Use the const variable Ln2 in math/const.go for function acosh.
Change-Id: I5381d03dd3142c227ae5773ece9be6c8f377615e
Reviewed-on: https://go-review.googlesource.com/c/go/+/232517
Reviewed-by: Robert Griesemer <gri@golang.org>
Trust: Robert Griesemer <gri@golang.org>
Trust: Giovanni Bajo <rasky@develer.com>
While reading the source code of the math/big package, I found the SetString function example of float type missing.
Change-Id: Id8c16a58e2e24f9463e8ff38adbc98f8c418ab26
Reviewed-on: https://go-review.googlesource.com/c/go/+/232804
Run-TryBot: Ian Lance Taylor <iant@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
Simplifying some code without compromising performance.
My CPU is Intel Xeon Gold 6161, 2.20GHz, 64-bit operating system.
The memory is 8GB. This is my test environment, I hope to help you judge.
Benchmark:
name old time/op new time/op delta
Log1p-4 21.8ns ± 5% 21.8ns ± 4% ~ (p=0.973 n=20+20)
Change-Id: Icd8f96f1325b00007602d114300b92d4c57de409
Reviewed-on: https://go-review.googlesource.com/c/go/+/233940
Reviewed-by: Robert Griesemer <gri@golang.org>
Replaced almost every use of Bytes with FillBytes.
Note that the approved proposal was for
func (*Int) FillBytes(buf []byte)
while this implements
func (*Int) FillBytes(buf []byte) []byte
because the latter was far nicer to use in all callsites.
Fixes#35833
Change-Id: Ia912df123e5d79b763845312ea3d9a8051343c0a
Reviewed-on: https://go-review.googlesource.com/c/go/+/230397
Reviewed-by: Robert Griesemer <gri@golang.org>
Implement special case handling and testing to ensure
conformance with the C99 standard annex G.6 Complex arithmetic.
Fixes#29320
Change-Id: Id72eb4c5a35d5a54b4b8690d2f7176ab11028f1b
Reviewed-on: https://go-review.googlesource.com/c/go/+/220689
Reviewed-by: Robert Griesemer <gri@golang.org>
When I browsed the source code, I saw that there is no corresponding example of this function. I am not sure if there is a need for an increase, this is my first time to submit CL.
Change-Id: Idbf4e1e1ed2995176a76959d561e152263a2fd26
Reviewed-on: https://go-review.googlesource.com/c/go/+/230741
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
Originally, we use an assembly function that returns a boolean result to
tell whether the machine has vector facility or not. It is now no longer
needed when we can directly use cpu.S390X.HasVX variable.
Change-Id: Ic1dae851982532bcfd9a9453416c112347f21d87
Reviewed-on: https://go-review.googlesource.com/c/go/+/230318
Reviewed-by: Michael Munday <mike.munday@ibm.com>
Run-TryBot: Michael Munday <mike.munday@ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Originally, we use an assembly function that returns a boolean result to
tell whether the machine has vector facility or not. It is now no longer
needed when we can directly use cpu.S390X.HasVX variable.
Change-Id: Ic3ffeb9e63238ef41406d97cdc42502145ddb454
Reviewed-on: https://go-review.googlesource.com/c/go/+/230319
Reviewed-by: Michael Munday <mike.munday@ibm.com>
Run-TryBot: Michael Munday <mike.munday@ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
This CL optimizes code that uses a carry from a function such as
bits.Add64 as the condition in an if statement. For example:
x, c := bits.Add64(a, b, 0)
if c != 0 {
panic("overflow")
}
Rather than converting the carry into a 0 or a 1 value and using
that as an input to a comparison instruction the carry flag is now
used as the input to a conditional branch directly. This typically
removes an ADD LOGICAL WITH CARRY instruction when user code is
doing overflow detection and is closer to the code that a user
would expect to generate.
Change-Id: I950431270955ab72f1b5c6db873b6abe769be0da
Reviewed-on: https://go-review.googlesource.com/c/go/+/219757
Run-TryBot: Michael Munday <mike.munday@ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
This CL looks big but it only does formatting changes to arith_s390x.s.
The file was formatted using asmfmt(https://github.com/klauspost/asmfmt)
, so there should not be any functional impact. I verified that the
generated assembly of big.test file is identical.
