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
169 lines
5.3 KiB
C
169 lines
5.3 KiB
C
/* @(#)e_rem_pio2.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_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
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#endif
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/* __ieee754_rem_pio2(x,y)
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*
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* return the remainder of x rem pi/2 in y[0]+y[1]
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* use __kernel_rem_pio2()
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*/
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#include "math.h"
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#include "math_private.h"
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/*
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* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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*/
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static const int32_t two_over_pi[] = {
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
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0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
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0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
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0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
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0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
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0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
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};
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static const int32_t npio2_hw[] = {
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0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
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0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
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0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
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0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
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0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
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0x404858EB, 0x404921FB,
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};
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/*
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* invpio2: 53 bits of 2/pi
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* pio2_1: first 33 bit of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 33 bit of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 33 bit of pi/2
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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*/
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static const double
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zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
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pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
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pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
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pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
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pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
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pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
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pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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int32_t
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__ieee754_rem_pio2(double x, double *y)
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{
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double z,w,t,r,fn;
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double tx[3];
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int32_t e0,i,j,nx,n,ix,hx;
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u_int32_t low;
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z = 0;
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GET_HIGH_WORD(hx,x); /* high word of x */
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ix = hx&0x7fffffff;
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if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
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{y[0] = x; y[1] = 0; return 0;}
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if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
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if(hx>0) {
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z = x - pio2_1;
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if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
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y[0] = z - pio2_1t;
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y[1] = (z-y[0])-pio2_1t;
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} else { /* near pi/2, use 33+33+53 bit pi */
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z -= pio2_2;
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y[0] = z - pio2_2t;
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y[1] = (z-y[0])-pio2_2t;
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}
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return 1;
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} else { /* negative x */
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z = x + pio2_1;
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if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
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y[0] = z + pio2_1t;
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y[1] = (z-y[0])+pio2_1t;
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} else { /* near pi/2, use 33+33+53 bit pi */
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z += pio2_2;
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y[0] = z + pio2_2t;
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y[1] = (z-y[0])+pio2_2t;
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}
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return -1;
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}
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}
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if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
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t = fabs(x);
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n = (int32_t) (t*invpio2+half);
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fn = (double)n;
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r = t-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 85 bit */
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if(n<32&&ix!=npio2_hw[n-1]) {
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y[0] = r-w; /* quick check no cancellation */
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} else {
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u_int32_t high;
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j = ix>>20;
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y[0] = r-w;
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GET_HIGH_WORD(high,y[0]);
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i = j-((high>>20)&0x7ff);
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if(i>16) { /* 2nd iteration needed, good to 118 */
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t = r;
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w = fn*pio2_2;
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r = t-w;
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w = fn*pio2_2t-((t-r)-w);
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y[0] = r-w;
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GET_HIGH_WORD(high,y[0]);
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i = j-((high>>20)&0x7ff);
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if(i>49) { /* 3rd iteration need, 151 bits acc */
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t = r; /* will cover all possible cases */
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w = fn*pio2_3;
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r = t-w;
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w = fn*pio2_3t-((t-r)-w);
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y[0] = r-w;
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}
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}
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}
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y[1] = (r-y[0])-w;
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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else return n;
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}
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/*
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* all other (large) arguments
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*/
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if(ix>=0x7ff00000) { /* x is inf or NaN */
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y[0]=y[1]=x-x; return 0;
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}
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/* set z = scalbn(|x|,ilogb(x)-23) */
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GET_LOW_WORD(low,x);
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SET_LOW_WORD(z,low);
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e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
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SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
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for(i=0;i<2;i++) {
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tx[i] = (double)((int32_t)(z));
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z = (z-tx[i])*two24;
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}
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tx[2] = z;
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nx = 3;
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while(tx[nx-1]==zero) nx--; /* skip zero term */
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n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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return n;
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}
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