diff --git a/stdlib/public/Darwin/CoreGraphics/CGFloat.swift.gyb b/stdlib/public/Darwin/CoreGraphics/CGFloat.swift.gyb
index 0ad49ea..73685e2 100644
--- a/stdlib/public/Darwin/CoreGraphics/CGFloat.swift.gyb
+++ b/stdlib/public/Darwin/CoreGraphics/CGFloat.swift.gyb
@@ -513,18 +513,111 @@
 // tgmath
 //===----------------------------------------------------------------------===//
 
+%from SwiftMathFunctions import *
+extension CGFloat: Real {
+% for func in ElementaryFunctions + RealFunctions:
+
+  @_alwaysEmitIntoClient
+  public static func ${func.decl("CGFloat")} {
+    return CGFloat(NativeType.${func.swiftName}(${func.params("", ".native")}))
+  }
+% end
+
+  @_alwaysEmitIntoClient
+  public static func pow(_ x: CGFloat, _ y: CGFloat) -> CGFloat {
+    return CGFloat(NativeType.pow(x.native, y.native))
+  }
+
+  @_alwaysEmitIntoClient
+  public static func pow(_ x: CGFloat, _ n: Int) -> CGFloat {
+    return CGFloat(NativeType.pow(x.native, n))
+  }
+
+  @_alwaysEmitIntoClient
+  public static func root(_ x: CGFloat, _ n: Int) -> CGFloat {
+    return CGFloat(NativeType.root(x.native, n))
+  }
+
+  @_alwaysEmitIntoClient
+  public static func atan2(y: CGFloat, x: CGFloat) -> CGFloat {
+    return CGFloat(NativeType.atan2(y: y.native, x: x.native))
+  }
+
+#if !os(Windows)
+  @_alwaysEmitIntoClient
+  public static func logGamma(_ x: CGFloat) -> CGFloat {
+    return CGFloat(NativeType.logGamma(x.native))
+  }
+#endif
+}
+
+@available(swift, deprecated: 5.1, message: "Use `root(x, 3)`.")
+@_transparent
+public func cbrt(_ x: CGFloat) -> CGFloat {
+  return CGFloat.root(x, 3)
+}
+
+@available(swift, deprecated: 5.1, message: "Use CGFloat.minimum( ) or Swift.min( )")
+@_transparent
+public func fmin(_ x: CGFloat, _ y: CGFloat) -> CGFloat {
+  return .minimum(x, y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use CGFloat.maximum( ) or Swift.max( )")
+@_transparent
+public func fmax(_ x: CGFloat, _ y: CGFloat) -> CGFloat {
+  return .maximum(x, y)
+}
+
+#if !os(Windows)
+@available(swift, deprecated: 5.1, message: "Use (logGamma(x), signGamma(x)).")
+@_transparent
+public func lgamma(_ x: CGFloat) -> (CGFloat, Int) {
+  return (CGFloat.logGamma(x), CGFloat.signGamma(x) == .plus ? 1 : -1)
+}
+#endif
+
+@available(swift, deprecated: 5.1, message: "Use `x.exponent` or `floor(log2(x))`.")
+@_transparent
+public func logb(_ x: CGFloat) -> CGFloat {
+  return CGFloat.log2(x).rounded(.down)
+}
+
+@available(swift, deprecated: 5.1, message: "Swift does not model dynamic rounding modes, use x.rounded(.toNearestOrEven).")
+@_transparent
+public func nearbyint(_ x: CGFloat) -> CGFloat {
+  return x.rounded(.toNearestOrEven)
+}
+
+@available(swift, deprecated: 5.1, message: "Use the .nextUp or .nextDown property.")
+@_transparent
+public func nextafter(_ x: CGFloat, _ y: CGFloat) -> CGFloat {
+  return y > x ? x.nextUp : (y < x ? x.nextDown : y)
+}
+
+@available(swift, deprecated: 5.1, message: "Swift does not model dynamic rounding modes, use x.rounded(.toNearestOrEven).")
+@_transparent
+public func rint(_ x: CGFloat) -> CGFloat {
+  return x.rounded(.toNearestOrEven)
+}
+
+@available(swift, deprecated: 5.1, message: "Use `gamma(x)`.")
+@_transparent
+public func tgamma(_ x: CGFloat) -> CGFloat {
+  return CGFloat.gamma(x)
+}
+
 %{
 UnaryFunctions = [
   'acos', 'asin', 'atan', 'cos', 'sin', 'tan',
   'acosh', 'asinh', 'atanh', 'cosh', 'sinh', 'tanh',
   'exp', 'exp2', 'expm1',
-  'log', 'log10', 'log1p', 'log2', 'logb',
-  'cbrt', 'erf', 'erfc', 'tgamma',
-  'nearbyint', 'rint'
+  'log', 'log10', 'log1p', 'log2',
+  'erf', 'erfc',
 ]
 
 BinaryFunctions = [
-  'atan2', 'hypot', 'pow', 'copysign', 'nextafter', 'fdim', 'fmax', 'fmin'
+  'atan2', 'hypot', 'pow', 'copysign', 'fdim'
 ]
 }%
 
@@ -571,19 +664,13 @@
   return CGFloat(ldexp(x.native, n))
 }
 
-@available(swift, deprecated: 4.2, message: "use the exponent property.")
+@available(swift, deprecated: 4.2, obsoleted: 5.1, message: "use the exponent property.")
 @_transparent
 public func ilogb(_ x: CGFloat) -> Int {
   return Int(x.exponent)
 }
 
 @_transparent
-public func lgamma(_ x: CGFloat) -> (CGFloat, Int) {
-  let (value, sign) = lgamma(x.native)
-  return (CGFloat(value), sign)
-}
-
-@_transparent
 public func remquo(_ x: CGFloat, _ y: CGFloat) -> (CGFloat, Int) {
   let (rem, quo) = remquo(x.native, y.native)
   return (CGFloat(rem), quo)
diff --git a/stdlib/public/Platform/tgmath.swift.gyb b/stdlib/public/Platform/tgmath.swift.gyb
index 4f3f279..dc22df6 100644
--- a/stdlib/public/Platform/tgmath.swift.gyb
+++ b/stdlib/public/Platform/tgmath.swift.gyb
@@ -2,7 +2,7 @@
 //
 // This source file is part of the Swift.org open source project
 //
-// Copyright (c) 2014 - 2017 Apple Inc. and the Swift project authors
+// Copyright (c) 2014 - 2019 Apple Inc. and the Swift project authors
 // Licensed under Apache License v2.0 with Runtime Library Exception
 //
 // See https://swift.org/LICENSE.txt for license information
@@ -14,11 +14,12 @@
 
 // Generic functions implementable directly on FloatingPoint.
 @_transparent
-@available(swift, deprecated: 4.2, renamed: "abs")
+@available(swift, deprecated: 4.2, obsoleted: 5.1, renamed: "Swift.abs")
 public func fabs<T: FloatingPoint>(_ x: T) -> T {
   return x.magnitude
 }
 
+@available(swift, obsoleted: 5.1, message: "Use Swift.sqrt(x) or x.squareRoot().")
 @_transparent
 public func sqrt<T: FloatingPoint>(_ x: T) -> T {
   return x.squareRoot()
@@ -112,7 +113,7 @@
 @available(*, unavailable, message: "use the sign property.")
 public func signbit<T: FloatingPoint>(_ value: T) -> Int { fatalError() }
 
-@available(swift, deprecated: 4.2, message: "use the exponent property.")
+@available(swift, deprecated: 4.2, obsoleted: 5.1, message: "use the exponent property.")
 public func ilogb<T: BinaryFloatingPoint>(_ x: T) -> Int {
   return Int(x.exponent)
 }
@@ -155,44 +156,20 @@
     'acos', 'asin', 'atan', 'tan',
     'acosh', 'asinh', 'atanh', 'cosh', 'sinh', 'tanh',
     'expm1',
-    'log1p', 'logb',
-    'cbrt', 'erf', 'erfc', 'tgamma',
+    'log1p',
+    'erf', 'erfc',
 ]
 
 # These functions have a corresponding LLVM intrinsic
-# We call this intrinsic via the Builtin method so keep this list in
-# sync with core/BuiltinMath.swift.gyb
 UnaryIntrinsicFunctions = [
-    'cos', 'sin',
-    'exp', 'exp2',
-    'log', 'log10', 'log2',
-    'nearbyint', 'rint',
+    'cos', 'sin', 'exp', 'exp2', 'log', 'log10', 'log2', 'nearbyint', 'rint'
 ]
 
 # (T, T) -> T
 BinaryFunctions = [
-    'atan2', 'hypot', 'pow',
-    'copysign', 'nextafter', 'fdim', 'fmax', 'fmin'
+    'atan2', 'hypot', 'fdim', 'copysign'
 ]
 
-# These functions have special implementations.
-OtherFunctions = [
-    'scalbn', 'lgamma', 'remquo', 'nan', 'jn', 'yn'
-]
-
-# These functions are imported correctly as-is.
-OkayFunctions = ['j0', 'j1', 'y0', 'y1']
-
-# These functions are not supported for various reasons.
-UnhandledFunctions = [
-    'math_errhandling', 'scalbln',
-    'lrint', 'lround', 'llrint', 'llround', 'nexttoward',
-    'isgreater', 'isgreaterequal', 'isless', 'islessequal',
-    'islessgreater', 'isunordered', '__exp10',
-    '__sincos', '__cospi', '__sinpi', '__tanpi', '__sincospi'
-]
-
-
 def AllFloatTypes():
     for bits in allFloatBits:
         yield floatName(bits), cFloatName(bits), cFuncSuffix(bits)
@@ -226,50 +203,74 @@
 %  end
 @_transparent
 public func ${ufunc}(_ x: ${T}) -> ${T} {
-  return ${T}(${ufunc}${f}(${CT}(x)))
+  return ${T}.${ufunc}(x)
 }
 %  if T == 'Float80':
 #endif
 %  end
 
 % end
+@available(swift, deprecated: 5.1, message: "Use `root(x, 3)`.")
+@_transparent
+public func cbrt(_ x: Float) -> Float {
+  return Float.root(x, 3)
+}
 
-#if os(macOS) || os(iOS) || os(tvOS) || os(watchOS)
+@available(swift, deprecated: 5.1, message: "Use `x.exponent` or `floor(log2(x))`.")
+@_transparent
+public func logb(_ x: Float) -> Float {
+  return Float.log2(x).rounded(.down)
+}
+
+@available(swift, deprecated: 5.1, message: "Use `gamma(x)`.")
+@_transparent
+public func tgamma(_ x: Float) -> Float {
+  return Float.gamma(x)
+}
+
+#if (arch(i386) || arch(x86_64)) && !os(Windows)
+@available(swift, deprecated: 5.1, message: "Use `root(x, 3)`.")
+@_transparent
+public func cbrt(_ x: Float80) -> Float80 {
+  return Float80.root(x, 3)
+}
+
+@available(swift, deprecated: 5.1, message: "Use `x.exponent` or `floor(log2(x))`.")
+@_transparent
+public func logb(_ x: Float80) -> Float80 {
+  return Float80.log2(x).rounded(.down)
+}
+
+@available(swift, deprecated: 5.1, message: "Use `gamma(x)`.")
+@_transparent
+public func tgamma(_ x: Float80) -> Float80 {
+  return Float80.gamma(x)
+}
+#endif
+
 // Unary intrinsic functions
 // Note these have a corresponding LLVM intrinsic
 % for T, ufunc in TypedUnaryIntrinsicFunctions():
 %  if T == 'Float80':
 #if (arch(i386) || arch(x86_64)) && !os(Windows)
 %  end
+%  if ufunc[-3:] != 'int':
 @_transparent
 public func ${ufunc}(_ x: ${T}) -> ${T} {
-  return _${ufunc}(x)
+  return ${T}.${ufunc}(x)
 }
+%  else:
+@available(swift, deprecated: 5.1, message: "Swift does not model dynamic rounding modes, use x.rounded(.toNearestOrEven) instead.")
+@_transparent
+public func ${ufunc}(_ x: ${T}) -> ${T} {
+  return x.rounded(.toNearestOrEven)
+}
+%  end
 %  if T == 'Float80':
 #endif
 %  end
 
