* Return tangent function of x.
*
* kernel function:
- * __kernel_tanl ... tangent function on [-pi/4,pi/4]
- * __ieee754_rem_pio2l ... argument reduction routine
+ * __kernel_tanl ... tangent function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2l ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
- * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
- * in [-pi/4 , +pi/4], and let n = k mod 4.
- * We have
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
- * 0 S C T
- * 1 C -S -1/T
- * 2 -S -C T
- * 3 -C S -1/T
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* trig(NaN) is that NaN;
*
* Accuracy:
- * TRIG(x) returns trig(x) nearly rounded
+ * TRIG(x) returns trig(x) nearly rounded
*/
#include "trigl.h"
-#ifdef HAVE_SINL
-#ifdef HAVE_COSL
-#include "trigl.c"
-#endif
-#endif
-#include "isnanl.h"
/*
* ====================================================
* -1/tan (if k= -1) is returned.
*
* Algorithm
- * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
- * 2. if x < 2^-57, return x with inexact if x!=0.
- * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
+ * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ * 2. if x < 2^-57, return x with inexact if x!=0.
+ * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
* on [0,0.67433].
*
- * Note: tan(x+y) = tan(x) + tan'(x)*y
- * ~ tan(x) + (1+x*x)*y
- * Therefore, for better accuracy in computing tan(x+y), let
- * r = x^3 * R(x^2)
- * then
- * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
+ * Note: tan(x+y) = tan(x) + tan'(x)*y
+ * ~ tan(x) + (1+x*x)*y
+ * Therefore, for better accuracy in computing tan(x+y), let
+ * r = x^3 * R(x^2)
+ * then
+ * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
*
* 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
- * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
- * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
/* 1.000000000000000000000000000000000000000E0 */
-long double
+static long double
kernel_tanl (long double x, long double y, int iy)
{
long double z, r, v, w, s, u, u1;
- int flag, sign;
+ int invert = 0, sign;
sign = 1;
if (x < 0)
if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* x < 2**-57 */
{
if ((int) x == 0)
- { /* generate inexact */
- if (iy == -1 && x == 0.0)
- return 1.0L / fabs (x);
- else
- return (iy == 1) ? x : -1.0L / x;
- }
+ { /* generate inexact */
+ if (iy == -1 && x == 0.0)
+ return 1.0L / fabs (x);
+ else
+ return (iy == 1) ? x : -1.0L / x;
+ }
}
if (x >= 0.6743316650390625) /* |x| >= 0.6743316650390625 */
{
- flag = 1;
+ invert = 1;
z = pio4hi - x;
w = pio4lo - y;
r = y + z * (s * r + y);
r += TH * s;
w = x + r;
- if (flag)
+ if (invert)
{
v = (long double) iy;
w = (v - 2.0 * (x - (w * w / (w + v) - r)));
if (sign < 0)
- w = -w;
+ w = -w;
return w;
}
if (iy == 1)
return w;
else
- { /* if allow error up to 2 ulp,
- simply return -1.0/(x+r) here */
+ { /* if allow error up to 2 ulp,
+ simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
u1 = (double) w;
v = r - (u1 - x);
/* tanl(Inf) is NaN, tanl(0) is 0 */
else if (x + x == x)
- return x - x; /* NaN */
+ return x - x; /* NaN */
/* argument reduction needed */
else