/* * Classified Tydeman Consulting Proprietary * Copyright (C) 1996, 2012 Tydeman Consulting. All rights reserved. * * Fred J. Tydeman tydeman@tybor.com * * Any person is hereby authorized to copy, use, and distribute, this * one sample test, subject to the following conditions: * * 1. the software may not be redistributed for a fee except as * reasonable to cover media costs; * 2. any copy of the software must include this notice, as well as * any other embedded copyright notices; and * 3. any distribution of this software or derivative works thereof * must comply with all applicable U.S. export control laws. * * Floating-Point C Extensions (FPCE) have been added to C99 (the * revision of the C language finished in late 1999). If you are * interested in other sample tests of the FPCE Test Suite, which * tests the floating-point and numerics capabilities of C/C++ * compilers and libraries, please see the FTP site: * ftp://ftp.tybor.com * user ID: anonymous * password: your email address * ***************************************************************** * * How accurate is sin(355.0)? * * The program computes the approximate number of bits in error in the * answer returned from the sin() math function for one particular * argument. The number of ULPs (Units in Last Place) of error would be * about 2 ** BitsWrong. So, the entries with 7.09 bits wrong have about * 135 ULPs error. * * The old C standard, C89 as amended, had no requirements on the * accuracy of the math library; it is a quality of implementation issue. * C99, the revision of C89 finished in late 1999, has added the requirement * that implementations document the accuracy of their math library. * C11 (the current C standard) has retained that requirement. * * While C99 has no requirement on the accuracy of the math library that * all implementations must follow (such as 5 ULP accuracy), there are * other "standards" that do have accuracy requirements on the math library. * * One "standard" is Draft international standard ISO/IEC 10967-2, * Language Independent Arithmetic (LIA) Part 2: Elementary Numerical * Functions. LIA-2 should be added to ISO/ANSI C sometime in the future * (it may be several years). LIA-2 says the error limit on sin() is * 1.5 * rounding_error as long as the magnitude of the argument is * less than max_arg_sin, an implementation defined value. * * Proposed Standard for a Generic Package of Elementary Functions for Ada, * ISO-IEC/JTC1/SC22/WG9 (Ada) Numerics Rapporteur Group, 1990 is another * "standard". It says that the maximum relative error allowed is * 2.0 * epsilon as long as the magnitude of the argument is less than * an implementation-dependent threshold, which must not be less than * radix ** (mantissa digits/2). * * Both "standards" have similar requirements of about 2 ULPs error. In * terms of this program, for IEEE-754 double which has 53 mantissa bits, * an error of 2 bits or less for arguments smaller than 94,906,265 would * meet Ada. So, testing with an argument of 355 is well within the domain * where sin() must