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math: fix asin, atan, log1p, tanh to raise underflow on subnormal

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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
This commit is contained in:
Szabolcs Nagy
2013-08-15 10:14:46 +00:00
parent cd18dc8525
commit c599f4f4d7
9 changed files with 39 additions and 26 deletions
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14
src/math/tanh.c
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@ -9,7 +9,7 @@ double tanh(double x)
union {double f; uint64_t i;} u = {.f = x};
uint32_t w;
int sign;
double t;
double_t t;
/* x = |x| */
sign = u.i >> 63;
@ -22,8 +22,7 @@ double tanh(double x)
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);
t = 1 - 0/x;
} else {
t = expm1(2*x);
t = 1 - 2/(t+2);
@ -32,10 +31,15 @@ double tanh(double x)
/* |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] */
} else if (w >= 0x00100000) {
/* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
t = expm1(-2*x);
t = -t/(t+2);
} else {
/* |x| is subnormal */
/* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
FORCE_EVAL((float)x);
t = x;
}
return sign ? -t : t;
}