more formatting changes

Author: wldfngrs

libc/src/math/generic/cospif16.cpp

@@ -39,7 +39,7 @@ LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
   // Once k and y are computed, we then deduce the answer by the sine of sum
   // formula:
   //   cos(x * pi) = cos((k + y) * pi/32)
-  //               = cos(k * pi/32) * cos(y * pi/32) + 
+  //               = cos(k * pi/32) * cos(y * pi/32) +
   //                 sin(y * pi/32) * sin(k * pi/32)
 
   // For signed zeros

libc/src/math/generic/sincosf16_utils.h

@@ -54,25 +54,17 @@ LIBC_INLINE void sincospif16_eval(float xf, float &sin_k, float &cos_k,
   sin_k = SIN_K_PI_OVER_32[k & 63];
   cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
 
-  // Recall;
-  // sin(x * pi/32) = sin((k + y) * pi/32)
-  // 		    = sin(y * pi/32) * cos(k * pi/32) +
-  // 		      cos(y * pi/32) * sin(k * pi/32) 
   // Recall, after range reduction, -0.5 <= y <= 0.5. For very small values of
   // y, calculating sin(y * p/32) can be inaccurate. Generating a polynomial for
   // sin(y * p/32)/y instead significantly reduces the relative errors.
   float ysq = y * y;
 
   // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
-  // with: > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
+  // with: 
+  // > Q = fpminimax(sin(y * pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
   sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,
                                0x1.a03354p-21f, -0x1.ad02d2p-20f);
 
-  // Note that cosm1_y = cos(y*pi/32) - 1 = cos_y - 1
-  // Derivation:
-  // sin(x * pi) = sin((k + y) * pi/32)
-  //             = sin_y * cos_k + cos_y * sin_k
-  //             = cos_k * sin_y + sin_k * (1 + cos_y - 1)
   // Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya with:
   // > P = fpminimax(cos(y * pi/32), [|0, 2, 4, 6|],[|1, SG...|], [0, 0.5]);
   cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3ccp-8f, 0x1.03a61ap-18f,

libc/src/math/generic/sinpif16.cpp

@@ -6,15 +6,14 @@
 //
 //===----------------------------------------------------------------------===//
 
-
 #include "src/math/sinpif16.h"
 #include "hdr/errno_macros.h"
 #include "hdr/fenv_macros.h"
+#include "sincosf16_utils.h"
 #include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/FPUtil/cast.h"
 #include "src/__support/FPUtil/multiply_add.h"
-#include "sincosf16_utils.h"
 
 namespace LIBC_NAMESPACE_DECL {
 LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
@@ -41,7 +40,7 @@ LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
   //   sin(x * pi) = sin((k + y) * pi/32)
   //               = sin(k * pi/32) * cos(y * pi/32) +
   //                 sin(y * pi/32) * cos(k * pi/32)
-  
+
   // For signed zeros
   if (LIBC_UNLIKELY(x_abs == 0U))
     return x;