Print this page
11175 libm should use signbit() correctly
11188 c99 math macros should return strictly backward compatible values
*** 66,76 ****
two = 2.0L,
zero = 0.0L,
one = 1.0L;
GENERIC
! jnl(n, x) int n; GENERIC x; {
int i, sgn;
GENERIC a, b, temp, z, w;
/*
* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
--- 66,77 ----
two = 2.0L,
zero = 0.0L,
one = 1.0L;
GENERIC
! jnl(int n, GENERIC x)
! {
int i, sgn;
GENERIC a, b, temp, z, w;
/*
* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
*** 111,140 ****
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch (n&3) {
! case 0: temp = cosl(x)+sinl(x); break;
! case 1: temp = -cosl(x)+sinl(x); break;
! case 2: temp = -cosl(x)-sinl(x); break;
! case 3: temp = cosl(x)-sinl(x); break;
}
b = invsqrtpi*temp/sqrtl(x);
} else {
a = j0l(x);
b = j1l(x);
for (i = 1; i < n; i++) {
temp = b;
! b = b*((GENERIC)(i+i)/x) - a; /* avoid underflow */
a = temp;
}
}
} else {
if (x < 1e-17L) { /* use J(n,x) = 1/n!*(x/2)^n */
b = powl(0.5L*x, (GENERIC)n);
if (b != zero) {
! for (a = one, i = 1; i <= n; i++) a *= (GENERIC)i;
b = b/a;
}
} else {
/* use backward recurrence */
/*
--- 112,151 ----
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch (n&3) {
! case 0:
! temp = cosl(x)+sinl(x);
! break;
! case 1:
! temp = -cosl(x)+sinl(x);
! break;
! case 2:
! temp = -cosl(x)-sinl(x);
! break;
! case 3:
! temp = cosl(x)-sinl(x);
! break;
}
b = invsqrtpi*temp/sqrtl(x);
} else {
a = j0l(x);
b = j1l(x);
for (i = 1; i < n; i++) {
temp = b;
! /* avoid underflow */
! b = b*((GENERIC)(i+i)/x) - a;
a = temp;
}
}
} else {
if (x < 1e-17L) { /* use J(n,x) = 1/n!*(x/2)^n */
b = powl(0.5L*x, (GENERIC)n);
if (b != zero) {
! for (a = one, i = 1; i <= n; i++)
! a *= (GENERIC)i;
b = b/a;
}
} else {
/* use backward recurrence */
/*
*** 163,185 ****
* 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 quaduple
*/
! /* determin k */
GENERIC t, v;
! double q0, q1, h, tmp; int 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 < 1.0e17) {
! 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)) > ...
--- 174,203 ----
* 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 quaduple
*/
! /* determine k */
GENERIC t, v;
! double q0, q1, h, tmp;
! int 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 < 1.0e17) {
! 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)) > ...
*** 211,228 ****
}
}
b = (t*j0l(x)/b);
}
}
! if (sgn == 1)
return (-b);
else
return (b);
}
! GENERIC ynl(n, x)
! int n; GENERIC x; {
int i;
int sign;
GENERIC a, b, temp;
if (x != x)
--- 229,247 ----
}
}
b = (t*j0l(x)/b);
}
}
! if (sgn != 0)
return (-b);
else
return (b);
}
! GENERIC
! ynl(int n, GENERIC x)
! {
int i;
int sign;
GENERIC a, b, temp;
if (x != x)
*** 243,270 ****
if (n == 1)
return (sign*y1l(x));
if (!finitel(x))
return (zero);
! if (x > 1.0e91L) { /* 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
*/
switch (n&3) {
! case 0: temp = sinl(x)-cosl(x); break;
! case 1: temp = -sinl(x)-cosl(x); break;
! case 2: temp = -sinl(x)+cosl(x); break;
! case 3: temp = sinl(x)+cosl(x); break;
}
b = invsqrtpi*temp/sqrtl(x);
} else {
a = y0l(x);
b = y1l(x);
--- 262,299 ----
if (n == 1)
return (sign*y1l(x));
if (!finitel(x))
return (zero);
! if (x > 1.0e91L) {
! /*
! * 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
*/
switch (n&3) {
! case 0:
! temp = sinl(x)-cosl(x);
! break;
! case 1:
! temp = -sinl(x)-cosl(x);
! break;
! case 2:
! temp = -sinl(x)+cosl(x);
! break;
! case 3:
! temp = sinl(x)+cosl(x);
! break;
}
b = invsqrtpi*temp/sqrtl(x);
} else {
a = y0l(x);
b = y1l(x);