tanh.c 996 字节
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#include "libm.h"

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/* 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)
 */
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double tanh(double x)
{
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	union {double f; uint64_t i;} u = {.f = x};
	uint32_t w;
	int sign;
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	double_t t;
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	/* x = |x| */
	sign = u.i >> 63;
	u.i &= (uint64_t)-1/2;
	x = u.f;
	w = u.i >> 32;
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	if (w > 0x3fe193ea) {
		/* |x| > log(3)/2 ~= 0.5493 or nan */
		if (w > 0x40340000) {
			/* |x| > 20 or nan */
			/* note: this branch avoids raising overflow */
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			t = 1 - 0/x;
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		} else {
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			t = expm1(2*x);
			t = 1 - 2/(t+2);
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		}
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	} else if (w > 0x3fd058ae) {
		/* |x| > log(5/3)/2 ~= 0.2554 */
		t = expm1(2*x);
		t = t/(t+2);
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	} else if (w >= 0x00100000) {
		/* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
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		t = expm1(-2*x);
		t = -t/(t+2);
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	} else {
		/* |x| is subnormal */
		/* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
		FORCE_EVAL((float)x);
		t = x;
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	}
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	return sign ? -t : t;
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}