ARM/libroot: Add more floating point code to get UCI happy
This commit is contained in:
Ithamar R. Adema
@@ -33,14 +33,41 @@ local genericSources =
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s_isinf.c s_isinff.c
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s_isinf.c s_isinff.c
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s_isnan.c s_isnanf.c
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s_isnan.c s_isnanf.c
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s_signbit.c s_signbitf.c s_signbitl.c
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s_signbit.c s_signbitf.c s_signbitl.c
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s_floor.c
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s_ceil.c s_ceilf.c
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s_modf.c
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w_pow.c e_pow.c slowpow.c
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e_exp.c slowexp.c
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dosincos.c
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doasin.c
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sincos32.c
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branred.c
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halfulp.c
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mpa.c mplog.c mpexp.c
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s_sin.c
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s_atan.c
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s_tan.c
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e_asin.c w_asin.c
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e_log10.c w_log10.c
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e_acos.c w_acos.c
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e_atan2.c w_atan2.c mpatan2.c mpatan.c mptan.c mpsqrt.c
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e_fmod.c w_fmod.c
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e_log.c w_log.c
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s_ldexp.c s_ldexpf.c
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;
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;
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MergeObject posix_gnu_arch_$(TARGET_ARCH)_generic.o :
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MergeObject posix_gnu_arch_$(TARGET_ARCH)_generic.o :
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$(genericSources)
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$(genericSources)
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;
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;
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MergeObject posix_gnu_arch_$(TARGET_ARCH)_others.o :
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e_sqrt.c
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;
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MergeObjectFromObjects posix_gnu_arch_$(TARGET_ARCH).o : :
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MergeObjectFromObjects posix_gnu_arch_$(TARGET_ARCH).o : :
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posix_gnu_arch_$(TARGET_ARCH)_generic.o
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posix_gnu_arch_$(TARGET_ARCH)_generic.o
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posix_gnu_arch_$(TARGET_ARCH)_others.o
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;
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;
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SEARCH on [ FGristFiles $(genericSources) ]
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SEARCH on [ FGristFiles $(genericSources) ]
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@@ -0,0 +1,203 @@
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/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001 Free Software Foundation
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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*/
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/*********************************************************************/
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/* */
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/* MODULE_NAME:ulog.c */
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/* */
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/* FUNCTION:ulog */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
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/* mpexp.c mplog.c mpa.c */
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/* ulog.tbl */
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/* */
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of log(x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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#include "endian.h"
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#include "dla.h"
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#include "mpa.h"
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#include "MathLib.h"
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#include "math_private.h"
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void __mplog(mp_no *, mp_no *, int);
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/*********************************************************************/
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of log(x). */
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/*********************************************************************/
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double __ieee754_log(double x) {
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#define M 4
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static const int pr[M]={8,10,18,32};
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int i,j,n,ux,dx,p;
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#if 0
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int k;
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#endif
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double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj,
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sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb,
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t1,t2,t3,t4,t5,t6,t7,t8,t,ra,rb,ww,
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a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c;
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number num;
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mp_no mpx,mpy,mpy1,mpy2,mperr;
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#include "ulog.tbl"
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#include "ulog.h"
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/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
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num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
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n=0;
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if (ux < 0x00100000) {
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if (((ux & 0x7fffffff) | dx) == 0) return MHALF/ZERO; /* return -INF */
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if (ux < 0) return (x-x)/ZERO; /* return NaN */
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n -= 54; x *= two54.d; /* scale x */
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num.d = x;
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}
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if (ux >= 0x7ff00000) return x+x; /* INF or NaN */
