Refactor the generic implementation to use math_config.h definitions,
and add an alternative one if the ABI supports truncf instructions
(gated through math-use-builtins-trunc.h).
The generic implementation generates similar code on x86_64, while
the optimization one for aarch64 (where truncf is supported as a
builtin by through frintz), the improvements are:
reciprocal-throughput master patch difference
workload-0_1 3.0595 3.0698 -0.34%
workload-1_maxint 5.1747 3.0542 40.98%
workload-maxint_maxfloat 3.4391 3.0349 11.75%
workload-integral 3.2732 3.0293 7.45%
latency master patch difference
workload-0_1 3.5267 4.7107 -33.57%
workload-1_maxint 6.9074 4.7282 31.55%
workload-maxint_maxfloat 3.7210 4.7506 -27.67%
workload-integral 3.8634 4.8137 -24.60%
Checked on aarch64-linux-gnu and x86_64-linux-gnu.
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
It removes the wrapper by moving the error/EDOM handling to an
out-of-line implementation (__math_invalid_i/__math_invalid_li).
Also, __glibc_unlikely is used on errors case since it helps
code generation on recent gcc.
The code now builds to with gcc-14 on aarch64:
0000000000000000 <__ilogb>:
0: 9e660000 fmov x0, d0
4: d374f801 ubfx x1, x0, #52, #11
8: 340000e1 cbz w1, 24 <__ilogb+0x24>
c: 510ffc20 sub w0, w1, #0x3ff
10: 711ffc3f cmp w1, #0x7ff
14: 54000040 b.eq 1c <__ilogb+0x1c> // b.none
18: d65f03c0 ret
1c: 12b00000 mov w0, #0x7fffffff // #2147483647
20: 14000000 b 0 <__math_invalid_i>
24: d374cc00 lsl x0, x0, #12
28: b40000a0 cbz x0, 3c <__ilogb+0x3c>
2c: dac01000 clz x0, x0
30: 12807fc1 mov w1, #0xfffffc01 // #-1023
34: 4b000020 sub w0, w1, w0
38: d65f03c0 ret
3c: 320107e0 mov w0, #0x80000001 // #-2147483647
40: 14000000 b 0 <__math_invalid_i>
Some ABI requires additional adjustments:
* i386 and m68k requires to use the template version, since
both provide __ieee754_ilogb implementatations.
* loongarch uses a custom implementation as well.
* powerpc64le also has a custom implementation for POWER9, which
is also used for float and float128 version. The generic
e_ilogb.c implementation is moved on powerpc to keep the
current code as-is.
Checked on aarch64-linux-gnu and x86_64-linux-gnu.
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
GCC aligns global data to 16 bytes if their size is >= 16 bytes. This patch
changes the exp_data struct slightly so that the fields are better aligned
and without gaps. As a result on targets that support them, more load-pair
instructions are used in exp. Exp10 is improved by moving invlog10_2N later
so that neglog10_2hiN and neglog10_2loN can be loaded using load-pair.
The exp benchmark improves 2.5%, "144bits" by 7.2%, "768bits" by 12.7% on
Neoverse V2. Exp10 improves by 1.5%.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
New implementation is based on the existing exp/exp2, with different
reduction constants and polynomial. Worst-case error in round-to-
nearest is 0.513 ULP.
The exp/exp2 shared table is reused for exp10 - .rodata size of
e_exp_data increases by 64 bytes.
As for exp/exp2, targets with single-instruction rounding/conversion
intrinsics can use them by toggling TOINT_INTRINSICS=1 and adding the
necessary code to their math_private.h.
Improvements on Neoverse V1 compared to current GLIBC master:
exp10 thruput: 3.3x in [-0x1.439b746e36b52p+8 0x1.34413509f79ffp+8]
exp10 latency: 1.8x in [-0x1.439b746e36b52p+8 0x1.34413509f79ffp+8]
Tested on:
aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and
x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction)
Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
Replace the loop-over-scalar placeholder routines with optimised
implementations from Arm Optimized Routines (AOR).
Also add some headers containing utilities for aarch64 libmvec
routines, and update libm-test-ulps.
Data tables for new routines are used via a pointer with a
barrier on it, in order to prevent overly aggressive constant
inlining in GCC. This allows a single adrp, combined with offset
loads, to be used for every constant in the table.
Special-case handlers are marked NOINLINE in order to confine the
save/restore overhead of switching from vector to normal calling
standard. This way we only incur the extra memory access in the
exceptional cases. NOINLINE definitions have been moved to
math_private.h in order to reduce duplication.
