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| 2 | /* @(#)e_exp.c 5.1 93/09/24 */
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| 3 | /*
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| 4 | * ====================================================
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 6 | *
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 8 | * Permission to use, copy, modify, and distribute this
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| 9 | * software is freely granted, provided that this notice
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| 10 | * is preserved.
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| 11 | * ====================================================
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| 12 | */
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| 13 |
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| 14 | /* __ieee754_exp(x)
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| 15 | * Returns the exponential of x.
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| 16 | *
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| 17 | * Method
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| 18 | * 1. Argument reduction:
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| 19 | * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
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| 20 | * Given x, find r and integer k such that
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| 21 | *
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| 22 | * x = k*ln2 + r, |r| <= 0.5*ln2.
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| 23 | *
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| 24 | * Here r will be represented as r = hi-lo for better
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| 25 | * accuracy.
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| 26 | *
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| 27 | * 2. Approximation of exp(r) by a special rational function on
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| 28 | * the interval [0,0.34658]:
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| 29 | * Write
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| 30 | * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
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| 31 | * We use a special Reme algorithm on [0,0.34658] to generate
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| 32 | * a polynomial of degree 5 to approximate R. The maximum error
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| 33 | * of this polynomial approximation is bounded by 2**-59. In
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