[NFC][compiler-rt][builtins] Tidy and match comments for floating point operations

compiler-rt/lib/builtins/divdf3.c

-//===-- lib/divdf3.c - Double-precision division ------------------*- C -*-===//
+//===-- lib/divdf3.c - Double-precision division ------------------*- C -*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements double-precision soft-float division
 // with the IEEE-754 default rounding (to nearest, ties to even).
 //
 // For simplicity, this implementation currently flushes denormals to zero.
 // It should be a fairly straightforward exercise to implement gradual
 // underflow with correct rounding.
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #define DOUBLE_PRECISION
 #include "fp_lib.h"
 
 COMPILER_RT_ABI fp_t __divdf3(fp_t a, fp_t b) {
 
   const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
   const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
if (!aAbs) {
       // zero / anything else = +/- zero
       else
         return fromRep(quotientSign);
     }
     // anything else / zero = +/- infinity
     if (!bAbs)
       return fromRep(infRep | quotientSign);
 
-    // one or both of a or b is denormal, the other (if applicable) is a
+    // One or both of a or b is denormal.  The other (if applicable) is a
     // normal number.  Renormalize one or both of a and b, and set scale to
     // include the necessary exponent adjustment.
     if (aAbs < implicitBit)
       scale += normalize(&aSignificand);
     if (bAbs < implicitBit)
       scale -= normalize(&bSignificand);
   }
 
-  // Or in the implicit significand bit.  (If we fell through from the
+  // Set the implicit significand bit.  If we fell through from the
   // denormal path it was already set by normalize( ), but setting it twice
-  // won't hurt anything.)
+  // won't hurt anything.
   aSignificand |= implicitBit;
   bSignificand |= implicitBit;
   int quotientExponent = aExponent - bExponent + scale;
 
   // Align the significand of b as a Q31 fixed-point number in the range
   // [1, 2.0) and get a Q32 approximate reciprocal using a small minimax
   // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2.  This
   // is accurate to about 3.5 binary digits.
   const uint32_t q31b = bSignificand >> 21;
   uint32_t recip32 = UINT32_C(0x7504f333) - q31b;
+  // 0x7504F333 / 2^32 + 1 = 3/4 + 1/sqrt(2)
 
   // Now refine the reciprocal estimate using a Newton-Raphson iteration:
   //
   //     x1 = x0 * (2 - x0 * b)
   //
   // This doubles the number of correct binary digits in the approximation
-  // with each iteration, so after three iterations, we have about 28 binary
-  // digits of accuracy.
+  // with each iteration.
   uint32_t correction32;
   correction32 = -((uint64_t)recip32 * q31b >> 32);
   recip32 = (uint64_t)recip32 * correction32 >> 31;
   correction32 = -((uint64_t)recip32 * q31b >> 32);
   recip32 = (uint64_t)recip32 * correction32 >> 31;
   correction32 = -((uint64_t)recip32 * q31b >> 32);
   recip32 = (uint64_t)recip32 * correction32 >> 31;
 
-  // recip32 might have overflowed to exactly zero in the preceding
-  // computation if the high word of b is exactly 1.0.  This would sabotage
-  // the full-width final stage of the computation that follows, so we adjust
-  // recip32 downward by one bit.
+  // The reciprocal may have overflowed to zero if the upper half of b is
+  // exactly 1.0.  This would sabatoge the full-width final stage of the
+  // computation that follows, so we adjust the reciprocal down by one bit.
   recip32--;
 
-  // We need to perform one more iteration to get us to 56 binary digits;
+  // We need to perform one more iteration to get us to 56 binary digits.
   // The last iteration needs to happen with extra precision.
   const uint32_t q63blo = bSignificand << 11;
   uint64_t correction, reciprocal;
   correction = -((uint64_t)recip32 * q31b + ((uint64_t)recip32 * q63blo >> 32));
   uint32_t cHi = correction >> 32;
   uint32_t cLo = correction;
   reciprocal = (uint64_t)recip32 * cHi + ((uint64_t)recip32 * cLo >> 32);
 
-  // We already adjusted the 32-bit estimate, now we need to adjust the final
-  // 64-bit reciprocal estimate downward to ensure that it is strictly smaller
-  // than the infinitely precise exact reciprocal.  Because the computation
-  // of the Newton-Raphson step is truncating at every step, this adjustment
-  // is small; most of the work is already done.
+  // Adjust the final 64-bit reciprocal estimate downward to ensure that it is
+  // strictly smaller than the infinitely precise exact reciprocal.  Because
+  // the computation of the Newton-Raphson step is truncating at every step,
+  // this adjustment is small; most of the work is already done.
   reciprocal -= 2;
 
   // The numerical reciprocal is accurate to within 2^-56, lies in the
   // interval [0.5, 1.0), and is strictly smaller than the true reciprocal
   // of b.  Multiplying a by this reciprocal thus gives a numerical q = a/b
   // in Q53 with the following properties:
   //
   //    1. q < a/b
   //    2. q is in the interval [0.5, 2.0)
-  //    3. the error in q is bounded away from 2^-53 (actually, we have a
+  //    3. The error in q is bounded away from 2^-53 (actually, we have a
   //       couple of bits to spare, but this is all we need).
 
