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diff --git a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
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-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* Modifications for 128-bit long double are
- Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
- 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
- the following terms:
-
- This library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- This library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with this library; if not, write to the Free Software
- Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
-
-/*
- * __ieee754_jn(n, x), __ieee754_yn(n, x)
- * floating point Bessel's function of the 1st and 2nd kind
- * of order n
- *
- * Special cases:
- * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
- * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
- * Note 2. About jn(n,x), yn(n,x)
- * For n=0, j0(x) is called,
- * for n=1, j1(x) is called,
- * for n<x, forward recursion us used starting
- * from values of j0(x) and j1(x).
- * for n>x, a continued fraction approximation to
- * j(n,x)/j(n-1,x) is evaluated and then backward
- * recursion is used starting from a supposed value
- * for j(n,x). The resulting value of j(0,x) is
- * compared with the actual value to correct the
- * supposed value of j(n,x).
- *
- * yn(n,x) is similar in all respects, except
- * that forward recursion is used for all
- * values of n>1.
- *
- */
-
-#include "math.h"
-#include "math_private.h"
-
-#ifdef __STDC__
-static const long double
-#else
-static long double
-#endif
- invsqrtpi = 5.6418958354775628694807945156077258584405E-1L,
- two = 2.0e0L,
- one = 1.0e0L,
- zero = 0.0L;
-
-
-#ifdef __STDC__
-long double
-__ieee754_jnl (int n, long double x)
-#else
-long double
-__ieee754_jnl (n, x)
- int n;
- long double x;
-#endif
-{
- u_int32_t se;
- int32_t i, ix, sgn;
- long double a, b, temp, di;
- long double z, w;
- ieee854_long_double_shape_type u;
-
-
- /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
- * Thus, J(-n,x) = J(n,-x)
- */
-
- u.value = x;
- se = u.parts32.w0;
- ix = se & 0x7fffffff;
-
- /* if J(n,NaN) is NaN */
- if (ix >= 0x7ff00000)
- {
- if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
- | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
- return x + x;
- }
-
- if (n < 0)
- {
- n = -n;
- x = -x;
- se ^= 0x80000000;
- }
- if (n == 0)
- return (__ieee754_j0l (x));
- if (n == 1)
- return (__ieee754_j1l (x));
- sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */
- x = fabsl (x);
-
- if (x == 0.0L || ix >= 0x7ff00000) /* if x is 0 or inf */
- b = zero;
- else if ((long double) n <= x)
- {
- /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
- if (ix >= 0x52d00000)
- { /* x > 2**302 */
-
- /* ??? Could use an expansion for large x here. */
-
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- long double s;
- long double c;
- __sincosl (x, &s, &c);
- switch (n & 3)
- {
- case 0:
- temp = c + s;
- break;
- case 1:
- temp = -c + s;
- break;
- case 2:
- temp = -c - s;
- break;
- case 3:
- temp = c - s;
- break;
- }
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
- }
- else
- {
- a = __ieee754_j0l (x);
- b = __ieee754_j1l (x);
- for (i = 1; i < n; i++)
- {
- temp = b;
- b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
- a = temp;
- }
- }
- }
- else
- {
- if (ix < 0x3e100000)
- { /* x < 2**-29 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
- * J(n,x) = 1/n!*(x/2)^n - ...
- */
- if (n >= 33) /* underflow, result < 10^-300 */
- b = zero;
- else
- {
- temp = x * 0.5;
- b = temp;
- for (a = one, i = 2; i <= n; i++)
- {
- a *= (long double) i; /* a = n! */
- b *= temp; /* b = (x/2)^n */
- }
- b = b / a;
- }
- }
- else
- {
- /* use backward recurrence */
- /* x x^2 x^2
- * J(n,x)/J(n-1,x) = ---- ------ ------ .....
- * 2n - 2(n+1) - 2(n+2)
- *
- * 1 1 1
- * (for large x) = ---- ------ ------ .....
- * 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
- * x x x
- *
- * Let w = 2n/x and h=2/x, then the above quotient
- * is equal to the continued fraction:
- * 1
- * = -----------------------
- * 1
- * w - -----------------
- * 1
- * w+h - ---------
- * w+2h - ...
- *
- * To determine how many terms needed, let
- * Q(0) = w, Q(1) = w(w+h) - 1,
- * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
- */
- /* determine k */
- long double t, v;
- long double q0, q1, h, tmp;
- int32_t k, m;
- w = (n + n) / (long double) x;
- h = 2.0L / (long double) x;
- q0 = w;
- z = w + h;
- q1 = w * z - 1.0L;
- k = 1;
- while (q1 < 1.0e17L)
- {
- k += 1;
- z += h;
- tmp = z * q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- m = n + n;
- for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
- t = one / (i / x - t);
- a = t;
- b = one;
- /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
- * Hence, if n*(log(2n/x)) > ...
- * single 8.8722839355e+01
- * double 7.09782712893383973096e+02
- * long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
- * likely underflow to zero
- */
- tmp = n;
- v = two / x;
- tmp = tmp * __ieee754_logl (fabsl (v * tmp));
-
- if (tmp < 1.1356523406294143949491931077970765006170e+04L)
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- }
- }
- else
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- /* scale b to avoid spurious overflow */
- if (b > 1e100L)
- {
- a /= b;
- t /= b;
- b = one;
- }
- }
- }
- b = (t * __ieee754_j0l (x) / b);
- }
- }
- if (sgn == 1)
- return -b;
- else
- return b;
-}
-
-#ifdef __STDC__
-long double
-__ieee754_ynl (int n, long double x)
-#else
-long double
-__ieee754_ynl (n, x)
- int n;
- long double x;
-#endif
-{
- u_int32_t se;
- int32_t i, ix;
- int32_t sign;
- long double a, b, temp;
- ieee854_long_double_shape_type u;
-
- u.value = x;
- se = u.parts32.w0;
- ix = se & 0x7fffffff;
-
- /* if Y(n,NaN) is NaN */
- if (ix >= 0x7ff00000)
- {
- if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
- | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
- return x + x;
- }
- if (x <= 0.0L)
- {
- if (x == 0.0L)
- return -HUGE_VALL + x;
- if (se & 0x80000000)
- return zero / (zero * x);
- }
- sign = 1;
- if (n < 0)
- {
- n = -n;
- sign = 1 - ((n & 1) << 1);
- }
- if (n == 0)
- return (__ieee754_y0l (x));
- if (n == 1)
- return (sign * __ieee754_y1l (x));
- if (ix >= 0x7ff00000)
- return zero;
- if (ix >= 0x52D00000)
- { /* x > 2**302 */
-
- /* ??? See comment above on the possible futility of this. */
-
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- long double s;
- long double c;
- __sincosl (x, &s, &c);
- switch (n & 3)
- {
- case 0:
- temp = s - c;
- break;
- case 1:
- temp = -s - c;
- break;
- case 2:
- temp = -s + c;
- break;
- case 3:
- temp = s + c;
- break;
- }
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
- }
- else
- {
- a = __ieee754_y0l (x);
- b = __ieee754_y1l (x);
- /* quit if b is -inf */
- u.value = b;
- se = u.parts32.w0 & 0xfff00000;
- for (i = 1; i < n && se != 0xfff00000; i++)
- {
- temp = b;
- b = ((long double) (i + i) / x) * b - a;
- u.value = b;
- se = u.parts32.w0 & 0xfff00000;
- a = temp;
- }
- }
- if (sign > 0)
- return b;
- else
- return -b;
-}