diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_jn.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_jn.c | 347 |
1 files changed, 0 insertions, 347 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_jn.c b/sysdeps/ieee754/dbl-64/e_jn.c deleted file mode 100644 index 3fecf82f10..0000000000 --- a/sysdeps/ieee754/dbl-64/e_jn.c +++ /dev/null @@ -1,347 +0,0 @@ -/* @(#)e_jn.c 5.1 93/09/24 */ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* - * __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 overflow 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 double - invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ - two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ - one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ - -static const double zero = 0.00000000000000000000e+00; - -double -__ieee754_jn (int n, double x) -{ - int32_t i, hx, ix, lx, sgn; - double a, b, temp, di, ret; - double z, w; - - /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) - * Thus, J(-n,x) = J(n,-x) - */ - EXTRACT_WORDS (hx, lx, x); - ix = 0x7fffffff & hx; - /* if J(n,NaN) is NaN */ - if (__glibc_unlikely ((ix | ((u_int32_t) (lx | -lx)) >> 31) > 0x7ff00000)) - return x + x; - if (n < 0) - { - n = -n; - x = -x; - hx ^= 0x80000000; - } - if (n == 0) - return (__ieee754_j0 (x)); - if (n == 1) - return (__ieee754_j1 (x)); - sgn = (n & 1) & (hx >> 31); /* even n -- 0, odd n -- sign(x) */ - x = fabs (x); - { - SET_RESTORE_ROUND (FE_TONEAREST); - if (__glibc_unlikely ((ix | lx) == 0 || ix >= 0x7ff00000)) - /* if x is 0 or inf */ - return sgn == 1 ? -zero : zero; - else if ((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 */ - { /* (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 - */ - double s; - double c; - __sincos (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_sqrt (x); - } - else - { - a = __ieee754_j0 (x); - b = __ieee754_j1 (x); - for (i = 1; i < n; i++) - { - temp = b; - b = b * ((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 */ - b = zero; - else - { - temp = x * 0.5; b = temp; - for (a = one, i = 2; i <= n; i++) - { - a *= (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 */ - double t, v; - double q0, q1, h, tmp; int32_t k, m; - w = (n + n) / (double) x; h = 2.0 / (double) x; - q0 = w; z = w + h; q1 = w * z - 1.0; k = 1; - while (q1 < 1.0e9) - { - 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_log (fabs (v * tmp)); - if (tmp < 7.09782712893383973096e+02) - { - for (i = n - 1, di = (double) (i + i); i > 0; i--) - { - temp = b; - b *= di; - b = b / x - a; - a = temp; - di -= two; - } - } - else - { - for (i = n - 1, di = (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 > 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_j0 (x); - w = __ieee754_j1 (x); - if (fabs (z) >= fabs (w)) - b = (t * z / b); - else - b = (t * w / a); - } - } - if (sgn == 1) - ret = -b; - else - ret = b; - ret = math_narrow_eval (ret); - } - if (ret == 0) - { - ret = math_narrow_eval (__copysign (DBL_MIN, ret) * DBL_MIN); - __set_errno (ERANGE); - } - else - math_check_force_underflow (ret); - return ret; -} -strong_alias (__ieee754_jn, __jn_finite) - -double -__ieee754_yn (int n, double x) -{ - int32_t i, hx, ix, lx; - int32_t sign; - double a, b, temp, ret; - - EXTRACT_WORDS (hx, lx, x); - ix = 0x7fffffff & hx; - /* if Y(n,NaN) is NaN */ - if (__glibc_unlikely ((ix | ((u_int32_t) (lx | -lx)) >> 31) > 0x7ff00000)) - return x + x; - if (__glibc_unlikely ((ix | lx) == 0)) - return -HUGE_VAL + x; - /* -inf and overflow exception. */; - if (__glibc_unlikely (hx < 0)) - return zero / (zero * x); - sign = 1; - if (n < 0) - { - n = -n; - sign = 1 - ((n & 1) << 1); - } - if (n == 0) - return (__ieee754_y0 (x)); - { - SET_RESTORE_ROUND (FE_TONEAREST); - if (n == 1) - { - ret = sign * __ieee754_y1 (x); - goto out; - } - if (__glibc_unlikely (ix == 0x7ff00000)) - return zero; - if (ix >= 0x52D00000) /* x > 2**302 */ - { /* (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 - */ - double c; - double s; - __sincos (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_sqrt (x); - } - else - { - u_int32_t high; - a = __ieee754_y0 (x); - b = __ieee754_y1 (x); - /* quit if b is -inf */ - GET_HIGH_WORD (high, b); - for (i = 1; i < n && high != 0xfff00000; i++) - { - temp = b; - b = ((double) (i + i) / x) * b - a; - GET_HIGH_WORD (high, b); - 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 = __copysign (DBL_MAX, ret) * DBL_MAX; - return ret; -} -strong_alias (__ieee754_yn, __yn_finite) |