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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>
/* A NaN whose bit pattern conforms to JS::Value's bit pattern restrictions. */
extern double js_NaN;
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)
{
MOZ_STATIC_ASSERT(mozilla::IsUnsigned<ResultType>::value,
"ResultType must be an unsigned type");
uint64_t bits = mozilla::BitwiseCast<uint64_t>(d);
// 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::DoubleExponentBits) >> mozilla::DoubleExponentShift) -
int_fast16_t(mozilla::DoubleExponentBias);
// 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 >= mozilla::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)).
MOZ_STATIC_ASSERT(sizeof(ResultType) <= sizeof(uint64_t),
"Left-shifting below would lose upper bits");
ResultType result = (exponent > mozilla::DoubleExponentShift)
? ResultType(bits << (exponent - mozilla::DoubleExponentShift))
: ResultType(bits >> (mozilla::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::DoubleSignBit) ? ~result + 1 : result;
}
template<typename ResultType>
inline ResultType
ToIntWidth(double d)
{
MOZ_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(__ANDROID__) && defined(__clang__)
#define ANDROID_CLANG 1
#endif
#if defined (__arm__) && defined (__GNUC__) && !defined(ANDROID_CLANG)
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
#undef ANDROID_CLANG
}
/* 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;
}
bool neg = (d < 0);
d = floor(neg ? -d : d);
return neg ? -d : d;
}
} /* namespace js */
#endif /* vm_NumericConversions_h */