[libc][math] Add float-only option for atan2f. (llvm#122979)

For targets that have single precision FPU but not double precision FPU
such as Cortex M4, only using float-float in the intermediate
computations might reduce the code size compared to using double. In
this case, when the exact pass is skipped, the float-only option for
atan2f implemented in this PR reduces the code size of this function by
~1 KB compared to the double precision version.

Author: lntue

libc/src/__support/FPUtil/double_double.h

@@ -20,41 +20,52 @@ namespace fputil {
 
 #define DEFAULT_DOUBLE_SPLIT 27
 
-using DoubleDouble = LIBC_NAMESPACE::NumberPair<double>;
+template <typename T> struct DefaultSplit;
+template <> struct DefaultSplit<float> {
+  static constexpr size_t VALUE = 12;
+};
+template <> struct DefaultSplit<double> {
+  static constexpr size_t VALUE = DEFAULT_DOUBLE_SPLIT;
+};
+
+using DoubleDouble = NumberPair<double>;
+using FloatFloat = NumberPair<float>;
 
 // The output of Dekker's FastTwoSum algorithm is correct, i.e.:
 //   r.hi + r.lo = a + b exactly
 //   and |r.lo| < eps(r.lo)
 // Assumption: |a| >= |b|, or a = 0.
-template <bool FAST2SUM = true>
-LIBC_INLINE constexpr DoubleDouble exact_add(double a, double b) {
-  DoubleDouble r{0.0, 0.0};
+template <bool FAST2SUM = true, typename T = double>
+LIBC_INLINE constexpr NumberPair<T> exact_add(T a, T b) {
+  NumberPair<T> r{0.0, 0.0};
   if constexpr (FAST2SUM) {
     r.hi = a + b;
-    double t = r.hi - a;
+    T t = r.hi - a;
     r.lo = b - t;
   } else {
     r.hi = a + b;
-    double t1 = r.hi - a;
-    double t2 = r.hi - t1;
-    double t3 = b - t1;
-    double t4 = a - t2;
+    T t1 = r.hi - a;
+    T t2 = r.hi - t1;
+    T t3 = b - t1;
+    T t4 = a - t2;
     r.lo = t3 + t4;
   }
   return r;
 }
 
 // Assumption: |a.hi| >= |b.hi|
-LIBC_INLINE constexpr DoubleDouble add(const DoubleDouble &a,
-                                       const DoubleDouble &b) {
-  DoubleDouble r = exact_add(a.hi, b.hi);
-  double lo = a.lo + b.lo;
+template <typename T>
+LIBC_INLINE constexpr NumberPair<T> add(const NumberPair<T> &a,
+                                        const NumberPair<T> &b) {
+  NumberPair<T> r = exact_add(a.hi, b.hi);
+  T lo = a.lo + b.lo;
   return exact_add(r.hi, r.lo + lo);
 }
 
 // Assumption: |a.hi| >= |b|
-LIBC_INLINE constexpr DoubleDouble add(const DoubleDouble &a, double b) {
-  DoubleDouble r = exact_add<false>(a.hi, b);
+template <typename T>
+LIBC_INLINE constexpr NumberPair<T> add(const NumberPair<T> &a, T b) {
+  NumberPair<T> r = exact_add<false>(a.hi, b);
   return exact_add(r.hi, r.lo + a.lo);
 }
 
@@ -63,12 +74,12 @@ LIBC_INLINE constexpr DoubleDouble add(const DoubleDouble &a, double b) {
 //   Zimmermann, P., "Note on the Veltkamp/Dekker Algorithms with Directed
 //   Roundings," https://inria.hal.science/hal-04480440.
 // Default splitting constant = 2^ceil(prec(double)/2) + 1 = 2^27 + 1.
-template <size_t N = DEFAULT_DOUBLE_SPLIT>
-LIBC_INLINE constexpr DoubleDouble split(double a) {
-  DoubleDouble r{0.0, 0.0};
+template <typename T = double, size_t N = DefaultSplit<T>::VALUE>
+LIBC_INLINE constexpr NumberPair<T> split(T a) {
+  NumberPair<T> r{0.0, 0.0};
   // CN = 2^N.
-  constexpr double CN = static_cast<double>(1 << N);
-  constexpr double C = CN + 1.0;
+  constexpr T CN = static_cast<T>(1 << N);
+  constexpr T C = CN + 1.0;
   double t1 = C * a;
   double t2 = a - t1;
   r.hi = t1 + t2;
@@ -77,16 +88,15 @@ LIBC_INLINE constexpr DoubleDouble split(double a) {
 }
 
