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 /* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-

  * vim: set ts=8 sts=4 et sw=4 tw=99:

  * This Source Code Form is subject to the terms of the Mozilla Public

  * License, v. 2.0. If a copy of the MPL was not distributed with this

  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

 #ifndef vm_NumericConversions_h

 #define vm_NumericConversions_h

 #include "mozilla/Assertions.h"

 #include "mozilla/Casting.h"

 #include "mozilla/FloatingPoint.h"

 #include "mozilla/TypeTraits.h"

 #include <math.h>

 namespace js {

 namespace detail {

 /*

  * Convert a double value to ResultType (an unsigned integral type) using

  * ECMAScript-style semantics (that is, in like manner to how ECMAScript's

  * ToInt32 converts to int32_t).

  *

  *   If d is infinite or NaN, return 0.

  *   Otherwise compute d2 = sign(d) * floor(abs(d)), and return the ResultType

  *   value congruent to d2 mod 2**(bit width of ResultType).

  *

  * The algorithm below is inspired by that found in

  * <http://trac.webkit.org/changeset/67825/trunk/JavaScriptCore/runtime/JSValue.cpp>

  * but has been generalized to all integer widths.

  */

 template<typename ResultType>

 inline ResultType

 ToUintWidth(double d)

 {

     static_assert(mozilla::IsUnsigned<ResultType>::value,

                   "ResultType must be an unsigned type");

     uint64_t bits = mozilla::BitwiseCast<uint64_t>(d);

     unsigned DoubleExponentShift = mozilla::FloatingPoint<double>::ExponentShift;

     // Extract the exponent component.  (Be careful here!  It's not technically

     // the exponent in NaN, infinities, and subnormals.)

     int_fast16_t exp =

         int_fast16_t((bits & mozilla::FloatingPoint<double>::ExponentBits) >> DoubleExponentShift) -

         int_fast16_t(mozilla::FloatingPoint<double>::ExponentBias);

     // If the exponent's less than zero, abs(d) < 1, so the result is 0.  (This

     // also handles subnormals.)

     if (exp < 0)

         return 0;

     uint_fast16_t exponent = mozilla::SafeCast<uint_fast16_t>(exp);

     // If the exponent is greater than or equal to the bits of precision of a

     // double plus ResultType's width, the number is either infinite, NaN, or

     // too large to have lower-order bits in the congruent value.  (Example:

     // 2**84 is exactly representable as a double.  The next exact double is

     // 2**84 + 2**32.  Thus if ResultType is int32_t, an exponent >= 84 implies

     // floor(abs(d)) == 0 mod 2**32.)  Return 0 in all these cases.

     const size_t ResultWidth = CHAR_BIT * sizeof(ResultType);

     if (exponent >= DoubleExponentShift + ResultWidth)

         return 0;

     // The significand contains the bits that will determine the final result.

     // Shift those bits left or right, according to the exponent, to their

     // locations in the unsigned binary representation of floor(abs(d)).

     static_assert(sizeof(ResultType) <= sizeof(uint64_t),

                   "Left-shifting below would lose upper bits");

     ResultType result = (exponent > DoubleExponentShift)

                         ? ResultType(bits << (exponent - DoubleExponentShift))

                         : ResultType(bits >> (DoubleExponentShift - exponent));

     // Two further complications remain.  First, |result| may contain bogus

     // sign/exponent bits.  Second, IEEE-754 numbers' significands (excluding

     // subnormals, but we already handled those) have an implicit leading 1

     // which may affect the final result.

     //

     // It may appear that there's complexity here depending on how ResultWidth

     // and DoubleExponentShift relate, but it turns out there's not.

     //

     // Assume ResultWidth < DoubleExponentShift:

     //   Only right-shifts leave bogus bits in |result|.  For this to happen,

     //   we must right-shift by > |DoubleExponentShift - ResultWidth|, implying

     //   |exponent < ResultWidth|.

     //   The implicit leading bit only matters if it appears in the final

     //   result -- if |2**exponent mod 2**ResultWidth != 0|.  This implies

     //   |exponent < ResultWidth|.

