Patchwork [v2] Add powf bench tests

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Submitter Paul Clarke
Date June 12, 2017, 8:19 p.m.
Message ID <d50b8d5e-b53b-3bd5-35ae-c33f6a0793ad@us.ibm.com>
Download mbox | patch
Permalink /patch/20973/
State Superseded
Delegated to: Joseph Myers
Headers show

Comments

Paul Clarke - June 12, 2017, 8:19 p.m.
2017-06-12  Paul A. Clarke  <pc@us.ibm.com>

Add powf() bench test with input which covers these cases:
- positive base to positive exponent
- exponent 0
- exponent 1
- exponent -1
- squared
- squareroot
- negative base to even exponent
- negative base to odd exponent
- negative base to non-integer exponent
- base 0
- 1 to negative exponent
- -1 to negative exponent
- -1 to non-integer exponent
- -1 to odd exponent
- -1 to even exponent
- small base
- small exponent

	* benchtests/Makefile (bench-math): Add powf.
	* benchtests/powf-inputs: New file.
---
Changes in v2:
Joseph caught me being lazy by using the input for pow tests, which often results in bad/uninteresting input data.  (Good catch!)  I've now created a new input file which covers a lot of the special cases and the fairly generic case as well.

 benchtests/Makefile    |   2 +-
 benchtests/powf-inputs | 410 +++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 411 insertions(+), 1 deletion(-)
 create mode 100644 benchtests/powf-inputs
Joseph Myers - June 12, 2017, 8:28 p.m.
On Mon, 12 Jun 2017, Paul Clarke wrote:

> +## name: negative base to even exponent
> +-0x1.fffffep+127, -0x1.8p+3
> +-0x1.fffffep+127, -0x1.cccccep+2
> +-0x1.fffffep+127, -0x1.33333p+1
> +-0x1.fffffep+127, 0x1.333338p+1
> +-0x1.fffffep+127, 0x1.ccccdp+2

Many of these are obviously not integer exponents.

> +## name: negative base to odd exponent
> +-0x1.fffffep+127, -0x1.6p+3
> +-0x1.fffffep+127, -0x1.8cccccp+2
> +-0x1.fffffep+127, -0x1.66666p+0
> +-0x1.fffffep+127, 0x1.b33338p+1
> +-0x1.fffffep+127, 0x1.066668p+3

Likewise.

I don't actually think the cases with NaN results (and other special 
cases) are particularly interesting for benchmarking; they're thoroughly 
covered in the tests of correctness, but if NaN results are common enough 
in your application that it's worth optimizing for that case, there's 
something wrong with your application.  That is, there should be a lot 
more of the ordinary cases (ones where powf actually has to compute a log 
and do exponentiation) in the benchmark than of the special cases.

Patch

diff --git a/benchtests/Makefile b/benchtests/Makefile
index 7f5fda5..f49e9a0 100644
--- a/benchtests/Makefile
+++ b/benchtests/Makefile
@@ -23,7 +23,7 @@  subdir := benchtests
 include ../Makeconfig
 bench-math := acos acosh asin asinh atan atanh cos cosh exp exp2 log log2 \
 	      modf pow rint sin sincos sinh sqrt tan tanh fmin fmax fminf \
-	      fmaxf
+	      fmaxf powf
 
