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Diffstat (limited to 'sysdeps/ieee754/ldbl-128/e_jnl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_jnl.c | 419 |
1 files changed, 0 insertions, 419 deletions
diff --git a/sysdeps/ieee754/ldbl-128/e_jnl.c b/sysdeps/ieee754/ldbl-128/e_jnl.c deleted file mode 100644 index 470631e600..0000000000 --- a/sysdeps/ieee754/ldbl-128/e_jnl.c +++ /dev/null @@ -1,419 +0,0 @@ -/* - * ==================================================== - * 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, see - <http://www.gnu.org/licenses/>. */ - -/* - * __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 <errno.h> -#include <float.h> -#include <math.h> -#include <math_private.h> - -static const _Float128 - invsqrtpi = L(5.6418958354775628694807945156077258584405E-1), - two = 2, - one = 1, - zero = 0; - - -_Float128 -__ieee754_jnl (int n, _Float128 x) -{ - u_int32_t se; - int32_t i, ix, sgn; - _Float128 a, b, temp, di, ret; - _Float128 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 >= 0x7fff0000) - { - if ((u.parts32.w0 & 0xffff) | u.parts32.w1 | u.parts32.w2 | 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); - - { - SET_RESTORE_ROUNDL (FE_TONEAREST); - if (x == 0 || ix >= 0x7fff0000) /* if x is 0 or inf */ - return sgn == 1 ? -zero : zero; - else if ((_Float128) n <= x) - { - /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ - if (ix >= 0x412D0000) - { /* 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 - */ - _Float128 s; - _Float128 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 * ((_Float128) (i + i) / x) - a; /* avoid underflow */ - a = temp; - } - } - } - else - { - if (ix < 0x3fc60000) - { /* x < 2**-57 */ - /* x is tiny, return the first Taylor expansion of J(n,x) - * J(n,x) = 1/n!*(x/2)^n - ... - */ - if (n >= 400) /* underflow, result < 10^-4952 */ - b = zero; - else - { - temp = x * 0.5; - b = temp; - for (a = one, i = 2; i <= n; i++) - { - a *= (_Float128) 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 */ - _Float128 t, v; - _Float128 q0, q1, h, tmp; - int32_t k, m; - w = (n + n) / (_Float128) x; - h = 2 / (_Float128) x; - q0 = w; - z = w + h; - q1 = w * z - 1; - k = 1; - while (q1 < L(1.0e17)) - { - 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 < L(1.1356523406294143949491931077970765006170e+04)) - { - for (i = n - 1, di = (_Float128) (i + i); i > 0; i--) - { - temp = b; - b *= di; - b = b / x - a; - a = temp; - di -= two; - } - } - else - { - for (i = n - 1, di = (_Float128) (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 > L(1e100)) - { - a /= b; - t /= b; - b = one; - } - } - } - /* j0() and j1() suffer enormous loss of precision at and - * near zero; however, we know that their zero points never - * coincide, so just choose the one further away from zero. - */ - z = __ieee754_j0l (x); - w = __ieee754_j1l (x); - if (fabsl (z) >= fabsl (w)) - b = (t * z / b); - else - b = (t * w / a); - } - } - if (sgn == 1) - ret = -b; - else - ret = b; - } - if (ret == 0) - { - ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN; - __set_errno (ERANGE); - } - else - math_check_force_underflow (ret); - return ret; -} -strong_alias (__ieee754_jnl, __jnl_finite) - -_Float128 -__ieee754_ynl (int n, _Float128 x) -{ - u_int32_t se; - int32_t i, ix; - int32_t sign; - _Float128 a, b, temp, ret; - ieee854_long_double_shape_type u; - - u.value = x; - se = u.parts32.w0; - ix = se & 0x7fffffff; - - /* if Y(n,NaN) is NaN */ - if (ix >= 0x7fff0000) - { - if ((u.parts32.w0 & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) - return x + x; - } - if (x <= 0) - { - if (x == 0) - return ((n < 0 && (n & 1) != 0) ? 1 : -1) / L(0.0); - 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)); - { - SET_RESTORE_ROUNDL (FE_TONEAREST); - if (n == 1) - { - ret = sign * __ieee754_y1l (x); - goto out; - } - if (ix >= 0x7fff0000) - return zero; - if (ix >= 0x412D0000) - { /* 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 - */ - _Float128 s; - _Float128 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 & 0xffff0000; - for (i = 1; i < n && se != 0xffff0000; i++) - { - temp = b; - b = ((_Float128) (i + i) / x) * b - a; - u.value = b; - se = u.parts32.w0 & 0xffff0000; - a = temp; - } - } - /* If B is +-Inf, set up errno accordingly. */ - if (! isfinite (b)) - __set_errno (ERANGE); - if (sign > 0) - ret = b; - else - ret = -b; - } - out: - if (isinf (ret)) - ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX; - return ret; -} -strong_alias (__ieee754_ynl, __ynl_finite) |