MathCommon.h   [plain text]


/*
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#pragma once

#include <cmath>
#include <wtf/Optional.h>

namespace JSC {

const int32_t maxExponentForIntegerMathPow = 1000;
double JIT_OPERATION operationMathPow(double x, double y) WTF_INTERNAL;
int32_t JIT_OPERATION operationToInt32(double) WTF_INTERNAL;
int32_t JIT_OPERATION operationToInt32SensibleSlow(double) WTF_INTERNAL;

inline constexpr double maxSafeInteger()
{
    // 2 ^ 53 - 1
    return 9007199254740991.0;
}

inline constexpr double minSafeInteger()
{
    // -(2 ^ 53 - 1)
    return -9007199254740991.0;
}

// This in the ToInt32 operation is defined in section 9.5 of the ECMA-262 spec.
// Note that this operation is identical to ToUInt32 other than to interpretation
// of the resulting bit-pattern (as such this method is also called to implement
// ToUInt32).
//
// The operation can be described as round towards zero, then select the 32 least
// bits of the resulting value in 2s-complement representation.
enum ToInt32Mode {
    Generic,
    AfterSensibleConversionAttempt,
};
template<ToInt32Mode Mode>
ALWAYS_INLINE int32_t toInt32Internal(double number)
{
    uint64_t bits = WTF::bitwise_cast<uint64_t>(number);
    int32_t exp = (static_cast<int32_t>(bits >> 52) & 0x7ff) - 0x3ff;

    // If exponent < 0 there will be no bits to the left of the decimal point
    // after rounding; if the exponent is > 83 then no bits of precision can be
    // left in the low 32-bit range of the result (IEEE-754 doubles have 52 bits
    // of fractional precision).
    // Note this case handles 0, -0, and all infinite, NaN, & denormal value.

    // We need to check exp > 83 because:
    // 1. exp may be used as a left shift value below in (exp - 52), and
    // 2. Left shift amounts that exceed 31 results in undefined behavior. See:
    //    http://en.cppreference.com/w/cpp/language/operator_arithmetic#Bitwise_shift_operators
    //
    // Using an unsigned comparison here also gives us a exp < 0 check for free.
    if (static_cast<uint32_t>(exp) > 83u)
        return 0;

    // Select the appropriate 32-bits from the floating point mantissa. If the
    // exponent is 52 then the bits we need to select are already aligned to the
    // lowest bits of the 64-bit integer representation of the number, no need
    // to shift. If the exponent is greater than 52 we need to shift the value
    // left by (exp - 52), if the value is less than 52 we need to shift right
    // accordingly.
    uint32_t result = (exp > 52)
        ? static_cast<uint32_t>(bits << (exp - 52))
        : static_cast<uint32_t>(bits >> (52 - exp));

    // IEEE-754 double precision values are stored omitting an implicit 1 before
    // the decimal point; we need to reinsert this now. We may also the shifted
    // invalid bits into the result that are not a part of the mantissa (the sign
    // and exponent bits from the floatingpoint representation); mask these out.
    // Note that missingOne should be held as uint32_t since ((1 << 31) - 1) causes
    // int32_t overflow.
    if (Mode == ToInt32Mode::AfterSensibleConversionAttempt) {
        if (exp == 31) {
            // This is an optimization for when toInt32() is called in the slow path
            // of a JIT operation. Currently, this optimization is only applicable for
            // x86 ports. This optimization offers 5% performance improvement in
            // kraken-crypto-pbkdf2.
            //
            // On x86, the fast path does a sensible double-to-int32 conversion, by
            // first attempting to truncate the double value to int32 using the
            // cvttsd2si_rr instruction. According to Intel's manual, cvttsd2si performs
            // the following truncate operation:
            //
            //     If src = NaN, +-Inf, or |(src)rz| > 0x7fffffff and (src)rz != 0x80000000,
            //     then the result becomes 0x80000000. Otherwise, the operation succeeds.
            //
            // Note that the ()rz notation means rounding towards zero.
            // We'll call the slow case function only when the above cvttsd2si fails. The
            // JIT code checks for fast path failure by checking if result == 0x80000000.
            // Hence, the slow path will only see the following possible set of numbers:
            //
            //     NaN, +-Inf, or |(src)rz| > 0x7fffffff.
            //
            // As a result, the exp of the double is always >= 31. We can take advantage
            // of this by specifically checking for (exp == 31) and give the compiler a
            // chance to constant fold the operations below.
            const constexpr uint32_t missingOne = 1U << 31;
            result &= missingOne - 1;
            result += missingOne;
        }
    } else {
        if (exp < 32) {
            const uint32_t missingOne = 1U << exp;
            result &= missingOne - 1;
            result += missingOne;
        }
    }

    // If the input value was negative (we could test either 'number' or 'bits',
    // but testing 'bits' is likely faster) invert the result appropriately.
    return static_cast<int64_t>(bits) < 0 ? -static_cast<int32_t>(result) : static_cast<int32_t>(result);
}

ALWAYS_INLINE int32_t toInt32(double number)
{
    return toInt32Internal<ToInt32Mode::Generic>(number);
}

// This implements ToUInt32, defined in ECMA-262 9.6.
inline uint32_t toUInt32(double number)
{
    // As commented in the spec, the operation of ToInt32 and ToUint32 only differ
    // in how the result is interpreted; see NOTEs in sections 9.5 and 9.6.
    return toInt32(number);
}

inline std::optional<double> safeReciprocalForDivByConst(double constant)
{
    // No "weird" numbers (NaN, Denormal, etc).
    if (!constant || !std::isnormal(constant))
        return std::nullopt;

    int exponent;
    if (std::frexp(constant, &exponent) != 0.5)
        return std::nullopt;

    // Note that frexp() returns the value divided by two
    // so we to offset this exponent by one.
    exponent -= 1;

    // A double exponent is between -1022 and 1023.
    // Nothing we can do to invert 1023.
    if (exponent == 1023)
        return std::nullopt;

    double reciprocal = std::ldexp(1, -exponent);
    ASSERT(std::isnormal(reciprocal));
    ASSERT(1. / constant == reciprocal);
    ASSERT(constant == 1. / reciprocal);
    ASSERT(1. == constant * reciprocal);

    return reciprocal;
}

extern "C" {
double JIT_OPERATION jsRound(double value) REFERENCED_FROM_ASM WTF_INTERNAL;

// On Windows we need to wrap fmod; on other platforms we can call it directly.
// On ARMv7 we assert that all function pointers have to low bit set (point to thumb code).
#if CALLING_CONVENTION_IS_STDCALL || CPU(ARM_THUMB2)
double JIT_OPERATION jsMod(double x, double y) REFERENCED_FROM_ASM WTF_INTERNAL;
#else
#define jsMod fmod
#endif
}

namespace Math {

using std::sin;
using std::sinh;
using std::cos;
using std::cosh;
using std::tan;
using std::tanh;
using std::asin;
using std::asinh;
using std::acos;
using std::acosh;
using std::atan;
using std::atanh;
using std::log;
using std::log10;
using std::log2;
using std::cbrt;
using std::exp;
using std::expm1;

double JIT_OPERATION log1p(double) WTF_INTERNAL;

} // namespace Math
} // namespace JSC