Change-Id: I8b4035ef082a4d0357881869327e25253f2d8be1
Reviewed-on: https://go-review.googlesource.com/c/go/+/229302
Reviewed-by: Michael Munday <mike.munday@ibm.com>
Run-TryBot: Michael Munday <mike.munday@ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
The Float.Sqrt method switches (for performance reasons) between
direct (uses Quo) and inverse (doesn't) computation, depending on the
precision, with threshold 128.
Unfortunately the implementation of recursive division in CL 172018
made Quo slightly slower exactly in the range around and below the
threshold Sqrt is using, so this strategy is no longer profitable.
The new division algorithm allocates more, and this has increased the
amount of allocations performed by Sqrt when using the direct method;
on low precisions the computation is fast, so additional allocations
have an negative impact on performance.
Interestingly, only using the inverse method doesn't just reverse the
effects of the Quo algorithm change, but it seems to make performances
better overall for small precisions:
name old time/op new time/op delta
FloatSqrt/64-4 643ns ± 1% 635ns ± 1% -1.24% (p=0.000 n=10+10)
FloatSqrt/128-4 1.44µs ± 1% 1.02µs ± 1% -29.25% (p=0.000 n=10+10)
FloatSqrt/256-4 1.49µs ± 1% 1.49µs ± 1% ~ (p=0.752 n=10+10)
FloatSqrt/1000-4 3.71µs ± 1% 3.74µs ± 1% +0.87% (p=0.001 n=10+10)
FloatSqrt/10000-4 35.3µs ± 1% 35.6µs ± 1% +0.82% (p=0.002 n=10+9)
FloatSqrt/100000-4 844µs ± 1% 844µs ± 0% ~ (p=0.549 n=10+9)
FloatSqrt/1000000-4 69.5ms ± 0% 69.6ms ± 0% ~ (p=0.222 n=9+9)
name old alloc/op new alloc/op delta
FloatSqrt/64-4 280B ± 0% 200B ± 0% -28.57% (p=0.000 n=10+10)
FloatSqrt/128-4 504B ± 0% 248B ± 0% -50.79% (p=0.000 n=10+10)
FloatSqrt/256-4 344B ± 0% 344B ± 0% ~ (all equal)
FloatSqrt/1000-4 1.30kB ± 0% 1.30kB ± 0% ~ (all equal)
FloatSqrt/10000-4 13.5kB ± 0% 13.5kB ± 0% ~ (p=0.237 n=10+10)
FloatSqrt/100000-4 123kB ± 0% 123kB ± 0% ~ (p=0.247 n=10+10)
FloatSqrt/1000000-4 1.83MB ± 1% 1.83MB ± 3% ~ (p=0.779 n=8+10)
name old allocs/op new allocs/op delta
FloatSqrt/64-4 8.00 ± 0% 5.00 ± 0% -37.50% (p=0.000 n=10+10)
FloatSqrt/128-4 11.0 ± 0% 5.0 ± 0% -54.55% (p=0.000 n=10+10)
FloatSqrt/256-4 5.00 ± 0% 5.00 ± 0% ~ (all equal)
FloatSqrt/1000-4 6.00 ± 0% 6.00 ± 0% ~ (all equal)
FloatSqrt/10000-4 6.00 ± 0% 6.00 ± 0% ~ (all equal)
FloatSqrt/100000-4 6.00 ± 0% 6.00 ± 0% ~ (all equal)
FloatSqrt/1000000-4 10.3 ±13% 10.3 ±13% ~ (p=1.000 n=10+10)
For example, 1.02µs for FloatSqrt/128 is actually better than what I
was getting on the same machine before the Quo changes.
The .8% slowdown on /1000 and /10000 appears to be real and it is
quite baffling (that codepath was not touched at all); it may be
caused by code alignment changes.
Change-Id: Ib03761cdc1055674bc7526d4f3a23d7a25094029
Reviewed-on: https://go-review.googlesource.com/c/go/+/228062
Run-TryBot: Alberto Donizetti <alb.donizetti@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
Fixes#38304
Also change `If m > 0, y < 0, ...` to `If m != 0, y < 0, ...` since `Exp` will return `nil`
whatever `m`'s sign is.
Change-Id: I17d7337ccd1404318cea5d42a8de904ad185fd00
GitHub-Last-Rev: 2399510300
GitHub-Pull-Request: golang/go#38390
Reviewed-on: https://go-review.googlesource.com/c/go/+/228000
Reviewed-by: Robert Griesemer <gri@golang.org>
The divBasic function computes the quotient of big nats u/v word by word.