be accurate. The integer value 355 was chosen for a * reason; for the details, see the file v1150001.h on the above FTP site. * * Depending upon how floating-point numbers are represented internally, * the number of bits wrong can vary by as much as one. For machines * that use the same representation (such as all the IEEE-754 ones), that * is not a problem for using these numbers for comparison. * * For example, consider the 15-bit binary numbers (one near the top and * the other near the bottom of the same binade): * * 111111111000001 100000000001001 F = computed value * 111111111000000 100000000001000 f = correct value * 1 1 absolute error * 1/111111111000000 1/100000000001000 relative error * (3.06e-5) (6.10e-5) relative error in decimal * -10.395 -9.704 log(relative error) * 14.9972 14.0007 bits "correct" * 0.0028 0.9993 bits "wrong" * * Results of running this test on various compilers: * (as reported by several users of this test; your mileage may vary) * * BitsWrong Hardware Operating system Compiler, version, and options * * 0.00 ARM + FPU RiscOS Norcroft ARM v4.69 C [no options] * 0.00 Apple Mac PPC 603e Tenon MachTen gcc 2.7.2.1 + Tim Prince sin() * 0.00 Apple Mac PPC G4 Mac OS X 10.3.7 Gnu gcc 3.3 (build 1495) * 0.00 Apple Mac PPC G4 Mac OS X 10.3.7 IBM XL C 6.0 + Gnu gcc 3.3 * 0.00 DEC Alpha OSF/1 3.2 DEC cc * 0.00 DEC Alpha OSF/1 3.2 Gnu gcc 2.7.2.1 * 0.00 DEC Alpha OpenVMS 7.1 DEC C V5.7 (G float format) * 0.00 DEC Alpha Windows NT 4.0 SP4 Visual C++ 5.0 * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /bin/c89 * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /bin/cc * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /bin/cxx -x cxx * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/bin/c89 * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/bin/cc * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/ccs/bin/c89 * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/ccs/bin/cc * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/local/bin/g++ * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/local/bin/gcc * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/local/bin/lcc -A -A * 0.00 DEC Alpha 2100-5/250 OSF/1 3.2 /usr/ucb/cc * 0.00 DEC Alpha 250 4/266 OSF/1 V4.0 cc (DEC C V5.2-023) * 0.00 DEC Alpha 4000/610 OSF/1 V3.2C cc * 0.00 DEC Alpha 4100 5/600 Digital Unix V4.0D cc (DEC C V5.6-079) * 0.00 HP 9000 750 HP-UX B.10.20 c89 (A.10.32.03) * 0.00 HP 9000/735 HP-UX 10.01 /bin/CC * 0.00 HP 9000/735 HP-UX 10.01 /bin/c89 * 0.00 HP 9000/735 HP-UX 10.01 /usr/bin/CC * 0.00 HP 9000/735 HP-UX 10.01 /usr/bin/c89 * 0.00 HP 9000/735 HP-UX 10.01 /usr/local/bin/g++ * 0.00 HP 9000/735 HP-UX 10.01 /usr/local/bin/gcc * 0.00 HP 9000/770 HP-UX B.10.01 Gnu gcc 2.7.0 * 0.00 HP 9000/770 HP-UX B.10.01 HP cc A.10.11 + libc 76.3 -Ae * 0.00 HP Integrity HP-UX 11i V3 HP c99, A.06.23, +decfp * 0.00 Hitachi 3027-G32/3050 HI-UX 04.00 c89 (1.2) * 0.00 IBM PowerPC 43P AIX 4.1 /bin/c89 * 0.00 IBM PowerPC 43P AIX 4.1 /bin/cc * 0.00 IBM PowerPC 43P AIX 4.1 /bin/xlC * 0.00 IBM PowerPC 43P AIX 4.1 /usr/bin/c89 * 0.00 IBM PowerPC 43P AIX 4.1 /usr/bin/cc * 0.00 IBM PowerPC 43P AIX 4.1 /usr/local/bin/g++ * 0.00 IBM PowerPC 43P AIX 4.1 /usr/local/bin/gcc * 0.00 IBM PowerPC 43P AIX 4.2 /bin/c89 * 0.00 IBM PowerPC 43P AIX 4.2 /bin/cc * 0.00 IBM PowerPC 43P AIX 4.2 /bin/xlC * 0.00 IBM PowerPC 43P AIX 4.2 /usr/bin/c89 * 0.00 IBM PowerPC 43P AIX 4.2 /usr/bin/cc * 0.00 IBM PowerPC 43P AIX 4.2 /usr/local/bin/g++ * 0.00 IBM PowerPC 43P AIX 4.2 /usr/local/bin/gcc * 0.00 IBM RS6000 6015/DD1 AIX 4.1.2.0 c89 (xlC.C 3.1.1.0) * 0.00 IBM RS6000 7006/42T AIX 4.2.0.0 c89 (xlC.C 3.1.3.5) * 0.00 IBM RS6000 7010/250 AIX 4.1.4.0 c89 (xlC.C 3.1.3.5) * 0.00 IBM RS6000 7011/230 AIX 3.2.5.0 c89 (xlCcmp.* 2.1.3.0) * 0.00 IBM RS6000 7030/3AT AIX 4.1.5.0 c89 (xlC.C 3.1.4.0) * 0.00 IBM S/390 OS/390 V2R5 IBM C/C++ V2R4 * 0.00 Intel Core i5-64 Linux Fedora 15 gcc 4.6.0-9 (2011/05/30) + glibc-2.14-3 (x86_64) * 0.00 Intel PPro 150MHz Solaris 2.5.1 gcc v2.7.2, -O -ffloat-store * 0.00 Intel PPro 150MHz Solaris 2.5.1 sun cc PC3.0.1 21 Jan 1995, -O -fsimple * 0.00 Intel Pentium OS/2 Warp IBM Visual Age C++ 3.0 * 0.00 Intel Pentium 4 Windows XP LCC 2002/06/17 * 0.00 Intel Pentium 4 Windows XP Microsoft C/C++ V 14.00 aka Visual Studio 8 * 0.00 Intel Pentium 4 IA-32 Linux Fedora 10 Intel C/C++ icc 11.1 -std=c99 -strict-ansi -fp-model strict -O0 * 0.00 Intel Pentium/90 Windows NT 4.0 IBM Visual Age C/C++ V3.5 * 0.00 Intel x86 Solaris 2.6 cc (Workshop 4.2) * 0.00 Intel x86 Solaris 7 cc (Workshop 5.0) * 0.00 Intel x86? SCO UnixWare 7.1 cc 3.2 * 0.00 Mips SGI Irix cc -n32 -mips3 -O -lm * 0.00 SGI O2 R10000-SC IRIX 6.3 /usr/local/bin/g++ * 0.00 SGI O2 R10000-SC IRIX 6.3 /usr/local/bin/gcc * 0.00 SGI Origin/200-4 IRIX 6.4 /bin/CC * 0.00 SGI Origin/200-4 IRIX 6.4 /bin/c89 * 0.00 SGI Origin/200-4 IRIX 6.4 /bin/cc * 0.00 SGI Origin/200-4 IRIX 6.4 /usr/bin/CC * 0.00 SGI Origin/200-4 IRIX 6.4 /usr/bin/c89 * 0.00 SGI Origin/200-4 IRIX 6.4 /usr/bin/cc * 0.00 SGI Origin/200-4 IRIX 6.4 /usr/local/bin/g++ * 0.00 SGI Origin/200-4 IRIX 6.4 /usr/local/bin/gcc * 0.00 StrongARM+FPE 1.07M RiscBSD 1.2 gcc 2.7.2.1 * 0.00 Sun 4m sparc Solaris 2.3 Gnu gcc 2.7.0 * 0.00 Sun 4m sparc Solaris 2.3 Sun cc * 0.00 Sun 4m sparc Sun OS 4.1.4 Sun acc 3.0.1 * 0.00 Sun 4m sparc Sun OS 5.4 Gnu gcc 2.7.0 * 0.00 Sun 4m sparc Sun OS 5.4 Sun C 4.0 * 0.00 Sun 4m sparc Sun OS 5.4 cc (C 4.0) * 0.00 Sun SPARC 20/512 Solaris 2.6 /opt/SUNWspro/bin/CC * 0.00 Sun SPARC 20/512 Solaris 2.6 /opt/SUNWspro/bin/c89 * 0.00 Sun SPARC 20/512 Solaris 2.6 /opt/SUNWspro/bin/cc * 0.00 Sun SPARC 20/512 Solaris 2.6 /usr/local/bin/g++ * 0.00 Sun SPARC 20/512 Solaris 2.6 /usr/local/bin/gcc * 0.00 Sun SPARC 20/512 Solaris 2.6 /usr/local/bin/lcc -A -A * 0.00 Sun SPARC 20/512 Solaris 2.6 /usr/ucb/cc * 0.00 Sun SparcStation4 Solaris 2.5.1 gcc v2.7.2, -O -ffloat-store * 0.00 Sun SparcStation4 Solaris 2.5.1 sun cc SC4.0 18 Oct 1995 C 4.0, -O -fsimple=0 * 0.00 Sun sparc Sun OS 5.5.1 ACE CoSy cc * 0.00 Ultra Sparc UXP/DS V20L10 fcc (Fujitsu C V12L10) * 0.02 Amiga1200 68030/882 AmigaOS v39 (3.0) SAS/C 6.58 math=ffp [double