float
__ieee754_expf (float x)
{
static const float himark = 88.72283935546875;
static const float lomark = -103.972084045410;
/* Check for usual case. */
if (isless (x, himark) && isgreater (x, lomark))
{
static const float THREEp42 = 13194139533312.0;
static const float THREEp22 = 12582912.0;
/* 1/ln(2). */
#undef M_1_LN2
static const float M_1_LN2 = 1.44269502163f;
/* ln(2) */
#undef M_LN2
static const double M_LN2 = .6931471805599452862;
int tval;
double x22, t, result, dx;
float n, delta;
union ieee754_double ex2_u;
{
SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
/* Calculate n. */
n = x * M_1_LN2 + THREEp22;
n -= THREEp22;
dx = x - n*M_LN2;
/* Calculate t/512. */
t = dx + THREEp42;
t -= THREEp42;
dx -= t;
/* Compute tval = t. */
tval = (int) (t * 512.0);
if (t >= 0)
delta = - __exp_deltatable[tval];
else
delta = __exp_deltatable[-tval];
/* Compute ex2 = 2^n e^(t/512+delta[t]). */
ex2_u.d = __exp_atable[tval+177];
ex2_u.ieee.exponent += (int) n;
/* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
with maximum error in [-2^-10-2^-28,2^-10+2^-28]
less than 5e-11. */
x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
}
/* Return result. */
result = x22 * ex2_u.d + ex2_u.d;
return (float) result;
}
/* Exceptional cases: */
else if (isless (x, himark))
{
if (isinf (x))
/* e^-inf == 0, with no error. */
return 0;
else
/* Underflow */
return TWOM100 * TWOM100;
}
else
/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
return TWO127*x;
}
float
__ieee754_exp2f (float x)
{
static const float himark = (float) FLT_MAX_EXP;
static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1);
/* Check for usual case. */
if (isless (x, himark) && isgreaterequal (x, lomark))
{
static const float THREEp14 = 49152.0;
int tval, unsafe;
float rx, x22, result;
union ieee754_float ex2_u, scale_u;
if (fabsf (x) < FLT_EPSILON / 4.0f)
return 1.0f + x;
{
SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
/* 1. Argument reduction.
Choose integers ex, -128 <= t < 128, and some real
-1/512 <= x1 <= 1/512 so that
x = ex + t/512 + x1.
First, calculate rx = ex + t/256. */
rx = x + THREEp14;
rx -= THREEp14;
x -= rx; /* Compute x=x1. */
/* Compute tval = (ex*256 + t)+128.
Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %;
and /-round-to-nearest not the usual c integer /]. */
tval = (int) (rx * 256.0f + 128.0f);
/* 2. Adjust for accurate table entry.
Find e so that
x = ex + t/256 + e + x2
where -7e-4 < e < 7e-4, and
(float)(2^(t/256+e))
is accurate to one part in 2^-64. */
/* 'tval & 255' is the same as 'tval%256' except that it's always
positive.
Compute x = x2. */
x -= __exp2f_deltatable[tval & 255];
/* 3. Compute ex2 = 2^(t/255+e+ex). */
ex2_u.f = __exp2f_atable[tval & 255];
tval >>= 8;
/* x2 is an integer multiple of 2^-30; avoid intermediate
underflow from the calculation of x22 * x. */
unsafe = abs(tval) >= -FLT_MIN_EXP - 32;
ex2_u.ieee.exponent += tval >> unsafe;
scale_u.f = 1.0;
scale_u.ieee.exponent += tval - (tval >> unsafe);
/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
less than 1.3e-10. */
x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
}
/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
result = x22 * x + ex2_u.f;
if (!unsafe)
return result;
else
{
result *= scale_u.f;
math_check_force_underflow_nonneg (result);
return result;
}
}
/* Exceptional cases: */
else if (isless (x, himark))
