[Bug libstdc++/103005] New: experimental simd sin and cos with big arguments returns values bigger than 1

[Bug libstdc++/103005] New: experimental simd sin and cos with big arguments returns values bigger than 1

[andreas_roever at web dot de]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=103005

            Bug ID: 103005
           Summary: experimental simd sin and cos with big arguments
                    returns values bigger than 1
           Product: gcc
           Version: 11.2.0
            Status: UNCONFIRMED
          Severity: normal
          Priority: P3
         Component: libstdc++
          Assignee: unassigned at gcc dot gnu.org
          Reporter: andreas_roever at web dot de
  Target Milestone: ---

Created attachment 51704
  --> https://gcc.gnu.org/bugzilla/attachment.cgi?id=51704&action=edit
example program displaying the problem

there seems to be a bug in the sin and cos functions for the experimental/simd
header.

When giving a very big argument to those functions they return values outside
the range -1 .. 1. I understand that the result will be quite meaningless for
such big values. But I'd argue that it should always be in the range -1..1.

so calculating sin(-2985064393126969344) gives 2527133379.389218


This is on Linux

compiled with

g++-11.2.0 -g -march=native --std=c++20 test1.cpp

here the CPU info (for one core)

processor       : 0
vendor_id       : GenuineIntel
cpu family      : 6
model           : 94
model name      : Intel(R) Core(TM) i5-6500 CPU @ 3.20GHz
stepping        : 3
microcode       : 0xc2
cpu MHz         : 3301.335
cache size      : 6144 KB
physical id     : 0
siblings        : 4
core id         : 0
cpu cores       : 4
apicid          : 0
initial apicid  : 0
fpu             : yes
fpu_exception   : yes
cpuid level     : 22
wp              : yes
flags           : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov
pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb
rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology
nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est
tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid sse4_1 sse4_2 x2apic movbe popcnt
tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch
cpuid_fault invpcid_single pti ibrs ibpb stibp tpr_shadow vnmi flexpriority ept
vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm mpx
rdseed adx smap clflushopt intel_pt xsaveopt xsavec xgetbv1 xsaves dtherm ida
arat pln pts hwp hwp_notify hwp_act_window hwp_epp
vmx flags       : vnmi preemption_timer invvpid ept_x_only ept_ad ept_1gb
flexpriority tsc_offset vtpr mtf vapic ept vpid unrestricted_guest ple
shadow_vmcs pml
bugs            : cpu_meltdown spectre_v1 spectre_v2 spec_store_bypass l1tf mds
swapgs taa itlb_multihit srbds
bogomips        : 6399.96
clflush size    : 64
cache_alignment : 64
address sizes   : 39 bits physical, 48 bits virtual

[Bug libstdc++/103005] experimental simd sin and cos with big arguments returns values bigger than 1

[marxin at gcc dot gnu.org]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=103005

Martin Liška <marxin at gcc dot gnu.org> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
   Last reconfirmed|                            |2021-11-01
     Ever confirmed|0                           |1
                 CC|                            |marxin at gcc dot gnu.org,
                   |                            |redi at gcc dot gnu.org
             Status|UNCONFIRMED                 |NEW

--- Comment #1 from Martin Liška <marxin at gcc dot gnu.org> ---
Confirmed.

[Bug libstdc++/103005] experimental simd sin and cos with big arguments returns values bigger than 1

[andreas_roever at web dot de]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=103005

--- Comment #2 from Andreas Röver <andreas_roever at web dot de> ---
I think the source of the problem is function

__fold_input(const simd<double, _Abi>& __x)

in simd_math.h

this function should return values between -pi/4 and pi/4 but doesn't for the
big argument. E.g for 

2985064393126969344

it returns

27.678747

according to wolfram alpha it should return 

0.189812

This "big" value throws off the calculation of the power series that is
performed after this


the 27.678646 is the result of a rounding error

2985064393126969344 / (pi/2) is (according to wolfram alpha again) 

1900351014455063569.620838

but the CPU gets

1900351014455063552

This seems to be the closest value that the CPU can get to the real value.

the difference between those 2 times pi/2 is the above mentioned 27.67...

... now my numerics skills are not good enough to find a cure for that problem.

[Bug libstdc++/103005] experimental simd sin and cos with big arguments returns values bigger than 1

[andreas_roever at web dot de]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=103005

--- Comment #3 from Andreas Röver <andreas_roever at web dot de> ---
I think the source of the problem is function

__fold_input(const simd<double, _Abi>& __x)

in simd_math.h

this function should return values between -pi/4 and pi/4 but doesn't for the
big argument. E.g for 

2985064393126969344

it returns

27.678747

according to wolfram alpha it should return 

0.189812

This "big" value throws off the calculation of the power series that is
performed after this


the 27.678646 is the result of a rounding error

2985064393126969344 / (pi/2) is (according to wolfram alpha again) 

1900351014455063569.620838

but the CPU gets

1900351014455063552

This seems to be the closest value that the CPU can get to the real value.

the difference between those 2 times pi/2 is the above mentioned 27.67...

... now my numerics skills are not good enough to find a cure for that problem.