 bench-pthread := pthread_once
 
diff --git a/benchtests/powf-inputs b/benchtests/powf-inputs
new file mode 100644
index 0000000..6cdb05b
--- /dev/null
+++ b/benchtests/powf-inputs
@@ -0,0 +1,410 @@ 
+## args: float:float
+## ret: float
+## includes: math.h
+## name: positive base to positive exponent
+0x0p+0, 0x0p+0
+0x0p+0, 0x1.22e8bap+2
+0x0p+0, 0x1.22e8bap+3
+0x0p+0, 0x1.b45d18p+3
+0x0p+0, 0x1.22e8bap+4
+0x0p+0, 0x1.6ba2eap+4
+0x0p+0, 0x1.b45d18p+4
+0x0p+0, 0x1.fd1746p+4
+0x0p+0, 0x1.22e8bap+5
+0x0p+0, 0x1.4745d2p+5
+0x0p+0, 0x1.6ba2eap+5
+0x0p+0, 0x1.9p+5
+0x1.22e8bap+2, 0x0p+0
+0x1.22e8bap+2, 0x1.22e8bap+2
+0x1.22e8bap+2, 0x1.22e8bap+3
+0x1.22e8bap+2, 0x1.b45d18p+3
+0x1.22e8bap+2, 0x1.22e8bap+4
+0x1.22e8bap+2, 0x1.6ba2eap+4
+0x1.22e8bap+2, 0x1.b45d18p+4
+0x1.22e8bap+2, 0x1.fd1746p+4
+0x1.22e8bap+2, 0x1.22e8bap+5
+0x1.22e8bap+2, 0x1.4745d2p+5
+0x1.22e8bap+2, 0x1.6ba2eap+5
+0x1.22e8bap+2, 0x1.9p+5
+0x1.22e8bap+3, 0x0p+0
+0x1.22e8bap+3, 0x1.22e8bap+2
+0x1.22e8bap+3, 0x1.22e8bap+3
+0x1.22e8bap+3, 0x1.b45d18p+3
+0x1.22e8bap+3, 0x1.22e8bap+4
+0x1.22e8bap+3, 0x1.6ba2eap+4
+0x1.22e8bap+3, 0x1.b45d18p+4
+0x1.22e8bap+3, 0x1.fd1746p+4
+0x1.22e8bap+3, 0x1.22e8bap+5
+0x1.22e8bap+3, 0x1.4745d2p+5
+0x1.22e8bap+3, 0x1.6ba2eap+5
+0x1.22e8bap+3, 0x1.9p+5
+0x1.b45d18p+3, 0x0p+0
+0x1.b45d18p+3, 0x1.22e8bap+2
+0x1.b45d18p+3, 0x1.22e8bap+3
+0x1.b45d18p+3, 0x1.b45d18p+3
+0x1.b45d18p+3, 0x1.22e8bap+4
+0x1.b45d18p+3, 0x1.6ba2eap+4
+0x1.b45d18p+3, 0x1.b45d18p+4
+0x1.b45d18p+3, 0x1.fd1746p+4
+0x1.b45d18p+3, 0x1.22e8bap+5
+0x1.b45d18p+3, 0x1.4745d2p+5
+0x1.b45d18p+3, 0x1.6ba2eap+5
+0x1.b45d18p+3, 0x1.9p+5
+0x1.22e8bap+4, 0x0p+0
+0x1.22e8bap+4, 0x1.22e8bap+2
+0x1.22e8bap+4, 0x1.22e8bap+3
+0x1.22e8bap+4, 0x1.b45d18p+3
+0x1.22e8bap+4, 0x1.22e8bap+4
+0x1.22e8bap+4, 0x1.6ba2eap+4
+0x1.22e8bap+4, 0x1.b45d18p+4
+0x1.22e8bap+4, 0x1.fd1746p+4
+0x1.22e8bap+4, 0x1.22e8bap+5
+0x1.22e8bap+4, 0x1.4745d2p+5
+0x1.22e8bap+4, 0x1.6ba2eap+5
+0x1.22e8bap+4, 0x1.9p+5
+0x1.6ba2eap+4, 0x0p+0
+0x1.6ba2eap+4, 0x1.22e8bap+2
+0x1.6ba2eap+4, 0x1.22e8bap+3
+0x1.6ba2eap+4, 0x1.b45d18p+3
+0x1.6ba2eap+4, 0x1.22e8bap+4
+0x1.6ba2eap+4, 0x1.6ba2eap+4
+0x1.6ba2eap+4, 0x1.b45d18p+4
+0x1.6ba2eap+4, 0x1.fd1746p+4
+0x1.6ba2eap+4, 0x1.22e8bap+5
+0x1.6ba2eap+4, 0x1.4745d2p+5
+0x1.6ba2eap+4, 0x1.6ba2eap+5
+0x1.6ba2eap+4, 0x1.9p+5
+0x1.b45d18p+4, 0x0p+0
+0x1.b45d18p+4, 0x1.22e8bap+2
+0x1.b45d18p+4, 0x1.22e8bap+3
