[libc][math] Implement scalbn, scalbnf, scalbnl.

[renyichen]

Summary

Implement scalbn via fptuil::ldexp for FLT_RADIX==2 case.
"unimplemented" otherwise.

[renyichen]

include other commits.

[renyichen]

Add darwin as well.

[renyichen]

Add scalbn.

[renyichen]

Add newline at end of file.

[renyichen]

• small fix

[renyichen]

Add scalbn, scalbnf, scalbnl.

[renyichen]

scalbn is supposed to compute more efficiently than directly performing x*FLT_RADIX^n as described in C99 Standard (in existing implementations, it doesn't necessary holds).
A rough compare has been performed locally by fixing n and test over the range defined in the existing infra for scalbnf(x, n):

	llvmlibc	glibc	directly calc x*exp2f(n)
n = 10 denormal range
avg runtime (ns/op)	13.7849	57.5703	58.7697
n = 10 normal range
avg runtime (ns/op)	9.71103	10.7406	13.6085

llvmlibc outperforms both glibc and directly calc.

Current optimization mechanisms in fputil::ldexp(): 1. early return if n is outside [-MAX_EXPONENT-MantissaWidth-1, MAX_EXPONENT+MantissaWidth+1]. 2. bit manipulation.

[sivachandra]

Thanks for the patch. Please wait for @lntue also to approve this.

[lntue]

libc/src/__support/FPUtil/ManipulationFunctions.h

119–122 ↗

(On Diff #494447)

These are exceptional cases, adding unlikely to these 2 conditions could potentially speed up the main cases.

[lntue]

Can you also update the status table in math.rst?

[renyichen]

Implement scalbn.

libc/src/math/generic/scalbn.cpp

 //===-- Single-precision scalbn function ----------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
 #include "src/math/scalbn.h"
 #include "src/__support/FPUtil/ManipulationFunctions.h"
 #include "src/__support/common.h"
 
 namespace __llvm_libc {
 
 LLVM_LIBC_FUNCTION(double, scalbn, (double x, int n)) {
 #if !defined(__FLT_RADIX__)
-#error __FLT_RADIX__!=2.
-#elif __FLT_RADIX__ == 2
-  return fputil::ldexp(x, n);
-#else
 #error __FLT_RADIX__ undefined.
+#elif __FLT_RADIX__ != 2
+#error __FLT_RADIX__!=2, unimplemented.
+#else
+  return fputil::ldexp(x, n);
 #endif
 }
 
 } // namespace __llvm_libc

libc/src/math/generic/scalbnf.cpp

 #include "src/__support/common.h"
 
 namespace __llvm_libc {
 
 LLVM_LIBC_FUNCTION(float, scalbnf, (float x, int n)) {
 #if !defined(__FLT_RADIX__)
 #error __FLT_RADIX__ undefined.
 #elif __FLT_RADIX__ != 2
-#error __FLT_RADIX__!=2.
+#error __FLT_RADIX__!=2, unimplemented.
 #else
   return fputil::ldexp(x, n);
 #endif
 }
 
 } // namespace __llvm_libc

libc/src/math/generic/scalbnl.cpp

 #include "src/__support/common.h"
 
 namespace __llvm_libc {
 
 LLVM_LIBC_FUNCTION(long double, scalbnl, (long double x, int n)) {
 #if !defined(__FLT_RADIX__)
 #error __FLT_RADIX__ undefined.
 #elif __FLT_RADIX__ != 2
-#error __FLT_RADIX__!=2.
+#error __FLT_RADIX__!=2, unimplemented.
 #else
   return fputil::ldexp(x, n);
 #endif
 }
 
 } // namespace __llvm_libc