AOR exposes a config option, WANT_SIMD_EXCEPT, to enable
selective masking (and later fixing up) of invalid lanes, in
order to trigger fp exceptions correctly (AdvSIMD only). This is
tested and maintained in AOR, however it is configured off at
source level here for performance reasons. We keep the
WANT_SIMD_EXCEPT blocks in routine sources to greatly simplify
the upstreaming process from AOR to glibc.
Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
The error handling is moved to sysdeps/ieee754 version with no SVID
support. The compatibility symbol versions still use the wrapper
with SVID error handling around the new code. There is no new symbol
version nor compatibility code on !LIBM_SVID_COMPAT targets
(e.g. riscv).
The ia64 is unchanged, since it still uses the arch specific
__libm_error_region on its implementation. For both i686 and m68k,
which provive arch specific implementation, wrappers are added so
no new symbol are added (which would require to change the
implementations).
It shows an small improvement, the results for fmod:
Architecture | Input | master | patch
-----------------|-----------------|----------|--------
x86_64 (Ryzen 9) | subnormals | 12.5049 | 9.40992
x86_64 (Ryzen 9) | normal | 296.939 | 296.738
x86_64 (Ryzen 9) | close-exponents | 16.0244 | 13.119
aarch64 (N1) | subnormal | 6.81778 | 4.33313
aarch64 (N1) | normal | 155.620 | 152.915
aarch64 (N1) | close-exponents | 8.21306 | 5.76138
armhf (N1) | subnormal | 15.1083 | 14.5746
armhf (N1) | normal | 244.833 | 241.738
armhf (N1) | close-exponents | 21.8182 | 22.457
Checked on x86_64-linux-gnu, i686-linux-gnu, and aarch64-linux-gnu.
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
This uses a new algorithm similar to already proposed earlier [1].
With x = mx * 2^ex and y = my * 2^ey (mx, my, ex, ey being integers),
the simplest implementation is:
mx * 2^ex == 2 * mx * 2^(ex - 1)
while (ex > ey)
{
mx *= 2;
--ex;
mx %= my;
}
With mx/my being mantissa of double floating pointer, on each step the
argument reduction can be improved 11 (which is sizeo of uint64_t minus
MANTISSA_WIDTH plus the signal bit):
while (ex > ey)
{
mx << 11;
ex -= 11;
mx %= my;
} */
The implementation uses builtin clz and ctz, along with shifts to
convert hx/hy back to doubles. Different than the original patch,
this path assume modulo/divide operation is slow, so use multiplication
with invert values.
I see the following performance improvements using fmod benchtests
(result only show the 'mean' result):
Architecture | Input | master | patch
-----------------|-----------------|----------|--------
x86_64 (Ryzen 9) | subnormals | 19.1584 | 12.5049
x86_64 (Ryzen 9) | normal | 1016.51 | 296.939
x86_64 (Ryzen 9) | close-exponents | 18.4428 | 16.0244
aarch64 (N1) | subnormal | 11.153 | 6.81778
aarch64 (N1) | normal | 528.649 | 155.62
aarch64 (N1) | close-exponents | 11.4517 | 8.21306
I also see similar improvements on arm-linux-gnueabihf when running on
the N1 aarch64 chips, where it a lot of soft-fp implementation (for
modulo, clz, ctz, and multiplication):
Architecture | Input | master | patch
-----------------|-----------------|----------|--------
armhf (N1) | subnormal | 15.908 | 15.1083
armhf (N1) | normal | 837.525 | 244.833
armhf (N1) | close-exponents | 16.2111 | 21.8182
Instead of using the math_private.h definitions, I used the
math_config.h instead which is used on newer math implementations.
Co-authored-by: kirill <kirill.okhotnikov@gmail.com>
[1] https://sourceware.org/pipermail/libc-alpha/2020-November/119794.html
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
I used these shell commands:
../glibc/scripts/update-copyrights $PWD/../gnulib/build-aux/update-copyright
(cd ../glibc && git commit -am"[this commit message]")
and then ignored the output, which consisted lines saying "FOO: warning:
copyright statement not found" for each of 7061 files FOO.
I then removed trailing white space from math/tgmath.h,
support/tst-support-open-dev-null-range.c, and
sysdeps/x86_64/multiarch/strlen-vec.S, to work around the following
obscure pre-commit check failure diagnostics from Savannah. I don't
know why I run into these diagnostics whereas others evidently do not.
remote: *** 912-#endif
remote: *** 913:
remote: *** 914-
remote: *** error: lines with trailing whitespace found
...
remote: *** error: sysdeps/unix/sysv/linux/statx_cp.c: trailing lines
I used these shell commands:
../glibc/scripts/update-copyrights $PWD/../gnulib/build-aux/update-copyright
(cd ../glibc && git commit -am"[this commit message]")
and then ignored the output, which consisted lines saying "FOO: warning:
copyright statement not found" for each of 6694 files FOO.
