129 lines
3.5 KiB
C
129 lines
3.5 KiB
C
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/*
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* Exponential function, long double precision
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, expl();
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*
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* y = expl( x );
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*
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*
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* DESCRIPTION:
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*
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* Returns e (2.71828...) raised to the x power.
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*
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* Range reduction is accomplished by separating the argument
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* into an integer k and fraction f such that
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*
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* x k f
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* e = 2 e.
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*
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* A Pade' form of degree 5/6 is used to approximate exp(f) - 1
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* in the basic range [-0.5 ln 2, 0.5 ln 2].
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE +-10000 50000 1.12e-19 2.81e-20
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*
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*
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* Error amplification in the exponential function can be
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* a serious matter. The error propagation involves
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* exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
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* which shows that a 1 lsb error in representing X produces
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* a relative error of X times 1 lsb in the function.
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* While the routine gives an accurate result for arguments
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* that are exactly represented by a long double precision
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* computer number, the result contains amplified roundoff
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* error for large arguments not exactly represented.
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* exp underflow x < MINLOG 0.0
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* exp overflow x > MAXLOG MAXNUM
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*
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*/
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#include "libc/math/libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double expl(long double x)
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{
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return exp(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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static const long double P[3] = {
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1.2617719307481059087798E-4L,
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3.0299440770744196129956E-2L,
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9.9999999999999999991025E-1L,
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};
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static const long double Q[4] = {
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3.0019850513866445504159E-6L,
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2.5244834034968410419224E-3L,
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2.2726554820815502876593E-1L,
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2.0000000000000000000897E0L,
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};
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static const long double
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LN2HI = 6.9314575195312500000000E-1L,
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LN2LO = 1.4286068203094172321215E-6L,
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LOG2E = 1.4426950408889634073599E0L;
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long double expl(long double x)
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{
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long double px, xx;
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int k;
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if (isnan(x))
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return x;
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if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */
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return x * 0x1p16383L;
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if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */
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return -0x1p-16445L/x;
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/* Express e**x = e**f 2**k
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* = e**(f + k ln(2))
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*/
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px = floorl(LOG2E * x + 0.5);
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k = px;
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x -= px * LN2HI;
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x -= px * LN2LO;
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/* rational approximation of the fractional part:
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* e**x = 1 + 2x P(x**2)/(Q(x**2) - x P(x**2))
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*/
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xx = x * x;
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px = x * __polevll(xx, P, 2);
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x = px/(__polevll(xx, Q, 3) - px);
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x = 1.0 + 2.0 * x;
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return scalbnl(x, k);
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}
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#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
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// TODO: broken implementation to make things compile
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long double expl(long double x)
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{
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return exp(x);
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}
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#endif
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