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Date: Wed, 22 Apr 2020 19:16:02 +0200
From: Szabolcs Nagy <>
To: leijitang <>
Cc: "" <>,
	"zhangwentao (M)" <>,
	"wanghao (H)" <>,
	"Huangqiang (H)" <>
Subject: Re: Unexpected exceptions in  math functions

* leijitang <> [2020-04-22 13:56:46 +0000]:
> Hi all,
> Recently we update musl in our project from 1.1.2 to version 1.2.0. But there are some errors about math functions when running
> the opensource test cases for musl, which are passed in musl 1.1.2. These errors are about exp2(), pow() and powf().
> Logs are listed below.
> According to the commit message, the underflow exception is signaled if the result is in the subnormal range even if
> the result is exact (e.g. exp2(-1023.0)). But we got INEXACT exception at the same time, which is not as expected.
> Is this a problem?

underflow and inexact are always raised together.

since this implementation is not correctly rounded
it is expected that the result may have a tiny
error, which can result such failure. we also don't
guarantee correct inexact flag for math functions
other than the correctly rounded ones.
(note: spurious underflow is allowed by the standard,
musl avoids it when the result is not in the subnormal
range, but such exact subnormal cases may be wrong.)

to fix this the special case handling code would
need the original x and check if it's int when
dealing with subnormal results. this is not out
of question, but would increase register pressure
to keep x around.

> Otherwise, there is a overflow exception in powf(0x1.fffffep+127,0x1p+0) with FE_UPWARD rounding mode(log is also behind. As
> 0x1.fffffep+127 is the largest number that float can represent, there should not be INEXACT|OVERFLOW exceptions.
> If these are problems affirmed, is there any patch to fix this?

similar arugment can be made in this case: we return
inf so overflow is right and our result is only
incorrect by a tiny bit. on the other hand it would
be nice to get obvious exact cases right. unfortunately
this is not easy (the overflow problem can be fixed
like above, in the special case handling, but normal
range exact results may be off-by-one-ulp in non-nearest
rounding mode and that's hard to fix without slowdown).

i currently don't have a patch for these and i consider
them QoI issues not critical bugs.

> / $ ./exp2.exe
> src/math/special/exp2.h:12: bad fp exception: RN exp2(-0x1.ff8p+9)=0x1p-1023,  want 0 got INEXACT|UNDERFLOW
> src/math/special/exp2.h:18: bad fp exception: RN exp2(-0x1.ff8p+9)=0x1p-1023, want 0 got INEXACT|UNDERFLOW
> src/math/special/exp2.h:20: bad fp exception: RN exp2(-0x1p+10)=0x1p-1024, want 0 got INEXACT|UNDERFLOW
> src/math/special/exp2.h:21: bad fp exception: RN exp2(-0x1.004p+10)=0x1p-1025, want 0 got INEXACT|UNDERFLOW
> src/math/special/exp2.h:22: bad fp exception: RN exp2(-0x1.0c8p+10)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> / $ ./pow.exe
> src/math/crlibm/pow.h:13: bad fp exception: RN pow(0x1p+1,-0x1.0c8p+10)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:72: bad fp exception: RN pow(0x1p-1074,0x1p+0)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:73: bad fp exception: RN pow(0x1p-1042,0x1p+0)=0x1p-1042, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:75: bad fp exception: RN pow(-0x1p-1074,0x1p+0)=-0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:76: bad fp exception: RN pow(-0x1p-1042,0x1p+0)=-0x1p-1042, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:284: bad fp exception: RN pow(0x1p-1073,0x1p+0)=0x1p-1073, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:300: bad fp exception: RN pow(0x1p-1024,0x1p+0)=0x1p-1024, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:304: bad fp exception: RN pow(0x1p-1023,0x1p+0)=0x1p-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:310: bad fp exception: RN pow(0x1.ffffffffffffcp-1023,0x1p+0)=0x1.ffffffffffffcp-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:313: bad fp exception: RN pow(0x1.ffffffffffffep-1023,0x1p+0)=0x1.ffffffffffffep-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:338: bad fp exception: RN pow(0x1p-537,0x1p+1)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:437: bad fp exception: RN pow(0x1p+1,-0x1.0c8p+10)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:498: bad fp exception: RN pow(0x1p+350,-0x1.8p+1)=0x1p-1050, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:499: bad fp exception: RN pow(0x1p+700,-0x1.8p+0)=0x1p-1050, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:516: bad fp exception: RN pow(0x1p+1023,-0x1p+0)=0x1p-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:544: bad fp exception: RN pow(-0x1p-1073,0x1p+0)=-0x1p-1073, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:548: bad fp exception: RN pow(-0x1p-1024,0x1p+0)=-0x1p-1024, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:551: bad fp exception: RN pow(-0x1p-1023,0x1p+0)=-0x1p-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:557: bad fp exception: RN pow(-0x1.ffffffffffffcp-1023,0x1p+0)=-0x1.ffffffffffffcp-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:560: bad fp exception: RN pow(-0x1.ffffffffffffep-1023,0x1p+0)=-0x1.ffffffffffffep-1023, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:581: bad fp exception: RN pow(-0x1p-537,0x1p+1)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:655: bad fp exception: RN pow(-0x1p+1,-0x1.0c8p+10)=0x1p-1074, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:695: bad fp exception: RN pow(-0x1p+350,-0x1.8p+1)=-0x1p-1050, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/pow.h:708: bad fp exception: RN pow(-0x1p+1023,-0x1p+0)=-0x1p-1023, want 0 got INEXACT|UNDERFLOW
> / $ ./powf.exe
> src/math/ucb/powf.h:103: bad fp exception: RU powf(0x1.fffffep+127,0x1p+0)=0x1.fffffep+127, want 0 got INEXACT|OVERFLOW
> src/math/ucb/powf.h:530: bad fp exception: RN powf(0x1.fffff8p-127,0x1p+0)=0x1.fffff8p-127, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/powf.h:533: bad fp exception: RN powf(0x1.fffffcp-127,0x1p+0)=0x1.fffffcp-127, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/powf.h:719: bad fp exception: RN powf(-0x1.fffff8p-127,0x1p+0)=-0x1.fffff8p-127, want 0 got INEXACT|UNDERFLOW
> src/math/ucb/powf.h:722: bad fp exception: RN powf(-0x1.fffffcp-127,0x1p+0)=-0x1.fffffcp-127, want 0 got INEXACT|UNDERFLOW
> Regards

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