14  * jn(n, x), yn(n, x)
16  * of order n
19  *	y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
20  *	y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
21  * Note 2. About jn(n,x), yn(n,x)
22  *	For n=0, j0(x) is called,
23  *	for n=1, j1(x) is called,
24  *	for n<x, forward recursion us used starting
26  *	for n>x, a continued fraction approximation to
27  *	j(n,x)/j(n-1,x) is evaluated and then backward
29  *	for j(n,x). The resulting value of j(0,x) is
31  *	supposed value of j(n,x).
33  *	yn(n,x) is similar in all respects, except
35  *	values of n>1.
51 jn64(int n, __float64 x)  in jn64()  argument
63     /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)  in jn64()
64      * Thus, J(-n,x) = J(n,-x)  in jn64()
69     if (n < 0) {  in jn64()
70         n = -n;  in jn64()
74     if (n == 0)  in jn64()
76     if (n == 1)  in jn64()
78     sgn = (n & 1) & (hx >> 31); /* even n -- 0, odd n -- sign(x) */  in jn64()
82     else if ((__float64)n <= x) {  in jn64()
83         /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */  in jn64()
85             /* (x >> n**2)  in jn64()
86      *	    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)  in jn64()
87      *	    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)  in jn64()
89      *		xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then  in jn64()
91      *		   n	sin(xn)*sqt2	cos(xn)*sqt2  in jn64()
98             switch (n & 3) {  in jn64()
117             for (i = 1; i < n; i++) {  in jn64()
125             /* x is tiny, return the first Taylor expansion of J(n,x)  in jn64()
126      * J(n,x) = 1/n!*(x/2)^n  - ...  in jn64()
128             if (n > 33) /* underflow */  in jn64()
133                 for (a = one, i = 2; i <= n; i++) {  in jn64()
134                     a *= (__float64)i; /* a = n! */  in jn64()
135                     b *= temp; /* b = (x/2)^n */  in jn64()
142 		 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....  in jn64()
143 		 *			2n  - 2(n+1) - 2(n+2)  in jn64()
147 		 *			2n   2(n+1)   2(n+2)  in jn64()
151 		 * Let w = 2n/x and h=2/x, then the above quotient  in jn64()
172             w = (n + n) / (__float64)x;  in jn64()
185             m = n + n;  in jn64()
186             for (t = zero, i = 2 * (n + k); i >= m; i -= 2)  in jn64()
190             /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)  in jn64()
191 		 *  Hence, if n*(log(2n/x)) > ...  in jn64()
198             tmp = n;  in jn64()
202                 for (i = n - 1, di = (__float64)(i + i); i > 0; i--) {  in jn64()
210                 for (i = n - 1, di = (__float64)(i + i); i > 0; i--) {  in jn64()
236 yn64(int n, __float64 x)  in _MATH_ALIAS_d_id()
244     /* if Y(n,NaN) is NaN */  in _MATH_ALIAS_d_id()
259     if (n < 0) {  in _MATH_ALIAS_d_id()
260         n = -n;  in _MATH_ALIAS_d_id()
261         sign = 1 - ((n & 1) << 1);  in _MATH_ALIAS_d_id()
263     if (n == 0)  in _MATH_ALIAS_d_id()
265     if (n == 1)  in _MATH_ALIAS_d_id()
269         /* (x >> n**2)  in _MATH_ALIAS_d_id()
270      *	    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)  in _MATH_ALIAS_d_id()
271      *	    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)  in _MATH_ALIAS_d_id()
273      *		xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then  in _MATH_ALIAS_d_id()
275      *		   n	sin(xn)*sqt2	cos(xn)*sqt2  in _MATH_ALIAS_d_id()
282         switch (n & 3) {  in _MATH_ALIAS_d_id()
304         for (i = 1; i < n && high != 0xfff00000; i++) {  in _MATH_ALIAS_d_id()