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/* Regular values of x */
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w = x-ONE;
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if (ABS(w) > U03) { goto case_03; }
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/*--- Stage I, the case abs(x-1) < 0.03 */
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t8 = MHALF*w;
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EMULV(t8,w,a,aa,t1,t2,t3,t4,t5)
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EADD(w,a,b,bb)
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/* Evaluate polynomial II */
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polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+
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w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w;
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c = (aa+bb)+polII;
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/* End stage I, case abs(x-1) < 0.03 */
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if ((y=b+(c+b*E2)) == b+(c-b*E2)) return y;
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/*--- Stage II, the case abs(x-1) < 0.03 */
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a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+
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w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d))))))));
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EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5)
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ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(w,ZERO, s3,ss3, b, bb,t1,t2)
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/* End stage II, case abs(x-1) < 0.03 */
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if ((y=b+(bb+b*E4)) == b+(bb-b*E4)) return y;
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goto stage_n;
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/*--- Stage I, the case abs(x-1) > 0.03 */
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case_03:
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/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
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n += (num.i[HIGH_HALF] >> 20) - 1023;
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num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
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if (num.d > SQRT_2) { num.d *= HALF; n++; }
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u = num.d; dbl_n = (double) n;
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/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
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num.d += h1.d;
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i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
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/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
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num.d = u*Iu[i].d + h2.d;
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j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
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/* Compute w=(u-ui*vj)/(ui*vj) */
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p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V);
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q=u-p0; r0=Iu[i].d*Iv[j].d; w=q*r0;
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/* Evaluate polynomial I */
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polI = w+(a2.d+a3.d*w)*w*w;
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/* Add up everything */
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nln2a = dbl_n*LN2A;
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luai = Lu[i][0].d; lubi = Lu[i][1].d;
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lvaj = Lv[j][0].d; lvbj = Lv[j][1].d;
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EADD(luai,lvaj,sij,ssij)
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EADD(nln2a,sij,A ,ttij)
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B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B;
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B = polI+B0;
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/* End stage I, case abs(x-1) >= 0.03 */
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if ((y=A+(B+E1)) == A+(B-E1)) return y;
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/*--- Stage II, the case abs(x-1) > 0.03 */
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/* Improve the accuracy of r0 */
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EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5)
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t=r0*((ONE-sa)-sb);
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EADD(r0,t,ra,rb)
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/* Compute w */
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MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8)
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EADD(A,B0,a0,aa0)
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/* Evaluate polynomial III */
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s1 = (c3.d+(c4.d+c5.d*w)*w)*w;
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EADD(c2.d,s1,s2,ss2)
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MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(s2,ss2,w,ww,s3,ss3,t1,t2)
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ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2)
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/* End stage II, case abs(x-1) >= 0.03 */
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if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y;
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/* Final stages. Use multi-precision arithmetic. */
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stage_n:
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for (i=0; i<M; i++) {
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p = pr[i];
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__dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p);
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__mplog(&mpx,&mpy,p);
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__dbl_mp(e[i].d,&mperr,p);
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__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
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|
__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
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if (y1==y2) return y1;
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}
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return y1;
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}
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@@ -0,0 +1,88 @@
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|
/*
|
||||||
|
* IBM Accurate Mathematical Library
|
||||||
|
* written by International Business Machines Corp.
|
||||||
|
* Copyright (C) 2001 Free Software Foundation
|
||||||
|
*
|
||||||
|
* This program is free software; you can redistribute it and/or modify
|
||||||
|
* it under the terms of the GNU Lesser General Public License as published by
|
||||||
|
* the Free Software Foundation; either version 2.1 of the License, or
|
||||||
|
* (at your option) any later version.
|
||||||
|
*
|
||||||
|
* This program is distributed in the hope that it will be useful,
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
* GNU Lesser General Public License for more details.