+0x1.b45d18p+4, 0x1.b45d18p+3
+0x1.b45d18p+4, 0x1.22e8bap+4
+0x1.b45d18p+4, 0x1.6ba2eap+4
+0x1.b45d18p+4, 0x1.b45d18p+4
+0x1.b45d18p+4, 0x1.fd1746p+4
+0x1.b45d18p+4, 0x1.22e8bap+5
+0x1.b45d18p+4, 0x1.4745d2p+5
+0x1.b45d18p+4, 0x1.6ba2eap+5
+0x1.b45d18p+4, 0x1.9p+5
+0x1.fd1746p+4, 0x0p+0
+0x1.fd1746p+4, 0x1.22e8bap+2
+0x1.fd1746p+4, 0x1.22e8bap+3
+0x1.fd1746p+4, 0x1.b45d18p+3
+0x1.fd1746p+4, 0x1.22e8bap+4
+0x1.fd1746p+4, 0x1.6ba2eap+4
+0x1.fd1746p+4, 0x1.b45d18p+4
+0x1.fd1746p+4, 0x1.fd1746p+4
+0x1.fd1746p+4, 0x1.22e8bap+5
+0x1.fd1746p+4, 0x1.4745d2p+5
+0x1.fd1746p+4, 0x1.6ba2eap+5
+0x1.fd1746p+4, 0x1.9p+5
+0x1.22e8bap+5, 0x0p+0
+0x1.22e8bap+5, 0x1.22e8bap+2
+0x1.22e8bap+5, 0x1.22e8bap+3
+0x1.22e8bap+5, 0x1.b45d18p+3
+0x1.22e8bap+5, 0x1.22e8bap+4
+0x1.22e8bap+5, 0x1.6ba2eap+4
+0x1.22e8bap+5, 0x1.b45d18p+4
+0x1.22e8bap+5, 0x1.fd1746p+4
+0x1.22e8bap+5, 0x1.22e8bap+5
+0x1.22e8bap+5, 0x1.4745d2p+5
+0x1.22e8bap+5, 0x1.6ba2eap+5
+0x1.22e8bap+5, 0x1.9p+5
+0x1.4745d2p+5, 0x0p+0
+0x1.4745d2p+5, 0x1.22e8bap+2
+0x1.4745d2p+5, 0x1.22e8bap+3
+0x1.4745d2p+5, 0x1.b45d18p+3
+0x1.4745d2p+5, 0x1.22e8bap+4
+0x1.4745d2p+5, 0x1.6ba2eap+4
+0x1.4745d2p+5, 0x1.b45d18p+4
+0x1.4745d2p+5, 0x1.fd1746p+4
+0x1.4745d2p+5, 0x1.22e8bap+5
+0x1.4745d2p+5, 0x1.4745d2p+5
+0x1.4745d2p+5, 0x1.6ba2eap+5
+0x1.4745d2p+5, 0x1.9p+5
+0x1.6ba2eap+5, 0x0p+0
+0x1.6ba2eap+5, 0x1.22e8bap+2
+0x1.6ba2eap+5, 0x1.22e8bap+3
+0x1.6ba2eap+5, 0x1.b45d18p+3
+0x1.6ba2eap+5, 0x1.22e8bap+4
+0x1.6ba2eap+5, 0x1.6ba2eap+4
+0x1.6ba2eap+5, 0x1.b45d18p+4
+0x1.6ba2eap+5, 0x1.fd1746p+4
+0x1.6ba2eap+5, 0x1.22e8bap+5
+0x1.6ba2eap+5, 0x1.4745d2p+5
+0x1.6ba2eap+5, 0x1.6ba2eap+5
+0x1.6ba2eap+5, 0x1.9p+5
+0x1.9p+5, 0x0p+0
+0x1.9p+5, 0x1.22e8bap+2
+0x1.9p+5, 0x1.22e8bap+3
+0x1.9p+5, 0x1.b45d18p+3
+0x1.9p+5, 0x1.22e8bap+4
+0x1.9p+5, 0x1.6ba2eap+4
+0x1.9p+5, 0x1.b45d18p+4
+0x1.9p+5, 0x1.fd1746p+4
+0x1.9p+5, 0x1.22e8bap+5
+0x1.9p+5, 0x1.4745d2p+5
+0x1.9p+5, 0x1.6ba2eap+5
+0x1.9p+5, 0x1.9p+5
+## name: exponent 0
+-0x1.fffffep+127, 0x0p+0
+-0x1.333332p+127, 0x0p+0
+-0x1.999998p+125, 0x0p+0
+0x1.999998p+125, 0x0p+0
+0x1.333332p+127, 0x0p+0
+0x1.fffffep+127, 0x0p+0
+## name: negative base to even exponent
+-0x1.fffffep+127, -0x1.8p+3
+-0x1.fffffep+127, -0x1.cccccep+2
+-0x1.fffffep+127, -0x1.33333p+1
+-0x1.fffffep+127, 0x1.333338p+1
+-0x1.fffffep+127, 0x1.ccccdp+2
+-0x1.fffffep+127, 0x1.8p+3
+-0x1.999998p+127, -0x1.8p+3
