<h3><details><summary>Original Reporter info from Mantis: <small>Wolfgang Ehrhardt</small></summary><small> - **Reporter name:** </small></details></h3> ## Description: The RTL function math.ldexp is implemented as ``` pascal function ldexp(x : float;const p : Integer) : float; begin ldexp:=x*intpower(2.0,p); end; ``` This will give spurious overflows if the absolute value<br/> abs(p) of the exponent is greater than 1023 (for double). ## Steps to reproduce: Compile and run the following program with the 64-bit compiler ``` pascal program ldexpp; {$apptype console} {$mode delphi} uses sysutils, math; var x,y,d: double; begin writeln('Spurious overflows in ldexp'); try writeln('Test 1'); d := 1; x := ldexp(d, -1030); writeln('x = ldexp(d, -1030) = ',x); except on E: Exception do writeln('x = ldexp(1, -1030) should be 8.6916947597937E-311 : ', E.Message); end; try writeln('Test 2'); d := 1; x := ldexp(d, -800); writeln('x = ldexp(d, -800) = ',x); y := ldexp(x, 1500); writeln('y = ldexp(x, 1500) = ',y); except on E: Exception do writeln('y = ldexp(x, 1500) should be 5.26013590154837E+210 : ', E.Message); end; try writeln('Test 3'); d := 1; x := ldexp(d, 700); writeln('x = ldexp(d, 700) = ',x); y := ldexp(x, -1200); writeln('y = ldexp(x, -1200) = ',y); except on E: Exception do writeln('y = ldexp(x, -1200) should be 3.0549363634996E-151 : ', E.Message); end; end. ``` D:\Work\DAMath\fpcbugs>D:\FPC304\bin\i386-win32\ppcrossx64.exe ldexpp.pas<br/> Free Pascal Compiler version 3.0.4 [2017/10/06] for x86_64<br/> Copyright (c) 1993-2017 by Florian Klaempfl and others<br/> Target OS: Win64 for x64<br/> Compiling ldexpp.pas<br/> Linking ldexpp.exe<br/> 42 lines compiled, 0.2 sec, 72400 bytes code, 4948 bytes data<br/> D:\Work\DAMath\fpcbugs>ldexpp.exe<br/> Spurious overflows in ldexp<br/> Test 1<br/> x = ldexp(1, -1030) should be 8.6916947597937E-311 : Floating point overflow<br/> Test 2<br/> x = ldexp(d, -800) = 1.4996968138956310E-241<br/> y = ldexp(x, 1500) should be 5.26013590154837E+210 : Floating point overflow<br/> Test 3<br/> x = ldexp(d, 700) = 5.2601359015483735E+210<br/> y = ldexp(x, -1200) should be 3.0549363634996E-151 : Floating point overflow D:\Work\DAMath\fpcbugs>D:\FPC311\bin\i386-win32\ppcrossx64.exe ldexpp.pas<br/> Free Pascal Compiler version 3.1.1-r20:38794 [2018/04/22] for x86_64<br/> Copyright (c) 1993-2018 by Florian Klaempfl and others<br/> Target OS: Win64 for x64<br/> Compiling ldexpp.pas<br/> Linking ldexpp.exe<br/> 42 lines compiled, 0.2 sec, 70832 bytes code, 5172 bytes data<br/> D:\Work\DAMath\fpcbugs>ldexpp.exe<br/> Spurious overflows in ldexp<br/> Test 1<br/> x = ldexp(1, -1030) should be 8.6916947597937E-311 : Floating point overflow<br/> Test 2<br/> x = ldexp(d, -800) = 1.4996968138956310E-241<br/> y = ldexp(x, 1500) should be 5.26013590154837E+210 : Floating point overflow<br/> Test 3<br/> x = ldexp(d, 700) = 5.2601359015483735E+210<br/> y = ldexp(x, -1200) should be 3.0549363634996E-151 : Floating point overflow The 32-bit version prints the correct results D:\Work\DAMath\fpcbugs>fpc304 ldexpp.pas<br/> D:\Work\DAMath\fpcbugs>D:\FPC304\bin\i386-win32\fpc.exe ldexpp.pas<br/> Free Pascal Compiler version 3.0.4 [2017/10/06] for i386<br/> Copyright (c) 1993-2017 by Florian Klaempfl and others<br/> Target OS: Win32 for i386<br/> Compiling ldexpp.pas<br/> Linking ldexpp.exe<br/> 42 lines compiled, 0.2 sec, 65856 bytes code, 4132 bytes data<br/> D:\Work\DAMath\fpcbugs>ldexpp.exe<br/> Spurious overflows in ldexp<br/> Test 1<br/> x = ldexp(d, -1030) = 8.6916947597937554E-311<br/> Test 2<br/> x = ldexp(d, -800) = 1.4996968138956310E-241<br/> y = ldexp(x, 1500) = 5.2601359015483735E+210<br/> Test 3<br/> x = ldexp(d, 700) = 5.2601359015483735E+210<br/> y = ldexp(x, -1200) = 3.0549363634996047E-151 ## Additional information: Other compilers/libraries compute ldexp by manipulation of<br/> the exponent field of x. Delphi Tokyo uses helper types for 64-bit and the X87 FSCALE<br/> instruction for 32-bit (as does Virtual Pascal). C libraries uses a more directly exponent manipulation, see e.g.<br/> FDLIBM s_ldexp.c (http://www.netlib.org/fdlibm/s_ldexp.c)<br/> and s_scalbn.c (http://www.netlib.org/fdlibm/s_scalbn.c) This bug is also present for extended with larger exponents. Source code indicates that ldexp will also produce overflows for other platforms. This bug is related to issue ID 34124<br/> (https://bugs.freepascal.org/view.php?id=34124) ## Mantis conversion info: - **Mantis ID:** 34125 - **OS:** Windows - **OS Build:** Win7 / 64 - **Platform:** X86_64 (X86) - **Version:** 3.0.4