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/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include "libm.h"
static const float ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
*/
Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
float expm1f(float x)
{
float_t y, hi, lo, c, t, e, hxs, hfx, r1, twopk;
union {
float f;
uint32_t i;
} u = { x };
uint32_t hx = u.i & 0x7fffffff;
int k, sign = u.i >> 31;
/* filter out huge and non-finite argument */
if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
if (hx > 0x7f800000) /* NaN */
return x;
if (sign)
return -1;
if (hx > 0x42b17217) { /* x > log(FLT_MAX) */
x *= 0x1p127f;
return x;
}
}
/* argument reduction */
if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
if (!sign) {
hi = x - ln2_hi;
lo = ln2_lo;
k = 1;
} else {
hi = x + ln2_hi;
lo = -ln2_lo;
k = -1;
}
} else {
k = invln2 * x + (sign ? -0.5f : 0.5f);
t = k;
hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
lo = t * ln2_lo;
}
x = hi - lo;
c = (hi - x) - lo;
} else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
if (hx < 0x00800000)
FORCE_EVAL(x * x);
return x;
} else
k = 0;
/* x is now in primary range */
hfx = 0.5f * x;
hxs = x * hfx;
r1 = 1.0f + hxs * (Q1 + hxs * Q2);
t = 3.0f - r1 * hfx;
e = hxs * ((r1 - t) / (6.0f - x * t));
if (k == 0) /* c is 0 */
return x - (x * e - hxs);
e = x * (e - c) - c;
e -= hxs;
/* exp(x) ~ 2^k (x_reduced - e + 1) */
if (k == -1)
return 0.5f * (x - e) - 0.5f;
if (k == 1) {
if (x < -0.25f)
return -2.0f * (e - (x + 0.5f));
return 1.0f + 2.0f * (x - e);
}
u.i = (0x7f + k) << 23; /* 2^k */
twopk = u.f;
if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
y = x - e + 1.0f;
if (k == 128)
y = y * 2.0f * 0x1p127f;
else
y = y * twopk;
return y - 1.0f;
}
u.i = (0x7f - k) << 23; /* 2^-k */
if (k < 23)
y = (x - e + (1 - u.f)) * twopk;
else
y = (x - (e + u.f) + 1) * twopk;
return y;
}
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