[libc][math] Implement atan2f correctly rounded to all rounding modes. (#86716)

We compute atan2f(y, x) in 2 stages:
- Fast step: perform computations in double precision , with relative
errors < 2^-50
- Accurate step: if the result from the Fast step fails Ziv's rounding
test, then we perform computations in double-double precision, with
relative errors < 2^-100.

On Ryzen 5900X, worst-case latency is ~ 200 clocks, compared to average
latency ~ 60 clocks, and average reciprocal throughput ~ 20 clocks.

Author: lntue

libc/config/baremetal/arm/entrypoints.txt

@@ -207,6 +207,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.ceil

libc/config/baremetal/riscv/entrypoints.txt

@@ -207,6 +207,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.ceil

libc/config/darwin/arm/entrypoints.txt

@@ -118,6 +118,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.copysign

libc/config/linux/aarch64/entrypoints.txt

@@ -330,6 +330,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.copysign

libc/config/linux/arm/entrypoints.txt

@@ -198,6 +198,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.ceil

libc/config/linux/riscv/entrypoints.txt

@@ -338,6 +338,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.copysign

libc/config/linux/x86_64/entrypoints.txt

@@ -348,6 +348,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.canonicalize

libc/config/windows/entrypoints.txt

@@ -116,6 +116,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
+    libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.copysign

libc/docs/math/index.rst

@@ -422,7 +422,7 @@ Higher Math Functions
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | atan2      |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| atan2f     |         |         |         |         |         |         |         |         |         |         |         |         |
+| atan2f     | |check| | |check| | |check| | |check| | |check| |         |         | |check| | |check| | |check| |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | atan2l     |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
@@ -591,6 +591,7 @@ acosh          |check|
 asin           |check|
 asinh          |check|
 atan           |check|
+atan2          |check|
 atanh          |check|
 cos            |check|          large
 cosh           |check|

libc/spec/stdc.td

@@ -620,10 +620,14 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"tanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 
           FunctionSpec<"acosf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+
           FunctionSpec<"asinf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"asin", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
+
           FunctionSpec<"atanf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 
+          FunctionSpec<"atan2f", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
+
           FunctionSpec<"acoshf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"asinhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"atanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

libc/src/math/generic/CMakeLists.txt

@@ -2854,6 +2854,24 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  atan2f
+  SRCS
+    atan2f.cpp
+  HDRS
+    ../atan2f.h
+  COMPILE_OPTIONS
+    -O3
+  DEPENDS
+    .inv_trigf_utils
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.nearest_integer
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.rounding_mode
+    libc.src.__support.macros.optimization
+)
+
 add_entrypoint_object(
   scalbn
   SRCS