is 24 bits] * 0.02 DECstation 5000/200 ULTRIX 4.3 /bin/cc * 0.02 DECstation 5000/200 ULTRIX 4.3 /usr/bin/cc * 0.02 DECstation 5000/200 ULTRIX 4.3 /usr/local/bin/g++ * 0.02 DECstation 5000/200 ULTRIX 4.3 /usr/local/bin/gcc * 0.02 DECstation 5000/200 ULTRIX 4.3 /usr/local/bin/lcc -A -A * 0.02 IBM AS/400 IBM OS/400 IBM C/C++ ? * 0.02 Motorola M-CORE SDS simulator dcc (Diab Data 4.3a) * 0.02 Motorola M-CORE SDS simulator dcc (Diab Data 4.3b) * 0.02 Sun UltraSPARC Sun Solaris 2.5 Apogee-C SPARC rel 4.0 -fast * 0.02 Unisys A18 MCP (SSR 44.1) A Series C++ * 1.60 HP 9000 715 HP-UX A.09.05 c89 (A.09.61) * 1.60 HP 9000 715 HP-UX A.09.05 c89 (A.09.77) * 1.60 HP 9000 735 HP-UX A.09.07 c89 (A.09.73) * 1.60 HP 9000 777/C100 HP-UX A.09.07 c89 (A.09.77) * 1.60 HP 9000/735 HP-UX A.09.07 Gnu gcc 2.7.0 * 1.60 HP 9000/735 HP-UX A.09.07 HP cc 9.73 -Ae * 3.34 MIPS R10000 UX/4800 R13.5 NEC R13.5 * 3.34 MIPS R4400 UX/4800 R11.5 NEC R11.5 * 4.48 Intel x86 DG/UX 5.4? cc (Data General 4.20MU04?) * 7.09 Intel 80486 ISC 4.0.1 cc * 7.09 Intel 80486DX OS/2 Warp Gnu gcc 2.5.7 + emx 0.8h * 7.09 Intel 80486DX OS/2 Warp Gnu gcc 2.7.2 + emx 0.9b + fix05 * 7.09 Intel 80486DX OS/2 Warp Gnu gcc 2.7.2.1 + emx 0.9c + fix02 * 7.09 Intel 80486DX PC DOS Borland C/C++ 4.00 in C mode * 7.09 Intel 80486DX PC DOS Borland Turbo C 2.01 * 7.09 Intel 80486DX PC DOS Symantec C/C++ 7.0r1x in C mode * 7.09 Intel 80486DX PC DOS Symantec C/C++ 7.0r1x in C++ mode * 7.09 Intel 80486DX Windows 3.1 Borland C/C++ 4.00 in C++ mode * 7.09 Intel Core2 Duo Linux Fedora 14 Gnu gcc 4.5.1-4 + glibc 2.12.90-15; -std=gnu99 -frounding-math * 7.09 Intel Core2 Duo Linux Fedora 15 Gnu gcc 4.6.1-9 + glibc 2.14-5; -std=gnu99 -frounding-math * 7.09 Intel Core2 Duo Linux Fedora 16 Gnu gcc 4.6.2-1 + glibc 2.14.90-21; -std=gnu99 -frounding-math * 7.09 Intel Core2 Duo Linux Fedora 16 clang 2.9-6 + glibc-2.14.90-24 * 7.09 Intel Core2 Duo Linux Fedora 16 pcc 1.0.0-2 (2011/12/16) + glibc-2.14.90-24 * 7.09 Intel Core2 Duo OS/2 eCS 2.0 Open Watcom C/C++ v1.8 * 7.09 Intel Core2 Duo OS/2 eCS 2.0 Open Watcom C/C++ v1.9 * 7.09 Intel Pentium 4 Linux Fedora 6 gcc 4.1.2-13.fc6 + glibc2.5-18.fc6 * 7.09 Intel Pentium 4 RedHat Linux 8 gcc 3.2 + glibc 2.2.93-5 * 7.09 Intel Pentium 4 SuSE Linux 9.1 gcc 3.3.3-41 + glibc 2.3.3-97 * 7.09 Intel Pentium 4 Windows XP Metrowerks CodeWarrior Pro 8.3 * 7.09 Intel Pentium 4 Windows XP Metrowerks CodeWarrior Pro 9.2 * 7.09 Intel Pentium 4 Linux Fedora 10 gcc 4.3.2-7, glibc 2.9-3; -std=gnu99 -frounding-math * 7.09 Intel Pentium 4 Linux Fedora 11 gcc 4.4.0-4, glibc 2.10.1-2; -std=gnu99 -frounding-math * 7.09 Intel Pentium 4 Linux Fedora 11 gcc 4.4.1-2, glibc 2.10.1-5; -std=gnu99 -frounding-math * 7.09 Intel Pentium 4 Linux Fedora 14 gcc 4.5.1-4 + glibc 2.12.90-15; -std=gnu99 -frounding-math * 7.09 Intel Pentium 4 OS/2 eCS 1.1 Open Watcom C/C++ v1.3 * 7.09 Intel Pentium 4 OS/2 eCS 1.1 Open Watcom C/C++ v1.4 * 7.09 Intel Pentium 4 OS/2 eCS 1.1 Open Watcom C/C++ v1.5 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.16 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.19 