[ieee754] Import ANSIfied msun log from FreeBSD.
Instead of manually adopting the ancient fdlibm sources, import the msun versions from FreeBSD instead, which were already adopted to ANSI C. Still under the same copyright. R=yangguo@chromium.org BUG=v8:5065,v8:5086 Review-Url: https://codereview.chromium.org/2065473002 Cr-Commit-Position: refs/heads/master@{#36913}
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@ -26,52 +26,142 @@ namespace ieee754 {
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namespace {
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union Float64 {
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double v;
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uint64_t w;
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struct {
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#if V8_TARGET_LITTLE_ENDIAN
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uint32_t lw;
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uint32_t hw;
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#else
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uint32_t hw;
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uint32_t lw;
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/* Fix-up typedefs so we can use the FreeBSD msun code mostly unmodified. */
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#if V8_OS_WIN
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typedef uint32_t u_int32_t;
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typedef uint64_t u_int64_t;
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#endif
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} words;
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};
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// Extract the less significant 32-bit word from a double.
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V8_INLINE uint32_t extractLowWord32(double v) {
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Float64 f;
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f.v = v;
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return f.words.lw;
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}
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/* Disable "potential divide by 0" warning in Visual Studio compiler. */
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// Extract the most significant 32-bit word from a double.
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V8_INLINE uint32_t extractHighWord32(double v) {
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Float64 f;
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f.v = v;
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return f.words.hw;
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}
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#if V8_CC_MSVC
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// Insert the most significant 32-bit word into a double.
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V8_INLINE double insertHighWord32(double v, uint32_t hw) {
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Float64 f;
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f.v = v;
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f.words.hw = hw;
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return f.v;
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}
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#pragma warning(disable : 4723)
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double const kLn2Hi = 6.93147180369123816490e-01; // 3fe62e42 fee00000
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double const kLn2Lo = 1.90821492927058770002e-10; // 3dea39ef 35793c76
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double const kTwo54 = 1.80143985094819840000e+16; // 43500000 00000000
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double const kLg1 = 6.666666666666735130e-01; // 3FE55555 55555593
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double const kLg2 = 3.999999999940941908e-01; // 3FD99999 9997FA04
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double const kLg3 = 2.857142874366239149e-01; // 3FD24924 94229359
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double const kLg4 = 2.222219843214978396e-01; // 3FCC71C5 1D8E78AF
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double const kLg5 = 1.818357216161805012e-01; // 3FC74664 96CB03DE
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double const kLg6 = 1.531383769920937332e-01; // 3FC39A09 D078C69F
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double const kLg7 = 1.479819860511658591e-01; // 3FC2F112 DF3E5244
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#endif
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/*
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* The original fdlibm code used statements like:
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* n0 = ((*(int*)&one)>>29)^1; * index of high word *
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* ix0 = *(n0+(int*)&x); * high word of x *
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* ix1 = *((1-n0)+(int*)&x); * low word of x *
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* to dig two 32 bit words out of the 64 bit IEEE floating point
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* value. That is non-ANSI, and, moreover, the gcc instruction
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* scheduler gets it wrong. We instead use the following macros.
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* Unlike the original code, we determine the endianness at compile
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* time, not at run time; I don't see much benefit to selecting
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* endianness at run time.
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*/
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/*
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* A union which permits us to convert between a double and two 32 bit
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* ints.
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*/
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#if V8_TARGET_LITTLE_ENDIAN
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typedef union {
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double value;
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struct {
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u_int32_t lsw;
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u_int32_t msw;
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} parts;
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struct {
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u_int64_t w;
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} xparts;
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} ieee_double_shape_type;
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#else
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typedef union {
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double value;
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struct {
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u_int32_t msw;
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u_int32_t lsw;
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} parts;
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struct {
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u_int64_t w;
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} xparts;
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} ieee_double_shape_type;
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#endif
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/* Get two 32 bit ints from a double. */
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#define EXTRACT_WORDS(ix0, ix1, d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} while (0)
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/* Get a 64-bit int from a double. */
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#define EXTRACT_WORD64(ix, d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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(ix) = ew_u.xparts.w; \
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} while (0)
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/* Get the more significant 32 bit int from a double. */
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#define GET_HIGH_WORD(i, d) \
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do { \
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ieee_double_shape_type gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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} while (0)
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/* Get the less significant 32 bit int from a double. */
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#define GET_LOW_WORD(i, d) \
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do { \
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ieee_double_shape_type gl_u; \
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gl_u.value = (d); \
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(i) = gl_u.parts.lsw; \
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} while (0)
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/* Set a double from two 32 bit ints. */
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#define INSERT_WORDS(d, ix0, ix1) \
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do { \
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ieee_double_shape_type iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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} while (0)
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/* Set a double from a 64-bit int. */
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#define INSERT_WORD64(d, ix) \
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do { \
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ieee_double_shape_type iw_u; \
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iw_u.xparts.w = (ix); \
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(d) = iw_u.value; \
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} while (0)
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/* Set the more significant 32 bits of a double from an int. */
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#define SET_HIGH_WORD(d, v) \
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do { \
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ieee_double_shape_type sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Set the less significant 32 bits of a double from an int. */
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#define SET_LOW_WORD(d, v) \
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do { \
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ieee_double_shape_type sl_u; \
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sl_u.value = (d); \
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sl_u.parts.lsw = (v); \
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(d) = sl_u.value; \
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} while (0)
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} // namespace
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@ -126,44 +216,58 @@ double const kLg7 = 1.479819860511658591e-01; // 3FC2F112 DF3E5244
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* to produce the hexadecimal values shown.
