[Support] Add mathematical constants

Add own version of the mathematical constants from the upcoming C++20 `std::numbers`.

Differential revision: https://reviews.llvm.org/D68257

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@374207 91177308-0d34-0410-b5e6-96231b3b80d8

include/llvm/Support/MathExtras.h

@@ -39,6 +39,7 @@ unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
 #endif
 
 namespace llvm {
+
 /// The behavior an operation has on an input of 0.
 enum ZeroBehavior {
   /// The returned value is undefined.
@@ -49,6 +50,42 @@ enum ZeroBehavior {
   ZB_Width
 };
 
+/// Mathematical constants.
+namespace numbers {
+// TODO: Track C++20 std::numbers.
+// TODO: Favor using the hexadecimal FP constants (requires C++17).
+constexpr double e          = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
+                 egamma     = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
+                 ln2        = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
+                 ln10       = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
+                 log2e      = 1.4426950408889634074, // (0x1.71547652b82feP+0)
+                 log10e     = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
+                 pi         = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
+                 inv_pi     = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
+                 sqrtpi     = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
+                 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
+                 sqrt2      = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
+                 inv_sqrt2  = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
+                 sqrt3      = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
+                 inv_sqrt3  = .57735026918962576451, // (0x1.279a74590331cP-1)
+                 phi        = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
+constexpr float ef          = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
+                egammaf     = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
+                ln2f        = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
+                ln10f       = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
+                log2ef      = 1.44269504F, // (0x1.715476P+0)
+                log10ef     = .434294482F, // (0x1.bcb7b2P-2)
+                pif         = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
+                inv_pif     = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
+                sqrtpif     = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
+                inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
+                sqrt2f      = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
+                inv_sqrt2f  = .707106781F, // (0x1.6a09e6P-1)
+                sqrt3f      = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
+                inv_sqrt3f  = .577350269F, // (0x1.279a74P-1)
+                phif        = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
+} // namespace numbers
+
 namespace detail {
 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
   static unsigned count(T Val, ZeroBehavior) {

lib/CodeGen/SelectionDAG/SelectionDAGBuilder.cpp

@@ -4974,12 +4974,11 @@ static SDValue expandExp(const SDLoc &dl, SDValue Op, SelectionDAG &DAG,
     // Put the exponent in the right bit position for later addition to the
     // final result:
     //
-    //   #define LOG2OFe 1.4426950f
-    //   t0 = Op * LOG2OFe
+    // t0 = Op * log2(e)
 
     // TODO: What fast-math-flags should be set here?
     SDValue t0 = DAG.getNode(ISD::FMUL, dl, MVT::f32, Op,
-                             getF32Constant(DAG, 0x3fb8aa3b, dl));
+                             DAG.getConstantFP(numbers::log2ef, dl, MVT::f32));
     return getLimitedPrecisionExp2(t0, dl, DAG);
   }
 
@@ -4997,10 +4996,11 @@ static SDValue expandLog(const SDLoc &dl, SDValue Op, SelectionDAG &DAG,
       LimitFloatPrecision > 0 && LimitFloatPrecision <= 18) {
     SDValue Op1 = DAG.getNode(ISD::BITCAST, dl, MVT::i32, Op);
 
-    // Scale the exponent by log(2) [0.69314718f].
+    // Scale the exponent by log(2).
     SDValue Exp = GetExponent(DAG, Op1, TLI, dl);
-    SDValue LogOfExponent = DAG.getNode(ISD::FMUL, dl, MVT::f32, Exp,
-                                        getF32Constant(DAG, 0x3f317218, dl));
+    SDValue LogOfExponent =
+        DAG.getNode(ISD::FMUL, dl, MVT::f32, Exp,
+                    DAG.getConstantFP(numbers::ln2f, dl, MVT::f32));
 
     // Get the significand and build it into a floating-point number with
     // exponent of 1.

lib/Transforms/Utils/SimplifyLibCalls.cpp

@@ -48,7 +48,6 @@ static cl::opt<bool>
                          cl::desc("Enable unsafe double to float "
                                   "shrinking for math lib calls"));
 
-
 //===----------------------------------------------------------------------===//
 // Helper Functions
 //===----------------------------------------------------------------------===//
@@ -1941,9 +1940,8 @@ Value *LibCallSimplifier::optimizeLog(CallInst *Log, IRBuilder<> &B) {
            ArgID == Intrinsic::exp || ArgID == Intrinsic::exp2) {
     Constant *Eul;
     if (ArgLb == ExpLb || ArgID == Intrinsic::exp)
-      // FIXME: The Euler number should be M_E, but it's place of definition
-      // is not quite standard.
-      Eul = ConstantFP::get(Log->getType(), 2.7182818284590452354);
+      // FIXME: Add more precise value of e for long double.
+      Eul = ConstantFP::get(Log->getType(), numbers::e);
     else if (ArgLb == Exp2Lb || ArgID == Intrinsic::exp2)
       Eul = ConstantFP::get(Log->getType(), 2.0);
     else