It estimates each word qhat by performing a long division (top 2 words of u
divided by top word of v), looks at the next word to correct the estimate,
then perform a full multiplication (qhat*v) to catch any inaccuracy in the
estimate.
In the latter case, "negative" values appear temporarily and carries
must be carefully managed, and the recursive division refactoring
introduced a case where qhat*v has the same length as v, triggering an
out-of-bounds write in the case it happens when computing the top word
of the quotient.
Fixes#37499
Change-Id: I15089da4a4027beda43af497bf6de261eb792f94
Reviewed-on: https://go-review.googlesource.com/c/go/+/221980
Reviewed-by: Robert Griesemer <gri@golang.org>
The s390x assembly implementation was previously only handling this
case correctly for x = -Pi. Update the special case handling for
any y.
Fixes#35446
Change-Id: I355575e9ec8c7ce8bd9db10d74f42a22f39a2f38
Reviewed-on: https://go-review.googlesource.com/c/go/+/223420
Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Michael Munday <mike.munday@ibm.com>
Reviewed-by: Robert Griesemer <gri@golang.org>
Document that the Float.Sqrt method does not set the receiver's
Accuracy field.
Updates #37915
Change-Id: Ief1dcac07eacc0ef02f86bfac9044501477bca1c
Reviewed-on: https://go-review.googlesource.com/c/go/+/224497
Reviewed-by: Robert Griesemer <gri@golang.org>
s390x has inaccurate range reduction for the assembly routines
in math so these tests are diabled until these are corrected.
Updates #37854
Change-Id: I1e26acd6d09ae3e592a3dd90aec73a6844f5c6fe
Reviewed-on: https://go-review.googlesource.com/c/go/+/223457
Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Rob Pike <r@golang.org>
Tan has poles along the real axis. In order to accurately calculate
the value near these poles, a range reduction by Pi is performed and
the result calculated via a Taylor series. The prior implementation
of range reduction used Cody-Waite range reduction in three parts.
This fails when x is too large to accurately calculate the partial
products in the summation accurately. Above this threshold, Payne-Hanek
range reduction using a multiple precision value of 1/Pi is required.
Additionally, the threshold used in math/trig_reduce.go for Payne-Hanek
range reduction was not set conservatively enough. The prior threshold
ensured that catastrophic failure did not occur where the argument x
would not actually be reduced below Pi/4. However, errors in reduction
begin to occur at values much lower when z = ((x - y*PI4A) - y*PI4B) - y*PI4C
is not exact because y*PI4A cannot be exactly represented as a float64.
reduceThreshold is lowered to the proper value.
Fixes#31566
Change-Id: I0f39a4171a5be44f64305f18dc57f6c29f19dba7
Reviewed-on: https://go-review.googlesource.com/c/go/+/172838
Reviewed-by: Rob Pike <r@golang.org>
Provide an assembly implementation of mulWW - for now all others run the
Go code.
Change-Id: Icb594c31048255f131bdea8d64f56784fc9db4d1
Reviewed-on: https://go-review.googlesource.com/c/go/+/220919
Reviewed-by: Robert Griesemer <gri@golang.org>
It was removed in CL 217302 but was intentionally added in CL 217104.
Change-Id: I1a478d80ad1ec4f0a0184bfebf8f1a5e352cfe8c
Reviewed-on: https://go-review.googlesource.com/c/go/+/217941
Reviewed-by: Robert Griesemer <gri@golang.org>
We don't usually document past behavior (like "As of Go 1.14 ...") and
in isolation the current docs made it sound like a and b could only be
negative or zero.
Change-Id: I0d3c2b8579a9c01159ce528a3128b1478e99042a
Reviewed-on: https://go-review.googlesource.com/c/go/+/217302
Reviewed-by: Ian Lance Taylor <iant@golang.org>
The bounds in the last carry branch were wrong as there
is no reason for len(u) >= n+n/2 to always hold true.
We also adjust test to avoid using a remainder of 1
(in which case, the last step of the algorithm computes
(qhatv+1) - qhatv which rarely produces a carry).
Change-Id: I69fbab9c5e19d0db1c087fbfcd5b89352c2d26fb
Reviewed-on: https://go-review.googlesource.com/c/go/+/206839
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
There is a (theoretical, but possible) chance that the
random number values a, b used for TestDiv are 0 or 1,
in which case the test would fail.