   // We need a 64 x 64 multiply high to compute q, which isn't a basic
   // operation in C, so we need to be a little bit fussy.
   rep_t quotient, quotientLo;
   wideMultiply(aSignificand << 2, reciprocal, &quotient, &quotientLo);
 
   // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0).
   // In either case, we are going to compute a residual of the form
   //
   //     r = a - q*b
   //
   // We know from the construction of q that r satisfies:
   //
   //     0 <= r < ulp(q)*b
   //
-  // if r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
+  // If r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
   // already have the correct result.  The exact halfway case cannot occur.
   // We also take this time to right shift quotient if it falls in the [1,2)
   // range and adjust the exponent accordingly.
   rep_t residual;
   if (quotient < (implicitBit << 1)) {
     residual = (aSignificand << 53) - quotient * bSignificand;
     quotientExponent--;
   } else {
else if (writtenExponent < 1) {
     }
     // Flush denormals to zero.  In the future, it would be nice to add
     // code to round them correctly.
     return fromRep(quotientSign);
   }
 
   else {
     const bool round = (residual << 1) > bSignificand;
-    // Clear the implicit bit
+    // Clear the implicit bit.
     rep_t absResult = quotient & significandMask;
-    // Insert the exponent
+    // Insert the exponent.
     absResult |= (rep_t)writtenExponent << significandBits;
-    // Round
+    // Round.
     absResult += round;
-    // Insert the sign and return
+    // Insert the sign and return.
     const double result = fromRep(absResult | quotientSign);
     return result;
   }
 }
 
 #if defined(__ARM_EABI__)
 #if defined(COMPILER_RT_ARMHF_TARGET)
 AEABI_RTABI fp_t __aeabi_ddiv(fp_t a, fp_t b) { return __divdf3(a, b); }
 #else
 COMPILER_RT_ALIAS(__divdf3, __aeabi_ddiv)
 #endif
 #endif

compiler-rt/lib/builtins/divsf3.c

if (!aAbs) {
       // zero / anything else = +/- zero
       else
         return fromRep(quotientSign);
     }
     // anything else / zero = +/- infinity
     if (!bAbs)
       return fromRep(infRep | quotientSign);
 
-    // one or both of a or b is denormal, the other (if applicable) is a
+    // One or both of a or b is denormal.  The other (if applicable) is a
     // normal number.  Renormalize one or both of a and b, and set scale to
     // include the necessary exponent adjustment.
     if (aAbs < implicitBit)
       scale += normalize(&aSignificand);
     if (bAbs < implicitBit)
       scale -= normalize(&bSignificand);
   }
 
-  // Or in the implicit significand bit.  (If we fell through from the
+  // Set the implicit significand bit.  If we fell through from the
   // denormal path it was already set by normalize( ), but setting it twice
-  // won't hurt anything.)
+  // won't hurt anything.
   aSignificand |= implicitBit;
   bSignificand |= implicitBit;
   int quotientExponent = aExponent - bExponent + scale;
+  // 0x7504F333 / 2^32 + 1 = 3/4 + 1/sqrt(2)
 
   // Align the significand of b as a Q31 fixed-point number in the range
   // [1, 2.0) and get a Q32 approximate reciprocal using a small minimax
   // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2.  This
   // is accurate to about 3.5 binary digits.
   uint32_t q31b = bSignificand << 8;
   uint32_t reciprocal = UINT32_C(0x7504f333) - q31b;
 
   // Now refine the reciprocal estimate using a Newton-Raphson iteration:
   //
   //     x1 = x0 * (2 - x0 * b)
   //
   // This doubles the number of correct binary digits in the approximation
-  // with each iteration, so after three iterations, we have about 28 binary
-  // digits of accuracy.
+  // with each iteration.
   uint32_t correction;
   correction = -((uint64_t)reciprocal * q31b >> 32);
   reciprocal = (uint64_t)reciprocal * correction >> 31;
   correction = -((uint64_t)reciprocal * q31b >> 32);
   reciprocal = (uint64_t)reciprocal * correction >> 31;
   correction = -((uint64_t)reciprocal * q31b >> 32);
   reciprocal = (uint64_t)reciprocal * correction >> 31;
 