|
||||||
|
*
|
||||||
|
* You should have received a copy of the GNU Lesser General Public License
|
||||||
|
* along with this program; if not, write to the Free Software
|
||||||
|
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
|
||||||
|
*/
|
||||||
|
/*********************************************************************/
|
||||||
|
/* MODULE_NAME: uroot.c */
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||||||
|
/* */
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||||||
|
/* FUNCTION: usqrt */
|
||||||
|
/* */
|
||||||
|
/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
|
||||||
|
/* uroot.tbl */
|
||||||
|
/* */
|
||||||
|
/* An ultimate sqrt routine. Given an IEEE double machine number x */
|
||||||
|
/* it computes the correctly rounded (to nearest) value of square */
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||||||
|
/* root of x. */
|
||||||
|
/* Assumption: Machine arithmetic operations are performed in */
|
||||||
|
/* round to nearest mode of IEEE 754 standard. */
|
||||||
|
/* */
|
||||||
|
/*********************************************************************/
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||||||
|
|
||||||
|
#include "endian.h"
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||||||
|
#include "mydefs.h"
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||||||
|
#include "dla.h"
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||||||
|
#include "MathLib.h"
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||||||
|
#include "root.tbl"
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||||||
|
#include "math_private.h"
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||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
/* An ultimate sqrt routine. Given an IEEE double machine number x */
|
||||||
|
/* it computes the correctly rounded (to nearest) value of square */
|
||||||
|
/* root of x. */
|
||||||
|
/*********************************************************************/
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||||||
|
double __ieee754_sqrt(double x) {
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|
#include "uroot.h"
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||||||
|
static const double
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||||||
|
rt0 = 9.99999999859990725855365213134618E-01,
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||||||
|
rt1 = 4.99999999495955425917856814202739E-01,
|
||||||
|
rt2 = 3.75017500867345182581453026130850E-01,
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||||||
|
rt3 = 3.12523626554518656309172508769531E-01;
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||||||
|
static const double big = 134217728.0;
|
||||||
|
double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
|
||||||
|
mynumber a,c={{0,0}};
|
||||||
|
int4 k;
|
||||||
|
|
||||||
|
a.x=x;
|
||||||
|
k=a.i[HIGH_HALF];
|
||||||
|
a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
|
||||||
|
t=inroot[(k&0x001fffff)>>14];
|
||||||
|
s=a.x;
|
||||||
|
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
|
||||||
|
if (k>0x000fffff && k<0x7ff00000) {
|
||||||
|
y=1.0-t*(t*s);
|
||||||
|
t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
|
||||||
|
c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
|
||||||
|
y=t*s;
|
||||||
|
hy=(y+big)-big;
|
||||||
|
del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
|
||||||
|
res=y+del;
|
||||||
|
if (res == (res+1.002*((y-res)+del))) return res*c.x;
|
||||||
|
else {
|
||||||
|
res1=res+1.5*((y-res)+del);
|
||||||
|
EMULV(res,res1,z,zz,p,hx,tx,hy,ty); /* (z+zz)=res*res1 */
|
||||||
|
return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
if ((k & 0x7ff00000) == 0x7ff00000)
|
||||||
|
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
|
||||||
|
if (x==0) return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
|
||||||
|
if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
|
||||||
|
return tm256.x*__ieee754_sqrt(x*t512.x);
|
||||||
|
}
|
||||||
|
}
|
||||||
@@ -0,0 +1,44 @@
|
|||||||
|
/*
|
||||||
|
* IBM Accurate Mathematical Library
|
||||||
|
* Written by International Business Machines Corp.
|
||||||
|
* Copyright (C) 2001 Free Software Foundation, Inc.
|
||||||
|
*
|
||||||
|
* This program is free software; you can redistribute it and/or modify
|
||||||
|
* it under the terms of the GNU Lesser General Public License as published by
|
||||||
|
* the Free Software Foundation; either version 2.1 of the License, or
|
||||||
|
* (at your option) any later version.
|
||||||
|
*
|
||||||
|
* This program is distributed in the hope that it will be useful,
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
* GNU Lesser General Public License for more details.
|
||||||
|
*
|
||||||
|
* You should have received a copy of the GNU Lesser General Public License
|
||||||
|
* along with this program; if not, write to the Free Software
|
||||||
|
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/******************************************************************/
|
||||||
|
/* */
|
||||||
|
/* MODULE_NAME:uroot.h */
|
||||||
|
/* */
|
||||||
|
/* common data and variables prototype and definition */
|
||||||
|
/******************************************************************/
|
||||||
|
|
||||||
|
#ifndef UROOT_H
|
||||||
|
#define UROOT_H
|
||||||
|
|
||||||
|
#ifdef BIG_ENDI
|
||||||
|
static const mynumber
|
||||||
|
/**/ t512 = {{0x5ff00000, 0x00000000 }}, /* 2^512 */
|
||||||
|
/**/ tm256 = {{0x2ff00000, 0x00000000 }}; /* 2^-256 */
|
||||||
|
|
||||||
|
#else
|
||||||
|
#ifdef LITTLE_ENDI
|
||||||
|
static const mynumber
|
||||||
|
/**/ t512 = {{0x00000000, 0x5ff00000 }}, /* 2^512 */
|
||||||
|
/**/ tm256 = {{0x00000000, 0x2ff00000 }}; /* 2^-256 */
|
||||||
|
#endif
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#endif
|
||||||
@@ -0,0 +1,58 @@
|
|||||||
|
/* Copyright (C) 1997, 1998, 1999 Free Software Foundation, Inc.