 % end
-#else
-// FIXME: As of now, we cannot declare 64-bit (Double/CDouble) overlays here.
-// Since CoreFoundation also exports libc functions, they will conflict with
-// Swift overlays when building Foundation. For now, just like normal
-// UnaryFunctions, we define overlays only for OverlayFloatTypes.
-% for ufunc in UnaryIntrinsicFunctions:
-%  for T, CT, f in OverlayFloatTypes():
-%   if T == 'Float80':
-#if (arch(i386) || arch(x86_64)) && !os(Windows)
-%   end
-@_transparent
-public func ${ufunc}(_ x: ${T}) -> ${T} {
-  return ${T}(${ufunc}${f}(${CT}(x)))
-}
-%   if T == 'Float80':
-#endif
-%   end
-%  end
-% end
-#endif
 
 // Binary functions
 
@@ -287,6 +288,54 @@
 
 % end
 
+@_transparent
+public func pow(_ x: Float, _ y: Float) -> Float {
+  return Float.pow(x, y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use the .nextUp and .nextDown properties.")
+@_transparent
+public func nextafter(_ x: Float, _ y: Float) -> Float {
+  return y > x ? x.nextUp : (y < x ? x.nextDown : y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use Float.minimum( ) or Swift.min( )")
+@_transparent
+public func fmin(_ x: Float, _ y: Float) -> Float {
+  return .minimum(x, y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use Float.maximum( ) or Swift.max( )")
+@_transparent
+public func fmax(_ x: Float, _ y: Float) -> Float {
+  return .maximum(x, y)
+}
+
+#if (arch(i386) || arch(x86_64)) && !os(Windows)
+@_transparent
+public func pow(_ x: Float80, _ y: Float80) -> Float80 {
+  return Float80.pow(x, y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use the .nextUp and .nextDown properties.")
+@_transparent
+public func nextafter(_ x: Float80, _ y: Float80) -> Float80 {
+  return y > x ? x.nextUp : (y < x ? x.nextDown : y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use Float80.minimum( ) or Swift.min( )")
+@_transparent
+public func fmin(_ x: Float80, _ y: Float80) -> Float80 {
+  return Float80.minimum(x, y)
+}
+
+@available(swift, deprecated: 5.1, message: "Use Float80.maximum( ) or Swift.max( )")
+@_transparent
+public func fmax(_ x: Float80, _ y: Float80) -> Float80 {
+  return Float80.maximum(x, y)
+}
+#endif
+
 % # This is AllFloatTypes not OverlayFloatTypes because of the tuple return.
 % for T, CT, f in AllFloatTypes():
 %  if T == 'Float80':
@@ -295,11 +344,10 @@
 //  lgamma not available on Windows, apparently?
 #if !os(Windows)
 %  end
+@available(swift, deprecated: 5.1, message: "Use (logGamma(x), signGamma(x)).")
 @_transparent
 public func lgamma(_ x: ${T}) -> (${T}, Int) {
-  var sign = Int32(0)
-  let value = lgamma${f}_r(${CT}(x), &sign)
-  return (${T}(value), Int(sign))
+  return (${T}.logGamma(x), ${T}.signGamma(x) == .plus ? 1 : -1)
 }
 #endif
 
@@ -326,8 +374,8 @@
 %  if T == 'Float80':
 #if (arch(i386) || arch(x86_64)) && !os(Windows)
 %  end
-@available(swift, deprecated: 4.2, message:
-           "use ${T}(nan: ${T}.RawSignificand) instead.")
+@available(swift, deprecated: 4.2, obsoleted: 5.1, message:
+           "use ${T}(nan: ${T}.RawSignificand).")
 @_transparent
 public func nan(_ tag: String) -> ${T} {
   return ${T}(nan${f}(tag))
diff --git a/stdlib/public/SwiftShims/LibcShims.h b/stdlib/public/SwiftShims/LibcShims.h
index ff99bc7..e495d56 100644
--- a/stdlib/public/SwiftShims/LibcShims.h
+++ b/stdlib/public/SwiftShims/LibcShims.h
@@ -127,46 +127,338 @@
 
 // Math library functions
 static inline SWIFT_ALWAYS_INLINE
-float _stdlib_remainderf(float _self, float _other) {
-  return __builtin_remainderf(_self, _other);
+float _swift_stdlib_remainderf(float _self, float other) {
+  return __builtin_remainderf(_self, other);
 }
   
 static inline SWIFT_ALWAYS_INLINE
-float _stdlib_squareRootf(float _self) {
+float _swift_stdlib_squareRootf(float _self) {
   return __builtin_sqrtf(_self);
 }
-
+  
 static inline SWIFT_ALWAYS_INLINE
-double _stdlib_remainder(double _self, double _other) {
-  return __builtin_remainder(_self, _other);
+float _swift_stdlib_tanf(float x) {
+  return __builtin_tanf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_acosf(float x) {
+  return __builtin_acosf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_asinf(float x) {
+  return __builtin_asinf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_atanf(float x) {
+  return __builtin_atanf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_atan2f(float y, float x) {
+  return __builtin_atan2f(y, x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_coshf(float x) {
+  return __builtin_coshf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_sinhf(float x) {
+  return __builtin_sinhf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_tanhf(float x) {
+  return __builtin_tanhf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_acoshf(float x) {
+  return __builtin_acoshf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_asinhf(float x) {
+  return __builtin_asinhf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_atanhf(float x) {
+  return __builtin_atanhf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_exp10f(float x) {
+#if defined __APPLE__
+  extern float __exp10f(float);
+  return __exp10f(x);
+#else
+  return __builtin_powf(10, x);
+#endif
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_expm1f(float x) {
+  return __builtin_expm1f(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_log1pf(float x) {
+  return __builtin_log1pf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_hypotf(float x, float y) {
+  return __builtin_hypotf(x, y);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_erff(float x) {
+  return __builtin_erff(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_erfcf(float x) {
+  return __builtin_erfcf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_tgammaf(float x) {
+  return __builtin_tgammaf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+float _swift_stdlib_lgammaf(float x) {
+  extern float lgammaf_r(float x, int *psigngam);
+  int dontCare;
+  return lgammaf_r(x, &dontCare);
 }
 
 static inline SWIFT_ALWAYS_INLINE
-double _stdlib_squareRoot(double _self) {
+double _swift_stdlib_remainder(double _self, double other) {
+  return __builtin_remainder(_self, other);
+}
+
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_squareRoot(double _self) {
   return __builtin_sqrt(_self);
 }
 
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_tan(double x) {
+  return __builtin_tan(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_acos(double x) {
+  return __builtin_acos(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_asin(double x) {
+  return __builtin_asin(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_atan(double x) {
+  return __builtin_atan(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_atan2(double y, double x) {
+  return __builtin_atan2(y, x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_cosh(double x) {
+  return __builtin_cosh(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_sinh(double x) {
+  return __builtin_sinh(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_tanh(double x) {
+  return __builtin_tanh(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_acosh(double x) {
+  return __builtin_acosh(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_asinh(double x) {
+  return __builtin_asinh(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_atanh(double x) {
+  return __builtin_atanh(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_exp10(double x) {
+#if defined __APPLE__
+  extern double __exp10(double);
+  return __exp10(x);
+#else
+  return __builtin_pow(10, x);
+#endif
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_expm1(double x) {
+  return __builtin_expm1(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_log1p(double x) {
+  return __builtin_log1p(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_hypot(double x, double y) {
+  return __builtin_hypot(x, y);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_erf(double x) {
+  return __builtin_erf(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_erfc(double x) {
+  return __builtin_erfc(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_tgamma(double x) {
+  return __builtin_tgamma(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+double _swift_stdlib_lgamma(double x) {
+  extern double lgamma_r(double x, int *psigngam);
+  int dontCare;
+  return lgamma_r(x, &dontCare);
+}
+
 #if !defined _WIN32 && (defined __i386__ || defined __x86_64__)
 static inline SWIFT_ALWAYS_INLINE
-long double _stdlib_remainderl(long double _self, long double _other) {
-  return __builtin_remainderl(_self, _other);
+long double _swift_stdlib_remainderl(long double _self, long double other) {
+  return __builtin_remainderl(_self, other);
+}
+
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_squareRootl(long double _self) {
+  return __builtin_sqrtl(_self);
+}
+
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_tanl(long double x) {
+  return __builtin_tanl(x);
 }
   
 static inline SWIFT_ALWAYS_INLINE
-long double _stdlib_squareRootl(long double _self) {
-  return __builtin_sqrtl(_self);
+long double _swift_stdlib_acosl(long double x) {
+  return __builtin_acosl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_asinl(long double x) {
+  return __builtin_asinl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_atanl(long double x) {
+  return __builtin_atanl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_atan2l(long double y, long double x) {
+  return __builtin_atan2l(y, x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_coshl(long double x) {
+  return __builtin_coshl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_sinhl(long double x) {
+  return __builtin_sinhl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_tanhl(long double x) {
+  return __builtin_tanhl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_acoshl(long double x) {
+  return __builtin_acoshl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_asinhl(long double x) {
+  return __builtin_asinhl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_atanhl(long double x) {
+  return __builtin_atanhl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_exp10l(long double x) {
+  return __builtin_powl(10, x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_expm1l(long double x) {
+  return __builtin_expm1l(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_log1pl(long double x) {
+  return __builtin_log1pl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_hypotl(long double x, long double y) {
+  return __builtin_hypotl(x, y);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_erfl(long double x) {
+  return __builtin_erfl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_erfcl(long double x) {
+  return __builtin_erfcl(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_tgammal(long double x) {
+  return __builtin_tgammal(x);
+}
+  
+static inline SWIFT_ALWAYS_INLINE
+long double _swift_stdlib_lgammal(long double x) {
+  extern long double lgammal_r(long double x, int *psigngam);
+  int dontCare;
+  return lgammal_r(x, &dontCare);
 }
 #endif
 
