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
136 lines
4.3 KiB
C
136 lines
4.3 KiB
C
/* @(#)e_log.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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#if defined(LIBM_SCCS) && !defined(lint)
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__RCSID("$NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
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#endif
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/* __ieee754_log(x)
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* Return the logrithm of x
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*
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* Method :
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* 1. Argument Reduction: find k and f such that
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* x = 2^k * (1+f),
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* where sqrt(2)/2 < 1+f < sqrt(2) .
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*
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* 2. Approximation of log(1+f).
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* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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* = 2s + s*R
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* We use a special Reme algorithm on [0,0.1716] to generate
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* a polynomial of degree 14 to approximate R The maximum error
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* of this polynomial approximation is bounded by 2**-58.45. In
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* other words,
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* 2 4 6 8 10 12 14
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* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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* (the values of Lg1 to Lg7 are listed in the program)
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* and
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* | 2 14 | -58.45
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* | Lg1*s +...+Lg7*s - R(z) | <= 2
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* | |
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* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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* In order to guarantee error in log below 1ulp, we compute log
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* by
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* log(1+f) = f - s*(f - R) (if f is not too large)
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* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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*
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* 3. Finally, log(x) = k*ln2 + log(1+f).
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* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
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* Here ln2 is split into two floating point number:
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* ln2_hi + ln2_lo,
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* where n*ln2_hi is always exact for |n| < 2000.
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*
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* Special cases:
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* log(x) is NaN with signal if x < 0 (including -INF) ;
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* log(+INF) is +INF; log(0) is -INF with signal;
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* log(NaN) is that NaN with no signal.
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*
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* Accuracy:
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* according to an error analysis, the error is always less than
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* 1 ulp (unit in the last place).
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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#include "math.h"
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#include "math_private.h"
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static const double
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ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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static const double zero = 0.0;
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double
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__ieee754_log(double x)
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{
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double hfsq,f,s,z,R,w,t1,t2,dk;
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int32_t k,hx,i,j;
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u_int32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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k=0;
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if (hx < 0x00100000) { /* x < 2**-1022 */
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if (((hx&0x7fffffff)|lx)==0)
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return -two54/zero; /* log(+-0)=-inf */
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if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
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k -= 54; x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD(hx,x);
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}
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if (hx >= 0x7ff00000) return x+x;
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k += (hx>>20)-1023;
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hx &= 0x000fffff;
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i = (hx+0x95f64)&0x100000;
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SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
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k += (i>>20);
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f = x-1.0;
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if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
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if(f==zero) { if(k==0) return zero; else {dk=(double)k;
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return dk*ln2_hi+dk*ln2_lo;}
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}
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R = f*f*(0.5-0.33333333333333333*f);
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if(k==0) return f-R; else {dk=(double)k;
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return dk*ln2_hi-((R-dk*ln2_lo)-f);}
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}
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s = f/(2.0+f);
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dk = (double)k;
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z = s*s;
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i = hx-0x6147a;
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w = z*z;
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j = 0x6b851-hx;
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t1= w*(Lg2+w*(Lg4+w*Lg6));
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t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
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i |= j;
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R = t2+t1;
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if(i>0) {
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hfsq=0.5*f*f;
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if(k==0) return f-(hfsq-s*(hfsq+R)); else
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return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
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} else {
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if(k==0) return f-s*(f-R); else
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return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
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}
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}
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