e-21 */ -#ifdef __STDC__ static const long double qr3[7] = { -#else -static long double qr3[7] = { -#endif -3.618746299358445926506719188614570588404E-6L, -2.951146018465419674063882650970344502798E-4L, -7.728518171262562194043409753656506795258E-3L, @@ -547,11 +455,7 @@ static long double qr3[7] = { -4.858192581793118040782557808823460276452E-1L, -1.592399251246473643510898335746432479373E-1L, }; -#ifdef __STDC__ static const long double qs3[7] = { -#else -static long double qs3[7] = { -#endif 3.529139957987837084554591421329876744262E-5L, 2.973602667215766676998703687065066180115E-3L, 8.273534546240864308494062287908662592100E-2L, @@ -566,11 +470,7 @@ static long double qs3[7] = { Q1(x) = z(.375 + z^2 R(z^2)), z=1/x 2 <= x <= 2.85711669921875 Peak relative error 6.9e-22 */ -#ifdef __STDC__ static const long double qr2[7] = { -#else -static long double qr2[7] = { -#endif -1.372751603025230017220666013816502528318E-4L, -6.879190253347766576229143006767218972834E-3L, -1.061253572090925414598304855316280077828E-1L, @@ -579,11 +479,7 @@ static long double qr2[7] = { -1.087955310491078933531734062917489870754E0L, -1.826821119773182847861406108689273719137E-1L, }; -#ifdef __STDC__ static const long double qs2[7] = { -#else -static long double qs2[7] = { -#endif 1.338768933634451601814048220627185324007E-3L, 7.071099998918497559736318523932241901810E-2L, 1.200511429784048632105295629933382142221E0L, @@ -595,20 +491,10 @@ static long double qs2[7] = { }; -#ifdef __STDC__ static long double qone (long double x) -#else -static long double -qone (x) - long double x; -#endif { -#ifdef __STDC__ const long double *p, *q; -#else - long double *p, *q; -#endif static long double s, r, z; int32_t ix; u_int32_t se, i0, i1; |