43 * expm1l(-2x) + 2
44 * 2
45 * 1 <= x <= threshold : tanhl(x) := 1 - ---------------
46 * expm1l(2x) + 2
47 * threshold < x <= INF : tanhl(x) := 1.
48 *
49 * where
50 * single : small = 1.e-5 threshold = 11.0
51 * double : small = 1.e-10 threshold = 22.0
52 * quad : small = 1.e-20 threshold = 45.0
53 *
54 * Note: threshold was chosen so that
55 * fl(1.0+2/(expm1(2*threshold)+2)) == 1.
56 *
57 * Special cases:
58 * tanhl(NaN) is NaN;
59 * only tanhl(0.0)=0.0 is exact for finite argument.
60 */
61
62 #include "libm.h"
63
64 static const long double small = 1.0e-20L, one = 1.0, two = 2.0,
65 #ifndef lint
66 big = 1.0e+20L,
67 #endif
68 threshold = 45.0L;
69
70 long double
71 tanhl(long double x) {
72 long double t, y, z;
73 int signx;
74
75 if (isnanl(x))
76 return (x + x); /* x is NaN */
77 signx = signbitl(x);
78 t = fabsl(x);
79 z = one;
80 if (t <= threshold) {
81 if (t > one)
82 z = one - two / (expm1l(t + t) + two);
83 else if (t > small) {
84 y = expm1l(-t - t);
85 z = -y / (y + two);
86 } else {
87 #ifndef lint
88 volatile long double dummy = t + big;
89 /* inexact if t != 0 */
90 #endif
91 return (x);
92 }
93 } else if (!finitel(t))
94 return (copysignl(one, x));
95 else
96 return (signx ? -z + small * small : z - small * small);
97 return (signx ? -z : z);
98 }
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43 * expm1l(-2x) + 2
44 * 2
45 * 1 <= x <= threshold : tanhl(x) := 1 - ---------------
46 * expm1l(2x) + 2
47 * threshold < x <= INF : tanhl(x) := 1.
48 *
49 * where
50 * single : small = 1.e-5 threshold = 11.0
51 * double : small = 1.e-10 threshold = 22.0
52 * quad : small = 1.e-20 threshold = 45.0
53 *
54 * Note: threshold was chosen so that
55 * fl(1.0+2/(expm1(2*threshold)+2)) == 1.
56 *
57 * Special cases:
58 * tanhl(NaN) is NaN;
59 * only tanhl(0.0)=0.0 is exact for finite argument.
60 */
61
62 #include "libm.h"
63 #include "longdouble.h"
64
65 static const long double small = 1.0e-20L, one = 1.0, two = 2.0,
66 #ifndef lint
67 big = 1.0e+20L,
68 #endif
69 threshold = 45.0L;
70
71 long double
72 tanhl(long double x) {
73 long double t, y, z;
74 int signx;
75 volatile long double dummy;
76
77 if (isnanl(x))
78 return (x + x); /* x is NaN */
79 signx = signbitl(x);
80 t = fabsl(x);
81 z = one;
82 if (t <= threshold) {
83 if (t > one)
84 z = one - two / (expm1l(t + t) + two);
85 else if (t > small) {
86 y = expm1l(-t - t);
87 z = -y / (y + two);
88 } else {
89 #ifndef lint
90 dummy = t + big;
91 /* inexact if t != 0 */
92 #endif
93 return (x);
94 }
95 } else if (!finitel(t))
96 return (copysignl(one, x));
97 else
98 return (signx ? -z + small * small : z - small * small);
99 return (signx ? -z : z);
100 }
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