-  // Exhaustive testing shows that the error in reciprocal after three steps
-  // is in the interval [-0x1.f58108p-31, 0x1.d0e48cp-29], in line with our
-  // expectations.  We bump the reciprocal by a tiny value to force the error
-  // to be strictly positive (in the range [0x1.4fdfp-37,0x1.287246p-29], to
-  // be specific).  This also causes 1/1 to give a sensible approximation
-  // instead of zero (due to overflow).
+  // Adust the final 32-bit reciprocal estimate downward to ensure that it is
+  // strictly smaller than the infinitely precise exact reciprocal.  Because
+  // the computation of the Newton-Raphson step is truncating at every step,
+  // this adjustment is small; most of the work is already done.
   reciprocal -= 2;
 
   // The numerical reciprocal is accurate to within 2^-28, lies in the
   // interval [0x1.000000eep-1, 0x1.fffffffcp-1], and is strictly smaller
   // than the true reciprocal of b.  Multiplying a by this reciprocal thus
   // gives a numerical q = a/b in Q24 with the following properties:
   //
   //    1. q < a/b
   //    2. q is in the interval [0x1.000000eep-1, 0x1.fffffffcp0)
-  //    3. the error in q is at most 2^-24 + 2^-27 -- the 2^24 term comes
+  //    3. The error in q is at most 2^-24 + 2^-27 -- the 2^24 term comes
   //       from the fact that we truncate the product, and the 2^27 term
   //       is the error in the reciprocal of b scaled by the maximum
   //       possible value of a.  As a consequence of this error bound,
-  //       either q or nextafter(q) is the correctly rounded
+  //       either q or nextafter(q) is the correctly rounded.
   rep_t quotient = (uint64_t)reciprocal * (aSignificand << 1) >> 32;
 
   // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0).
   // In either case, we are going to compute a residual of the form
   //
   //     r = a - q*b
   //
   // We know from the construction of q that r satisfies:
   //
   //     0 <= r < ulp(q)*b
   //
-  // if r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
+  // If r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
   // already have the correct result.  The exact halfway case cannot occur.
   // We also take this time to right shift quotient if it falls in the [1,2)
   // range and adjust the exponent accordingly.
   rep_t residual;
   if (quotient < (implicitBit << 1)) {
     residual = (aSignificand << 24) - quotient * bSignificand;
     quotientExponent--;
   } else {
else if (writtenExponent < 1) {
     }
     // Flush denormals to zero.  In the future, it would be nice to add
     // code to round them correctly.
     return fromRep(quotientSign);
   }
 
   else {
     const bool round = (residual << 1) > bSignificand;
-    // Clear the implicit bit
+    // Clear the implicit bit.
     rep_t absResult = quotient & significandMask;
-    // Insert the exponent
+    // Insert the exponent.
     absResult |= (rep_t)writtenExponent << significandBits;
-    // Round
+    // Round.
     absResult += round;
-    // Insert the sign and return
+    // Insert the sign and return.
     return fromRep(absResult | quotientSign);
   }
 }
 
 #if defined(__ARM_EABI__)
 #if defined(COMPILER_RT_ARMHF_TARGET)
 AEABI_RTABI fp_t __aeabi_fdiv(fp_t a, fp_t b) { return __divsf3(a, b); }
 #else
 COMPILER_RT_ALIAS(__divsf3, __aeabi_fdiv)
 #endif
 #endif

compiler-rt/lib/builtins/divtf3.c

-//===-- lib/divtf3.c - Quad-precision division --------------------*- C -*-===//
+//===-- lib/divtf3.c - Quad-precision division --------------------*- C -*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements quad-precision soft-float division
 // with the IEEE-754 default rounding (to nearest, ties to even).
 //
 // For simplicity, this implementation currently flushes denormals to zero.
 // It should be a fairly straightforward exercise to implement gradual
 // underflow with correct rounding.
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #define QUAD_PRECISION
 #include "fp_lib.h"
 
 #if defined(CRT_HAS_128BIT) && defined(CRT_LDBL_128BIT)
 COMPILER_RT_ABI fp_t __divtf3(fp_t a, fp_t b) {
 
   const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
if (!aAbs) {
       // zero / anything else = +/- zero
       else
         return fromRep(quotientSign);
     }
     // anything else / zero = +/- infinity
     if (!bAbs)
       return fromRep(infRep | quotientSign);
 
-    // one or both of a or b is denormal, the other (if applicable) is a
+    // One or both of a or b is denormal.  The other (if applicable) is a
     // normal number.  Renormalize one or both of a and b, and set scale to
     // include the necessary exponent adjustment.
     if (aAbs < implicitBit)
       scale += normalize(&aSignificand);
     if (bAbs < implicitBit)
       scale -= normalize(&bSignificand);
   }
 