 // Helper for non-fma exact mult where the first number is already split.
-template <size_t SPLIT_B = DEFAULT_DOUBLE_SPLIT>
-LIBC_INLINE DoubleDouble exact_mult(const DoubleDouble &as, double a,
-                                    double b) {
-  DoubleDouble bs = split<SPLIT_B>(b);
-  DoubleDouble r{0.0, 0.0};
+template <typename T = double, size_t SPLIT_B = DefaultSplit<T>::VALUE>
+LIBC_INLINE NumberPair<T> exact_mult(const NumberPair<T> &as, T a, T b) {
+  NumberPair<T> bs = split<T, SPLIT_B>(b);
+  NumberPair<T> r{0.0, 0.0};
 
   r.hi = a * b;
-  double t1 = as.hi * bs.hi - r.hi;
-  double t2 = as.hi * bs.lo + t1;
-  double t3 = as.lo * bs.hi + t2;
+  T t1 = as.hi * bs.hi - r.hi;
+  T t2 = as.hi * bs.lo + t1;
+  T t3 = as.lo * bs.hi + t2;
   r.lo = as.lo * bs.lo + t3;
 
   return r;
@@ -99,18 +109,18 @@ LIBC_INLINE DoubleDouble exact_mult(const DoubleDouble &as, double a,
 // Using Theorem 1 in the paper above, without FMA instruction, if we restrict
 // the generated constants to precision <= 51, and splitting it by 2^28 + 1,
 // then a * b = r.hi + r.lo is exact for all rounding modes.
-template <size_t SPLIT_B = 27>
-LIBC_INLINE DoubleDouble exact_mult(double a, double b) {
-  DoubleDouble r{0.0, 0.0};
+template <typename T = double, size_t SPLIT_B = DefaultSplit<T>::VALUE>
+LIBC_INLINE NumberPair<T> exact_mult(T a, T b) {
+  NumberPair<T> r{0.0, 0.0};
 
 #ifdef LIBC_TARGET_CPU_HAS_FMA
   r.hi = a * b;
   r.lo = fputil::multiply_add(a, b, -r.hi);
 #else
   // Dekker's Product.
-  DoubleDouble as = split(a);
+  NumberPair<T> as = split(a);
 
-  r = exact_mult<SPLIT_B>(as, a, b);
+  r = exact_mult<T, SPLIT_B>(as, a, b);
 #endif // LIBC_TARGET_CPU_HAS_FMA
 
   return r;
@@ -125,7 +135,7 @@ LIBC_INLINE DoubleDouble quick_mult(double a, const DoubleDouble &b) {
 template <size_t SPLIT_B = 27>
 LIBC_INLINE DoubleDouble quick_mult(const DoubleDouble &a,
                                     const DoubleDouble &b) {
-  DoubleDouble r = exact_mult<SPLIT_B>(a.hi, b.hi);
+  DoubleDouble r = exact_mult<double, SPLIT_B>(a.hi, b.hi);
   double t1 = multiply_add(a.hi, b.lo, r.lo);
   double t2 = multiply_add(a.lo, b.hi, t1);
   r.lo = t2;
@@ -157,19 +167,20 @@ LIBC_INLINE DoubleDouble multiply_add<DoubleDouble>(const DoubleDouble &a,
 //   rl = q * (ah - bh * rh) + q * (al - bl * rh)
 // as accurate as possible, then the error is bounded by:
 //   |(ah + al) / (bh + bl) - (rh + rl)| < O(bl/bh) * (2^-52 + al/ah + bl/bh)
-LIBC_INLINE DoubleDouble div(const DoubleDouble &a, const DoubleDouble &b) {
-  DoubleDouble r;
-  double q = 1.0 / b.hi;
+template <typename T>
+LIBC_INLINE NumberPair<T> div(const NumberPair<T> &a, const NumberPair<T> &b) {
+  NumberPair<T> r;
+  T q = T(1) / b.hi;
   r.hi = a.hi * q;
 