     // Otherwise assume ResultWidth >= DoubleExponentShift:

     //   Any left-shift less than |ResultWidth - DoubleExponentShift| leaves

     //   bogus bits in |result|.  This implies |exponent < ResultWidth|.  Any

     //   right-shift less than |ResultWidth| does too, which implies

     //   |DoubleExponentShift - ResultWidth < exponent|.  By assumption, then,

     //   |exponent| is negative, but we excluded that above.  So bogus bits

     //   need only |exponent < ResultWidth|.

     //   The implicit leading bit matters identically to the other case, so

     //   again, |exponent < ResultWidth|.

     if (exponent < ResultWidth) {

         ResultType implicitOne = ResultType(1) << exponent;

         result &= implicitOne - 1; // remove bogus bits

         result += implicitOne; // add the implicit bit

     }

     // Compute the congruent value in the signed range.

     return (bits & mozilla::FloatingPoint<double>::SignBit) ? ~result + 1 : result;

 }

 template<typename ResultType>

 inline ResultType

 ToIntWidth(double d)

 {

     static_assert(mozilla::IsSigned<ResultType>::value,

                   "ResultType must be a signed type");

     const ResultType MaxValue = (1ULL << (CHAR_BIT * sizeof(ResultType) - 1)) - 1;

     const ResultType MinValue = -MaxValue - 1;

     typedef typename mozilla::MakeUnsigned<ResultType>::Type UnsignedResult;

     UnsignedResult u = ToUintWidth<UnsignedResult>(d);

     if (u <= UnsignedResult(MaxValue))

         return static_cast<ResultType>(u);

     return (MinValue + static_cast<ResultType>(u - MaxValue)) - 1;

 }

 } /* namespace detail */

 /* ES5 9.5 ToInt32 (specialized for doubles). */

 inline int32_t

 ToInt32(double d)

 {

 #if defined (__arm__) && defined (__GNUC__)

     int32_t i;

     uint32_t    tmp0;

     uint32_t    tmp1;

     uint32_t    tmp2;

     asm (

     // We use a pure integer solution here. In the 'softfp' ABI, the argument

     // will start in r0 and r1, and VFP can't do all of the necessary ECMA

     // conversions by itself so some integer code will be required anyway. A

     // hybrid solution is faster on A9, but this pure integer solution is

     // notably faster for A8.

     // %0 is the result register, and may alias either of the %[QR]1 registers.

     // %Q4 holds the lower part of the mantissa.

     // %R4 holds the sign, exponent, and the upper part of the mantissa.

     // %1, %2 and %3 are used as temporary values.

     // Extract the exponent.

 "   mov     %1, %R4, LSR #20\n"

 "   bic     %1, %1, #(1 << 11)\n"  // Clear the sign.

     // Set the implicit top bit of the mantissa. This clobbers a bit of the

     // exponent, but we have already extracted that.

 "   orr     %R4, %R4, #(1 << 20)\n"

     // Special Cases

     //   We should return zero in the following special cases:

     //    - Exponent is 0x000 - 1023: +/-0 or subnormal.

     //    - Exponent is 0x7ff - 1023: +/-INFINITY or NaN

     //      - This case is implicitly handled by the standard code path anyway,

     //        as shifting the mantissa up by the exponent will result in '0'.

     //

     // The result is composed of the mantissa, prepended with '1' and

     // bit-shifted left by the (decoded) exponent. Note that because the r1[20]

     // is the bit with value '1', r1 is effectively already shifted (left) by

     // 20 bits, and r0 is already shifted by 52 bits.

     // Adjust the exponent to remove the encoding offset. If the decoded

     // exponent is negative, quickly bail out with '0' as such values round to

     // zero anyway. This also catches +/-0 and subnormals.

 "   sub     %1, %1, #0xff\n"

 "   subs    %1, %1, #0x300\n"

 "   bmi     8f\n"

     //  %1 = (decoded) exponent >= 0

     //  %R4 = upper mantissa and sign

     // ---- Lower Mantissa ----

 "   subs    %3, %1, #52\n"         // Calculate exp-52

 "   bmi     1f\n"

     // Shift r0 left by exp-52.

     // Ensure that we don't overflow ARM's 8-bit shift operand range.