-// Apple's math.h does not declare lgamma_r() etc by default, but they're
-// unconditionally exported by libsystem_m.dylib in all OS versions that
-// support Swift development; we simply need to provide declarations here.
-#if defined(__APPLE__)
-float lgammaf_r(float x, int *psigngam);
-double lgamma_r(double x, int *psigngam);
-long double lgammal_r(long double x, int *psigngam);
-#endif // defined(__APPLE__)
-
 #ifdef __cplusplus
 }} // extern "C", namespace swift
 #endif
diff --git a/stdlib/public/core/AssertCommon.swift b/stdlib/public/core/AssertCommon.swift
index f4d401a..b225cfe 100644
--- a/stdlib/public/core/AssertCommon.swift
+++ b/stdlib/public/core/AssertCommon.swift
@@ -115,7 +115,8 @@
 ) -> Never {
   prefix.withUTF8Buffer {
     (prefix) -> Void in
-    message._withUnsafeBufferPointerToUTF8 {
+    var message = message
+    message.withUTF8 {
       (messageUTF8) -> Void in
       file.withUTF8Buffer {
         (file) -> Void in
@@ -145,7 +146,8 @@
 ) -> Never {
   prefix.withUTF8Buffer {
     (prefix) -> Void in
-    message._withUnsafeBufferPointerToUTF8 {
+    var message = message
+    message.withUTF8 {
       (messageUTF8) -> Void in
       _swift_stdlib_reportFatalError(
         prefix.baseAddress!, CInt(prefix.count),
diff --git a/stdlib/public/core/BuiltinMath.swift.gyb b/stdlib/public/core/BuiltinMath.swift.gyb
deleted file mode 100644
index 69db331..0000000
--- a/stdlib/public/core/BuiltinMath.swift.gyb
+++ /dev/null
@@ -1,78 +0,0 @@
-//===--- BuiltinMath.swift.gyb --------------------------------*- swift -*-===//
-//
-// This source file is part of the Swift.org open source project
-//
-// Copyright (c) 2014 - 2017 Apple Inc. and the Swift project authors
-// Licensed under Apache License v2.0 with Runtime Library Exception
-//
-// See https://swift.org/LICENSE.txt for license information
-// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
-//
-//===----------------------------------------------------------------------===//
-
-%{
-
-# Don't need 64-bit (Double/CDouble) overlays. The ordinary C imports work fine.
-overlayFloatBits = [32, 80]
-allFloatBits = [32, 64, 80]
-
-def floatName(bits):
-    if bits == 32:
-        return 'Float'
-    if bits == 64:
-        return 'Double'
-    if bits == 80:
-        return 'Float80'
-
-def cFloatName(bits):
-    if bits == 32:
-        return 'CFloat'
-    if bits == 64:
-        return 'CDouble'
-    if bits == 80:
-        return 'CLongDouble'
-
-def cFuncSuffix(bits):
-    if bits == 32:
-        return 'f'
-    if bits == 64:
-        return ''
-    if bits == 80:
-        return 'l'
-
-# Each of the following lists is ordered to match math.h
-
-# These functions have a corresponding LLVM intrinsic
-# Note, keep this up to date with Darwin/tgmath.swift.gyb
-UnaryIntrinsicFunctions = [
-    'cos', 'sin',
-    'exp', 'exp2',
-    'log', 'log10', 'log2',
-    'nearbyint', 'rint',
-]
-
-def TypedUnaryIntrinsicFunctions():
-    for ufunc in UnaryIntrinsicFunctions:
-        for bits in allFloatBits:
-            yield floatName(bits), cFloatName(bits), bits, ufunc
-
-}%
-
-// Unary intrinsic functions
-// Note these have a corresponding LLVM intrinsic
-% for T, CT, bits, ufunc in TypedUnaryIntrinsicFunctions():
-%  if bits == 80:
-#if !os(Windows) && (arch(i386) || arch(x86_64))
-%  end
-@_transparent
-public func _${ufunc}(_ x: ${T}) -> ${T} {
-  return ${T}(Builtin.int_${ufunc}_FPIEEE${bits}(x._value))
-}
-%  if bits == 80:
-#endif
-%  end
-% end
-
-// ${'Local Variables'}:
-// eval: (read-only-mode 1)
-// End:
diff --git a/stdlib/public/core/CMakeLists.txt b/stdlib/public/core/CMakeLists.txt
index f7874df..849a883 100644
--- a/stdlib/public/core/CMakeLists.txt
+++ b/stdlib/public/core/CMakeLists.txt
@@ -184,7 +184,6 @@
 
 set(SWIFTLIB_ESSENTIAL_GYB_SOURCES
   AtomicInt.swift.gyb
-  BuiltinMath.swift.gyb
   Codable.swift.gyb
   FixedArray.swift.gyb
   FloatingPointParsing.swift.gyb
@@ -218,10 +217,11 @@
   )
 
 set(SWIFTLIB_GYB_SOURCES
-    ${SWIFTLIB_ESSENTIAL_GYB_SOURCES}
-    ExistentialCollection.swift.gyb
-    SIMDVectorTypes.swift.gyb
-    Tuple.swift.gyb
+  ${SWIFTLIB_ESSENTIAL_GYB_SOURCES}
+  ExistentialCollection.swift.gyb
+  MathFunctions.swift.gyb
+  SIMDVectorTypes.swift.gyb
+  Tuple.swift.gyb
   )
 set(GROUP_INFO_JSON_FILE ${CMAKE_CURRENT_SOURCE_DIR}/GroupInfo.json)
 set(swift_core_link_flags "${SWIFT_RUNTIME_SWIFT_LINK_FLAGS}")
diff --git a/stdlib/public/core/ContiguouslyStored.swift b/stdlib/public/core/ContiguouslyStored.swift
index 2a6d3ad..55b625e 100644
--- a/stdlib/public/core/ContiguouslyStored.swift
+++ b/stdlib/public/core/ContiguouslyStored.swift
@@ -80,22 +80,11 @@
   }
 
   @inlinable @inline(__always)
-  internal func _withUTF8<R>(
-    _ body: (UnsafeBufferPointer<UInt8>) throws -> R
-  ) rethrows -> R {
-    if _fastPath(self._guts.isFastUTF8) {
-      return try self._guts.withFastUTF8 {
-        try body($0)
-      }
-    }
-    return try String._copying(self)._guts.withFastUTF8 { try body($0) }
-  }
-
-  @inlinable @inline(__always)
   internal func withUnsafeBytes<R>(
     _ body: (UnsafeRawBufferPointer) throws -> R
   ) rethrows -> R {
-    return try self._withUTF8 { return try body(UnsafeRawBufferPointer($0)) }
+    var copy = self
+    return try copy.withUTF8 { return try body(UnsafeRawBufferPointer($0)) }
   }
 }
 extension Substring: _HasContiguousBytes {
@@ -105,21 +94,10 @@
   }
 
   @inlinable @inline(__always)
-  internal func _withUTF8<R>(
-    _ body: (UnsafeBufferPointer<UInt8>) throws -> R
-  ) rethrows -> R {
-    if _fastPath(_wholeGuts.isFastUTF8) {
-      return try _wholeGuts.withFastUTF8(range: self._offsetRange) {
-        return try body($0)
-      }
-    }
-    return try String._copying(self)._guts.withFastUTF8 { try body($0) }
-  }
-
-  @inlinable @inline(__always)
   internal func withUnsafeBytes<R>(
     _ body: (UnsafeRawBufferPointer) throws -> R
   ) rethrows -> R {
-    return try self._withUTF8 { return try body(UnsafeRawBufferPointer($0)) }
+    var copy = self
+    return try copy.withUTF8 { return try body(UnsafeRawBufferPointer($0)) }
   }
 }
diff --git a/stdlib/public/core/FloatingPoint.swift b/stdlib/public/core/FloatingPoint.swift
index 6933ca3..ccb4fdd 100644
--- a/stdlib/public/core/FloatingPoint.swift
+++ b/stdlib/public/core/FloatingPoint.swift
@@ -1898,10 +1898,6 @@
   ///   other is NaN.
   @inlinable
   public static func minimum(_ x: Self, _ y: Self) -> Self {
-    if x.isSignalingNaN || y.isSignalingNaN {
-      //  Produce a quiet NaN matching platform arithmetic behavior.
-      return x + y
-    }
     if x <= y || y.isNaN { return x }
     return y
   }
@@ -1935,10 +1931,6 @@
   ///   other is NaN.
   @inlinable
   public static func maximum(_ x: Self, _ y: Self) -> Self {
-    if x.isSignalingNaN || y.isSignalingNaN {
-      //  Produce a quiet NaN matching platform arithmetic behavior.
-      return x + y
-    }
     if x > y || y.isNaN { return x }
     return y
   }
@@ -1974,10 +1966,6 @@
   ///   a number if the other is NaN.
   @inlinable
   public static func minimumMagnitude(_ x: Self, _ y: Self) -> Self {
-    if x.isSignalingNaN || y.isSignalingNaN {
-      //  Produce a quiet NaN matching platform arithmetic behavior.
-      return x + y
-    }
     if x.magnitude <= y.magnitude || y.isNaN { return x }
     return y
   }
@@ -2013,10 +2001,6 @@
   ///   a number if the other is NaN.
   @inlinable
   public static func maximumMagnitude(_ x: Self, _ y: Self) -> Self {
-    if x.isSignalingNaN || y.isSignalingNaN {
-      //  Produce a quiet NaN matching platform arithmetic behavior.
-      return x + y
-    }
     if x.magnitude > y.magnitude || y.isNaN { return x }
     return y
   }
diff --git a/stdlib/public/core/FloatingPointTypes.swift.gyb b/stdlib/public/core/FloatingPointTypes.swift.gyb
index 6c7c9b4..074d88c 100644
--- a/stdlib/public/core/FloatingPointTypes.swift.gyb
+++ b/stdlib/public/core/FloatingPointTypes.swift.gyb
@@ -1115,7 +1115,7 @@
   @inlinable // FIXME(inline-always)
   @inline(__always)
   public mutating func formRemainder(dividingBy other: ${Self}) {
-    self = _stdlib_remainder${cFuncSuffix}(self, other)
+    self = _swift_stdlib_remainder${cFuncSuffix}(self, other)
   }
 
   /// Replaces this value with the remainder of itself divided by the given
@@ -1157,7 +1157,7 @@
   /// value.
   @_transparent
   public mutating func formSquareRoot( ) {
-    self = _stdlib_squareRoot${cFuncSuffix}(self)
+    self = _swift_stdlib_squareRoot${cFuncSuffix}(self)
   }
 
   /// Adds the product of the two given values to this value in place, computed
diff --git a/stdlib/public/core/GroupInfo.json b/stdlib/public/core/GroupInfo.json
index 06ba858..aa25068 100644
--- a/stdlib/public/core/GroupInfo.json
+++ b/stdlib/public/core/GroupInfo.json
@@ -158,7 +158,7 @@
   ],
   "Math": [
     "SetAlgebra.swift",
-    "BuiltinMath.swift",
+    "MathFunctions.swift",
     {
     "Integers": [
       "Integers.swift",
diff --git a/stdlib/public/core/LegacyABI.swift b/stdlib/public/core/LegacyABI.swift
index 6f64dfd..604a86b 100644
--- a/stdlib/public/core/LegacyABI.swift
+++ b/stdlib/public/core/LegacyABI.swift
@@ -39,3 +39,24 @@
   internal var _wholeString: String { return base }
 }
 