+-0x1.999998p+127, -0x1.cccccep+2
+-0x1.999998p+127, -0x1.33333p+1
+-0x1.999998p+127, 0x1.333338p+1
+-0x1.999998p+127, 0x1.ccccdp+2
+-0x1.999998p+127, 0x1.8p+3
+-0x1.333332p+127, -0x1.8p+3
+-0x1.333332p+127, -0x1.cccccep+2
+-0x1.333332p+127, -0x1.33333p+1
+-0x1.333332p+127, 0x1.333338p+1
+-0x1.333332p+127, 0x1.ccccdp+2
+-0x1.333332p+127, 0x1.8p+3
+-0x1.999998p+126, -0x1.8p+3
+-0x1.999998p+126, -0x1.cccccep+2
+-0x1.999998p+126, -0x1.33333p+1
+-0x1.999998p+126, 0x1.333338p+1
+-0x1.999998p+126, 0x1.ccccdp+2
+-0x1.999998p+126, 0x1.8p+3
+-0x1.999998p+125, -0x1.8p+3
+-0x1.999998p+125, -0x1.cccccep+2
+-0x1.999998p+125, -0x1.33333p+1
+-0x1.999998p+125, 0x1.333338p+1
+-0x1.999998p+125, 0x1.ccccdp+2
+-0x1.999998p+125, 0x1.8p+3
+0x0p+0, -0x1.8p+3
+0x0p+0, -0x1.cccccep+2
+0x0p+0, -0x1.33333p+1
+0x0p+0, 0x1.333338p+1
+0x0p+0, 0x1.ccccdp+2
+0x0p+0, 0x1.8p+3
+## name: negative base to odd exponent
+-0x1.fffffep+127, -0x1.6p+3
+-0x1.fffffep+127, -0x1.8cccccp+2
+-0x1.fffffep+127, -0x1.66666p+0
+-0x1.fffffep+127, 0x1.b33338p+1
+-0x1.fffffep+127, 0x1.066668p+3
+-0x1.fffffep+127, 0x1.ap+3
+-0x1.999998p+127, -0x1.6p+3
+-0x1.999998p+127, -0x1.8cccccp+2
+-0x1.999998p+127, -0x1.66666p+0
+-0x1.999998p+127, 0x1.b33338p+1
+-0x1.999998p+127, 0x1.066668p+3
+-0x1.999998p+127, 0x1.ap+3
+-0x1.333332p+127, -0x1.6p+3
+-0x1.333332p+127, -0x1.8cccccp+2
+-0x1.333332p+127, -0x1.66666p+0
+-0x1.333332p+127, 0x1.b33338p+1
+-0x1.333332p+127, 0x1.066668p+3
+-0x1.333332p+127, 0x1.ap+3
+-0x1.999998p+126, -0x1.6p+3
+-0x1.999998p+126, -0x1.8cccccp+2
+-0x1.999998p+126, -0x1.66666p+0
+-0x1.999998p+126, 0x1.b33338p+1
+-0x1.999998p+126, 0x1.066668p+3
+-0x1.999998p+126, 0x1.ap+3
+-0x1.999998p+125, -0x1.6p+3
+-0x1.999998p+125, -0x1.8cccccp+2
+-0x1.999998p+125, -0x1.66666p+0
+-0x1.999998p+125, 0x1.b33338p+1
+-0x1.999998p+125, 0x1.066668p+3
+-0x1.999998p+125, 0x1.ap+3
+0x0p+0, -0x1.6p+3
+0x0p+0, -0x1.8cccccp+2
+0x0p+0, -0x1.66666p+0
+0x0p+0, 0x1.b33338p+1
+0x0p+0, 0x1.066668p+3
+0x0p+0, 0x1.ap+3
+## name: negative base to non-integer exponent
+-0x1.fffffep+127, -0x1.7p+3
+-0x1.fffffep+127, -0x1.acccccp+2
+-0x1.fffffep+127, -0x1.e66668p+0
+-0x1.fffffep+127, 0x1.733338p+1
+-0x1.fffffep+127, 0x1.ecccccp+2
+-0x1.fffffep+127, 0x1.9p+3
+-0x1.999998p+127, -0x1.7p+3
+-0x1.999998p+127, -0x1.acccccp+2
+-0x1.999998p+127, -0x1.e66668p+0
+-0x1.999998p+127, 0x1.733338p+1
+-0x1.999998p+127, 0x1.ecccccp+2
