inline void eval_ldexp(float128_backend& result, const float128_backend& arg, int exp)
{
result.value() = ldexpq(arg.value(), exp);
}
__float128
expm1q (__float128 x)
{
__float128 px, qx, xx;
int32_t ix, sign;
ieee854_float128 u;
int k;
/* Detect infinity and NaN. */
u.value = x;
ix = u.words32.w0;
sign = ix & 0x80000000;
ix &= 0x7fffffff;
if (!sign && ix >= 0x40060000)
{
/* If num is positive and exp >= 6 use plain exp. */
return expq (x);
}
if (ix >= 0x7fff0000)
{
/* Infinity. */
if (((ix & 0xffff) | u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
{
if (sign)
return -1.0Q;
else
return x;
}
/* NaN. No invalid exception. */
return x;
}
/* expm1(+- 0) = +- 0. */
if ((ix == 0) && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
return x;
/* Overflow. */
if (x > maxlog)
{
errno = ERANGE;
return (HUGE_VALQ * HUGE_VALQ);
}
/* Minimum value. */
if (x < minarg)
return (4.0/HUGE_VALQ - 1.0Q);
/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
xx = C1 + C2; /* ln 2. */
px = floorq (0.5 + x / xx);
k = px;
/* remainder times ln 2 */
x -= px * C1;
x -= px * C2;
/* Approximate exp(remainder ln 2). */
px = (((((((P7 * x
+ P6) * x
+ P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x;
qx = (((((((x
+ Q7) * x
+ Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
xx = x * x;
qx = x + (0.5 * xx + xx * px / qx);
/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
We have qx = exp(remainder ln 2) - 1, so
exp(x) - 1 = 2^k (qx + 1) - 1
= 2^k qx + 2^k - 1. */
px = ldexpq (1.0Q, k);
x = px * qx + (px - 1.0);
return x;
}
