diff -r 000000000000 -r 6474c204b198 js/src/vm/NumericConversions.h --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/js/src/vm/NumericConversions.h Wed Dec 31 06:09:35 2014 +0100 @@ -0,0 +1,298 @@ +/* -*- 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 + +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 + * + * but has been generalized to all integer widths. + */ +template +inline ResultType +ToUintWidth(double d) +{ + static_assert(mozilla::IsUnsigned::value, + "ResultType must be an unsigned type"); + + uint64_t bits = mozilla::BitwiseCast(d); + unsigned DoubleExponentShift = mozilla::FloatingPoint::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::ExponentBits) >> DoubleExponentShift) - + int_fast16_t(mozilla::FloatingPoint::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(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::SignBit) ? ~result + 1 : result; +} + +template +inline ResultType +ToIntWidth(double d) +{ + static_assert(mozilla::IsSigned::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::Type UnsignedResult; + UnsignedResult u = ToUintWidth(d); + if (u <= UnsignedResult(MaxValue)) + return static_cast(u); + return (MinValue + static_cast(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(d); +#endif +} + +/* ES5 9.6 (specialized for doubles). */ +inline uint32_t +ToUint32(double d) +{ + return detail::ToUintWidth(d); +} + +/* WEBIDL 4.2.10 */ +inline int64_t +ToInt64(double d) +{ + return detail::ToIntWidth(d); +} + +/* WEBIDL 4.2.11 */ +inline uint64_t +ToUint64(double d) +{ + return detail::ToUintWidth(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 */