 #ifdef LIBC_TARGET_CPU_HAS_FMA
-  double e_hi = fputil::multiply_add(b.hi, -r.hi, a.hi);
-  double e_lo = fputil::multiply_add(b.lo, -r.hi, a.lo);
+  T e_hi = fputil::multiply_add(b.hi, -r.hi, a.hi);
+  T e_lo = fputil::multiply_add(b.lo, -r.hi, a.lo);
 #else
-  DoubleDouble b_hi_r_hi = fputil::exact_mult(b.hi, -r.hi);
-  DoubleDouble b_lo_r_hi = fputil::exact_mult(b.lo, -r.hi);
-  double e_hi = (a.hi + b_hi_r_hi.hi) + b_hi_r_hi.lo;
-  double e_lo = (a.lo + b_lo_r_hi.hi) + b_lo_r_hi.lo;
+  NumberPair<T> b_hi_r_hi = fputil::exact_mult(b.hi, -r.hi);
+  NumberPair<T> b_lo_r_hi = fputil::exact_mult(b.lo, -r.hi);
+  T e_hi = (a.hi + b_hi_r_hi.hi) + b_hi_r_hi.lo;
+  T e_lo = (a.lo + b_lo_r_hi.hi) + b_lo_r_hi.lo;
 #endif // LIBC_TARGET_CPU_HAS_FMA
 
   r.lo = q * (e_hi + e_lo);

libc/src/__support/macros/optimization.h

@@ -45,6 +45,7 @@ LIBC_INLINE constexpr bool expects_bool_condition(T value, T expected) {
 #define LIBC_MATH_FAST                                                         \
   (LIBC_MATH_SKIP_ACCURATE_PASS | LIBC_MATH_SMALL_TABLES |                     \
    LIBC_MATH_NO_ERRNO | LIBC_MATH_NO_EXCEPT)
+#define LIBC_MATH_INTERMEDIATE_COMP_IN_FLOAT 0x10
 
 #ifndef LIBC_MATH
 #define LIBC_MATH 0
@@ -58,4 +59,8 @@ LIBC_INLINE constexpr bool expects_bool_condition(T value, T expected) {
 #define LIBC_MATH_HAS_SMALL_TABLES
 #endif
 
+#if (LIBC_MATH & LIBC_MATH_INTERMEDIATE_COMP_IN_FLOAT)
+#define LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT
+#endif
+
 #endif // LLVM_LIBC_SRC___SUPPORT_MACROS_OPTIMIZATION_H

libc/src/math/generic/CMakeLists.txt

@@ -4052,8 +4052,10 @@ add_entrypoint_object(
     atan2f.cpp
   HDRS
     ../atan2f.h
+    atan2f_float.h
   DEPENDS
     .inv_trigf_utils
+    libc.src.__support.FPUtil.double_double
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.multiply_add
     libc.src.__support.FPUtil.nearest_integer

libc/src/math/generic/atan2f.cpp

@@ -17,6 +17,14 @@
 #include "src/__support/macros/config.h"
 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
 
+#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS) &&                               \
+    defined(LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT)
+
+// We use float-float implementation to reduce size.
+#include "src/math/generic/atan2f_float.h"
+
+#else
+
 namespace LIBC_NAMESPACE_DECL {
 
 namespace {
@@ -324,3 +332,5 @@ LLVM_LIBC_FUNCTION(float, atan2f, (float y, float x)) {
 }
 
 } // namespace LIBC_NAMESPACE_DECL
+
+#endif