-  // Or in the implicit significand bit.  (If we fell through from the
+  // Set the implicit significand bit.  If we fell through from the
   // denormal path it was already set by normalize( ), but setting it twice
-  // won't hurt anything.)
+  // won't hurt anything.
   aSignificand |= implicitBit;
   bSignificand |= implicitBit;
   int quotientExponent = aExponent - bExponent + scale;
 
   // Align the significand of b as a Q63 fixed-point number in the range
   // [1, 2.0) and get a Q64 approximate reciprocal using a small minimax
   // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2.  This
   // is accurate to about 3.5 binary digits.
COMPILER_RT_ABI fp_t __divtf3(fp_t a, fp_t b) {
   recip64 = (rep_t)recip64 * correction64 >> 63;
   correction64 = -((rep_t)recip64 * q63b >> 64);
   recip64 = (rep_t)recip64 * correction64 >> 63;
   correction64 = -((rep_t)recip64 * q63b >> 64);
   recip64 = (rep_t)recip64 * correction64 >> 63;
   correction64 = -((rep_t)recip64 * q63b >> 64);
   recip64 = (rep_t)recip64 * correction64 >> 63;
 
-  // recip64 might have overflowed to exactly zero in the preceeding
-  // computation if the high word of b is exactly 1.0.  This would sabotage
-  // the full-width final stage of the computation that follows, so we adjust
-  // recip64 downward by one bit.
+  // The reciprocal may have overflowed to zero if the upper half of b is
+  // exactly 1.0.  This would sabatoge the full-width final stage of the
+  // computation that follows, so we adjust the reciprocal down by one bit.
   recip64--;
 
   // We need to perform one more iteration to get us to 112 binary digits;
   // The last iteration needs to happen with extra precision.
   const uint64_t q127blo = bSignificand << 15;
   rep_t correction, reciprocal;
 
   // NOTE: This operation is equivalent to __multi3, which is not implemented
   //       in some architechure
   rep_t r64q63, r64q127, r64cH, r64cL, dummy;
   wideMultiply((rep_t)recip64, (rep_t)q63b, &dummy, &r64q63);
   wideMultiply((rep_t)recip64, (rep_t)q127blo, &dummy, &r64q127);
 
   correction = -(r64q63 + (r64q127 >> 64));
 
   uint64_t cHi = correction >> 64;
   uint64_t cLo = correction;
 
   wideMultiply((rep_t)recip64, (rep_t)cHi, &dummy, &r64cH);
   wideMultiply((rep_t)recip64, (rep_t)cLo, &dummy, &r64cL);
 
   reciprocal = r64cH + (r64cL >> 64);
 
-  // We already adjusted the 64-bit estimate, now we need to adjust the final
-  // 128-bit reciprocal estimate downward to ensure that it is strictly smaller
-  // than the infinitely precise exact reciprocal.  Because the computation
-  // of the Newton-Raphson step is truncating at every step, this adjustment
-  // is small; most of the work is already done.
+  // Adjust the final 128-bit reciprocal estimate downward to ensure that it
+  // is strictly smaller than the infinitely precise exact reciprocal. Because
+  // the computation of the Newton-Raphson step is truncating at every step,
+  // this adjustment is small; most of the work is already done.
   reciprocal -= 2;
 
   // The numerical reciprocal is accurate to within 2^-112, lies in the
   // interval [0.5, 1.0), and is strictly smaller than the true reciprocal
   // of b.  Multiplying a by this reciprocal thus gives a numerical q = a/b
   // in Q127 with the following properties:
   //
   //    1. q < a/b
   //    2. q is in the interval [0.5, 2.0)
-  //    3. the error in q is bounded away from 2^-113 (actually, we have a
+  //    3. The error in q is bounded away from 2^-113 (actually, we have a
   //       couple of bits to spare, but this is all we need).
 
   // We need a 128 x 128 multiply high to compute q, which isn't a basic
   // operation in C, so we need to be a little bit fussy.
   rep_t quotient, quotientLo;
   wideMultiply(aSignificand << 2, reciprocal, &quotient, &quotientLo);
 
   // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0).
   // In either case, we are going to compute a residual of the form
   //
   //     r = a - q*b
   //
   // We know from the construction of q that r satisfies:
   //
   //     0 <= r < ulp(q)*b
   //
-  // if r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
+  // If r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
   // already have the correct result.  The exact halfway case cannot occur.
   // We also take this time to right shift quotient if it falls in the [1,2)
   // range and adjust the exponent accordingly.
   rep_t residual;
   rep_t qb;
 
   if (quotient < (implicitBit << 1)) {
     wideMultiply(quotient, bSignificand, &dummy, &qb);
if (writtenExponent == 0) {
         return fromRep(absResult | quotientSign);
       }
     }
     // Flush denormals to zero.  In the future, it would be nice to add
     // code to round them correctly.
     return fromRep(quotientSign);
   } else {
     const bool round = (residual << 1) >= bSignificand;
-    // Clear the implicit bit
+    // Clear the implicit bit.
     rep_t absResult = quotient & significandMask;
-    // Insert the exponent
+    // Insert the exponent.
     absResult |= (rep_t)writtenExponent << significandBits;
-    // Round
+    // Round.
     absResult += round;
-    // Insert the sign and return
+    // Insert the sign and return.
     const long double result = fromRep(absResult | quotientSign);
     return result;
   }
 }
 
 #endif

compiler-rt/lib/builtins/fp_add_impl.inc

-//===----- lib/fp_add_impl.inc - floaing point addition -----------*- C -*-===//
+//===----- lib/fp_add_impl.inc - floaing point addition -----------*- C -*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements soft-float addition with the IEEE-754 default rounding
 // (to nearest, ties to even).
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #include "fp_lib.h"
 
 static __inline fp_t __addXf3__(fp_t a, fp_t b) {
   rep_t aRep = toRep(a);
   rep_t bRep = toRep(b);
   const rep_t aAbs = aRep & absMask;
   const rep_t bAbs = bRep & absMask;
if (aAbs - REP_C(1) >= infRep - REP_C(1) ||
     }
 
     // anything remaining + +/-infinity = +/-infinity
     if (bAbs == infRep)
       return b;
 
     // zero + anything = anything
     if (!aAbs) {
-      // but we need to get the sign right for zero + zero
+      // We need to get the sign right for zero + zero.
       if (!bAbs)
         return fromRep(toRep(a) & toRep(b));
       else
         return b;
     }
 
     // anything + zero = anything
     if (!bAbs)
static __inline fp_t __addXf3__(fp_t a, fp_t b) {
 
   // Normalize any denormals, and adjust the exponent accordingly.
   if (aExponent == 0)
     aExponent = normalize(&aSignificand);
   if (bExponent == 0)
     bExponent = normalize(&bSignificand);
 
   // The sign of the result is the sign of the larger operand, a.  If they
-  // have opposite signs, we are performing a subtraction; otherwise addition.
+  // have opposite signs, we are performing a subtraction.  Otherwise, we
+  // perform addition.
   const rep_t resultSign = aRep & signBit;
   const bool subtraction = (aRep ^ bRep) & signBit;
 
-  // Shift the significands to give us round, guard and sticky, and or in the
-  // implicit significand bit.  (If we fell through from the denormal path it
+  // Shift the significands to give us round, guard and sticky, and set the
+  // implicit significand bit.  If we fell through from the denormal path it
   // was already set by normalize( ), but setting it twice won't hurt
-  // anything.)
+  // anything.
   aSignificand = (aSignificand | implicitBit) << 3;
   bSignificand = (bSignificand | implicitBit) << 3;
 
   // Shift the significand of b by the difference in exponents, with a sticky
   // bottom bit to get rounding correct.
   const unsigned int align = aExponent - bExponent;
   if (align) {
     if (align < typeWidth) {
       const bool sticky = bSignificand << (typeWidth - align);
       bSignificand = bSignificand >> align | sticky;
     } else {
-      bSignificand = 1; // sticky; b is known to be non-zero.
+      bSignificand = 1; // Set the sticky bit.  b is known to be non-zero.
     }
   }
   if (subtraction) {
     aSignificand -= bSignificand;
     // If a == -b, return +zero.
     if (aSignificand == 0)
       return fromRep(0);
 
     // If partial cancellation occured, we need to left-shift the result
-    // and adjust the exponent:
+    // and adjust the exponent.
     if (aSignificand < implicitBit << 3) {
       const int shift = rep_clz(aSignificand) - rep_clz(implicitBit << 3);
       aSignificand <<= shift;
       aExponent -= shift;
     }
   } else /* addition */ {
     aSignificand += bSignificand;
 
     // If the addition carried up, we need to right-shift the result and
-    // adjust the exponent:
+    // adjust the exponent.
     if (aSignificand & implicitBit << 4) {
       const bool sticky = aSignificand & 1;
       aSignificand = aSignificand >> 1 | sticky;
       aExponent += 1;
     }
   }
 
-  // If we have overflowed the type, return +/- infinity:
+  // If we have overflowed the type, return +/- infinity.
   if (aExponent >= maxExponent)
     return fromRep(infRep | resultSign);
 
   if (aExponent <= 0) {
-    // Result is denormal before rounding; the exponent is zero and we
+    // The result is denormal before rounding.  The exponent is zero and we
     // need to shift the significand.
     const int shift = 1 - aExponent;
     const bool sticky = aSignificand << (typeWidth - shift);
     aSignificand = aSignificand >> shift | sticky;
     aExponent = 0;
   }
 
