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* Method: (equally-spaced tables)
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* x = 2**k + y, for integer k and |y| <= 1/2.
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* x = k + y, for integer k and |y| <= 1/2.
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* Thus we have exp2f(x) = 2**k * exp2(y).
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float exp2f(float x)
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double tv, twopk, u, z;
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uint32_t hx, ix, i0, k;
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union {float f; uint32_t i;} u = {x};
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union {double f; uint64_t i;} uk;
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/* Filter out exceptional cases. */
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GET_FLOAT_WORD(hx, x);
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if (ix >= 0x43000000) { /* |x| >= 128 */
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if (ix >= 0x7f800000) {
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if (hx == 0xff800000) /* -inf */
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ix = u.i & 0x7fffffff;
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if (ix > 0x42fc0000) { /* |x| > 126 */
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if (u.i >= 0x43000000 && u.i < 0x80000000) { /* x >= 128 */
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if (u.i >= 0x80000000) { /* x < -126 */
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if (u.i >= 0xc3160000 || (u.i & 0x0000ffff))
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FORCE_EVAL(-0x1p-149f/x);
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if (u.i >= 0xc3160000) /* x <= -150 */
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STRICT_ASSIGN(float, x, x * 0x1p127f);
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STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
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} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
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/* Reduce x, computing z, i0, and k. */
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STRICT_ASSIGN(float, t, x + redux);
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GET_FLOAT_WORD(i0, t);
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i0 += TBLSIZE / 2;
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k = (i0 / TBLSIZE) << 20;
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uk.i = (uint64_t)(0x3ff + k)<<52;
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i0 &= TBLSIZE - 1;
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INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
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/* Compute r = exp2(y) = exp2ft[i0] * p(z). */
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tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
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r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
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/* Scale by 2**(k>>20). */