84d9c625bf
- Fix for possible unset uid/gid in toproto
- Fix for default mtree style
- Update libelf
- Importing libexecinfo
- Resynchronize GCC, mpc, gmp, mpfr
- build.sh: Replace params with show-params.
This has been done as the make target has been renamed in the same
way, while a new target named params has been added. This new
target generates a file containing all the parameters, instead of
printing it on the console.
- Update test48 with new etc/services (Fix by Ben Gras <ben@minix3.org)
get getservbyport() out of the inner loop
Change-Id: Ie6ad5226fa2621ff9f0dee8782ea48f9443d2091
146 lines
3.5 KiB
C
146 lines
3.5 KiB
C
/*-
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
* Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*
|
|
* The argument reduction and testing for exceptional cases was
|
|
* written by Steven G. Kargl with input from Bruce D. Evans
|
|
* and David A. Schultz.
|
|
*/
|
|
|
|
#include <sys/cdefs.h>
|
|
__RCSID("$NetBSD: s_cbrtl.c,v 1.1 2013/11/19 19:24:34 joerg Exp $");
|
|
#if 0
|
|
__FBSDID("$FreeBSD: head/lib/msun/src/s_cbrtl.c 238924 2012-07-30 21:58:28Z kargl $");
|
|
#endif
|
|
|
|
#include "namespace.h"
|
|
#include <machine/ieee.h>
|
|
#include <float.h>
|
|
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
|
|
#ifdef __HAVE_LONG_DOUBLE
|
|
__weak_alias(cbrtl, _cbrtl)
|
|
|
|
static const unsigned
|
|
B1 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
|
|
|
|
long double
|
|
cbrtl(long double x)
|
|
{
|
|
union ieee_ext_u ux, vx;
|
|
long double r, s, t, w;
|
|
double dr, dt, dx;
|
|
float ft, fx;
|
|
uint32_t hx;
|
|
int k;
|
|
|
|
ux.extu_ld = x;
|
|
|
|
|
|
/*
|
|
* If x = +-Inf, then cbrt(x) = +-Inf.
|
|
* If x = NaN, then cbrt(x) = NaN.
|
|
*/
|
|
if (ux.extu_exp == EXT_EXP_INFNAN)
|
|
return (x + x);
|
|
if ((ux.extu_frach | ux.extu_fracl | ux.extu_exp) == 0)
|
|
return (x);
|
|
|
|
vx.extu_ld = 1;
|
|
vx.extu_ext.ext_sign = ux.extu_ext.ext_sign;
|
|
ux.extu_ext.ext_sign = 0;
|
|
if (ux.extu_exp == 0) {
|
|
/* Adjust subnormal numbers. */
|
|
ux.extu_ld *= 0x1.0p514;
|
|
k = ux.extu_exp - EXT_EXP_BIAS - 514;
|
|
} else {
|
|
k = ux.extu_exp - EXT_EXP_BIAS;
|
|
}
|
|
|
|
ux.extu_exp = EXT_EXP_BIAS;
|
|
x = ux.extu_ld;
|
|
switch (k % 3) {
|
|
case 1:
|
|
case -2:
|
|
x = 2*x;
|
|
k--;
|
|
break;
|
|
case 2:
|
|
case -1:
|
|
x = 4*x;
|
|
k -= 2;
|
|
break;
|
|
}
|
|
vx.extu_exp = EXT_EXP_BIAS + k / 3;
|
|
|
|
/*
|
|
* The following is the guts of s_cbrtf, with the handling of
|
|
* special values removed and extra care for accuracy not taken,
|
|
* but with most of the extra accuracy not discarded.
|
|
*/
|
|
|
|
/* ~5-bit estimate: */
|
|
fx = x;
|
|
GET_FLOAT_WORD(hx, fx);
|
|
SET_FLOAT_WORD(ft, ((hx & 0x7fffffff) / 3 + B1));
|
|
|
|
/* ~16-bit estimate: */
|
|
dx = x;
|
|
dt = ft;
|
|
dr = dt * dt * dt;
|
|
dt = dt * (dx + dx + dr) / (dx + dr + dr);
|
|
|
|
/* ~47-bit estimate: */
|
|
dr = dt * dt * dt;
|
|
dt = dt * (dx + dx + dr) / (dx + dr + dr);
|
|
|
|
#if LDBL_MANT_DIG == 64
|
|
/*
|
|
* dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8).
|
|
* Round it away from zero to 32 bits (32 so that t*t is exact, and
|
|
* away from zero for technical reasons).
|
|
*/
|
|
volatile double vd2 = 0x1.0p32;
|
|
volatile double vd1 = 0x1.0p-31;
|
|
#define vd ((long double)vd2 + vd1)
|
|
|
|
t = dt + vd - 0x1.0p32;
|
|
#elif LDBL_MANT_DIG == 113
|
|
/*
|
|
* Round dt away from zero to 47 bits. Since we don't trust the 47,
|
|
* add 2 47-bit ulps instead of 1 to round up. Rounding is slow and
|
|
* might be avoidable in this case, since on most machines dt will
|
|
* have been evaluated in 53-bit precision and the technical reasons
|
|
* for rounding up might not apply to either case in cbrtl() since
|
|
* dt is much more accurate than needed.
|
|
*/
|
|
t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60;
|
|
#else
|
|
#error "Unsupported long double format"
|
|
#endif
|
|
|
|
/*
|
|
* Final step Newton iteration to 64 or 113 bits with
|
|
* error < 0.667 ulps
|
|
*/
|
|
s=t*t; /* t*t is exact */
|
|
r=x/s; /* error <= 0.5 ulps; |r| < |t| */
|
|
w=t+t; /* t+t is exact */
|
|
r=(r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */
|
|
t=t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */
|
|
|
|
t *= vx.extu_ld;
|
|
return t;
|
|
}
|
|
|
|
#endif /* __HAVE_LONG_DOUBLE */
|