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c599f4f4d7
for these functions f(x)=x for small inputs, because f(0)=0 and f'(0)=1, but for subnormal values they should raise the underflow flag (required by annex F), if they are approximated by a polynomial around 0 then spurious underflow should be avoided (not required by annex F) all these functions should raise inexact flag for small x if x!=0, but it's not required by the standard and it does not seem a worthy goal, so support for it is removed in some cases. raising underflow: - x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0 - x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0 - in case of double subnormal x, store x as float - in case of float subnormal x, store x*x as float
46 lines
996 B
C
46 lines
996 B
C
#include "libm.h"
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/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
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* = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
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* = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
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*/
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double tanh(double x)
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{
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union {double f; uint64_t i;} u = {.f = x};
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uint32_t w;
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int sign;
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double_t t;
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/* x = |x| */
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sign = u.i >> 63;
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u.i &= (uint64_t)-1/2;
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x = u.f;
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w = u.i >> 32;
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if (w > 0x3fe193ea) {
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/* |x| > log(3)/2 ~= 0.5493 or nan */
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if (w > 0x40340000) {
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/* |x| > 20 or nan */
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/* 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);
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t = 1 - 2/(t+2);
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}
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} else if (w > 0x3fd058ae) {
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/* |x| > log(5/3)/2 ~= 0.2554 */
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t = expm1(2*x);
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t = t/(t+2);
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} else if (w >= 0x00100000) {
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/* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
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t = expm1(-2*x);
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t = -t/(t+2);
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} else {
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/* |x| is subnormal */
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/* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
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FORCE_EVAL((float)x);
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t = x;
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}
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return sign ? -t : t;
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}
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