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math: fix asin, atan, log1p, tanh to raise underflow on subnormal
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
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@ -23,8 +23,8 @@ double sinh(double x)
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t = expm1(absx);
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if (w < 0x3ff00000) {
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if (w < 0x3ff00000 - (26<<20))
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/* note: inexact is raised by expm1 */
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/* note: this branch avoids underflow */
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/* note: inexact and underflow are raised by expm1 */
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/* note: this branch avoids spurious underflow */
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return x;
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return h*(2*t - t*t/(t+1));
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}
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