doc: use ASCII in .texi files where UTF-8 isn't needed

[gnulib.git] / lib / tanl.c

diff --git a/lib/tanl.c b/lib/tanl.c
index 60e6637..ae70884 100644 (file)
--- a/lib/tanl.c
+++ b/lib/tanl.c
@@ -19,25 +19,38 @@
 /* Specification.  */
 #include <math.h>
 
+#if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
+
+long double
+tanl (long double x)
+{
+  return tan (x);
+}
+
+#else
+
+/* Code based on glibc/sysdeps/ieee754/ldbl-128/s_tanl.c
+   and           glibc/sysdeps/ieee754/ldbl-128/k_tanl.c.  */
+
 /* tanl(x)
  * 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:
@@ -46,15 +59,10 @@
  *      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 "trigl.h"
 
 /*
  * ====================================================
@@ -80,21 +88,21 @@
  * -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)))
  */
 
 
@@ -120,7 +128,7 @@ static const long double
   /* 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;
@@ -137,12 +145,12 @@ kernel_tanl (long double x, long double y, int iy)
   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 */
     {
@@ -167,14 +175,14 @@ kernel_tanl (long double x, long double y, int iy)
       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);
@@ -202,7 +210,7 @@ tanl (long double 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
@@ -213,16 +221,18 @@ tanl (long double x)
     }
 }
 
+#endif
+
 #if 0
 int
 main (void)
 {
-  printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492));
-  printf ("%.16Lg\n", tanl(-0.7853981633974483096156608458198757210492));
-  printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 *3));
-  printf ("%.16Lg\n", tanl(-0.7853981633974483096156608458198757210492 *31));
-  printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 / 2));
-  printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 * 3/2));
-  printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 * 5/2));
+  printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492));
+  printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492));
+  printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 *3));
+  printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492 *31));
+  printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 / 2));
+  printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 3/2));
+  printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 5/2));
 }
 #endif