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.20 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.35.6 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.38 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.39 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.47 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.48 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.50 * 7.09 Intel Pentium 4 Windows XP Digital Mars C/C++ V8.51 * 7.09 Intel Pentium 4 Windows XP LCC 2002/02/10 * 7.09 Intel Pentium 4 Windows XP LCC 2004/07/26 * 7.09 Intel Pentium 4 Windows XP LCC 2006/04/10 * 7.09 Intel Pentium 4 Windows XP LCC 2008/07/24 -ansic * 7.09 Intel Pentium 4 Windows XP Microsoft VC++ V 12.00 aka Visual Studio 6.0 * 7.09 Intel Pentium II MMX Linux 2.0.33 /usr/bin/cc * 7.09 Intel Pentium II MMX Linux 2.0.33 /usr/bin/g++ * 7.09 Intel Pentium II MMX Linux 2.0.33 /usr/bin/gcc * 7.09 Intel Pentium MMX 200 Linux 2.0.30 /usr/bin/cc * 7.09 Intel Pentium MMX 200 Linux 2.0.30 /usr/bin/g++ * 7.09 Intel Pentium MMX 200 Linux 2.0.30 /usr/bin/gcc * 7.09 Intel Pentium/90 Windows NT 4.0 Microsoft C/C++ Visual 4.2 * 7.09 Intel Pentium/90 Windows NT 4.0 Symantec C/C++ V7.01 * 7.09 Intel PentiumPro/200 OS/2 4 Merlin Gnu gcc 2.8.1 + emx 0.9d * 7.09 Intel PentiumPro/200 OS/2 4 Merlin Metrowerks CodeWarrior Pro 4 * 7.09 Intel PentiumPro/200 OS/2 4 Merlin Metrowerks CodeWarrior Pro 5 * 7.09 Intel PentiumPro/200 Windows NT 4.0 Intel C/C++ V2.4 -Op -Za -Od * 7.09 Intel PentiumPro/200 Windows NT 4.0 SP3 Borland C/C++ V5.01 (16-bit C mode) * 7.09 Intel PentiumPro/350 Windows NT 4.0 SP3 Microsoft VC++ V 12.00 aka Visual Studio 6.0 * 7.09 Intel x86 DYNIX/ptx V4.4.4 cc (Sequent V4.4.4) * 7.09 Intel x86 NCR 3.01.01 NCR cc 3.02 * 7.09 Intel x86 NCR 3.02 NCR cc 3.03 * 7.09 Intel x86 Windows NT 4.0 SP4 Visual C++ 5.0 * 7.09 Intel x86 Windows NT 4.0 SP4 Visual C++ 6.0 SP2 * 7.09 NeXT Turbostation Mach 3.3 /bin/cc * 7.09 NeXT Turbostation Mach 3.3 /usr/local/bin/g++ * 7.09 NeXT Turbostation Mach 3.3 /usr/local/bin/gcc * 7.09 Sun 4m sparc Sun OS 4.1.4 Gnu gcc 2.7.0 * 7.09 Sun SPARC 4/380 SunOS 4.1.3 /usr/lang/CC * 7.09 Sun SPARC 4/380 SunOS 4.1.3 /usr/lang/acc * 7.09 Sun SPARC 4/380 SunOS 4.1.3 /usr/local/bin/g++ * 7.09 Sun SPARC 4/380 SunOS 4.1.3 /usr/local/bin/gcc * 7.09 Sun SPARC 4/380 SunOS 4.1.3 /usr/local/bin/lcc -A -A * 7.11 Intel 80486DX ISC 4.0.1 gcc 2.7.2 * 7.13 Intel Pentium/90 Windows NT 4.0 Watcom v10.5 * 10.73 Intel Pentium/90 Windows NT 4.0 Borland C/C++ V5.01 * 10.73 MC68030/MC68882 System V.3 TAU ACE Expert C alfa-8.21 * 11.75 ARM + SWFP RiscOS Norcroft ARM v4.69 C [no options] * 21.98 Apple Mac PPC 603e Tenon MachTen gcc 2.7.2.1 * 21.98 Mips IP22 SGI Irix 5.2 Gnu gcc 2.7.2.f.1 * 21.98 Mips IP22 SGI Irix 5.2 cc * 21.98 Mips R4400+R4000 SGI Irix64 6.2 cc (C 6.2) * 21.98 Mips R4400+R4010 SGI Irix 5.3 cc (C 3.19) * 21.98 SGI Challenge L IRIX 5.3 /bin/CC * 21.98 SGI Challenge L IRIX 5.3 /bin/cc * 21.98 SGI Challenge L IRIX 5.3 /usr/bin/CC * 21.98 SGI Challenge L IRIX 5.3 /usr/bin/cc * 21.98 SGI Challenge L