Fixed tanh(-0.0) on ia64 and optimizeed tanh(x) for 2**-55 <= |x| <
2**-28 as a side effect, by merging with the float precision version of tanh() and the double precision version of sinh(). For tiny x, tanh(x) ~= x, and we used the expression x*(one+x) to return this value (x) and set the inexact flag iff x != 0. This doesn't work on ia64 since gcc -O does the dubious optimization x*(one+x) = x+x*x so as to use fma, so the sign of -0.0 was lost. Instead, handle tiny x in the same as sinh(), although this is imperfect: - return x directly and set the inexact flag in a less efficient way. - increased the threshold for non-tinyness from 2**-55 to 2**-28 so that many more cases are optimized than are pessimized. Updated some comments and fixed bugs in others (ranges for half-open intervals mostly had the open end backwards, and there were nearby style bugs).
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svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=160122
@ -24,14 +24,14 @@ static char rcsid[] = "$FreeBSD$";
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* x -x
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* e + e
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* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
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* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
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* 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
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* -t
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* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
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* 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
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* t + 2
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* 2
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* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
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* 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
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* t + 2
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* 22.0 < x <= INF : tanh(x) := 1.
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* 22 <= x <= INF : tanh(x) := 1.
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*
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* Special cases:
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* tanh(NaN) is NaN;
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@ -41,7 +41,7 @@ static char rcsid[] = "$FreeBSD$";
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#include "math.h"
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#include "math_private.h"
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static const double one=1.0, two=2.0, tiny = 1.0e-300;
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static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
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double
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tanh(double x)
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@ -49,7 +49,6 @@ tanh(double x)
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double t,z;
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int32_t jx,ix;
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/* High word of |x|. */
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GET_HIGH_WORD(jx,x);
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ix = jx&0x7fffffff;
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@ -61,8 +60,9 @@ tanh(double x)
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/* |x| < 22 */
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if (ix < 0x40360000) { /* |x|<22 */
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if (ix<0x3c800000) /* |x|<2**-55 */
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return x*(one+x); /* tanh(small) = small */
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if (ix<0x3e300000) { /* |x|<2**-28 */
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if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
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}
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if (ix>=0x3ff00000) { /* |x|>=1 */
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t = expm1(two*fabs(x));
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z = one - two/(t+two);
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@ -70,9 +70,9 @@ tanh(double x)
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t = expm1(-two*fabs(x));
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z= -t/(t+two);
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}
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/* |x| > 22, return +-1 */
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/* |x| >= 22, return +-1 */
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} else {
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z = one - tiny; /* raised inexact flag */
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z = one - tiny; /* raise inexact flag */
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}
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return (jx>=0)? z: -z;
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}
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