   // Low three bits are round, guard, and sticky.
   const int roundGuardSticky = aSignificand & 0x7;
 
   // Shift the significand into place, and mask off the implicit bit.
   rep_t result = aSignificand >> 3 & significandMask;
 
   // Insert the exponent and sign.
   result |= (rep_t)aExponent << significandBits;
   result |= resultSign;
 
-  // Final rounding.  The result may overflow to infinity, but that is the
-  // correct result in that case.
+  // Perform the final rounding.  The result may overflow to infinity, but
+  // that is the correct result in that case.
   if (roundGuardSticky > 0x4)
     result++;
   if (roundGuardSticky == 0x4)
     result += result & 1;
   return fromRep(result);
 }

compiler-rt/lib/builtins/fp_extend_impl.inc

-//=-lib/fp_extend_impl.inc - low precision -> high precision conversion -*-- -//
+//=-lib/fp_extend_impl.inc - low precision -> high precision conversion -*-- -
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements a fairly generic conversion from a narrower to a wider
 // IEEE-754 floating-point type.  The constants and types defined following the
 // includes below parameterize the conversion.
 //
 // It does not support types that don't use the usual IEEE-754 interchange
 // formats; specifically, some work would be needed to adapt it to
 // (for example) the Intel 80-bit format or PowerPC double-double format.
 //
 // Note please, however, that this implementation is only intended to support
 // *widening* operations; if you need to convert to a *narrower* floating-point
 // type (e.g. double -> float), then this routine will not do what you want it
 // to.
 //
 // It also requires that integer types at least as large as both formats
 // are available on the target platform; this may pose a problem when trying
 // to add support for quad on some 32-bit systems, for example.  You also may
 // run into trouble finding an appropriate CLZ function for wide source types;
 // you will likely need to roll your own on some platforms.
 //
 // Finally, the following assumptions are made:
 //
-// 1. floating-point types and integer types have the same endianness on the
-//    target platform
+// 1. Floating-point types and integer types have the same endianness on the
+//    target platform.
 //
-// 2. quiet NaNs, if supported, are indicated by the leading bit of the
-//    significand field being set
+// 2. Quiet NaNs, if supported, are indicated by the leading bit of the
+//    significand field being set.
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #include "fp_extend.h"
 
 static __inline dst_t __extendXfYf2__(src_t a) {
   // Various constants whose values follow from the type parameters.
   // Any reasonable optimizer will fold and propagate all of these.
   const int srcBits = sizeof(src_t) * CHAR_BIT;
   const int srcExpBits = srcBits - srcSigBits - 1;
static __inline dst_t __extendXfYf2__(src_t a) {
 
   const int dstBits = sizeof(dst_t) * CHAR_BIT;
   const int dstExpBits = dstBits - dstSigBits - 1;
   const int dstInfExp = (1 << dstExpBits) - 1;
   const int dstExpBias = dstInfExp >> 1;
 
   const dst_rep_t dstMinNormal = DST_REP_C(1) << dstSigBits;
 
-  // Break a into a sign and representation of the absolute value
+  // Break a into a sign and representation of the absolute value.
   const src_rep_t aRep = srcToRep(a);
   const src_rep_t aAbs = aRep & srcAbsMask;
   const src_rep_t sign = aRep & srcSignMask;
   dst_rep_t absResult;
 
   // If sizeof(src_rep_t) < sizeof(int), the subtraction result is promoted
   // to (signed) int.  To avoid that, explicitly cast to src_rep_t.
   if ((src_rep_t)(aAbs - srcMinNormal) < srcInfinity - srcMinNormal) {
else if (aAbs) {
     absResult |= (dst_rep_t)resultExponent << dstSigBits;
   }
 
   else {
     // a is zero.
     absResult = 0;
   }
 
-  // Apply the signbit to (dst_t)abs(a).
+  // Apply the signbit to the absolute value.
   const dst_rep_t result = absResult | (dst_rep_t)sign << (dstBits - srcBits);
   return dstFromRep(result);
 }

compiler-rt/lib/builtins/fp_fixint_impl.inc

-//===-- lib/fixdfsi.c - Double-precision -> integer conversion ----*- C -*-===//
+//===-- lib/fixdfsi.c - Double-precision -> integer conversion ----*- C -*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements float to integer conversion for the
 // compiler-rt library.
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #include "fp_lib.h"
 
 static __inline fixint_t __fixint(fp_t a) {
   const fixint_t fixint_max = (fixint_t)((~(fixuint_t)0) / 2);
   const fixint_t fixint_min = -fixint_max - 1;
-  // Break a into sign, exponent, significand
+  // Break a into sign, exponent, significand parts.
   const rep_t aRep = toRep(a);
   const rep_t aAbs = aRep & absMask;
   const fixint_t sign = aRep & signBit ? -1 : 1;
   const int exponent = (aAbs >> significandBits) - exponentBias;
   const rep_t significand = (aAbs & significandMask) | implicitBit;
 