+-0x1.999998p+127, 0x1.9p+3
+-0x1.333332p+127, -0x1.7p+3
+-0x1.333332p+127, -0x1.acccccp+2
+-0x1.333332p+127, -0x1.e66668p+0
+-0x1.333332p+127, 0x1.733338p+1
+-0x1.333332p+127, 0x1.ecccccp+2
+-0x1.333332p+127, 0x1.9p+3
+-0x1.999998p+126, -0x1.7p+3
+-0x1.999998p+126, -0x1.acccccp+2
+-0x1.999998p+126, -0x1.e66668p+0
+-0x1.999998p+126, 0x1.733338p+1
+-0x1.999998p+126, 0x1.ecccccp+2
+-0x1.999998p+126, 0x1.9p+3
+-0x1.999998p+125, -0x1.7p+3
+-0x1.999998p+125, -0x1.acccccp+2
+-0x1.999998p+125, -0x1.e66668p+0
+-0x1.999998p+125, 0x1.733338p+1
+-0x1.999998p+125, 0x1.ecccccp+2
+-0x1.999998p+125, 0x1.9p+3
+0x0p+0, -0x1.7p+3
+0x0p+0, -0x1.acccccp+2
+0x0p+0, -0x1.e66668p+0
+0x0p+0, 0x1.733338p+1
+0x0p+0, 0x1.ecccccp+2
+0x0p+0, 0x1.9p+3
+## name: exponent 1
+-0x1.fffffep+127, 0x1p+0
+-0x1.333332p+127, 0x1p+0
+-0x1.999998p+125, 0x1p+0
+0x1.999998p+125, 0x1p+0
+0x1.333332p+127, 0x1p+0
+0x1.fffffep+127, 0x1p+0
+## name: exponent -1
+-0x1.fffffep+127, -0x1p+0
+-0x1.333332p+127, -0x1p+0
+-0x1.999998p+125, -0x1p+0
+0x1.999998p+125, -0x1p+0
+0x1.333332p+127, -0x1p+0
+0x1.fffffep+127, -0x1p+0
+## name: squared
+-0x1.fffffep+127, 0x1p+1
+-0x1.333332p+127, 0x1p+1
+-0x1.999998p+125, 0x1p+1
+0x1.999998p+125, 0x1p+1
+0x1.333332p+127, 0x1p+1
+0x1.fffffep+127, 0x1p+1
+## name: squareroot
+-0x1.fffffep+127, 0x1p-1
+-0x1.333332p+127, 0x1p-1
+-0x1.999998p+125, 0x1p-1
+0x1.999998p+125, 0x1p-1
+0x1.333332p+127, 0x1p-1
+0x1.fffffep+127, 0x1p-1
+## name: 1 to negative exponent
+0x1p+0, -0x1.fffffep+127
+0x1p+0, -0x1.999998p+127
+0x1p+0, -0x1.333332p+127
+0x1p+0, -0x1.999998p+126
+0x1p+0, -0x1.999998p+125
+0x1p+0, 0x0p+0
+## name: -1 to negative exponent
+-0x1p+0, -0x1.fffffep+127
+-0x1p+0, -0x1.999998p+127
+-0x1p+0, -0x1.333332p+127
+-0x1p+0, -0x1.999998p+126
+-0x1p+0, -0x1.999998p+125
+-0x1p+0, 0x0p+0
+## name: -1 to non-integer exponent
+-0x1p+0, -0x1.7p+3
+-0x1p+0, -0x1.acccccp+2
+-0x1p+0, -0x1.e66668p+0
+-0x1p+0, 0x1.733338p+1
+-0x1p+0, 0x1.ecccccp+2
+-0x1p+0, 0x1.9p+3
+## name: -1 to odd exponent
+-0x1p+0, -0x1.6p+3
+-0x1p+0, -0x1.8cccccp+2
+-0x1p+0, -0x1.66666p+0
+-0x1p+0, 0x1.b33338p+1
+-0x1p+0, 0x1.066668p+3
+-0x1p+0, 0x1.ap+3
+## name: base 0
+0x0p+0, -0x1.fffffep+127
+0x0p+0, -0x1.333332p+127
+0x0p+0, -0x1.999998p+125
+0x0p+0, 0x1.999998p+125
+0x0p+0, 0x1.333332p+127
+0x0p+0, 0x1.fffffep+127
+## name: -1 to even exponent
+-0x1p+0, -0x1.8p+3
+-0x1p+0, -0x1.cccccep+2
