#include "libm.h"
-#define TBLBITS 4
-#define TBLSIZE (1 << TBLBITS)
+#define TBLSIZE 16
static const float
-huge = 0x1p100f,
redux = 0x1.8p23f / TBLSIZE,
P1 = 0x1.62e430p-1f,
P2 = 0x1.ebfbe0p-3f,
P3 = 0x1.c6b348p-5f,
P4 = 0x1.3b2c9cp-7f;
-static const volatile float twom100 = 0x1p-100f;
-
static const double exp2ft[TBLSIZE] = {
0x1.6a09e667f3bcdp-1,
0x1.7a11473eb0187p-1,
* Method: (equally-spaced tables)
*
* Reduce x:
- * x = 2**k + y, for integer k and |y| <= 1/2.
+ * x = k + y, for integer k and |y| <= 1/2.
* Thus we have exp2f(x) = 2**k * exp2(y).
*
* Reduce y:
*/
float exp2f(float x)
{
- double tv, twopk, u, z;
- float t;
- uint32_t hx, ix, i0;
- int32_t k;
+ double_t t, r, z;
+ union {float f; uint32_t i;} u = {x};
+ union {double f; uint64_t i;} uk;
+ uint32_t ix, i0, k;
/* Filter out exceptional cases. */
- GET_FLOAT_WORD(hx, x);
- ix = hx & 0x7fffffff;
- if (ix >= 0x43000000) { /* |x| >= 128 */
- if (ix >= 0x7f800000) {
- if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
- return x + x; /* x is NaN or +Inf */
- else
- return 0.0; /* x is -Inf */
+ ix = u.i & 0x7fffffff;
+ if (ix > 0x42fc0000) { /* |x| > 126 */
+ if (u.i >= 0x43000000 && u.i < 0x80000000) { /* x >= 128 */
+ x *= 0x1p127f;
+ return x;
+ }
+ if (u.i >= 0x80000000) { /* x < -126 */
+ if (u.i >= 0xc3160000 || (u.i & 0x0000ffff))
+ FORCE_EVAL(-0x1p-149f/x);
+ if (u.i >= 0xc3160000) /* x <= -150 */
+ return 0;
}
- if (x >= 0x1.0p7f)
- return huge * huge; /* overflow */
- if (x <= -0x1.2cp7f)
- return twom100 * twom100; /* underflow */
} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
return 1.0f + x;
}
/* Reduce x, computing z, i0, and k. */
- STRICT_ASSIGN(float, t, x + redux);
- GET_FLOAT_WORD(i0, t);
+ u.f = x + redux;
+ i0 = u.i;
i0 += TBLSIZE / 2;
- k = (i0 >> TBLBITS) << 20;
+ k = i0 / TBLSIZE;
+ uk.i = (uint64_t)(0x3ff + k)<<52;
i0 &= TBLSIZE - 1;
- t -= redux;
- z = x - t;
- INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
-
+ u.f -= redux;
+ z = x - u.f;
/* Compute r = exp2(y) = exp2ft[i0] * p(z). */
- tv = exp2ft[i0];
- u = tv * z;
- tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
+ r = exp2ft[i0];
+ t = r * z;
+ r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
- /* Scale by 2**(k>>20). */
- return tv * twopk;
+ /* Scale by 2**k */
+ return r * uk.f;
}