IRIX 5.3 /usr/local/bin/g++ * 21.98 SGI Challenge L IRIX 5.3 /usr/local/bin/gcc * 21.98 SGI Challenge L IRIX 5.3 /usr/local/bin/lcc -A -A * 21.98 SGI O2 R10000-SC IRIX 6.3 /bin/CC * 21.98 SGI O2 R10000-SC IRIX 6.3 /bin/c89 * 21.98 SGI O2 R10000-SC IRIX 6.3 /bin/cc * 21.98 SGI O2 R10000-SC IRIX 6.3 /usr/bin/CC * 21.98 SGI O2 R10000-SC IRIX 6.3 /usr/bin/c89 * 21.98 SGI O2 R10000-SC IRIX 6.3 /usr/bin/cc * 21.98 Sony NWS-5000 VP NEWS-OS 6.1.1 cc (ANSI C 3.18) * 23.40 Motorola M-CORE SDS simulator dcc (Diab Data 4.1a) * 23.40 Motorola M-CORE SDS simulator dcc (Diab Data 4.2a) * ??.?? HP 9000/735 HP-UX 10.01 /bin/cc [would not compile] * ??.?? HP 9000/735 HP-UX 10.01 /usr/bin/cc [would not compile] * ??.?? HP 9000/735 HP-UX 10.01 /usr/ccs/bin/cc [would not compile] * ??.?? SGI O2 R10000-SC IRIX 6.3 /usr/local/bin/lcc -A -A [would not link] * ??.?? SGI Origin/200-4 IRIX 6.4 /usr/local/bin/lcc -A -A [DBL_MANT_DIG is 0] * ??.?? Sun SPARC 4/380 SunOS 4.1.3 /bin/cc [no float.h] * ??.?? Sun SPARC 4/380 SunOS 4.1.3 /usr/bin/cc [no float.h] * ??.?? Sun SPARC 4/380 SunOS 4.1.3 /usr/ucb/cc [no float.h] * NaN NeXT Turbostation Mach 3.3 /usr/local/bin/lcc -A -A [FLT_RADIX is -1] * * I wish to acknowledge the following people for taking the time and effort * to run this test and sending me their results: * Nelson H. F. Beebe, Center for Scientific Computing, University of Utah * L. Busby * Rex Jaeschke, consultant * Larry Jones * David S. Schwab * Jonathan Ziebell * * MODIFICATION HISTORY: * * 1996/12/02 - Create; calculate approximate number of bits in error. * 1997/01/22 - Add in ULPs error calculation. * 1998/07/07 - Add many more system's results. * 1998/07/08 - Detect FLT_RADIX < 2. Detect small precision for double. * 1999/08/11 - Add many more system's results. * 2000/03/01 - Make classification explicit in each file. * 2000/03/01 - Remove confidential so can post to public ftp site. * 2000/07/23 - Add "using namespace std;" for C++ usage. * 2003/02/17 - Add Pass/Fail messages. * 2003/02/20 - Add ability to tailor via external file (TAILOR). * 2003/02/22 - Add FIX_IMPLICIT_FLUSH. * 2004/07/30 - Update DEBUG section. * 2006/07/25 - Indent #if's. * 2007/11/21 - Add const as per PC-Lint 8. * 2008/07/14 - Shorten marco symbols to less than 32 chars. * 2008/11/29 - Suppress info messages if RETVAL defined (part of test suite). * 2009/04/28 - Another suppress info messages if RETVAL defined. * 2009/07/01 - Update DEBUG section. * 2012/01/23 - Add C11 (which replaced C99 in December 2011). * ***********************************************************************/ #ifdef TAILOR /* A way to tailor via external file */ #include "tsin.h" /* A place to define overrides */ #endif #ifdef DEBUG /* local override of FIXes to force errors to show */ #ifdef DEBUG2 /* Kills some compilers */ #undef FIX_NAMESPACE_STD #endif #endif #include /* FLT_RADIX, DBL_MANT_DIG, DBL_EPSILON */ #include /* sin(), log() */ #include /* printf() */ #ifdef DEBUG /* local override of FIXes to force errors to show */ #ifdef DEBUG3 #endif #undef FIX_IMPLICIT_FLUSH #endif #ifdef DEBUG4 #undef RETVAL #endif #ifndef FIX_NAMESPACE_STD #ifdef __cplusplus /* For C++ to call C functions */ using namespace std; /* Add implicit std:: to each function call */ #endif #endif int main(void) { double const correct = -3.014435335948844921433028000865009959025e-5; double const base = (double) FLT_RADIX; double const prec = (double) DBL_MANT_DIG; double calculate; /* sin(355.0) */ double abs_error; /* absolute error */ double rel_error; /* relative error */ double ulp_error; /* unit last place error */ double eps; /* epsilon in terms of bits */ double bits_cor; /* number of bits correct in answer */ double bits_bad; /* number of bits bad in answer */ double bits_tot; /* total number of bits in double */ double log_2; /* log(2) */ #ifndef TAILOR (void)printf("Info: 'TAILOR' not defined => NOT using any bug workarounds.\n"); #endif calculate = sin(355.0); #ifndef RETVAL (void) printf("sin(355) = %.17e from math library.\n", calculate); #endif #if (FLT_RADIX < 2) (void) printf("Failed: FLT_RADIX has illegal value: %i", (int) FLT_RADIX); goto death; #endif eps = DBL_EPSILON / base; /* base ** -precision */ log_2 = log(2.0); switch (FLT_RADIX) { case 2: bits_tot = prec; break; case 4: bits_tot = 2.0 * prec; break; case 8: bits_tot = 3.0 * prec; break; case 16: bits_tot = 4.0 * prec; break; default: bits_tot = (log(base) / log_2) * prec; /* base-2 log( radix ) */ break; } /* * Absolute error */ abs_error = (calculate - correct); if (abs_error < 0.0) { abs_error = -abs_error; }; /* * Relative error */ rel_error = (abs_error) / correct; if (rel_error < 0.0) { rel_error = -rel_error; } if (0.0 == rel_error) { bits_bad = 0.0; } else { bits_cor = -log(rel_error) / log_2; bits_bad = bits_tot - bits_cor; } /* * 2**-16 < |sin(355)| < 2**-15 * |sin(355)| * 32768 = 0.98777, eg, in binade just below 1.0 * eps = base ** -prec = ULP spacing in binade just below 1.0 * eps / 32768 = ULP spacing of sin(355) in terms of base-2 * Absolute error / spacing of correct answer = ULPs error w.r.t. correct */ ulp_error = abs_error * 32768.0 / eps; if( 2.0 < ulp_error ) { (void) printf("sin(355) = %.17e is correct answer.\n", correct); (void) printf("About %.2f bits are wrong out of %.2f total bits.\n", bits_bad, bits_tot); (void) printf("That is about %.2f ULPs (Units Last Place) bits error.\n", ulp_error); } if (bits_tot < 33.22) { /* base-2 log of 10**10 */ (void) printf("ERROR: double has too small precision: %.2f", bits_tot); } #ifdef DEBUG (void) printf("eps =%.25g\n", eps); (void) printf("abs =%.25g\n", abs_error); (void) printf("ulp =%.25g\n", ulp_error); (void) printf("rad =%.25g\n", base); (void) printf("prec=%.25g\n", prec); #endif if( ulp_error <= 2.0 ){ (void)printf("Test ( Pass ) {} \n"); }else{ (void)printf("Test Failed due to ULPs error being too large.\n"); } #if (FLT_RADIX < 2) death:; #endif #ifdef FIX_IMPLICIT_FLUSH (void)fflush(stdout); /* need explicit flush */ #endif #if (defined RETVAL) && (defined STANDALONE_TEST) return RETVAL; /* Being run as part of test suite */ #else return 0; #endif }