+extension String {
+  @available(*, unavailable, renamed: "String.withUTF8")
+  @inlinable
+  internal func _withUTF8<R>(
+    _ body: (UnsafeBufferPointer<UInt8>) throws -> R
+  ) rethrows -> R {
+    var copy = self
+    return try copy.withUTF8(body)
+  }
+}
+
+extension Substring {
+  @available(*, unavailable, renamed: "Substring.withUTF8")
+  @inlinable
+  internal func _withUTF8<R>(
+    _ body: (UnsafeBufferPointer<UInt8>) throws -> R
+  ) rethrows -> R {
+    var copy = self
+    return try copy.withUTF8(body)
+  }
+}
diff --git a/stdlib/public/core/MathFunctions.swift.gyb b/stdlib/public/core/MathFunctions.swift.gyb
new file mode 100644
index 0000000..78ca724
--- /dev/null
+++ b/stdlib/public/core/MathFunctions.swift.gyb
@@ -0,0 +1,329 @@
+//===--- MathFunctions.swift ----------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift.org open source project
+//
+// Copyright (c) 2019 Apple Inc. and the Swift project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+//
+//===----------------------------------------------------------------------===//
+
+import SwiftShims
+%from SwiftMathFunctions import *
+%from SwiftFloatingPointTypes import all_floating_point_types
+
+/// A type that has elementary functions available.
+///
+/// An ["elementary function"][elfn] is a function built up from powers, roots,
+/// exponentials, logarithms, trigonometric functions (sin, cos, tan) and
+/// their inverses, and the hyperbolic functions (sinh, cosh, tanh) and their
+/// inverses.
+///
+/// Conformance to this protocol means that all of these building blocks are
+/// available as static functions on the type.
+///
+/// ```swift
+/// let x: Float = 1
+/// let y = Float.sin(x) // 0.84147096
+/// ```
+///
+/// All of these are made available as free functions by importing the Math
+/// module:
+///
+/// ```swift
+/// import Math
+/// let y = sin(x) // 0.84147096
+/// ```
+///
+/// Additional operations, such as `atan2(y:x:)`, `hypot(_:_:)` and some
+/// special functions, are provided on the Real protocol, which refines both
+/// ElementaryFunctions and FloatingPoint.
+///
+/// [elfn]: http://en.wikipedia.org/wiki/Elementary_function
+public protocol ElementaryFunctions {
+
+%for func in ElementaryFunctions:
+
+  ${func.comment}
+  static func ${func.decl("Self")}
+%end
+
+  /// `exp(y log(x))` computed without loss of intermediate precision.
+  ///
+  /// For real types, if `x` is negative the result is NaN, even if `y` has
+  /// an integral value. For complex types, there is a branch cut on the
+  /// negative real axis.
+  static func pow(_ x: Self, _ y: Self) -> Self
+
+  /// `x` raised to the `n`th power.
+  static func pow(_ x: Self, _ n: Int) -> Self
+
+  /// The `n`th root of `x`.
+  ///
+  /// For real types, if `x` is negative and `n` is even, the result is NaN.
+  /// For complex types, there is a branch cut along the negative real axis.
+  static func root(_ x: Self, _ n: Int) -> Self
+}
+
+/// A type that models the real numbers.
+public protocol Real: ElementaryFunctions, FloatingPoint {
+%for func in RealFunctions:
+
+  ${func.comment}
+  static func ${func.decl("Self")}
+%end
+
+  /// `atan(y/x)` with quadrant fixup.
+  ///
+  /// There is an infinite family of angles whose tangent is `y/x`. `atan2`
+  /// selects the representative that is the angle between the vector `(x, y)`
+  /// and the real axis in the range [-π, π].
+  static func atan2(y: Self, x: Self) -> Self
+
+#if !os(Windows)
+  //  lgamma is not available on Windows.
+  //  TODO: provide an implementation of lgamma with the stdlib to support
+  //  Windows so we can vend a uniform interface.
+
+  /// `log(gamma(x))` computed without undue overflow.
+  ///
+  /// `log(abs(gamma(x)))` is returned. To get the sign of `gamma(x)` cheaply,
+  /// use `signGamma(x)`.
+  static func logGamma(_ x: Self) -> Self
+#endif
+}
+
+extension Real {
+#if !os(Windows)
+  //  lgamma is not available on Windows; no lgamma means signGamma
+  //  is basically useless, so don't bother exposing it.
+
+  /// The sign of `gamma(x)`.
+  ///
+  /// This function is typically used in conjunction with `logGamma(x)`, which
+  /// computes `log(abs(gamma(x)))`, to recover the sign information that is
+  /// lost to the absolute value.
+  ///
+  /// `gamma(x)` has a simple pole at each non-positive integer and an
+  /// essential singularity at infinity; we arbitrarily choose to return
+  /// `.plus` for the sign in those cases. For all other values, `signGamma(x)`
+  /// is `.plus` if `x >= 0` or `trunc(x)` is odd, and `.minus` otherwise.
+  @_alwaysEmitIntoClient
+  public static func signGamma(_ x: Self) -> FloatingPointSign {
+    if x >= 0 { return .plus }
+    let trunc = x.rounded(.towardZero)
+    // Treat poles as gamma(x) == +inf. This is arbitrary, but we need to
+    // pick one sign or the other.
+    if x == trunc { return .plus }
+    // Result is .minus if trunc is even, .plus otherwise. To figure out if
+    // trunc is even or odd, check if trunc/2 is an integer.
+    let halfTrunc = trunc/2
+    if halfTrunc == halfTrunc.rounded(.towardZero) { return .minus }
+    return .plus
+  }
+#endif
+}
+
+%for type in all_floating_point_types():
+% if type.bits == 80:
+#if (arch(i386) || arch(x86_64)) && !os(Windows)
+% end
+% Self = type.stdlib_name
+extension ${Self}: Real {
+% for func in ElementaryFunctions + RealFunctions:
+
+  @_alwaysEmitIntoClient
+  public static func ${func.decl(Self)} {
+    return ${func.impl(type)}
+  }
+% end
+
+  @_alwaysEmitIntoClient
+  public static func pow(_ x: ${Self}, _ y: ${Self}) -> ${Self} {
+    guard x >= 0 else { return .nan }
+    return ${Self}(Builtin.int_pow_FPIEEE${type.bits}(x._value, y._value))
+  }
+
+  @_alwaysEmitIntoClient
+  public static func pow(_ x: ${Self}, _ n: Int) -> ${Self} {
+    // TODO: this implementation isn't quite right for n so large that
+    // the conversion to `${Self}` rounds. We could also consider using
+    // a multiply-chain implementation for small `n`; this would be faster
+    // for static `n`, but less accurate on platforms with a good `pow`
+    // implementation.
+    return ${Self}(Builtin.int_pow_FPIEEE${type.bits}(x._value, ${Self}(n)._value))
+  }
+
+  @_alwaysEmitIntoClient
+  public static func root(_ x: ${Self}, _ n: Int) -> ${Self} {
+    guard x >= 0 || n % 2 != 0 else { return .nan }
+    // TODO: this implementation isn't quite right for n so large that
+    // the conversion to `${Self}` rounds.
+    return ${Self}(signOf: x, magnitudeOf: pow(x, 1/${Self}(n)))
+  }
+
+  @_alwaysEmitIntoClient
+  public static func atan2(y: ${Self}, x: ${Self}) -> ${Self} {
+    return _swift_stdlib_atan2${type.cFuncSuffix}(y, x)
+  }
+
+#if !os(Windows)
+  @_alwaysEmitIntoClient
+  public static func logGamma(_ x: ${Self}) -> ${Self} {
+    return _swift_stdlib_lgamma${type.cFuncSuffix}(x)
+  }
+#endif
+}
+% if type.bits == 80:
+#endif
+% end
+%end
+
+// MARK: - Free functions defined on ElementaryFunctions:
+%from SwiftMathFunctions import *
+%for func in ElementaryFunctions:
+
+% if func.name == 'sqrt':
+// sqrt requires availability because it was previous generic on FloatingPoint.
+@available(swift, introduced: 5.1)
+% end
+@_alwaysEmitIntoClient
+public func ${func.free_decl()} {
+  return T.${func.swiftName}(${func.params()})
+}
+
+@_alwaysEmitIntoClient
+public func ${func.free_decl("T: SIMD, T.Scalar: ElementaryFunctions")} {
+  var r = T()
+  for i in r.indices { r[i] = T.Scalar.${func.swiftName}(${func.params("","[i]")}) }
+  return r
+}
+%end
+
+@_alwaysEmitIntoClient
+public func pow<T>(_ x: T, _ y: T) -> T where T: ElementaryFunctions {
+  return T.pow(x, y)
+}
+
+@_alwaysEmitIntoClient
+public func pow<T>(_ x: T, _ y: T) -> T where T: SIMD, T.Scalar: ElementaryFunctions {
+  var r = T()
+  for i in r.indices { r[i] = T.Scalar.pow(x[i], y[i]) }
+  return r
+}
+
+@_alwaysEmitIntoClient
+public func pow<T>(_ x: T, _ n: Int) -> T where T: ElementaryFunctions {
+  return T.pow(x, n)
+}
+
+@_alwaysEmitIntoClient
+public func pow<T>(_ x: T, _ n: Int) -> T where T: SIMD, T.Scalar: ElementaryFunctions {
+  var r = T()
+  for i in r.indices { r[i] = T.Scalar.pow(x[i], n) }
+  return r
+}
+
+@_alwaysEmitIntoClient
+public func root<T>(_ x: T, _ n: Int) -> T where T: ElementaryFunctions {
+  return T.root(x, n)
+}
+
+@_alwaysEmitIntoClient
+public func root<T>(_ x: T, _ n: Int) -> T where T: SIMD, T.Scalar: ElementaryFunctions {
+  var r = T()
+  for i in r.indices { r[i] = T.Scalar.root(x[i], n) }
+  return r
+}
+
+// MARK: - Free functions defined on Real:
+%for func in RealFunctions:
+
+@_alwaysEmitIntoClient
+public func ${func.free_decl("T: Real")} {
+  return T.${func.swiftName}(${func.params()})
+}
+
+@_alwaysEmitIntoClient
+public func ${func.free_decl("T: SIMD, T.Scalar: Real")} {
+  var r = T()
+  for i in r.indices { r[i] = T.Scalar.${func.swiftName}(${func.params("","[i]")}) }
+  return r
+}
+%end
+
+@_alwaysEmitIntoClient
+public func atan2<T>(y: T, x: T) -> T where T: Real {
+  return T.atan2(y: y, x: x)
+}
+
+@_alwaysEmitIntoClient
+public func atan2<T>(y: T, x: T) -> T where T: SIMD, T.Scalar: Real {
+  var r = T()
+  for i in r.indices { r[i] = T.Scalar.atan2(y: y[i], x: x[i]) }
+  return r
+}
+
+//  logGamma is not available on Windows.
+//  TODO: logGamma, signGamma for SIMD types.
+#if !os(Windows)
+@_alwaysEmitIntoClient
+public func logGamma<T>(_ x: T) -> T where T: Real {
+  return T.logGamma(x)
+}
+
+@_alwaysEmitIntoClient
+public func signGamma<T>(_ x: T) -> FloatingPointSign where T: Real {
+  return T.signGamma(x)
+}
+#endif
+
+// MARK: - Free functions defined on FloatingPoint:
+% for (func,dir) in [("ceil", ".up"), ("floor", ".down"), ("round", ""), ("trunc", ".towardZero")]:
+
+@_alwaysEmitIntoClient
+public func ${func}<T>(_ x: T) -> T where T: FloatingPoint {
+  return x.rounded(${dir})
+}
+
+@_alwaysEmitIntoClient
+public func ${func}<T>(_ x: T) -> T where T: SIMD, T.Scalar: FloatingPoint {
+  return x.rounded(${dir})
+}
+%end
+
+@_alwaysEmitIntoClient
+public func fma<T>(_ x: T, _ y: T, _ z: T) -> T where T: FloatingPoint {
+  return z.addingProduct(x, y)
+}
+
+@_alwaysEmitIntoClient
+public func fma<T>(_ x: T, _ y: T, _ z: T) -> T where T: SIMD, T.Scalar: FloatingPoint {
+  return z.addingProduct(x, y)
+}
+
+@_alwaysEmitIntoClient
+public func remainder<T>(_ dividend: T, _ divisor: T) -> T where T: FloatingPoint {
+  return dividend.remainder(dividingBy: divisor)
+}
+
+@_alwaysEmitIntoClient
+public func remainder<T>(_ dividend: T, _ divisor: T) -> T where T: SIMD, T.Scalar: FloatingPoint {
+  var r = T()
+  for i in r.indices { r[i] = dividend[i].remainder(dividingBy: divisor[i]) }
+  return r
+}
+
+@_alwaysEmitIntoClient
+public func copysign<T>(_ magnitude: T, _ sign: T) -> T where T: FloatingPoint {
+  return T(signOf: sign, magnitudeOf: magnitude)
+}
+
+@_alwaysEmitIntoClient
+public func copysign<T>(_ magnitude: T, _ sign: T) -> T where T: SIMD, T.Scalar: FloatingPoint {
+  var r = T()
+  for i in r.indices { r[i] = copysign(magnitude[i], sign[i]) }
+  return r
+}
diff --git a/stdlib/public/core/OutputStream.swift b/stdlib/public/core/OutputStream.swift
index 6303846..a4dbca9 100644
--- a/stdlib/public/core/OutputStream.swift
+++ b/stdlib/public/core/OutputStream.swift
@@ -521,7 +521,8 @@
   internal mutating func write(_ string: String) {
     if string.isEmpty { return }
 