+-0x1p+0, -0x1.33333p+1
+-0x1p+0, 0x1.333338p+1
+-0x1p+0, 0x1.ccccdp+2
+-0x1p+0, 0x1.8p+3
+## name: small base
+0x1.fffffp-1, -0x1.fffffep+127
+0x1.fffffp-1, -0x1.333332p+127
+0x1.fffffp-1, -0x1.999998p+125
+0x1.fffffp-1, 0x1.999998p+125
+0x1.fffffp-1, 0x1.333332p+127
+0x1.fffffp-1, 0x1.fffffep+127
+0x1.fffff8p-1, -0x1.fffffep+127
+0x1.fffff8p-1, -0x1.333332p+127
+0x1.fffff8p-1, -0x1.999998p+125
+0x1.fffff8p-1, 0x1.999998p+125
+0x1.fffff8p-1, 0x1.333332p+127
+0x1.fffff8p-1, 0x1.fffffep+127
+0x1p+0, -0x1.fffffep+127
+0x1p+0, -0x1.333332p+127
+0x1p+0, -0x1.999998p+125
+0x1p+0, 0x1.999998p+125
+0x1p+0, 0x1.333332p+127
+0x1p+0, 0x1.fffffep+127
+0x1.000004p+0, -0x1.fffffep+127
+0x1.000004p+0, -0x1.333332p+127
+0x1.000004p+0, -0x1.999998p+125
+0x1.000004p+0, 0x1.999998p+125
+0x1.000004p+0, 0x1.333332p+127
+0x1.000004p+0, 0x1.fffffep+127
+0x1.000008p+0, -0x1.fffffep+127
+0x1.000008p+0, -0x1.333332p+127
+0x1.000008p+0, -0x1.999998p+125
+0x1.000008p+0, 0x1.999998p+125
+0x1.000008p+0, 0x1.333332p+127
+0x1.000008p+0, 0x1.fffffep+127
+0x1.00001p+0, -0x1.fffffep+127
+0x1.00001p+0, -0x1.333332p+127
+0x1.00001p+0, -0x1.999998p+125
+0x1.00001p+0, 0x1.999998p+125
+0x1.00001p+0, 0x1.333332p+127
+0x1.00001p+0, 0x1.fffffep+127
+## name: small exponent
+-0x1.fffffep+127, -0x1p-32
+-0x1.fffffep+127, -0x1.333334p-33
+-0x1.fffffep+127, -0x1.99999cp-35
+-0x1.fffffep+127, 0x1.9999ap-35
+-0x1.fffffep+127, 0x1.333334p-33
+-0x1.fffffep+127, 0x1p-32
+-0x1.333332p+127, -0x1p-32
+-0x1.333332p+127, -0x1.333334p-33
+-0x1.333332p+127, -0x1.99999cp-35
+-0x1.333332p+127, 0x1.9999ap-35
+-0x1.333332p+127, 0x1.333334p-33
+-0x1.333332p+127, 0x1p-32
+-0x1.999998p+125, -0x1p-32
+-0x1.999998p+125, -0x1.333334p-33
+-0x1.999998p+125, -0x1.99999cp-35
+-0x1.999998p+125, 0x1.9999ap-35
+-0x1.999998p+125, 0x1.333334p-33
+-0x1.999998p+125, 0x1p-32
+0x1.999998p+125, -0x1p-32
+0x1.999998p+125, -0x1.333334p-33
+0x1.999998p+125, -0x1.99999cp-35
+0x1.999998p+125, 0x1.9999ap-35
+0x1.999998p+125, 0x1.333334p-33
+0x1.999998p+125, 0x1p-32
+0x1.333332p+127, -0x1p-32
+0x1.333332p+127, -0x1.333334p-33
+0x1.333332p+127, -0x1.99999cp-35
+0x1.333332p+127, 0x1.9999ap-35
+0x1.333332p+127, 0x1.333334p-33
+0x1.333332p+127, 0x1p-32
+0x1.fffffep+127, -0x1p-32
+0x1.fffffep+127, -0x1.333334p-33
+0x1.fffffep+127, -0x1.99999cp-35
+0x1.fffffep+127, 0x1.9999ap-35
+0x1.fffffep+127, 0x1.333334p-33
+0x1.fffffep+127, 0x1p-32