1 /* origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c */
3 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
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31 #define TBLSIZE (1 << TBLBITS)
35 redux = 0x1.8p23f / TBLSIZE,
41 static volatile float twom100 = 0x1p-100f;
43 static const double exp2ft[TBLSIZE] = {
63 * exp2f(x): compute the base 2 exponential of x
65 * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
67 * Method: (equally-spaced tables)
70 * x = 2**k + y, for integer k and |y| <= 1/2.
71 * Thus we have exp2f(x) = 2**k * exp2(y).
74 * y = i/TBLSIZE + z for integer i near y * TBLSIZE.
75 * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
76 * with |z| <= 2**-(TBLSIZE+1).
78 * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
79 * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
80 * Using double precision for everything except the reduction makes
81 * roundoff error insignificant and simplifies the scaling step.
83 * This method is due to Tang, but I do not use his suggested parameters:
85 * Tang, P. Table-driven Implementation of the Exponential Function
86 * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
90 double tv, twopk, u, z;
95 /* Filter out exceptional cases. */
96 GET_FLOAT_WORD(hx, x);
98 if (ix >= 0x43000000) { /* |x| >= 128 */
99 if (ix >= 0x7f800000) {
100 if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
101 return x + x; /* x is NaN or +Inf */
103 return 0.0; /* x is -Inf */
106 return huge * huge; /* overflow */
108 return twom100 * twom100; /* underflow */
109 } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
113 /* Reduce x, computing z, i0, and k. */
114 STRICT_ASSIGN(float, t, x + redux);
115 GET_FLOAT_WORD(i0, t);
117 k = (i0 >> TBLBITS) << 20;
121 INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
123 /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
126 tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
128 /* Scale by 2**(k>>20). */