-    _ = string._withUTF8 { utf8 in
+    var string = string
+    _ = string.withUTF8 { utf8 in
       _swift_stdlib_fwrite_stdout(utf8.baseAddress!, 1, utf8.count)
     }
   }
diff --git a/stdlib/public/core/SIMDVector.swift b/stdlib/public/core/SIMDVector.swift
index dce9b33..5bb6308 100644
--- a/stdlib/public/core/SIMDVector.swift
+++ b/stdlib/public/core/SIMDVector.swift
@@ -652,7 +652,7 @@
   }
   
   @_transparent
-  public func rounded(_ rule: FloatingPointRoundingRule) -> Self {
+  public func rounded(_ rule: FloatingPointRoundingRule = .toNearestOrEven) -> Self {
     var result = Self()
     for i in result.indices { result[i] = self[i].rounded(rule) }
     return result
diff --git a/stdlib/public/core/String.swift b/stdlib/public/core/String.swift
index 270a7ad..658ce7b 100644
--- a/stdlib/public/core/String.swift
+++ b/stdlib/public/core/String.swift
@@ -468,7 +468,8 @@
     encodedAs targetEncoding: TargetEncoding.Type,
     _ body: (UnsafePointer<TargetEncoding.CodeUnit>) throws -> Result
   ) rethrows -> Result {
-    return try self._withUTF8 { utf8 in
+    var copy = self
+    return try copy.withUTF8 { utf8 in
       var arg = Array<TargetEncoding.CodeUnit>()
       arg.reserveCapacity(1 &+ self._guts.count / 4)
       let repaired = transcode(
diff --git a/stdlib/public/core/StringCreate.swift b/stdlib/public/core/StringCreate.swift
index 648420e..62d7257 100644
--- a/stdlib/public/core/StringCreate.swift
+++ b/stdlib/public/core/StringCreate.swift
@@ -144,16 +144,6 @@
     return contents.withUnsafeBufferPointer { String._uncheckedFromUTF8($0) }
   }
 
-  internal func _withUnsafeBufferPointerToUTF8<R>(
-    _ body: (UnsafeBufferPointer<UTF8.CodeUnit>) throws -> R
-  ) rethrows -> R {
-    return try self.withUnsafeBytes { rawBufPtr in
-      return try body(UnsafeBufferPointer(
-        start: rawBufPtr.baseAddress?.assumingMemoryBound(to: UInt8.self),
-        count: rawBufPtr.count))
-    }
-  }
-
   @usableFromInline @inline(never) // slow-path
   internal static func _fromCodeUnits<
     Input: Collection,
@@ -218,4 +208,3 @@
     }
   }
 }
-
diff --git a/stdlib/public/core/StringProtocol.swift b/stdlib/public/core/StringProtocol.swift
index 4e31396..2b2f3fd 100644
--- a/stdlib/public/core/StringProtocol.swift
+++ b/stdlib/public/core/StringProtocol.swift
@@ -173,4 +173,98 @@
   }
 }
 
+// Contiguous UTF-8 strings
+extension String {
+  /// Returns whether this string is capable of providing access to
+  /// validly-encoded UTF-8 contents in contiguous memory in O(1) time.
+  ///
+  /// Contiguous strings always operate in O(1) time for withUTF8 and always
+  /// give a result for String.UTF8View.withContiguousStorageIfAvailable.
+  /// Contiguous strings also benefit from fast-paths and better optimizations.
+  ///
+  @_alwaysEmitIntoClient
+  public var isContiguousUTF8: Bool { return _guts.isFastUTF8 }
 
+  /// If this string is not contiguous, make it so. If this mutates the string,
+  /// it will invalidate any pre-existing indices.
+  ///
+  /// Complexity: O(n) if non-contiguous, O(1) if already contiguous
+  ///
+  @_alwaysEmitIntoClient
+  public mutating func makeContiguousUTF8() {
+    if _fastPath(isContiguousUTF8) { return }
+    self = String._copying(self)
+  }
+
+  /// Runs `body` over the content of this string in contiguous memory. If this
+  /// string is not contiguous, this will first make it contiguous, which will
+  /// also speed up subsequent access. If this mutates the string,
+  /// it will invalidate any pre-existing indices.
+  ///
+  /// Note that it is unsafe to escape the pointer provided to `body`. For
+  /// example, strings of up to 15 UTF-8 code units in length may be represented
+  /// in a small-string representation, and thus will be spilled into
+  /// temporary stack space which is invalid after `withUTF8` finishes
+  /// execution.
+  ///
+  /// Complexity: O(n) if non-contiguous, O(1) if already contiguous
+  ///
+  @_alwaysEmitIntoClient
+  public mutating func withUTF8<R>(
+    _ body: (UnsafeBufferPointer<UInt8>) throws -> R
+  ) rethrows -> R {
+    makeContiguousUTF8()
+    return try _guts.withFastUTF8(body)
+  }
+}
+
+// Contiguous UTF-8 strings
+extension Substring {
+  /// Returns whether this string is capable of providing access to
+  /// validly-encoded UTF-8 contents in contiguous memory in O(1) time.
+  ///
+  /// Contiguous strings always operate in O(1) time for withUTF8 and always
+  /// give a result for String.UTF8View.withContiguousStorageIfAvailable.
+  /// Contiguous strings also benefit from fast-paths and better optimizations.
+  ///
+  @_alwaysEmitIntoClient
+  public var isContiguousUTF8: Bool { return self.base.isContiguousUTF8 }
+
+  /// If this string is not contiguous, make it so. If this mutates the
+  /// substring, it will invalidate any pre-existing indices.
+  ///
+  /// Complexity: O(n) if non-contiguous, O(1) if already contiguous
+  ///
+  @_alwaysEmitIntoClient
+  public mutating func makeContiguousUTF8() {
+    if _fastPath(isContiguousUTF8) { return }
+    self = String._copying(self)[...]
+  }
+
+  /// Runs `body` over the content of this substring in contiguous memory. If
+  /// this substring is not contiguous, this will first make it contiguous,
+  /// which will also speed up subsequent access. If this mutates the substring,
+  /// it will invalidate any pre-existing indices.
+  ///
+  /// Note that it is unsafe to escape the pointer provided to `body`. For
+  /// example, strings of up to 15 UTF-8 code units in length may be represented
+  /// in a small-string representation, and thus will be spilled into
+  /// temporary stack space which is invalid after `withUTF8` finishes
+  /// execution.
+  ///
+  /// Complexity: O(n) if non-contiguous, O(1) if already contiguous
+  ///
+  @_alwaysEmitIntoClient
+  public mutating func withUTF8<R>(
+    _ body: (UnsafeBufferPointer<UInt8>) throws -> R
+  ) rethrows -> R {
+    if _fastPath(isContiguousUTF8) {
+      return try _wholeGuts.withFastUTF8(range: self._offsetRange) {
+        return try body($0)
+      }
+    }
+
+    makeContiguousUTF8()
+    return try _wholeGuts.withFastUTF8(body)
+  }
+}
diff --git a/test/Driver/profiling.swift b/test/Driver/profiling.swift
index 02676c9..28439dd 100644
--- a/test/Driver/profiling.swift
+++ b/test/Driver/profiling.swift
@@ -41,7 +41,7 @@
 // watchOS: {{(bin/)?ld(.exe)?"? }}
 // watchOS: lib{{(\\\\|/)}}swift{{(\\\\|/)}}clang{{(\\\\|/)}}lib{{(\\\\|/)}}darwin{{(\\\\|/)}}libclang_rt.profile_watchos.a
 
-// watchOS_SIM: {{(bin/)?ld"? }}
+// watchOS_SIM: {{(bin/)?ld(.exe)?"? }}
 // watchOS_SIM: lib{{(\\\\|/)}}swift{{(\\\\|/)}}clang{{(\\\\|/)}}lib{{(\\\\|/)}}darwin{{(\\\\|/)}}libclang_rt.profile_watchossim.a
 
 // LINUX: clang++{{(\.exe)?"? }}
diff --git a/test/IDE/complete_repl_identifier_prefix_1.swift b/test/IDE/complete_repl_identifier_prefix_1.swift
index 6d2bb25..99119f3 100644
--- a/test/IDE/complete_repl_identifier_prefix_1.swift
+++ b/test/IDE/complete_repl_identifier_prefix_1.swift
@@ -2,6 +2,8 @@
 
 // CHECK: Begin completions
 // CHECK-NEXT: {{^}}true: Bool{{$}}
+// CHECK-NEXT: {{^}}trunc(x: FloatingPoint) -> FloatingPoint
+// CHECK-NEXT: {{^}}trunc(x: SIMD) -> SIMD
 // CHECK-NEXT: End completions
 
 tru
diff --git a/test/IRGen/builtin_math.swift b/test/IRGen/builtin_math.swift
index 93a7938..b1d4afc 100644
--- a/test/IRGen/builtin_math.swift
+++ b/test/IRGen/builtin_math.swift
@@ -13,13 +13,7 @@
 // Make sure we use an intrinsic for functions such as exp.
 
 // CHECK-LABEL: define {{.*}}test1
-// CHECK-ios: call float @llvm.exp.f32
-// CHECK-macosx: call float @llvm.exp.f32
-// CHECK-tvos: call float @llvm.exp.f32
-// CHECK-watchos: call float @llvm.exp.f32
-// CHECK-darwin: call float @llvm.exp.f32
-// CHECK-linux-gnu: call float @expf
-// CHECK-windows: call float @expf
+// CHECK: call float @llvm.exp.f32
 
 public func test1(f : Float) -> Float {
   return exp(f)
@@ -29,7 +23,7 @@
 // CHECK: call double @llvm.exp.f64
 
 public func test2(f : Double) -> Double {
-  return _exp(f)
+  return exp(f)
 }
 
 // CHECK-LABEL: define {{.*}}test3
diff --git a/test/Parse/recovery.swift b/test/Parse/recovery.swift
index 1712d39..ca41457 100644
--- a/test/Parse/recovery.swift
+++ b/test/Parse/recovery.swift
@@ -33,8 +33,7 @@
   func exists() -> Bool { return true }
 }
 
-// expected-note @+2 {{did you mean 'test'?}}
-// expected-note @+1 {{'test' declared here}}
+// expected-note @+1 {{did you mean 'test'?}}
 func test(a: BadAttributes) -> () {
   _ = a.exists() // no-warning
 }
@@ -619,7 +618,7 @@
 func foo2(bar! = baz) {}// expected-note {{did you mean 'foo2'?}}
 