   // If exponent is negative, the result is zero.
   if (exponent < 0)

compiler-rt/lib/builtins/fp_fixuint_impl.inc

-//===-- lib/fixdfsi.c - Double-precision -> integer conversion ----*- C -*-===//
+//===-- lib/fixdfsi.c - Double-precision -> integer conversion ----*- C -*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements float to unsigned integer conversion for the
 // compiler-rt library.
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #include "fp_lib.h"
 
 static __inline fixuint_t __fixuint(fp_t a) {
-  // Break a into sign, exponent, significand
+  // Break a into sign, exponent, significand parts.
   const rep_t aRep = toRep(a);
   const rep_t aAbs = aRep & absMask;
   const int sign = aRep & signBit ? -1 : 1;
   const int exponent = (aAbs >> significandBits) - exponentBias;
   const rep_t significand = (aAbs & significandMask) | implicitBit;
 
   // If either the value or the exponent is negative, the result is zero.
   if (sign == -1 || exponent < 0)

compiler-rt/lib/builtins/fp_mul_impl.inc

-//===---- lib/fp_mul_impl.inc - floating point multiplication -----*- C -*-===//
+//===---- lib/fp_mul_impl.inc - floating point multiplication -----*- C -*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements soft-float multiplication with the IEEE-754 default
 // rounding (to nearest, ties to even).
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #include "fp_lib.h"
 
 static __inline fp_t __mulXf3__(fp_t a, fp_t b) {
   const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
   const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
   const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
 
if (aAbs == infRep) {
       if (bAbs)
         return fromRep(aAbs | productSign);
       // infinity * zero = NaN
       else
         return fromRep(qnanRep);
     }
 
     if (bAbs == infRep) {
-      //? non-zero * infinity = +/- infinity
+      // non-zero * infinity = +/- infinity
       if (aAbs)
         return fromRep(bAbs | productSign);
       // zero * infinity = NaN
       else
         return fromRep(qnanRep);
     }
 
     // zero * anything = +/- zero
     if (!aAbs)
       return fromRep(productSign);
     // anything * zero = +/- zero
     if (!bAbs)
       return fromRep(productSign);
 
-    // one or both of a or b is denormal, the other (if applicable) is a
+    // One or both of a or b is denormal.  The other (if applicable) is a
     // normal number.  Renormalize one or both of a and b, and set scale to
     // include the necessary exponent adjustment.
     if (aAbs < implicitBit)
       scale += normalize(&aSignificand);
     if (bAbs < implicitBit)
       scale += normalize(&bSignificand);
   }
 
-  // Or in the implicit significand bit.  (If we fell through from the
+  // Set the implicit significand bit.  If we fell through from the
   // denormal path it was already set by normalize( ), but setting it twice
-  // won't hurt anything.)
+  // won't hurt anything.
   aSignificand |= implicitBit;
   bSignificand |= implicitBit;
 
-  // Get the significand of a*b.  Before multiplying the significands, shift
-  // one of them left to left-align it in the field.  Thus, the product will
-  // have (exponentBits + 2) integral digits, all but two of which must be
-  // zero.  Normalizing this result is just a conditional left-shift by one
-  // and bumping the exponent accordingly.
+  // Perform a basic multiplication on the significands.  One of them must be
+  // shifted beforehand to be aligned with the exponent.
   rep_t productHi, productLo;
   wideMultiply(aSignificand, bSignificand << exponentBits, &productHi,
                &productLo);
 
   int productExponent = aExponent + bExponent - exponentBias + scale;
 
-  // Normalize the significand, adjust exponent if needed.
+  // Normalize the significand and adjust the exponent if needed.
   if (productHi & implicitBit)
     productExponent++;
   else
     wideLeftShift(&productHi, &productLo, 1);
 
   // If we have overflowed the type, return +/- infinity.
   if (productExponent >= maxExponent)
     return fromRep(infRep | productSign);
 
   if (productExponent <= 0) {
-    // Result is denormal before rounding
+    // The result is denormal before rounding.
     //
     // If the result is so small that it just underflows to zero, return
-    // a zero of the appropriate sign.  Mathematically there is no need to
+    // zero with the appropriate sign.  Mathematically, there is no need to
     // handle this case separately, but we make it a special case to
     // simplify the shift logic.
     const unsigned int shift = REP_C(1) - (unsigned int)productExponent;
     if (shift >= typeWidth)
       return fromRep(productSign);
 