This CL makes sure that a >= 1 and b >= 2 at all times.
Fixes#35523.
Change-Id: I6451feb94241249516a821cd0066e95a0c65b0ed
Reviewed-on: https://go-review.googlesource.com/c/go/+/206818
Run-TryBot: Robert Griesemer <gri@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
The current division algorithm produces one word of result at a time,
using 2-word division to compute the top word and mulAddVWW to compute
the remainder. The top word may need to be adjusted by 1 or 2 units.
The recursive version, based on Burnikel, Ziegler, "Fast Recursive Division",
uses the same principles, but in a multi-word setting, so that
multiplication benefits from the Karatsuba algorithm (and possibly later
improvements).
benchmark old ns/op new ns/op delta
BenchmarkDiv/20/10-4 38.2 38.3 +0.26%
BenchmarkDiv/40/20-4 38.7 38.5 -0.52%
BenchmarkDiv/100/50-4 62.5 62.6 +0.16%
BenchmarkDiv/200/100-4 238 259 +8.82%
BenchmarkDiv/400/200-4 311 338 +8.68%
BenchmarkDiv/1000/500-4 604 649 +7.45%
BenchmarkDiv/2000/1000-4 1214 1278 +5.27%
BenchmarkDiv/20000/10000-4 38279 36510 -4.62%
BenchmarkDiv/200000/100000-4 3022057 1359615 -55.01%
BenchmarkDiv/2000000/1000000-4 310827664 54012939 -82.62%
BenchmarkDiv/20000000/10000000-4 33272829421 1965401359 -94.09%
BenchmarkString/10/Base10-4 158 156 -1.27%
BenchmarkString/100/Base10-4 797 792 -0.63%
BenchmarkString/1000/Base10-4 3677 3814 +3.73%
BenchmarkString/10000/Base10-4 16633 17116 +2.90%
BenchmarkString/100000/Base10-4 5779029 1793808 -68.96%
BenchmarkString/1000000/Base10-4 889840820 85524031 -90.39%
BenchmarkString/10000000/Base10-4 134338236860 4935657026 -96.33%
Fixes#21960
Updates #30943
Change-Id: I134c6f81a47870c688ca95b6081eb9211def15a2
Reviewed-on: https://go-review.googlesource.com/c/go/+/172018
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
This reverts CL 169501.
Reason for revert: The new tests fail at least on s390x and MIPS. This is likely a minor bug in the compiler or runtime. But this point in the release cycle is not the time to debug these details, which are unlikely to be new. Let's try again for 1.15.
Updates #29320Fixes#35443
Change-Id: I2218b2083f8974b57d528e3742524393fc72b355
Reviewed-on: https://go-review.googlesource.com/c/go/+/206037
Run-TryBot: Ian Lance Taylor <iant@golang.org>
Reviewed-by: Bryan C. Mills <bcmills@google.com>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Implement special case handling and testing to ensure
conformance with the C99 standard annex G.6 Complex arithmetic.
Fixes#29320
Change-Id: Ieb0527191dd7fdea5b1aecb42b9e23aae3f74260
Reviewed-on: https://go-review.googlesource.com/c/go/+/169501
Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
This makes it a little less likely the portable FMA will be
broken without realizing it.
Change-Id: I7f7f4509b35160a9709f8b8a0e494c09ea6e410a
Reviewed-on: https://go-review.googlesource.com/c/go/+/205337
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
This API was added for #25819, where it was discussed as math.FMA.
The commit adding it used math.Fma, presumably for consistency
with the rest of the unusual names in package math
(Sincos, Acosh, Erfcinv, Float32bits, etc).
I believe that using an idiomatic Go name is more important here
than consistency with these other names, most of which are historical
baggage from C's standard library.
Early additions like Float32frombits happened before "uppercase for export"
(so they were originally like "float32frombits") and they were not properly
reconsidered when we uppercased the symbols to export them.
That's a mistake we live with.
The names of functions we have added since then, and even a few
that were legacy, are more properly Go-cased, such as IsNaN, IsInf,
and RoundToEven, rather than Isnan, Isinf, and Roundtoeven.
And also constants like MaxFloat32.
For new API, we should keep using proper Go-cased symbols
instead of minimally-upper-cased-C symbols.
So math.FMA, not math.Fma.