 // rdar://19605567
-// expected-error@+1{{use of unresolved identifier 'esp'; did you mean 'test'?}}
+// expected-error@+1{{use of unresolved identifier 'esp'; did you mean 'exp'?}}
 switch esp {
 case let (jeb):
   // expected-error@+5{{top-level statement cannot begin with a closure expression}}
diff --git a/test/ParseableInterface/ModuleCache/SDKDependencies.swift b/test/ParseableInterface/ModuleCache/SDKDependencies.swift
index 02728e3..d48ccac 100644
--- a/test/ParseableInterface/ModuleCache/SDKDependencies.swift
+++ b/test/ParseableInterface/ModuleCache/SDKDependencies.swift
@@ -12,9 +12,9 @@
 // RUN: llvm-bcanalyzer -dump %t/prebuilt-cache/SdkLib.swiftmodule | %FileCheck %s -check-prefix=PREBUILT
 //
 // PREBUILT: MODULE_BLOCK
-// PREBUILT-NOT: FILE_DEPENDENCY {{.*}}/MCP/{{.*}}
-// PREBUILT-NOT: FILE_DEPENDENCY {{.*}}/prebuilt-cache/{{.*}}
-// PREBUILD-NOT: FILE_DEPENDENCY {{.*}}/lib/swift/{{.*}}
+// PREBUILT-NOT: FILE_DEPENDENCY {{.*[/\\]MCP[/\\]}}
+// PREBUILT-NOT: FILE_DEPENDENCY {{.*[/\\]prebuilt-cache[/\\]}}
+// PREBUILD-NOT: FILE_DEPENDENCY {{.*[/\\]lib[/\\]swift[/\\]}}
 //
 // Re-build them in the opposite order
 // RUN: %empty-directory(%t/prebuilt-cache)
@@ -50,8 +50,8 @@
 // RUN: cat %t/dummy.d | %FileCheck %s -check-prefix=DEPFILE-NEGATIVE
 // RUN: cat %t/dummy.d | %FileCheck %s -check-prefix=DEPFILE
 //
-// DEPFILE-NEGATIVE-NOT: /MCP/
-// DEPFILE-NEGATIVE-NOT: /prebuilt-cache/
+// DEPFILE-NEGATIVE-NOT: {{[/\\]MCP[/\\]}}
+// DEPFILE-NEGATIVE-NOT: {{[/\\]prebuilt-cache[/\\]}}
 //
 // DEPFILE-DAG: SomeCModule.h
 // DEPFILE-DAG: SdkLib.swiftinterface
@@ -79,21 +79,21 @@
 // RUN: cat %t/MCP/SdkLib-*.swiftmodule | %FileCheck %s -check-prefixes=EXLIB,SDKLIB
 //
 // EXLIB: dependencies:
-// EXLIB-DAG: /my-sdk/usr/include/module.modulemap
-// EXLIB-DAG: /my-sdk/usr/include/SomeCModule.h
-// EXLIB-DAG: /my-sdk/ExportedLib.swiftinterface
-// SDKLIB-DAG: /my-sdk/SdkLib.swiftinterface
+// EXLIB-DAG: {{[/\\]my-sdk[/\\]usr[/\\]include[/\\]}}module.modulemap
+// EXLIB-DAG: {{[/\\]my-sdk[/\\]usr[/\\]include[/\\]}}SomeCModule.h
+// EXLIB-DAG: {{[/\\]my-sdk[/\\]}}ExportedLib.swiftinterface
+// SDKLIB-DAG: {{[/\\]my-sdk[/\\]}}SdkLib.swiftinterface
 //
 // Check they don't contain any dependencies from either cache other than themselves
 // RUN: cat %t/MCP/ExportedLib-*.swiftmodule | %FileCheck %s -check-prefix=NOCACHE -DLIB_NAME=ExportedLib
 // RUN: cat %t/MCP/SdkLib-*.swiftmodule | %FileCheck %s -check-prefix=NOCACHE -DLIB_NAME=SdkLib
 //
 // NOCACHE: dependencies:
-// NOCACHE-NOT: /prebuilt-cache/
-// NOCACHE-NOT: /MCP/
-// NOCACHE: /prebuilt-cache/[[LIB_NAME]].swiftmodule
-// NOCACHE-NOT: /prebuilt-cache/
-// NOCACHE-NOT: /MCP/
+// NOCACHE-NOT: {{[/\\]prebuilt-cache[/\\]}}
+// NOCACHE-NOT: {{[/\\]MCP[/\\]}}
+// NOCACHE: {{[/\\]prebuilt-cache[/\\]}}[[LIB_NAME]].swiftmodule
+// NOCACHE-NOT: {{[/\\]prebuilt-cache[/\\]}}
+// NOCACHE-NOT: {{[/\\]MCP[/\\]}}
 //
 // Check we didn't emit anything from the cache in the .d file either
 // RUN: cat %t/dummy.d | %FileCheck %s -check-prefix=DEPFILE-NEGATIVE
@@ -122,10 +122,10 @@
 // RUN: cat %t/MCP/ExportedLib-*.swiftmodule | %FileCheck %s -check-prefix=NEW-EXLIB
 // RUN: cat %t/MCP/SdkLib-*.swiftmodule | %FileCheck %s -check-prefixes=NEW-EXLIB,NEW-SDKLIB
 //
-// NEW-EXLIB-DAG: /my-new-sdk/usr/include/module.modulemap
-// NEW-EXLIB-DAG: /my-new-sdk/usr/include/SomeCModule.h
-// NEW-EXLIB-DAG: /my-new-sdk/ExportedLib.swiftinterface
-// NEW-SDKLIB-DAG: /my-new-sdk/SdkLib.swiftinterface
+// NEW-EXLIB-DAG: {{[/\\]my-new-sdk[/\\]usr[/\\]include[/\\]}}module.modulemap
+// NEW-EXLIB-DAG: {{[/\\]my-new-sdk[/\\]usr[/\\]include[/\\]}}SomeCModule.h
+// NEW-EXLIB-DAG: {{[/\\]my-new-sdk[/\\]}}ExportedLib.swiftinterface
+// NEW-SDKLIB-DAG: {{[/\\]my-new-sdk[/\\]}}SdkLib.swiftinterface
 //
 // Check they don't contain dependencies from the module cache, old prebuilt
 // cache, or new prebuilt cache
diff --git a/test/ParseableInterface/ModuleCache/SystemDependencies.swiftinterface b/test/ParseableInterface/ModuleCache/SystemDependencies.swiftinterface
index ecbedc6..2a13736 100644
--- a/test/ParseableInterface/ModuleCache/SystemDependencies.swiftinterface
+++ b/test/ParseableInterface/ModuleCache/SystemDependencies.swiftinterface
@@ -35,10 +35,12 @@
 
 // Check that it picked a different cache key.
 // RUN: %empty-directory(%t/MCP-combined)
-// RUN: cp -n %t/MCP/SystemDependencies*.swiftmodule %t/MCP-combined
-// RUN: cp -n %t/MCP-system/SystemDependencies*.swiftmodule %t/MCP-combined
+// RUN: cp %t/MCP/SystemDependencies*.swiftmodule %t/MCP-combined
+// RUN: cp %t/MCP-system/SystemDependencies*.swiftmodule %t/MCP-combined
+// RUN: ls -1 %t/MCP-combined | %FileCheck %s -check-prefix=MODULECACHE
 
 // NEGATIVE-NOT: SomeCModule.h
 // CHECK: SomeCModule.h
+// MODULECACHE-COUNT-2: SystemDependencies-{{[^ ]+}}.swiftmodule
 
 import SomeCModule
diff --git a/test/PlaygroundTransform/Inputs/not.py b/test/PlaygroundTransform/Inputs/not.py
index e7fd556..6e1c8b8 100644
--- a/test/PlaygroundTransform/Inputs/not.py
+++ b/test/PlaygroundTransform/Inputs/not.py
@@ -7,7 +7,8 @@
     sys.exit(0)
 
