Make log10 correctly rounded for non-FMA targets and improve its
performance.
Implemented fast pass and accurate pass:
**Fast Pass**:
- Range reduction step 0: Extract exponent and mantissa
```
x = 2^(e_x) * m_x
```
- Range reduction step 1: Use lookup tables of size 2^7 = 128 to reduce the argument to:
```
-2^-8 <= v = r * m_x - 1 < 2^-7
where r = 2^-8 * ceil( 2^8 * (1 - 2^-8) / (1 + k * 2^-7) )
and k = trunc( (m_x - 1) * 2^7 )
```
- Polynomial approximation: approximate `log(1 + v)` by a degree-7 polynomial generated by Sollya with:
```
> P = fpminimax((log(1 + x) - x)/x^2, 5, [|D...|], [-2^-8, 2^-7]);
```
- Combine the results:
```
log10(x) ~ ( e_x * log(2) - log(r) + v + v^2 * P(v) ) * log10(e)
```
- Perform additive Ziv's test with errors bounded by `P_ERR * v^2`. Return the result if Ziv's test passed.
**Accurate Pass**:
- Take `e_x`, `v`, and the lookup table index from the range reduction step of fast pass.
- Perform 3 more range reduction steps:
- Range reduction step 2: Use look-up tables of size 193 to reduce the argument to `[-0x1.3ffcp-15, 0x1.3e3dp-15]`
```
v2 = r2 * (1 + v) - 1 = (1 + s2) * (1 + v) - 1 = s2 + v + s2 * v
where r2 = 2^-16 * round ( 2^16 / (1 + k * 2^-14) )
and k = trunc( v * 2^14 + 0.5 ).
```
- Range reduction step 3: Use look-up tables of size 161 to reduce the argument to `[-0x1.01928p-22 , 0x1p-22]`
```
v3 = r3 * (1 + v2) - 1 = (1 + s3) * (1 + v2) - 1 = s3 + v2 + s3 * v2
where r3 = 2^-21 * round ( 2^21 / (1 + k * 2^-21) )
and k = trunc( v * 2^21 + 0.5 ).
```
- Range reduction step 4: Use look-up tables of size 130 to reduce the argument to `[-0x1.0002143p-29 , 0x1p-29]`
```
v4 = r4 * (1 + v3) - 1 = (1 + s4) * (1 + v3) - 1 = s4 + v3 + s4 * v3
where r4 = 2^-28 * round ( 2^28 / (1 + k * 2^-28) )
and k = trunc( v * 2^28 + 0.5 ).
```
- Polynomial approximation: approximate `log10(1 + v4)` by a degree-4 minimax polynomial generated by Sollya with:
```
> P = fpminimax(log10(1 + x)/x, 3, [|128...|], [-0x1.0002143p-29 , 0x1p-29]);
```
- Combine the results:
```
log10(x) ~ e_x * log10(2) - log10(r) - log10(r2) - log10(r3) - log10(r4) + v * P(v)
```
- The combined results are computed using floating points of 128-bit precision.
**Performance**
- For `0.5 <= x <= 2`, the fast pass hitting rate is about 99.92%.
- Reciprocal throughput from CORE-MATH's perf tool on Ryzen 5900X:
```
$ ./perf.sh log10
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH reciprocal throughput -- with FMA
[####################] 100 %
Ntrial = 20 ; Min = 20.402 + 0.589 clc/call; Median-Min = 0.277 clc/call; Max = 22.752 clc/call;
-- CORE-MATH reciprocal throughput -- without FMA (-march=x86-64-v2)
[####################] 100 %
Ntrial = 20 ; Min = 75.797 + 3.317 clc/call; Median-Min = 3.407 clc/call; Max = 79.371 clc/call;
-- System LIBC reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 22.668 + 0.184 clc/call; Median-Min = 0.181 clc/call; Max = 23.205 clc/call;
-- LIBC reciprocal throughput -- with FMA
[####################] 100 %
Ntrial = 20 ; Min = 25.977 + 0.183 clc/call; Median-Min = 0.138 clc/call; Max = 26.283 clc/call;
-- LIBC reciprocal throughput -- without FMA
[####################] 100 %
Ntrial = 20 ; Min = 22.140 + 0.980 clc/call; Median-Min = 0.853 clc/call; Max = 23.790 clc/call;
```
- Latency from CORE-MATH's perf tool on Ryzen 5900X:
```
$ ./perf.sh log10 --latency
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH latency -- with FMA
[####################] 100 %
Ntrial = 20 ; Min = 54.613 + 0.357 clc/call; Median-Min = 0.287 clc/call; Max = 55.701 clc/call;
-- CORE-MATH latency -- without FMA (-march=x86-64-v2)
[####################] 100 %
Ntrial = 20 ; Min = 79.681 + 0.482 clc/call; Median-Min = 0.294 clc/call; Max = 81.604 clc/call;
-- System LIBC latency --
[####################] 100 %
Ntrial = 20 ; Min = 61.532 + 0.208 clc/call; Median-Min = 0.199 clc/call; Max = 62.256 clc/call;
-- LIBC latency -- with FMA
[####################] 100 %
Ntrial = 20 ; Min = 41.510 + 0.205 clc/call; Median-Min = 0.244 clc/call; Max = 41.867 clc/call;
-- LIBC latency -- without FMA
[####################] 100 %
Ntrial = 20 ; Min = 55.669 + 0.240 clc/call; Median-Min = 0.280 clc/call; Max = 56.056 clc/call;
```
- Accurate pass latency:
```
$ ./perf.sh log10 --latency --simple_stat
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH latency -- with FMA
640.688
-- CORE-MATH latency -- without FMA (-march=x86-64-v2)
667.354
-- LIBC latency -- with FMA
495.593
-- LIBC latency -- without FMA
504.143
```
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D150014