     // Otherwise, shift the significand of the result so that the round
     // bit is the high bit of productLo.
     wideRightShiftWithSticky(&productHi, &productLo, shift);
   } else {
-    // Result is normal before rounding; insert the exponent.
+    // The result is normal before rounding.  Insert the exponent.
     productHi &= significandMask;
     productHi |= (rep_t)productExponent << significandBits;
   }
 
-  // Insert the sign of the result:
+  // Insert the sign of the result.
   productHi |= productSign;
 
-  // Final rounding.  The final result may overflow to infinity, or underflow
-  // to zero, but those are the correct results in those cases.  We use the
-  // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
+  // Perform the final rounding.  The final result may overflow to infinity,
+  // or underflow to zero, but those are the correct results in those cases.
+  // We use the default IEEE-754 round-to-nearest, ties-to-even rounding mode.
   if (productLo > signBit)
     productHi++;
   if (productLo == signBit)
     productHi += productHi & 1;
   return fromRep(productHi);
 }

compiler-rt/lib/builtins/fp_trunc_impl.inc

-//= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===//
+//= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 //
 // This file implements a fairly generic conversion from a wider to a narrower
 // IEEE-754 floating-point type in the default (round to nearest, ties to even)
 // rounding mode.  The constants and types defined following the includes below
 // parameterize the conversion.
 //
 // This routine can be trivially adapted to support conversions to
 // half-precision or from quad-precision. It does not support types that don't
 // use the usual IEEE-754 interchange formats; specifically, some work would be
 // needed to adapt it to (for example) the Intel 80-bit format or PowerPC
 // double-double format.
 //
 // Note please, however, that this implementation is only intended to support
 // *narrowing* operations; if you need to convert to a *wider* floating-point
 // type (e.g. float -> double), then this routine will not do what you want it
 // to.
 //
 // It also requires that integer types at least as large as both formats
 // are available on the target platform; this may pose a problem when trying
 // to add support for quad on some 32-bit systems, for example.
 //
 // Finally, the following assumptions are made:
 //
-// 1. floating-point types and integer types have the same endianness on the
-//    target platform
+// 1. Floating-point types and integer types have the same endianness on the
+//    target platform.
 //
-// 2. quiet NaNs, if supported, are indicated by the leading bit of the
-//    significand field being set
+// 2. Quiet NaNs, if supported, are indicated by the leading bit of the
+//    significand field being set.
 //
-//===----------------------------------------------------------------------===//
+//===----------------------------------------------------------------------===
 
 #include "fp_trunc.h"
 
 static __inline dst_t __truncXfYf2__(src_t a) {
   // Various constants whose values follow from the type parameters.
   // Any reasonable optimizer will fold and propagate all of these.
   const int srcBits = sizeof(src_t) * CHAR_BIT;
   const int srcExpBits = srcBits - srcSigBits - 1;
static __inline dst_t __truncXfYf2__(src_t a) {
   const int underflowExponent = srcExpBias + 1 - dstExpBias;
   const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
   const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
   const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;
 
   const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
   const dst_rep_t dstNaNCode = dstQNaN - 1;
 
-  // Break a into a sign and representation of the absolute value
+  // Break a into a sign and representation of the absolute value.
   const src_rep_t aRep = srcToRep(a);
   const src_rep_t aAbs = aRep & srcAbsMask;
   const src_rep_t sign = aRep & srcSignMask;
   dst_rep_t absResult;
 
   if (aAbs - underflow < aAbs - overflow) {
     // The exponent of a is within the range of normal numbers in the
     // destination format.  We can convert by simply right-shifting with
     // rounding and adjusting the exponent.
     absResult = aAbs >> (srcSigBits - dstSigBits);
     absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;
 
     const src_rep_t roundBits = aAbs & roundMask;
-    // Round to nearest
+    // Round to nearest.
     if (roundBits > halfway)
       absResult++;
-    // Ties to even
+    // Tie to even.
     else if (roundBits == halfway)
       absResult += absResult & 1;
   } else if (aAbs > srcInfinity) {
     // a is NaN.
     // Conjure the result by beginning with infinity, setting the qNaN
     // bit and inserting the (truncated) trailing NaN field.
     absResult = (dst_rep_t)dstInfExp << dstSigBits;
     absResult |= dstQNaN;
if (shift > srcSigBits) {
       if (roundBits > halfway)
         absResult++;
       // Ties to even
       else if (roundBits == halfway)
         absResult += absResult & 1;
     }
   }
 
-  // Apply the signbit to (dst_t)abs(a).
+  // Apply the signbit to the absolute value.
   const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
   return dstFromRep(result);
 }