This API has not yet been released, so this change does not break
the compatibility promise.
This CL also modifies cmd/compile, since the compiler knows
the name of the function. I could have stopped at changing the
string constants, but it seemed to make more sense to use a
consistent casing everywhere.
Change-Id: I0f6f3407f41e99bfa8239467345c33945088896e
Reviewed-on: https://go-review.googlesource.com/c/go/+/205317
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Allow the inputs a and b to be zero or negative to GCD
with the following definitions.
If x or y are not nil, GCD sets their value such that z = a*x + b*y.
Regardless of the signs of a and b, z is always >= 0.
If a == b == 0, GCD sets z = x = y = 0.
If a == 0 and b != 0, GCD sets z = |b|, x = 0, y = sign(b) * 1.
If a != 0 and b == 0, GCD sets z = |a|, x = sign(a) * 1, y = 0.
Fixes#28878
Change-Id: Ia83fce66912a96545c95cd8df0549bfd852652f3
Reviewed-on: https://go-review.googlesource.com/c/go/+/164972
Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
A Rat is represented via a quotient a/b where a and b are Int values.
To make it possible to use an uninitialized Rat value (with a and b
uninitialized and thus == 0), the implementation treats a 0 denominator
as 1.
Rat.Num and Rat.Denom return pointers to these values a and b. Because
b may be 0, Rat.Denom used to first initialize it to 1 and thus produce
an undesirable side-effect (by changing the Rat's denominator).
This CL changes Denom to return a new (not shared) *Int with value 1
in the rare case where the Rat was not initialized. This eliminates
the side effect and returns the correct denominator value.
While this is changing behavior of the API, the impact should now be
minor because together with (prior) CL https://golang.org/cl/202997,
which initializes Rats ASAP, Denom is unlikely used to access the
denominator of an uninitialized (and thus 0) Rat. Any operation that
will somehow set a Rat value will ensure that the denominator is not 0.
Fixes#33792.
Updates #3521.
Change-Id: I0bf15ac60513cf52162bfb62440817ba36f0c3fc
Reviewed-on: https://go-review.googlesource.com/c/go/+/203059
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
A Rat is represented via a quotient a/b where a and b are Int values.
To make it possible to use an uninitialized Rat value (with a and b
uninitialized and thus == 0), the implementation treats a 0 denominator
as 1.
For each operation we check if the denominator is 0, and then treat
it as 1 (if necessary). Operations that create a new Rat result,
normalize that value such that a result denominator 1 is represened
as 0 again.
This CL changes this behavior slightly: 0 denominators are still
interpreted as 1, but whenever we (safely) can, we set an uninitialized
0 denominator to 1. This simplifies the code overall.
Also: Improved some doc strings.
Preparation for addressing issue #33792.
Updates #33792.
Change-Id: I3040587c8d0dad2e840022f96ca027d8470878a0
Reviewed-on: https://go-review.googlesource.com/c/go/+/202997
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Currently, the precision of the float64 multiply-add operation
(x * y) + z varies across architectures. While generated code for
ppc64, s390x, and arm64 can guarantee that there is no intermediate
rounding on those platforms, other architectures like x86, mips, and
arm will exhibit different behavior depending on available instruction
set. Consequently, applications cannot rely on results being identical
across GOARCH-dependent codepaths.
This CL introduces a software implementation that performs an IEEE 754
double-precision fused-multiply-add operation. The only supported
rounding mode is round-to-nearest ties-to-even. Separate CLs include
hardware implementations when available. Otherwise, this software
fallback is given as the default implementation.
Specifically,
- arm64, ppc64, s390x: Uses the FMA instruction provided by all
of these ISAs.
- mips[64][le]: Falls back to this software implementation. Only
release 6 of the ISA includes a strict FMA instruction with
MADDF.D (not implementation defined). Because the number of R6
processors in the wild is scarce, the assembly implementation
is left as a future optimization.
- x86: Guards the use of VFMADD213SD by checking cpu.X86.HasFMA.
- arm: Guards the use of VFMA by checking cpu.ARM.HasVFPv4.
- software fallback: Uses mostly integer arithmetic except
for input that involves Inf, NaN, or zero.
Updates #25819.
Change-Id: Iadadff2219638bacc9fec78d3ab885393fea4a08
Reviewed-on: https://go-review.googlesource.com/c/go/+/127458
Run-TryBot: Ian Lance Taylor <iant@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
