-/* origin: FreeBSD /usr/src/lib/msun/src/s_tanh.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* Tanh(x)
- * Return the Hyperbolic Tangent of x
- *
- * Method :
- * x -x
- * e - e
- * 0. tanh(x) is defined to be -----------
- * x -x
- * e + e
- * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
- * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
- * -t
- * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
- * t + 2
- * 2
- * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
- * t + 2
- * 22 <= x <= INF : tanh(x) := 1.
- *
- * Special cases:
- * tanh(NaN) is NaN;
- * only tanh(0)=0 is exact for finite argument.
- */
-
#include "libm.h"
-static const double tiny = 1.0e-300, huge = 1.0e300;
-
+/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
+ * = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
+ * = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
+ */
double tanh(double x)
{
- double t,z;
- int32_t jx,ix;
-
- GET_HIGH_WORD(jx, x);
- ix = jx & 0x7fffffff;
+ union {double f; uint64_t i;} u = {.f = x};
+ uint32_t w;
+ int sign;
+ double t;
- /* x is INF or NaN */
- if (ix >= 0x7ff00000) {
- if (jx >= 0)
- return 1.0f/x + 1.0f; /* tanh(+-inf)=+-1 */
- else
- return 1.0f/x - 1.0f; /* tanh(NaN) = NaN */
- }
+ /* x = |x| */
+ sign = u.i >> 63;
+ u.i &= (uint64_t)-1/2;
+ x = u.f;
+ w = u.i >> 32;
- if (ix < 0x40360000) { /* |x| < 22 */
- if (ix < 0x3e300000) { /* |x| < 2**-28 */
- /* tanh(tiny) = tiny with inexact */
- if (huge+x > 1.0f)
- return x;
- }
- if (ix >= 0x3ff00000) { /* |x| >= 1 */
- t = expm1(2.0f*fabs(x));
- z = 1.0f - 2.0f/(t+2.0f);
+ if (w > 0x3fe193ea) {
+ /* |x| > log(3)/2 ~= 0.5493 or nan */
+ if (w > 0x40340000) {
+ /* |x| > 20 or nan */
+ /* note: this branch avoids raising overflow */
+ /* raise inexact if x!=+-inf and handle nan */
+ t = 1 + 0/(x + 0x1p-120f);
} else {
- t = expm1(-2.0f*fabs(x));
- z= -t/(t+2.0f);
+ t = expm1(2*x);
+ t = 1 - 2/(t+2);
}
- } else { /* |x| >= 22, return +-1 */
- z = 1.0f - tiny; /* raise inexact */
+ } else if (w > 0x3fd058ae) {
+ /* |x| > log(5/3)/2 ~= 0.2554 */
+ t = expm1(2*x);
+ t = t/(t+2);
+ } else {
+ /* |x| is small, up to 2ulp error in [0.1,0.2554] */
+ t = expm1(-2*x);
+ t = -t/(t+2);
}
- return jx >= 0 ? z : -z;
+ return sign ? -t : t;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_tanhf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
#include "libm.h"
-static const float
-tiny = 1.0e-30,
-huge = 1.0e30;
-
float tanhf(float x)
{
- float t,z;
- int32_t jx,ix;
+ union {float f; uint32_t i;} u = {.f = x};
+ uint32_t w;
+ int sign;
+ float t;
- GET_FLOAT_WORD(jx, x);
- ix = jx & 0x7fffffff;
+ /* x = |x| */
+ sign = u.i >> 31;
+ u.i &= 0x7fffffff;
+ x = u.f;
+ w = u.i;
- /* x is INF or NaN */
- if(ix >= 0x7f800000) {
- if (jx >= 0)
- return 1.0f/x + 1.0f; /* tanh(+-inf)=+-1 */
- else
- return 1.0f/x - 1.0f; /* tanh(NaN) = NaN */
- }
-
- if (ix < 0x41100000) { /* |x| < 9 */
- if (ix < 0x39800000) { /* |x| < 2**-12 */
- /* tanh(tiny) = tiny with inexact */
- if (huge+x > 1.0f)
- return x;
