#include "libm.h"
static const float
-one = 1.0,
-halF[2] = {0.5,-0.5,},
-huge = 1.0e+30,
-o_threshold = 8.8721679688e+01, /* 0x42b17180 */
-u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
-ln2HI[2] = { 6.9314575195e-01, /* 0x3f317200 */
- -6.9314575195e-01,},/* 0xbf317200 */
-ln2LO[2] = { 1.4286067653e-06, /* 0x35bfbe8e */
- -1.4286067653e-06,},/* 0xb5bfbe8e */
-invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
+half[2] = {0.5,-0.5},
+ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
+ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
+invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
*/
-P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
-P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
-
-static const volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
+P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
+P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
float expf(float x)
{
- float y,hi=0.0,lo=0.0,c,t,twopk;
- int32_t k=0,xsb;
+ float_t hi, lo, c, xx, y;
+ int k, sign;
uint32_t hx;
GET_FLOAT_WORD(hx, x);
- xsb = (hx>>31)&1; /* sign bit of x */
+ sign = hx >> 31; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
- /* filter out non-finite argument */
- if (hx >= 0x42b17218) { /* if |x|>=88.721... */
- if (hx > 0x7f800000) /* NaN */
- return x+x;
- if (hx == 0x7f800000) /* exp(+-inf)={inf,0} */
- return xsb==0 ? x : 0.0;
- if (x > o_threshold)
- return huge*huge; /* overflow */
- if (x < u_threshold)
- return twom100*twom100; /* underflow */
+ /* special cases */
+ if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */
+ if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */
+ /* overflow */
+ x *= 0x1p127f;
+ return x;
+ }
+ if (sign) {
+ /* underflow */
+ FORCE_EVAL(-0x1p-149f/x);
+ if (hx >= 0x42cff1b5) /* x <= -103.972084f */
+ return 0;
+ }
}
/* argument reduction */
- if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
- if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
- hi = x-ln2HI[xsb];
- lo = ln2LO[xsb];
- k = 1 - xsb - xsb;
- } else {
- k = invln2*x + halF[xsb];
- t = k;
- hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
- lo = t*ln2LO[0];
- }
- STRICT_ASSIGN(float, x, hi - lo);
- } else if(hx < 0x39000000) { /* |x|<2**-14 */
- /* raise inexact */
- if (huge+x > one)
- return one + x;
- } else
+ if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
+ if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
+ k = invln2*x + half[sign];
+ else
+ k = 1 - sign - sign;
+ hi = x - k*ln2hi; /* k*ln2hi is exact here */
+ lo = k*ln2lo;
+ x = hi - lo;
+ } else if (hx > 0x39000000) { /* |x| > 2**-14 */
k = 0;
+ hi = x;
+ lo = 0;
+ } else {
+ /* raise inexact */
+ FORCE_EVAL(0x1p127f + x);
+ return 1 + x;
+ }
/* x is now in primary range */
- t = x*x;
- if (k >= -125)
- SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
- else
- SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
- c = x - t*(P1+t*P2);
+ xx = x*x;
+ c = x - xx*(P1+xx*P2);
+ y = 1 + (x*c/(2-c) - lo + hi);
if (k == 0)
- return one - ((x*c)/(c - 2.0f) - x);
- y = one - ((lo - (x*c)/(2.0f - c)) - hi);
- if (k < -125)
- return y*twopk*twom100;
- if (k == 128)
- return y*2.0f*0x1p127f;
- return y*twopk;
+ return y;
+ return scalbnf(y, k);
}