2fe8fb192f
There is important information about booting non-ack images in docs/UPDATING. ack/aout-format images can't be built any more, and booting clang/ELF-format ones is a little different. Updating to the new boot monitor is recommended. Changes in this commit: . drop boot monitor -> allowing dropping ack support . facility to copy ELF boot files to /boot so that old boot monitor can still boot fairly easily, see UPDATING . no more ack-format libraries -> single-case libraries . some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases . drop several ack toolchain commands, but not all support commands (e.g. aal is gone but acksize is not yet). . a few libc files moved to netbsd libc dir . new /bin/date as minix date used code in libc/ . test compile fix . harmonize includes . /usr/lib is no longer special: without ack, /usr/lib plays no kind of special bootstrapping role any more and bootstrapping is done exclusively through packages, so releases depend even less on the state of the machine making them now. . rename nbsd_lib* to lib* . reduce mtree
139 lines
4.2 KiB
C
139 lines
4.2 KiB
C
/*-
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* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <sys/cdefs.h>
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__RCSID("$NetBSD: s_exp2f.c,v 1.1 2010/01/11 16:28:39 christos Exp $");
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#ifdef __FBSDID
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__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $");
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#endif
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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#define TBLBITS 4
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#define TBLSIZE (1 << TBLBITS)
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static const float
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huge = 0x1p100f,
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redux = 0x1.8p23f / TBLSIZE,
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P1 = 0x1.62e430p-1f,
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P2 = 0x1.ebfbe0p-3f,
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P3 = 0x1.c6b348p-5f,
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P4 = 0x1.3b2c9cp-7f;
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static volatile float twom100 = 0x1p-100f;
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static const double exp2ft[TBLSIZE] = {
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0x1.6a09e667f3bcdp-1,
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0x1.7a11473eb0187p-1,
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0x1.8ace5422aa0dbp-1,
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0x1.9c49182a3f090p-1,
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0x1.ae89f995ad3adp-1,
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0x1.c199bdd85529cp-1,
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0x1.d5818dcfba487p-1,
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0x1.ea4afa2a490dap-1,
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0x1.0000000000000p+0,
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0x1.0b5586cf9890fp+0,
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0x1.172b83c7d517bp+0,
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0x1.2387a6e756238p+0,
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0x1.306fe0a31b715p+0,
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0x1.3dea64c123422p+0,
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0x1.4bfdad5362a27p+0,
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0x1.5ab07dd485429p+0,
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};
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/*
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* exp2f(x): compute the base 2 exponential of x
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*
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* Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
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*
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* Method: (equally-spaced tables)
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*
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* Reduce x:
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* x = 2**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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*
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* Reduce y:
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* y = i/TBLSIZE + z for integer i near y * TBLSIZE.
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* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
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* with |z| <= 2**-(TBLSIZE+1).
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*
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* We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
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* degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
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* Using double precision for everything except the reduction makes
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* roundoff error insignificant and simplifies the scaling step.
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*
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* This method is due to Tang, but I do not use his suggested parameters:
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*
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* Tang, P. Table-driven Implementation of the Exponential Function
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* in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
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*/
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float
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exp2f(float x)
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{
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double tv, twopk, u, z;
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float t;
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uint32_t hx, ix, i0;
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int32_t k;
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/* Filter out exceptional cases. */
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff; /* high word of |x| */
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if(ix >= 0x43000000) { /* |x| >= 128 */
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if(ix >= 0x7f800000) {
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if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
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return (x + x); /* x is NaN or +Inf */
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else
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return (0.0); /* x is -Inf */
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}
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if(x >= 0x1.0p7f)
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return (huge * huge); /* overflow */
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if(x <= -0x1.2cp7f)
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return (twom100 * twom100); /* underflow */
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} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
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return (1.0f + x);
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}
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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 >> TBLBITS) << 20;
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i0 &= TBLSIZE - 1;
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t -= redux;
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z = x - t;
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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 = exp2ft[i0];
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u = tv * z;
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tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
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/* Scale by 2**(k>>20). */
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return (tv * twopk);
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}
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