- }
- if (ix >= 0x3f800000) { /* |x|>=1 */
- t = expm1f(2.0f*fabsf(x));
- z = 1.0f - 2.0f/(t+2.0f);
+ if (w > 0x3f0c9f54) {
+ /* |x| > log(3)/2 ~= 0.5493 or nan */
+ if (w > 0x41200000) {
+ /* |x| > 10 */
+ t = 1 + 0/(x + 0x1p-120f);
} else {
- t = expm1f(-2.0f*fabsf(x));
- z = -t/(t+2.0f);
+ t = expm1f(2*x);
+ t = 1 - 2/(t+2);
}
- } else { /* |x| >= 9, return +-1 */
- z = 1.0f - tiny; /* raise inexact */
+ } else if (w > 0x3e82c578) {
+ /* |x| > log(5/3)/2 ~= 0.2554 */
+ t = expm1f(2*x);
+ t = t/(t+2);
+ } else {
+ /* |x| is small */
+ t = expm1f(-2*x);
+ t = -t/(t+2);
}
- return jx >= 0 ? z : -z;
+ return sign ? -t : t;
}
-/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_tanhl.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* tanhl(x)
- * Return the Hyperbolic Tangent of x
- *
- * Method :
- * x -x
- * e - e
- * 0. tanhl(x) is defined to be -----------
- * x -x
- * e + e
- * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
- * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
- * -t
- * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
- * t + 2
- * 2
- * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
- * t + 2
- * 23.0 < x <= INF : tanhl(x) := 1.
- *
- * Special cases:
- * tanhl(NaN) is NaN;
- * only tanhl(0)=0 is exact for finite argument.
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return tanh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double tiny = 1.0e-4900L;
-
long double tanhl(long double x)
{
- long double t,z;
- int32_t se;
- uint32_t jj0,jj1,ix;
+ union {
+ long double f;
+ struct{uint64_t m; uint16_t se; uint16_t pad;} i;
+ } u = {.f = x};
+ unsigned ex = u.i.se & 0x7fff;
+ unsigned sign = u.i.se & 0x8000;
+ uint32_t w;
+ long double t;
- /* High word of |x|. */
- GET_LDOUBLE_WORDS(se, jj0, jj1, x);
- ix = se & 0x7fff;
-
- /* x is INF or NaN */
- if (ix == 0x7fff) {
- /* for NaN it's not important which branch: tanhl(NaN) = NaN */
- if (se & 0x8000)
- return 1.0/x-1.0; /* tanhl(-inf)= -1; */
- return 1.0/x+1.0; /* tanhl(+inf)= +1 */
- }
+ /* x = |x| */
+ u.i.se = ex;
+ x = u.f;
+ w = u.i.m >> 32;
- /* |x| < 23 */
- if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {
- if ((ix|jj0|jj1) == 0) /* x == +- 0 */
- return x;
- if (ix < 0x3fc8) /* |x| < 2**-55 */
- return x*(1.0+tiny); /* tanh(small) = small */
- if (ix >= 0x3fff) { /* |x| >= 1 */
- t = expm1l(2.0*fabsl(x));
- z = 1.0 - 2.0/(t+2.0);
+ if (ex > 0x3ffe || (ex == 0x3ffe && w > 0x8c9f53d5)) {
+ /* |x| > log(3)/2 ~= 0.5493 or nan */
+ if (ex >= 0x3fff+5) {
+ /* |x| >= 32 */
+ t = 1 + 0/(x + 0x1p-120f);
} else {
- t = expm1l(-2.0*fabsl(x));
- z = -t/(t+2.0);
+ t = expm1l(2*x);
+ t = 1 - 2/(t+2);
}
- /* |x| > 23, return +-1 */
+ } else if (ex > 0x3ffd || (ex == 0x3ffd && w > 0x82c577d4)) {
+ /* |x| > log(5/3)/2 ~= 0.2554 */
+ t = expm1l(2*x);
+ t = t/(t+2);
} else {
- z = 1.0 - tiny; /* raise inexact flag */
+ /* |x| is small */
+ t = expm1l(-2*x);
+ t = -t/(t+2);
}
- return se & 0x8000 ? -z : z;
+ return sign ? -t : t;
}
#endif
projects / oweals / musl.git / commitdiff