 try:
-    subprocess.check_call(shlex.split(sys.argv[1]))
+    isPosix = (sys.platform != "win32")
+    subprocess.check_call(shlex.split(sys.argv[1], posix=isPosix))
     sys.exit(1)
 except subprocess.CalledProcessError as e:
     sys.exit(0)
diff --git a/test/SourceKit/Sema/sema_symlink.swift.response b/test/SourceKit/Sema/sema_symlink.swift.response
index 87aebf7..782720e 100644
--- a/test/SourceKit/Sema/sema_symlink.swift.response
+++ b/test/SourceKit/Sema/sema_symlink.swift.response
@@ -12,7 +12,7 @@
     key.column: 16,
     key.filepath: real.swift,
     key.severity: source.diagnostic.severity.error,
-    key.description: "use of unresolved identifier 'goo'; did you mean 'Bool'?",
+    key.description: "use of unresolved identifier 'goo'",
     key.diagnostic_stage: source.diagnostic.stage.swift.sema,
     key.ranges: [
       {
@@ -20,20 +20,27 @@
         key.length: 3
       }
     ],
-    key.fixits: [
-      {
-        key.offset: 15,
-        key.length: 3,
-        key.sourcetext: "Bool"
-      }
-    ],
     key.diagnostics: [
       {
         key.line: 1,
         key.column: 16,
         key.filepath: real.swift,
         key.severity: source.diagnostic.severity.note,
-        key.description: "'Bool' declared here (Swift.Bool)"
+        key.description: "did you mean 'root'? (Swift.root)"
+      },
+      {
+        key.line: 1,
+        key.column: 16,
+        key.filepath: real.swift,
+        key.severity: source.diagnostic.severity.note,
+        key.description: "did you mean 'root'? (Swift.root)"
+      },
+      {
+        key.line: 1,
+        key.column: 16,
+        key.filepath: real.swift,
+        key.severity: source.diagnostic.severity.note,
+        key.description: "did you mean 'Bool'? (Swift.Bool)"
       }
     ]
   }
diff --git a/test/api-digester/Outputs/stability-stdlib-abi.swift.expected b/test/api-digester/Outputs/stability-stdlib-abi.swift.expected
index 8b13789..345e895 100644
--- a/test/api-digester/Outputs/stability-stdlib-abi.swift.expected
+++ b/test/api-digester/Outputs/stability-stdlib-abi.swift.expected
@@ -1 +1,51 @@
-
+Func _cos(_:) has been removed
+Func _cos(_:) has been renamed to Func cos(_:)
+Func _cos(_:) has generic signature change from to <τ_0_0 where τ_0_0 : ElementaryFunctions>
+Func _cos(_:) has generic signature change from to <τ_0_0 where τ_0_0 : SIMD, τ_0_0.Scalar : ElementaryFunctions>
+Func _cos(_:) has parameter 0 type change from Double to τ_0_0
+Func _cos(_:) has parameter 0 type change from Float to τ_0_0
+Func _cos(_:) has return type change from Double to τ_0_0
+Func _cos(_:) has return type change from Float to τ_0_0
+Func _exp(_:) has been removed
+Func _exp(_:) has been renamed to Func exp(_:)
+Func _exp(_:) has generic signature change from to <τ_0_0 where τ_0_0 : ElementaryFunctions>
+Func _exp(_:) has generic signature change from to <τ_0_0 where τ_0_0 : SIMD, τ_0_0.Scalar : ElementaryFunctions>
+Func _exp(_:) has parameter 0 type change from Double to τ_0_0
+Func _exp(_:) has parameter 0 type change from Float to τ_0_0
+Func _exp(_:) has return type change from Double to τ_0_0
+Func _exp(_:) has return type change from Float to τ_0_0
+Func _exp2(_:) has been removed
+Func _exp2(_:) has been renamed to Func exp2(_:)
+Func _exp2(_:) has generic signature change from to <τ_0_0 where τ_0_0 : ElementaryFunctions>
+Func _exp2(_:) has generic signature change from to <τ_0_0 where τ_0_0 : SIMD, τ_0_0.Scalar : ElementaryFunctions>
+Func _exp2(_:) has parameter 0 type change from Double to τ_0_0
+Func _exp2(_:) has parameter 0 type change from Float to τ_0_0
+Func _exp2(_:) has return type change from Double to τ_0_0
+Func _exp2(_:) has return type change from Float to τ_0_0
+Func _log(_:) has been removed
+Func _log10(_:) has been removed
+Func _log10(_:) has been renamed to Func log10(_:)
+Func _log10(_:) has generic signature change from to <τ_0_0 where τ_0_0 : ElementaryFunctions>
+Func _log10(_:) has generic signature change from to <τ_0_0 where τ_0_0 : SIMD, τ_0_0.Scalar : ElementaryFunctions>
+Func _log10(_:) has parameter 0 type change from Double to τ_0_0
+Func _log10(_:) has parameter 0 type change from Float to τ_0_0
+Func _log10(_:) has return type change from Double to τ_0_0
+Func _log10(_:) has return type change from Float to τ_0_0
+Func _log2(_:) has been removed
+Func _log2(_:) has been renamed to Func log2(_:)
+Func _log2(_:) has generic signature change from to <τ_0_0 where τ_0_0 : ElementaryFunctions>
+Func _log2(_:) has generic signature change from to <τ_0_0 where τ_0_0 : SIMD, τ_0_0.Scalar : ElementaryFunctions>
+Func _log2(_:) has parameter 0 type change from Double to τ_0_0
+Func _log2(_:) has parameter 0 type change from Float to τ_0_0
+Func _log2(_:) has return type change from Double to τ_0_0
+Func _log2(_:) has return type change from Float to τ_0_0
+Func _nearbyint(_:) has been removed
+Func _rint(_:) has been removed
+Func _sin(_:) has been removed
+Func _sin(_:) has been renamed to Func sin(_:)
+Func _sin(_:) has generic signature change from to <τ_0_0 where τ_0_0 : ElementaryFunctions>
+Func _sin(_:) has generic signature change from to <τ_0_0 where τ_0_0 : SIMD, τ_0_0.Scalar : ElementaryFunctions>
+Func _sin(_:) has parameter 0 type change from Double to τ_0_0
+Func _sin(_:) has parameter 0 type change from Float to τ_0_0
+Func _sin(_:) has return type change from Double to τ_0_0
+Func _sin(_:) has return type change from Float to τ_0_0
diff --git a/test/stdlib/MathFunctions.swift.gyb b/test/stdlib/MathFunctions.swift.gyb
new file mode 100644
index 0000000..03d6b8e
--- /dev/null
+++ b/test/stdlib/MathFunctions.swift.gyb
@@ -0,0 +1,168 @@
+//===--- Math.swift.gyb ---------------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift.org open source project
+//
+// Copyright (c) 2014 - 2019 Apple Inc. and the Swift project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+//
+//===----------------------------------------------------------------------===//
+// -*- swift -*-
+// RUN: %empty-directory(%t)
+// RUN: %gyb %s -o %t/tgmath.swift
+// RUN: %line-directive %t/tgmath.swift -- %target-build-swift %t/tgmath.swift -o %t/a.out
+// RUN: %target-codesign %t/a.out
+// RUN: %line-directive %t/tgmath.swift -- %target-run %t/a.out
+// REQUIRES: executable_test
+
+#if (arch(i386) || arch(x86_64)) && !os(Windows)
+  typealias TestLiteralType = Float80
+#else
+  typealias TestLiteralType = Double
+#endif
+
+import StdlibUnittest
+
+let MathTests = TestSuite("Math")
+
+func expectEqualWithTolerance<T>(_ expected: TestLiteralType, _ actual: T,
+                                 ulps allowed: T = 3,
+                                 file: String = #file, line: UInt = #line)
+                                 where T: BinaryFloatingPoint {
+  if actual == T(expected) || actual.isNaN && expected.isNaN {
+    return
+  }
+  //  Compute error in ulp, compare to tolerance.
+  let absoluteError = T(abs(TestLiteralType(actual) - expected))
+  let ulpError = absoluteError / T(expected).ulp
+  expectTrue(ulpError <= allowed,
+             "\(actual) != \(expected) as \(T.self)" +
+             "\n  \(ulpError)-ulp error exceeds \(allowed)-ulp tolerance.",
+             file: file, line: line)
+}
+
+%from SwiftMathFunctions import *
+
+internal extension ElementaryFunctions where Self: BinaryFloatingPoint {
+  static func elementaryFunctionTests() {
+    /* Default tolerance is 3 ulps unless specified otherwise. It's OK to relax
+     * this as needed for new platforms, as these tests are *not* intended to
+     * validate the math library--they are only intended to check that the
+     * Swift bindings are calling the right functions in the math library.    */
+    expectEqualWithTolerance(1.1863995522992575361931268186727044683, Self.acos(0.375))
+    expectEqualWithTolerance(0.3843967744956390830381948729670469737, Self.asin(0.375))
+    expectEqualWithTolerance(0.3587706702705722203959200639264604997, Self.atan(0.375))
+    expectEqualWithTolerance(0.9305076219123142911494767922295555080, Self.cos(0.375))
+    expectEqualWithTolerance(0.3662725290860475613729093517162641571, Self.sin(0.375))
+    expectEqualWithTolerance(0.3936265759256327582294137871012180981, Self.tan(0.375))
+    expectEqualWithTolerance(0.4949329230945269058895630995767185785, Self.acosh(1.125))
+    expectEqualWithTolerance(0.9670596312833237113713762009167286709, Self.asinh(1.125))
+    expectEqualWithTolerance(0.7331685343967135223291211023213964500, Self.atanh(0.625))
+    expectEqualWithTolerance(1.0711403467045867672994980155670160493, Self.cosh(0.375))
+    expectEqualWithTolerance(0.3838510679136145687542956764205024589, Self.sinh(0.375))
+    expectEqualWithTolerance(0.3583573983507859463193602315531580424, Self.tanh(0.375))
+    expectEqualWithTolerance(1.4549914146182013360537936919875185083, Self.exp(0.375))
+    expectEqualWithTolerance(1.2968395546510096659337541177924511598, Self.exp2(0.375))
+    expectEqualWithTolerance(2.3713737056616552616517527574788898386, Self.exp10(0.375))
+    expectEqualWithTolerance(0.4549914146182013360537936919875185083, Self.expm1(0.375))
+    expectEqualWithTolerance(-0.980829253011726236856451127452003999, Self.log(0.375))
+    expectEqualWithTolerance(-1.415037499278843818546261056052183491, Self.log2(0.375))
+    expectEqualWithTolerance(0.3184537311185346158102472135905995955, Self.log1p(0.375))
+    expectEqualWithTolerance(-0.425968732272281148346188780918363771, Self.log10(0.375))
+    expectEqualWithTolerance(0.7211247851537041911608191553900547941, Self.root(0.375, 3))
+    expectEqualWithTolerance(0.6123724356957945245493210186764728479, Self.sqrt(0.375))
+    expectEqualWithTolerance(0.54171335479545025876069682133938570, Self.pow(0.375, 0.625))
+    expectEqualWithTolerance(-0.052734375, Self.pow(-0.375, 3))
+
+    expectEqual(Self.acos(0.375), acos(0.375))
+    expectEqual(Self.asin(0.375), asin(0.375))
+    expectEqual(Self.atan(0.375), atan(0.375))
+    expectEqual(Self.cos(0.375), cos(0.375))
+    expectEqual(Self.sin(0.375), sin(0.375))
+    expectEqual(Self.tan(0.375), tan(0.375))
+    expectEqual(Self.acosh(1.125), acosh(1.125))
+    expectEqual(Self.asinh(1.125), asinh(1.125))
+    expectEqual(Self.atanh(0.625), atanh(0.625))
+    expectEqual(Self.cosh(0.375), cosh(0.375))
+    expectEqual(Self.sinh(0.375), sinh(0.375))
+    expectEqual(Self.tanh(0.375), tanh(0.375))
+    expectEqual(Self.exp(0.375), exp(0.375))
+    expectEqual(Self.exp2(0.375), exp2(0.375))
+    expectEqual(Self.exp10(0.375), exp10(0.375))
+    expectEqual(Self.expm1(0.375), expm1(0.375))
+    expectEqual(Self.log(0.375), log(0.375))
+    expectEqual(Self.log2(0.375), log2(0.375))
+    expectEqual(Self.log1p(0.375), log1p(0.375))
+    expectEqual(Self.log10(0.375), log10(0.375))
+    expectEqual(Self.sqrt(0.375), sqrt(0.375))
+    expectEqual(Self.pow(0.375, 0.625), pow(0.375, 0.625))
+    expectEqual(Self.root(0.375, 3), root(0.375, 3))
+    expectEqual(Self.pow(-0.375, 3), pow(-0.375, 3))
+  }
+}
+
+internal extension Real where Self: BinaryFloatingPoint {
+  static func realFunctionTests() {
+    expectEqualWithTolerance(0.54041950027058415544357836460859991, Self.atan2(y: 0.375, x: 0.625))
+    expectEqualWithTolerance(0.72886898685566255885926910969319788, Self.hypot(0.375, 0.625))
+    expectEqualWithTolerance(0.4041169094348222983238250859191217675, Self.erf(0.375))
+    expectEqualWithTolerance(0.5958830905651777016761749140808782324, Self.erfc(0.375))
+    expectEqualWithTolerance(2.3704361844166009086464735041766525098, Self.gamma(0.375))
+#if !os(Windows)
+    expectEqualWithTolerance( -0.11775527074107877445136203331798850, Self.logGamma(1.375), ulps: 16)
+    expectEqual(.plus,  Self.signGamma(1.375))
+    expectEqual(.minus, Self.signGamma(-2.375))
+#endif
+
+    expectEqual(Self.atan2(y: 0.375, x: 0.625), atan2(y: 0.375, x: 0.625))
+    expectEqual(Self.hypot(0.375, 0.625), hypot(0.375, 0.625))
+    expectEqual(Self.erf(0.375), erf(0.375))
+    expectEqual(Self.erfc(0.375), erfc(0.375))
+    expectEqual(Self.gamma(0.375), gamma(0.375))
+#if !os(Windows)
+    expectEqual(Self.logGamma(1.375), logGamma(1.375))
+    expectEqual(Self.signGamma(1.375), signGamma(1.375))
+    expectEqual(Self.signGamma(-2.375), signGamma(-2.375))
+#endif
+  }
+}
+
+internal extension BinaryFloatingPoint {
+  static func floatingPointFunctionTests() {
+    expectEqual(1 as Self, ceil(0.375))
+    expectEqual(0 as Self, floor(0.375))
+    expectEqual(0 as Self, Swift.round(0.375))
+    expectEqual(0 as Self, trunc(0.375))
+    expectEqual(0 as Self, ceil(-0.625))
+    expectEqual(-1 as Self, floor(-0.625))
+    expectEqual(-1 as Self, Swift.round(-0.625))
+    expectEqual(0 as Self, trunc(-0.625))
+    expectEqual(1 as Self, ceil(0.5))
+    expectEqual(0 as Self, floor(0.5))
+    expectEqual(1 as Self, Swift.round(0.5))
+    expectEqual(0 as Self, trunc(0.5))
+  }
+}
+
+%for T in ['Float', 'Double', 'CGFloat', 'Float80']:
+% if T == 'Float80':
+#if (arch(i386) || arch(x86_64)) && !os(Windows)
+% elif T == 'CGFloat':
+#if canImport(CoreGraphics)
+  import CoreGraphics
+% end
+
+MathTests.test("${T}") {
+  ${T}.elementaryFunctionTests()
+  ${T}.realFunctionTests()
+  ${T}.floatingPointFunctionTests()
+}
+
+% if T in ['CGFloat', 'Float80']:
+#endif
+% end
+%end
+
+runAllTests()
diff --git a/test/stdlib/tgmath.swift.gyb b/test/stdlib/tgmath.swift.gyb
index c3382fa..91748cb 100644
--- a/test/stdlib/tgmath.swift.gyb
+++ b/test/stdlib/tgmath.swift.gyb
@@ -18,7 +18,7 @@
 // REQUIRES: executable_test
 