I then removed trailing white space from benchtests/bench-pthread-locks.c
and iconvdata/tst-iconv-big5-hkscs-to-2ucs4.c, to work around this
diagnostic from Savannah:
remote: *** pre-commit check failed ...
remote: *** error: lines with trailing whitespace found
remote: error: hook declined to update refs/heads/master
The algorithm is exp(y * log(x)), where log(x) is computed with about
1.3*2^-68 relative error (1.5*2^-68 without fma), returning the result
in two doubles, and the exp part uses the same algorithm (and lookup
tables) as exp, but takes the input as two doubles and a sign (to handle
negative bases with odd integer exponent). The __exp1 internal symbol
is no longer necessary.
There is separate code path when fma is not available but the worst case
error is about 0.54 ULP in both cases. The lookup table and consts for
log are 4168 bytes. The .rodata+.text is decreased by 37908 bytes on
aarch64. The non-nearest rounding error is less than 1 ULP.
Improvements on Cortex-A72 compared to current glibc master:
pow thruput: 2.40x in [0.01 11.1]x[0.01 11.1]
pow latency: 1.84x in [0.01 11.1]x[0.01 11.1]
Tested on
aarch64-linux-gnu (defined __FP_FAST_FMA, TOINT_INTRINSICS) and
arm-linux-gnueabihf (!defined __FP_FAST_FMA, !TOINT_INTRINSICS) and
x86_64-linux-gnu (!defined __FP_FAST_FMA, !TOINT_INTRINSICS) and
powerpc64le-linux-gnu (defined __FP_FAST_FMA, !TOINT_INTRINSICS) targets.
* NEWS: Mention pow improvements.
* math/Makefile (type-double-routines): Add e_pow_log_data.
* sysdeps/generic/math_private.h (__exp1): Remove.
* sysdeps/i386/fpu/e_pow_log_data.c: New file.
* sysdeps/ia64/fpu/e_pow_log_data.c: New file.
* sysdeps/ieee754/dbl-64/Makefile (CFLAGS-e_pow.c): Allow fma
contraction.
* sysdeps/ieee754/dbl-64/e_exp.c (__exp1): Remove.
(exp_inline): Remove.
(__ieee754_exp): Only single double input is handled.
* sysdeps/ieee754/dbl-64/e_pow.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_pow_log_data.c: New file.
* sysdeps/ieee754/dbl-64/math_config.h (issignaling_inline): Define.
(__pow_log_data): Define.
* sysdeps/ieee754/dbl-64/upow.h: Remove.
* sysdeps/ieee754/dbl-64/upow.tbl: Remove.
* sysdeps/m68k/m680x0/fpu/e_pow_log_data.c: New file.
* sysdeps/x86_64/fpu/multiarch/Makefile (CFLAGS-e_pow-fma.c): Allow fma
contraction.
(CFLAGS-e_pow-fma4.c): Likewise.
Similar algorithm is used as in log: log2(2^k x) = k + log2(c) + log2(x/c)
where the last term is approximated by a polynomial of x/c - 1, the first
order coefficient is about 1/ln2 in this case.
There is separate code path when fma instruction is not available for
computing x/c - 1 precisely, for which the table size is doubled.
The worst case error is 0.547 ULP (0.55 without fma), the read only
global data size is 1168 bytes (2192 without fma) on aarch64. The
non-nearest rounding error is less than 1 ULP.
Improvements on Cortex-A72 compared to current glibc master:
log2 thruput: 2.00x in [0.01 11.1]
log2 latency: 2.04x in [0.01 11.1]
log2 thruput: 2.17x in [0.999 1.001]
log2 latency: 2.88x in [0.999 1.001]
Tested on
aarch64-linux-gnu (defined __FP_FAST_FMA)
arm-linux-gnueabihf (!defined __FP_FAST_FMA)
x86_64-linux-gnu (!defined __FP_FAST_FMA)
powerpc64le-linxu-gnu (defined __FP_FAST_FMA)
targets.
* NEWS: Mention log2 improvements.
* math/Makefile (type-double-routines): Add e_log2_data.
* sysdeps/i386/fpu/e_log2_data.c: New file.
* sysdeps/ia64/fpu/e_log2_data.c: New file.
* sysdeps/ieee754/dbl-64/e_log2.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_log2_data.c: New file.
* sysdeps/ieee754/dbl-64/math_config.h (__log2_data): Add.
* sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c: Remove.
* sysdeps/m68k/m680x0/fpu/e_log2_data.c: New file.
