#include "libm.h"
static const float
-one = 1.0,
-huge = 1.0e+30,
-tiny = 1.0e-30,
-o_threshold = 8.8721679688e+01, /* 0x42b17180 */
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
float expm1f(float x)
{
- float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
- int32_t k,xsb;
- uint32_t hx;
-
- GET_FLOAT_WORD(hx, x);
- xsb = hx&0x80000000; /* sign bit of x */
- hx &= 0x7fffffff; /* high word of |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 >= 0x42b17218) { /* if |x|>=88.721... */
- if (hx > 0x7f800000) /* NaN */
- return x+x;
- if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
- return xsb==0 ? x : -1.0;
- if (x > o_threshold)
- return huge*huge; /* overflow */
- }
- if (xsb != 0) { /* x < -27*ln2 */
- /* raise inexact */
- if (x+tiny < 0.0f)
- return tiny-one; /* return -1 */
+ 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 (xsb == 0) {
+ if (!sign) {
hi = x - ln2_hi;
lo = ln2_lo;
k = 1;
k = -1;
}
} else {
- k = invln2*x + (xsb==0 ? 0.5f : -0.5f);
+ 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;
}
- STRICT_ASSIGN(float, x, hi - lo);
+ x = hi-lo;
c = (hi-x)-lo;
} else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
- t = huge+x; /* return x with inexact flags when x!=0 */
- return x - (t-(huge+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 = one+hxs*(Q1+hxs*Q2);
+ 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);
- SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23)); /* 2^k */
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 one + 2.0f*(x-e);
+ return 1.0f + 2.0f*(x-e);
}
- if (k <= -2 || k > 56) { /* suffice to return exp(x)-1 */
- y = one - (e - x);
+ 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 - one;
- }
- t = one;
- if (k < 23) {
- SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
- y = t - (e - x);
- y = y*twopk;
- } else {
- SET_FLOAT_WORD(t, (0x7f-k)<<23); /* 2^-k */
- y = x - (e + t);
- y += one;
- 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;
}