diff --git a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
index bfa470dd5690d..3e6fbafe8a6b3 100644
--- a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
+++ b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
@@ -2687,10 +2687,10 @@ mlir::Value IntrinsicLibrary::genAcospi(mlir::Type resultType,
   mlir::FunctionType ftype =
       mlir::FunctionType::get(context, {resultType}, {args[0].getType()});
   mlir::Value acos = getRuntimeCallGenerator("acos", ftype)(builder, loc, args);
-  llvm::APFloat inv_pi = llvm::APFloat(llvm::numbers::inv_pi);
-  mlir::Value dfactor =
-      builder.createRealConstant(loc, mlir::Float64Type::get(context), inv_pi);
-  mlir::Value factor = builder.createConvert(loc, resultType, dfactor);
+  llvm::APFloat inv_pi =
+      llvm::APFloat(llvm::cast<mlir::FloatType>(resultType).getFloatSemantics(),
+                    llvm::numbers::inv_pis);
+  mlir::Value factor = builder.createRealConstant(loc, resultType, inv_pi);
   return mlir::arith::MulFOp::create(builder, loc, acos, factor);
 }
 
diff --git a/flang/test/Lower/Intrinsics/acospi.f90 b/flang/test/Lower/Intrinsics/acospi.f90
index dcacd25bca480..38c547fd5dd13 100644
--- a/flang/test/Lower/Intrinsics/acospi.f90
+++ b/flang/test/Lower/Intrinsics/acospi.f90
@@ -1,3 +1,4 @@
+! REQUIRES: flang-supports-f128-math
 ! RUN: bbc -emit-fir -hlfir=false %s -o - | FileCheck %s --check-prefixes="CHECK,CHECK-FAST"
 ! RUN: bbc --math-runtime=precise -emit-fir -hlfir=false %s -o - | FileCheck %s --check-prefixes="CHECK,CHECK-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -flang-deprecated-no-hlfir %s -o - | FileCheck %s --check-prefixes="CHECK,CHECK-FAST"
@@ -10,8 +11,7 @@ function test_real4(x)
 ! CHECK-LABEL: @_QPtest_real4
 ! CHECK-PRECISE: %[[acos:.*]] = fir.call @acosf({{%[A-Za-z0-9._]+}}) fastmath<contract> : (f32) -> f32
 ! CHECK-FAST: %[[acos:.*]] = math.acos %{{.*}} : f32
-! CHECK: %[[dpi:.*]] = arith.constant 0.31830988618379069 : f64
-! CHECK: %[[inv_pi:.*]] = fir.convert %[[dpi]] : (f64) -> f32
+! CHECK: %[[inv_pi:.*]] = arith.constant 0.318309873 : f32
 ! CHECK: %{{.*}} = arith.mulf %[[acos]], %[[inv_pi]] fastmath<contract> : f32
 
 function test_real8(x)
@@ -24,3 +24,13 @@ function test_real8(x)
 ! CHECK-FAST: %[[acos:.*]] = math.acos %{{.*}} : f64
 ! CHECK: %[[inv_pi:.*]] = arith.constant 0.31830988618379069 : f64
 ! CHECK: %{{.*}} = arith.mulf %[[acos]], %[[inv_pi]] fastmath<contract> : f64
+
+function test_real16(x)
+  real(16) :: x, test_real16
+  test_real16 = acospi(x)
+end function
+
+! CHECK-LABEL: @_QPtest_real16
+! CHECK: %[[acos:.*]] = fir.call @_FortranAAcosF128({{.*}}) fastmath<contract> : (f128) -> f128
+! CHECK: %[[inv_pi:.*]] = arith.constant 0.3183098861837906715377675267450{{.*}} : f128
+! CHECK: %{{.*}} = arith.mulf %[[acos]], %[[inv_pi]] fastmath<contract> : f128
diff --git a/llvm/include/llvm/Support/MathExtras.h b/llvm/include/llvm/Support/MathExtras.h
index 7bbf1b3aab761..c9dae7ae7346d 100644
--- a/llvm/include/llvm/Support/MathExtras.h
+++ b/llvm/include/llvm/Support/MathExtras.h
@@ -74,6 +74,10 @@ constexpr float ef          = 0x1.5bf0a8P+1F, // (2.71828183) https://oeis.org/A
                 sqrt3f      = 0x1.bb67aeP+0F, // (1.73205081) https://oeis.org/A002194
                 inv_sqrt3f  = 0x1.279a74P-1F, // (.577350269)
                 phif        = 0x1.9e377aP+0F; // (1.61803399) https://oeis.org/A001622
+// These string literals are taken from below:
+// https://github.com/bminor/glibc/blob/8543577b04ded6d979ffcc5a818930e4d74d0645/math/math.h#L1215-L1229
+constexpr const char *pis     = "3.141592653589793238462643383279502884",
+                     *inv_pis = "0.318309886183790671537767526745028724";
 // clang-format on
 } // namespace numbers