Optimized log using carefully generated lookup table with 1/c and log(c)
values for small intervalls around 1. The log(c) is very near a double
precision value, it has about 62 bits precision. The algorithm is
log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is
approximated by a polynomial of x/c - 1. Near 1 a single polynomial of
x - 1 is used.
There is separate code path when fma instruction is not available for
computing x/c - 1 precisely, in which case the table size is doubled.
The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined
as an instruction.
With the default configuration settings the worst case error is 0.519 ULP
(and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma).
The non-nearest rounding error is less than 1 ULP.
Improvements on Cortex-A72 compared to current glibc master:
log thruput: 3.28x in [0.01 11.1]
log latency: 2.23x in [0.01 11.1]
log thruput: 1.56x in [0.999 1.001]
log latency: 1.57x in [0.999 1.001]
Tested on
aarch64-linux-gnu (defined __FP_FAST_FMA)
arm-linux-gnueabihf (!defined __FP_FAST_FMA)
x86_64-linux-gnu (!defined __FP_FAST_FMA)
powerpc64le-linux-gnu (defined __FP_FAST_FMA)
targets.
* NEWS: Mention log improvement.
* math/Makefile (type-double-routines): Add e_log_data.
* sysdeps/i386/fpu/e_log_data.c: New file.
* sysdeps/ia64/fpu/e_log_data.c: New file.
* sysdeps/ieee754/dbl-64/e_log.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_log_data.c: New file.
* sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add.
* sysdeps/ieee754/dbl-64/ulog.h: Remove.
* sysdeps/ieee754/dbl-64/ulog.tbl: Remove.
* sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
Optimized exp and exp2 implementations using a lookup table for
fractional powers of 2. There are several variants, see e_exp_data.c,
they can be selected by modifying math_config.h allowing different
tradeoffs.
The default selection should be acceptable as generic libm code.
Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on
aarch64 the rodata size is 2160 bytes, shared between exp and exp2.
On aarch64 .text + .rodata size decreased by 24912 bytes.
The non-nearest rounding error is less than 1 ULP even on targets
without efficient round implementation (although the error rate is
higher in that case). Targets with single instruction, rounding mode
independent, to nearest integer rounding and conversion can use them
by setting TOINT_INTRINSICS and adding the necessary code to their
math_private.h.
The __exp1 code uses the same algorithm, so the error bound of pow
increased a bit.
New double precision error handling code was added following the
style of the single precision error handling code.
Improvements on Cortex-A72 compared to current glibc master:
exp thruput: 1.61x in [-9.9 9.9]
exp latency: 1.53x in [-9.9 9.9]
exp thruput: 1.13x in [0.5 1]
exp latency: 1.30x in [0.5 1]
exp2 thruput: 2.03x in [-9.9 9.9]
exp2 latency: 1.64x in [-9.9 9.9]
For small (< 1) inputs the current exp code uses a separate algorithm
so the speed up there is less.
Was tested on
aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and
arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and
x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) and
powerpc64le-linux-gnu (!TOINT_INTRINSICS, fma contraction) targets,
only non-nearest rounding ulp errors increase and they are within
acceptable bounds (ulp updates are in separate patches).
* NEWS: Mention exp and exp2 improvements.
* math/Makefile (libm-support): Remove t_exp.
(type-double-routines): Add math_err and e_exp_data.
* sysdeps/aarch64/libm-test-ulps: Update.
* sysdeps/arm/libm-test-ulps: Update.
* sysdeps/i386/fpu/e_exp_data.c: New file.
* sysdeps/i386/fpu/math_err.c: New file.
* sysdeps/i386/fpu/t_exp.c: Remove.
* sysdeps/ia64/fpu/e_exp_data.c: New file.
* sysdeps/ia64/fpu/math_err.c: New file.
* sysdeps/ia64/fpu/t_exp.c: Remove.
* sysdeps/ieee754/dbl-64/e_exp.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_exp_data.c: New file.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound.
* sysdeps/ieee754/dbl-64/eexp.tbl: Remove.
* sysdeps/ieee754/dbl-64/math_config.h: New file.
* sysdeps/ieee754/dbl-64/math_err.c: New file.
* sysdeps/ieee754/dbl-64/t_exp.c: Remove.
* sysdeps/ieee754/dbl-64/t_exp2.h: Remove.
* sysdeps/ieee754/dbl-64/uexp.h: Remove.
* sysdeps/ieee754/dbl-64/uexp.tbl: Remove.
* sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file.
* sysdeps/m68k/m680x0/fpu/math_err.c: New file.
* sysdeps/m68k/m680x0/fpu/t_exp.c: Remove.
* sysdeps/powerpc/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