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*/
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double log(double x) {
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double hfsq, f, s, z, r, w, t1, t2, dk;
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int32_t k = 0, i, j;
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int32_t hx = extractHighWord32(x);
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uint32_t lx = extractLowWord32(x);
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static const double /* -- */
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ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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static const double zero = 0.0;
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static volatile double vzero = 0.0;
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double hfsq, f, s, z, R, w, t1, t2, dk;
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int32_t k, hx, i, j;
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u_int32_t lx;
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EXTRACT_WORDS(hx, lx, x);
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k = 0;
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if (hx < 0x00100000) { /* x < 2**-1022 */
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if (((hx & 0x7fffffff) | lx) == 0) {
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return -std::numeric_limits<double>::infinity();
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}
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if (hx < 0) {
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return std::numeric_limits<double>::quiet_NaN();
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}
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if (((hx & 0x7fffffff) | lx) == 0)
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return -two54 / vzero; /* log(+-0)=-inf */
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if (hx < 0) return (x - x) / zero; /* log(-#) = NaN */
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k -= 54;
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x *= kTwo54; /* subnormal number, scale up x */
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hx = extractHighWord32(x);
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x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD(hx, x);
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}
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if (hx >= 0x7ff00000) return x + x;
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k += (hx >> 20) - 1023;
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hx &= 0x000fffff;
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i = (hx + 0x95f64) & 0x100000;
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x = insertHighWord32(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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k += (i >> 20);
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f = x - 1.0;
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if ((0x000fffff & (2 + hx)) < 3) { /* -2**-20 <= f < 2**-20 */
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if (f == 0.0) {
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if (f == zero) {
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if (k == 0) {
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return 0.0;
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return zero;
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} else {
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dk = static_cast<double>(k);
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return dk * kLn2Hi + dk * kLn2Lo;
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return dk * ln2_hi + dk * ln2_lo;
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}
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}
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r = f * f * (0.5 - 0.33333333333333333 * f);
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R = f * f * (0.5 - 0.33333333333333333 * f);
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if (k == 0) {
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return f - r;
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return f - R;
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} else {
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dk = static_cast<double>(k);
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return dk * kLn2Hi - ((r - dk * kLn2Lo) - f);
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return dk * ln2_hi - ((R - dk * ln2_lo) - f);
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}
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}
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s = f / (2.0 + f);
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@ -172,23 +276,21 @@ double log(double x) {
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i = hx - 0x6147a;
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w = z * z;
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j = 0x6b851 - hx;
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t1 = w * (kLg2 + w * (kLg4 + w * kLg6));
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t2 = z * (kLg1 + w * (kLg3 + w * (kLg5 + w * kLg7)));
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t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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i |= j;
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r = t2 + t1;
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R = t2 + t1;
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if (i > 0) {
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hfsq = 0.5 * f * f;
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if (k == 0) {
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return f - (hfsq - s * (hfsq + r));
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} else {
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return dk * kLn2Hi - ((hfsq - (s * (hfsq + r) + dk * kLn2Lo)) - f);
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}
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if (k == 0)
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return f - (hfsq - s * (hfsq + R));
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else
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return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - f);
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} else {
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if (k == 0) {
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return f - s * (f - r);
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} else {
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return dk * kLn2Hi - ((s * (f - r) - dk * kLn2Lo) - f);
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}
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if (k == 0)
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return f - s * (f - R);
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else
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return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
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}
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}
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