|
||||||
|
This file is part of the GNU C Library.
|
||||||
|
|
||||||
|
The GNU C Library is free software; you can redistribute it and/or
|
||||||
|
modify it under the terms of the GNU Lesser General Public
|
||||||
|
License as published by the Free Software Foundation; either
|
||||||
|
version 2.1 of the License, or (at your option) any later version.
|
||||||
|
|
||||||
|
The GNU C Library is distributed in the hope that it will be useful,
|
||||||
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||||
|
Lesser General Public License for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU Lesser General Public
|
||||||
|
License along with the GNU C Library; if not, write to the Free
|
||||||
|
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
|
||||||
|
02111-1307 USA. */
|
||||||
|
|
||||||
|
#ifndef _FENV_H
|
||||||
|
# error "Never use <bits/fenv.h> directly; include <fenv.h> instead."
|
||||||
|
#endif
|
||||||
|
|
||||||
|
/* Define bits representing exceptions in the FPU status word. */
|
||||||
|
enum
|
||||||
|
{
|
||||||
|
FE_INVALID = 1,
|
||||||
|
#define FE_INVALID FE_INVALID
|
||||||
|
FE_DIVBYZERO = 2,
|
||||||
|
#define FE_DIVBYZERO FE_DIVBYZERO
|
||||||
|
FE_OVERFLOW = 4,
|
||||||
|
#define FE_OVERFLOW FE_OVERFLOW
|
||||||
|
FE_UNDERFLOW = 8,
|
||||||
|
#define FE_UNDERFLOW FE_UNDERFLOW
|
||||||
|
};
|
||||||
|
|
||||||
|
/* Amount to shift by to convert an exception to a mask bit. */
|
||||||
|
#define FE_EXCEPT_SHIFT 16
|
||||||
|
|
||||||
|
/* All supported exceptions. */
|
||||||
|
#define FE_ALL_EXCEPT \
|
||||||
|
(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)
|
||||||
|
|
||||||
|
/* The ARM FPU basically only supports round-to-nearest. Other rounding
|
||||||
|
modes exist, but you have to encode them in the actual instruction. */
|
||||||
|
#define FE_TONEAREST 0
|
||||||
|
|
||||||
|
/* Type representing exception flags. */
|
||||||
|
typedef unsigned long int fexcept_t;
|
||||||
|
|
||||||
|
/* Type representing floating-point environment. */
|
||||||
|
typedef struct
|
||||||
|
{
|
||||||
|
unsigned long int __cw;
|
||||||
|
}
|
||||||
|
fenv_t;
|
||||||
|
|
||||||
|
/* If the default argument is used we use this value. */
|
||||||
|
#define FE_DFL_ENV ((fenv_t *) -1l)
|
||||||
@@ -30,6 +30,12 @@ typedef float float_t; /* `float' expressions are evaluated as
|
|||||||
typedef double double_t; /* `double' expressions are evaluated as
|
typedef double double_t; /* `double' expressions are evaluated as
|
||||||
`double'. */
|
`double'. */
|
||||||
|
|
||||||
|
/* Signal that both types are `long double'. */
|
||||||
|
# define FLT_EVAL_METHOD 2
|
||||||
|
|
||||||
|
/* Define `INFINITY' as value of type `float'. */
|
||||||
|
# define INFINITY HUGE_VALF
|
||||||
|
|
||||||
/* The values returned by `ilogb' for 0 and NaN respectively. */
|
/* The values returned by `ilogb' for 0 and NaN respectively. */
|
||||||
# define FP_ILOGB0 (-2147483647)
|
# define FP_ILOGB0 (-2147483647)
|
||||||
# define FP_ILOGBNAN (2147483647)
|
# define FP_ILOGBNAN (2147483647)
|
||||||
@@ -41,3 +47,6 @@ typedef double double_t; /* `double' expressions are evaluated as
|
|||||||
declaration of all the `long double' function variants. */
|
declaration of all the `long double' function variants. */
|
||||||
# define __NO_LONG_DOUBLE_MATH 1
|
# define __NO_LONG_DOUBLE_MATH 1
|
||||||
#endif
|
#endif
|
||||||
|
|
||||||
|
/* Number of decimal digits for the `long double' type. */
|
||||||
|
# define DECIMAL_DIG 21
|
||||||
|
|||||||
Reference in New Issue
Block a user