 #if os(macOS) || os(iOS) || os(tvOS) || os(watchOS)
-  import Darwin.C.tgmath
+  import Darwin
 #elseif os(Linux) || os(FreeBSD) || os(PS4) || os(Android) || os(Cygwin) || os(Haiku)
   import Glibc
 #elseif os(Windows)
@@ -61,7 +61,7 @@
   'cosh', 'sinh', 'tanh',
   'exp', 'exp2', 'expm1',
   'log', 'log2', 'log1p', 'log10', 'logb',
-  'fabs', 'cbrt', 'sqrt',
+  'fabs', 'cbrt',
   'erf', 'erfc',
   'tgamma',
   'ceil', 'floor', 'nearbyint', 'rint', 'trunc',
@@ -118,7 +118,6 @@
     expectEqual(-2, Self._logb(0.375))
     expectEqual(0.375, Self._fabs(-0.375))
     expectEqualWithTolerance(0.7211247851537041911608191553900547941, Self._cbrt(0.375))
-    expectEqualWithTolerance(0.6123724356957945245493210186764728479, Self._sqrt(0.375))
     expectEqualWithTolerance(0.4041169094348222983238250859191217675, Self._erf(0.375))
     expectEqualWithTolerance(0.5958830905651777016761749140808782324, Self._erfc(0.375))
     expectEqualWithTolerance(2.3704361844166009086464735041766525098, Self._tgamma(0.375))
@@ -181,21 +180,49 @@
 % end
 
 extension ${T}: TGMath {
+#if os(macOS) || os(iOS) || os(tvOS) || os(watchOS)
+% Module = 'CoreGraphics' if T == 'CGFloat' else 'Darwin'
 % for f in unary:
-  static func _${f}(_ x: ${T}) -> ${T} { return ${f}(x) }
+  static func _${f}(_ x: ${T}) -> ${T} { return ${Module}.${f}(x) }
 % end
 %for f in binary:
-  static func _${f}(_ x: ${T}, _ y: ${T}) -> ${T} { return ${f}(x, y) }
+  static func _${f}(_ x: ${T}, _ y: ${T}) -> ${T} { return ${Module}.${f}(x, y) }
 %end
-  static func _remquo(_ x: ${T}, _ y: ${T}) -> (${T}, Int) { return remquo(x, y) }
-  static func _fma(_ x: ${T}, _ y: ${T}, _ z: ${T}) -> ${T} { return fma(x, y, z) }
-#if !os(Windows)
-  static func _lgamma(_ x: ${T}) -> (${T}, Int) { return lgamma(x) }
+  static func _remquo(_ x: ${T}, _ y: ${T}) -> (${T}, Int) { return ${Module}.remquo(x, y) }
+  static func _fma(_ x: ${T}, _ y: ${T}, _ z: ${T}) -> ${T} { return ${Module}.fma(x, y, z) }
+  static func _lgamma(_ x: ${T}) -> (${T}, Int) { return ${Module}.lgamma(x) }
+  static func _modf(_ x: ${T}) -> (${T}, ${T}) { return ${Module}.modf(x) }
+  static func _scalbn(_ x: ${T}, _ n: Int) -> ${T} { return ${Module}.scalbn(x, n) }
+  static func _frexp(_ x: ${T}) -> (${T}, Int) { return ${Module}.frexp(x) }
+  static func _ilogb(_ x: ${T}) -> Int { return ${Module}.ilogb(x) }
+#elseif os(Linux) || os(FreeBSD) || os(PS4) || os(Android) || os(Cygwin) || os(Haiku)
+% for f in unary:
+  static func _${f}(_ x: ${T}) -> ${T} { return Glibc.${f}(x) }
+% end
+%for f in binary:
+  static func _${f}(_ x: ${T}, _ y: ${T}) -> ${T} { return Glibc.${f}(x, y) }
+%end
+  static func _remquo(_ x: ${T}, _ y: ${T}) -> (${T}, Int) { return Glibc.remquo(x, y) }
+  static func _fma(_ x: ${T}, _ y: ${T}, _ z: ${T}) -> ${T} { return Glibc.fma(x, y, z) }
+  static func _lgamma(_ x: ${T}) -> (${T}, Int) { return Glibc.lgamma(x) }
+  static func _modf(_ x: ${T}) -> (${T}, ${T}) { return Glibc.modf(x) }
+  static func _scalbn(_ x: ${T}, _ n: Int) -> ${T} { return Glibc.scalbn(x, n) }
+  static func _frexp(_ x: ${T}) -> (${T}, Int) { return Glibc.frexp(x) }
+  static func _ilogb(_ x: ${T}) -> Int { return Glibc.ilogb(x) }
+#elseif os(Windows)
+% for f in unary:
+  static func _${f}(_ x: ${T}) -> ${T} { return MSVCRT.${f}(x) }
+% end
+%for f in binary:
+  static func _${f}(_ x: ${T}, _ y: ${T}) -> ${T} { return MSVCRT.${f}(x, y) }
+%end
+  static func _remquo(_ x: ${T}, _ y: ${T}) -> (${T}, Int) { return MSVCRT.remquo(x, y) }
+  static func _fma(_ x: ${T}, _ y: ${T}, _ z: ${T}) -> ${T} { return MSVCRT.fma(x, y, z) }
+  static func _modf(_ x: ${T}) -> (${T}, ${T}) { return MSVCRT.modf(x) }
+  static func _scalbn(_ x: ${T}, _ n: Int) -> ${T} { return MSVCRT.scalbn(x, n) }
+  static func _frexp(_ x: ${T}) -> (${T}, Int) { return MSVCRT.frexp(x) }
+  static func _ilogb(_ x: ${T}) -> Int { return MSVCRT.ilogb(x) }
 #endif
-  static func _modf(_ x: ${T}) -> (${T}, ${T}) { return modf(x) }
-  static func _scalbn(_ x: ${T}, _ n: Int) -> ${T} { return scalbn(x, n) }
-  static func _frexp(_ x: ${T}) -> (${T}, Int) { return frexp(x) }
-  static func _ilogb(_ x: ${T}) -> Int { return ilogb(x) }
 }
 
 MathTests.test("${T}") {
diff --git a/utils/PathSanitizingFileCheck b/utils/PathSanitizingFileCheck
index ab01e6c..d7aecb1 100755
--- a/utils/PathSanitizingFileCheck
+++ b/utils/PathSanitizingFileCheck
@@ -12,6 +12,7 @@
 from __future__ import print_function
 
 import argparse
+import re
 import subprocess
 import sys
 
@@ -47,7 +48,7 @@
     stdin = sys.stdin.read()
     for s in args.sanitize_strings:
         replacement, pattern = s.split('=', 1)
-        stdin = stdin.replace(pattern, replacement)
+        stdin = re.sub(re.sub(r'/', r'[/\\\\]', pattern), replacement, stdin)
 
     p = subprocess.Popen(
         [args.file_check_path] + unknown_args, stdin=subprocess.PIPE)
diff --git a/utils/SwiftMathFunctions.py b/utils/SwiftMathFunctions.py
new file mode 100644
index 0000000..c1b82b2
--- /dev/null
+++ b/utils/SwiftMathFunctions.py
@@ -0,0 +1,74 @@
+class SwiftMathFunction(object):
+    def __init__(self, name, kind=None, swiftName=None, args="x", comment=None,
+                 platforms=None):
+        self.name = name
+        self.swiftName = swiftName if swiftName is not None else name
+        self.kind = kind if kind is not None else "library"
+        self.args = args
+        if comment is not None:
+            self.comment = comment
+        else:
+            self.comment = "/// The " + str(self.swiftName) + " function."
+        self.platforms = platforms
+
+    def params(self, prefix="", suffix=""):
+        return ", ".join(map(lambda a: prefix + a + suffix, self.args))
+
+    def decl(self, type):
+        return self.swiftName + "(" + self.params("_ ", ": " + type) + \
+            ") -> " + type
+
+    def free_decl(self, constraint="T: ElementaryFunctions"):
+        return self.swiftName + "<T>(" + self.params("_ ", ": T") + \
+            ") -> T where " + constraint
+
+    def impl(self, type):
+        if self.kind == "intrinsic":
+            builtin = "Builtin.int_" + self.name + "_FPIEEE" + str(type.bits)
+            return type.stdlib_name + "(" + builtin + "(" + \
+                self.params("", "._value") + "))"
+        return "_swift_stdlib_" + self.name + type.cFuncSuffix + "(" + \
+            self.params() + ")"
+
+
+ElementaryFunctions = [
+    SwiftMathFunction(name="sqrt", kind="intrinsic",
+                      comment="/// The square root of `x`."),
+    SwiftMathFunction(name="cos", kind="intrinsic",
+                      comment="/// The cosine of `x`."),
+    SwiftMathFunction(name="sin", kind="intrinsic",
+                      comment="/// The sine of `x`."),
+    SwiftMathFunction(name="tan",
+                      comment="/// The tangent of `x`."),
+    SwiftMathFunction(name="acos"),
+    SwiftMathFunction(name="asin"),
+    SwiftMathFunction(name="atan"),
+    SwiftMathFunction(name="cosh"),
+    SwiftMathFunction(name="sinh"),
+    SwiftMathFunction(name="tanh"),
+    SwiftMathFunction(name="acosh"),
+    SwiftMathFunction(name="asinh"),
+    SwiftMathFunction(name="atanh"),
+    SwiftMathFunction(name="exp", kind="intrinsic"),
+    SwiftMathFunction(name="exp2", kind="intrinsic"),
+    SwiftMathFunction(name="exp10"),
+    SwiftMathFunction(name="expm1"),
+    SwiftMathFunction(name="log", kind="intrinsic"),
+    SwiftMathFunction(name="log2", kind="intrinsic"),
+    SwiftMathFunction(name="log10", kind="intrinsic"),
+    SwiftMathFunction(name="log1p"),
+    # SwiftMathFunction(name="pow", kind="intrinsic", args="xy"), Handled
+    # separately for edge cases.
+    # SwiftMathFunction(name="root", args="xn"), Handled separately for
+    # implementation.
+]
+
+RealFunctions = [
+    # SwiftMathFunction(name="atan2"), Handled separately for explicit
+    # argument labels.
+    SwiftMathFunction(name="erf"),
+    SwiftMathFunction(name="erfc"),
+    SwiftMathFunction(name="hypot", args="xy"),
+    SwiftMathFunction(name="tgamma", swiftName="gamma"),
+    # SwiftMathFunction(name="lgamma"), Handled separately for sign result.
+]
diff --git a/utils/build-script-impl b/utils/build-script-impl
index 5b42241..ecac789 100755
--- a/utils/build-script-impl
+++ b/utils/build-script-impl
@@ -3089,6 +3089,7 @@
                     LIBDISPATCH_BUILD_DIR="$(build_directory ${host} libdispatch)"
                     FOUNDATION_BUILD_DIR=$(build_directory ${host} foundation)
                     DOTEST_EXTRA="-I${FOUNDATION_BUILD_DIR}"
+                    DOTEST_EXTRA="-Xcc -F${FOUNDATION_BUILD_DIR}"
                     DOTEST_EXTRA="-Xcc -F${FOUNDATION_BUILD_DIR}/CoreFoundation-prefix/System/Library/Frameworks"
                     DOTEST_EXTRA="${DOTEST_EXTRA} -I${FOUNDATION_BUILD_DIR}/swift"
                     DOTEST_EXTRA="${DOTEST_EXTRA} -I${LIBDISPATCH_SOURCE_DIR}"