     // We need to handle anything up to an 11-bit value here as we know that

     // 52 <= exp <= 1024 (0x400). Any shift beyond 31 bits results in zero

     // anyway, so as long as we don't touch the bottom 5 bits, we can use

     // a logical OR to push long shifts into the 32 <= (exp&0xff) <= 255 range.

 "   bic     %2, %3, #0xff\n"

 "   orr     %3, %3, %2, LSR #3\n"

     // We can now perform a straight shift, avoiding the need for any

     // conditional instructions or extra branches.

 "   mov     %Q4, %Q4, LSL %3\n"

 "   b       2f\n"

 "1:\n" // Shift r0 right by 52-exp.

     // We know that 0 <= exp < 52, and we can shift up to 255 bits so 52-exp

     // will always be a valid shift and we can sk%3 the range check for this case.

 "   rsb     %3, %1, #52\n"

 "   mov     %Q4, %Q4, LSR %3\n"

     //  %1 = (decoded) exponent

     //  %R4 = upper mantissa and sign

     //  %Q4 = partially-converted integer

 "2:\n"

     // ---- Upper Mantissa ----

     // This is much the same as the lower mantissa, with a few different

     // boundary checks and some masking to hide the exponent & sign bit in the

     // upper word.

     // Note that the upper mantissa is pre-shifted by 20 in %R4, but we shift

     // it left more to remove the sign and exponent so it is effectively

     // pre-shifted by 31 bits.

 "   subs    %3, %1, #31\n"          // Calculate exp-31

 "   mov     %1, %R4, LSL #11\n"     // Re-use %1 as a temporary register.

 "   bmi     3f\n"

     // Shift %R4 left by exp-31.

     // Avoid overflowing the 8-bit shift range, as before.

 "   bic     %2, %3, #0xff\n"

 "   orr     %3, %3, %2, LSR #3\n"

     // Perform the shift.

 "   mov     %2, %1, LSL %3\n"

 "   b       4f\n"

 "3:\n" // Shift r1 right by 31-exp.

     // We know that 0 <= exp < 31, and we can shift up to 255 bits so 31-exp

     // will always be a valid shift and we can skip the range check for this case.

 "   rsb     %3, %3, #0\n"          // Calculate 31-exp from -(exp-31)

 "   mov     %2, %1, LSR %3\n"      // Thumb-2 can't do "LSR %3" in "orr".

     //  %Q4 = partially-converted integer (lower)

     //  %R4 = upper mantissa and sign

     //  %2 = partially-converted integer (upper)

 "4:\n"

     // Combine the converted parts.

 "   orr     %Q4, %Q4, %2\n"

     // Negate the result if we have to, and move it to %0 in the process. To

     // avoid conditionals, we can do this by inverting on %R4[31], then adding

     // %R4[31]>>31.

 "   eor     %Q4, %Q4, %R4, ASR #31\n"

 "   add     %0, %Q4, %R4, LSR #31\n"

 "   b       9f\n"

 "8:\n"

     // +/-INFINITY, +/-0, subnormals, NaNs, and anything else out-of-range that

     // will result in a conversion of '0'.

 "   mov     %0, #0\n"

 "9:\n"

     : "=r" (i), "=&r" (tmp0), "=&r" (tmp1), "=&r" (tmp2), "=&r" (d)

     : "4" (d)

     : "cc"

         );

     return i;

 #else

     return detail::ToIntWidth<int32_t>(d);

 #endif

 }

 /* ES5 9.6 (specialized for doubles). */

 inline uint32_t

 ToUint32(double d)

 {

     return detail::ToUintWidth<uint32_t>(d);

 }

 /* WEBIDL 4.2.10 */

 inline int64_t

 ToInt64(double d)

 {

     return detail::ToIntWidth<int64_t>(d);

 }

 /* WEBIDL 4.2.11 */

 inline uint64_t

 ToUint64(double d)

 {

     return detail::ToUintWidth<uint64_t>(d);

 }

 /* ES5 9.4 ToInteger (specialized for doubles). */

 inline double

 ToInteger(double d)

 {

     if (d == 0)

         return d;

     if (!mozilla::IsFinite(d)) {

         if (mozilla::IsNaN(d))

             return 0;

         return d;

     }

     return d < 0 ? ceil(d) : floor(d);

 }

 } /* namespace js */

 #endif /* vm_NumericConversions_h */