[builtins] stop using imprecise fdlibm pow
This CL reinstates the old pow implementation which calls out to the system implementation of pow. Bug: v8:9622 Change-Id: I3df997888ced3fb8b5bd4b810098e967649aaa55 Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/1774898 Reviewed-by: Hannes Payer <hpayer@chromium.org> Reviewed-by: Georg Neis <neis@chromium.org> Commit-Queue: Georg Neis <neis@chromium.org> Cr-Commit-Position: refs/heads/master@{#66303}
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Gus Caplan
Commit Bot
parent
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commit
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@ -2587,314 +2587,38 @@ double cosh(double x) {
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}
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/*
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* ES2019 Draft 2019-01-02 12.6.4
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* Math.pow & Exponentiation Operator
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*
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* Return X raised to the Yth power
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*
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* Method:
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* Let x = 2 * (1+f)
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* 1. Compute and return log2(x) in two pieces:
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* log2(x) = w1 + w2,
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* where w1 has 53-24 = 29 bit trailing zeros.
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* 2. Perform y*log2(x) = n+y' by simulating muti-precision
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* arithmetic, where |y'|<=0.5.
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* 3. Return x**y = 2**n*exp(y'*log2)
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*
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* Special cases:
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* 1. (anything) ** 0 is 1
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* 2. (anything) ** 1 is itself
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* 3. (anything) ** NAN is NAN
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* 4. NAN ** (anything except 0) is NAN
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* 5. +-(|x| > 1) ** +INF is +INF
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* 6. +-(|x| > 1) ** -INF is +0
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* 7. +-(|x| < 1) ** +INF is +0
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* 8. +-(|x| < 1) ** -INF is +INF
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* 9. +-1 ** +-INF is NAN
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* 10. +0 ** (+anything except 0, NAN) is +0
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* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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* 12. +0 ** (-anything except 0, NAN) is +INF
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* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
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* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
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* 15. +INF ** (+anything except 0,NAN) is +INF
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* 16. +INF ** (-anything except 0,NAN) is +0
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* 17. -INF ** (anything) = -0 ** (-anything)
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* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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* 19. (-anything except 0 and inf) ** (non-integer) is NAN
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*
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* Accuracy:
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* pow(x,y) returns x**y nearly rounded. In particular,
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* pow(integer, integer) always returns the correct integer provided it is
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* representable.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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* ES2020 draft 08-18-2019, section 12.6.4
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* Math.pow, **
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*/
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double pow(double x, double y) {
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static const double
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bp[] = {1.0, 1.5},
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dp_h[] = {0.0, 5.84962487220764160156e-01}, // 0x3FE2B803, 0x40000000
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dp_l[] = {0.0, 1.35003920212974897128e-08}, // 0x3E4CFDEB, 0x43CFD006
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zero = 0.0, one = 1.0, two = 2.0,
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two53 = 9007199254740992.0, // 0x43400000, 0x00000000
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huge = 1.0e300, tiny = 1.0e-300,
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// poly coefs for (3/2)*(log(x)-2s-2/3*s**3
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L1 = 5.99999999999994648725e-01, // 0x3FE33333, 0x33333303
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L2 = 4.28571428578550184252e-01, // 0x3FDB6DB6, 0xDB6FABFF
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L3 = 3.33333329818377432918e-01, // 0x3FD55555, 0x518F264D
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L4 = 2.72728123808534006489e-01, // 0x3FD17460, 0xA91D4101
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L5 = 2.30660745775561754067e-01, // 0x3FCD864A, 0x93C9DB65
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L6 = 2.06975017800338417784e-01, // 0x3FCA7E28, 0x4A454EEF
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P1 = 1.66666666666666019037e-01, // 0x3FC55555, 0x5555553E
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P2 = -2.77777777770155933842e-03, // 0xBF66C16C, 0x16BEBD93
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P3 = 6.61375632143793436117e-05, // 0x3F11566A, 0xAF25DE2C
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P4 = -1.65339022054652515390e-06, // 0xBEBBBD41, 0xC5D26BF1
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P5 = 4.13813679705723846039e-08, // 0x3E663769, 0x72BEA4D0
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lg2 = 6.93147180559945286227e-01, // 0x3FE62E42, 0xFEFA39EF
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lg2_h = 6.93147182464599609375e-01, // 0x3FE62E43, 0x00000000
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lg2_l = -1.90465429995776804525e-09, // 0xBE205C61, 0x0CA86C39
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ovt = 8.0085662595372944372e-0017, // -(1024-log2(ovfl+.5ulp))
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cp = 9.61796693925975554329e-01, // 0x3FEEC709, 0xDC3A03FD =2/(3ln2)
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cp_h = 9.61796700954437255859e-01, // 0x3FEEC709, 0xE0000000 =(float)cp
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cp_l = -7.02846165095275826516e-09, // 0xBE3E2FE0, 0x145B01F5 =tail cp_h
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ivln2 = 1.44269504088896338700e+00, // 0x3FF71547, 0x652B82FE =1/ln2
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ivln2_h =
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1.44269502162933349609e+00, // 0x3FF71547, 0x60000000 =24b 1/ln2
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ivln2_l =
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1.92596299112661746887e-08; // 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail
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double z, ax, z_h, z_l, p_h, p_l;
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double y1, t1, t2, r, s, t, u, v, w;
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int i, j, k, yisint, n;
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int hx, hy, ix, iy;
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unsigned lx, ly;
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EXTRACT_WORDS(hx, lx, x);
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EXTRACT_WORDS(hy, ly, y);
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ix = hx & 0x7fffffff;
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iy = hy & 0x7fffffff;
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/* y==zero: x**0 = 1 */
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if ((iy | ly) == 0) return one;
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/* +-NaN return x+y */
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if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 ||
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((iy == 0x7ff00000) && (ly != 0))) {
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return x + y;
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if (y == 0.0) {
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return 1.0;
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}
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if (std::isnan(y) || ((x == 1 || x == -1) && std::isinf(y))) {
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return std::numeric_limits<double>::quiet_NaN();
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}
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#if (defined(__MINGW64_VERSION_MAJOR) && \
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(!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1)) || \
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defined(V8_OS_AIX)
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// MinGW64 and AIX have a custom implementation for pow. This handles certain
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// special cases that are different.
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if ((x == 0.0 || std::isinf(x)) && y != 0.0 && std::isfinite(y)) {
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double f;
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double result = ((x == 0.0) ^ (y > 0)) ? V8_INFINITY : 0;
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// retain sign if odd integer exponent
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return ((std::modf(y, &f) == 0.0) && (static_cast<int64_t>(y) & 1))
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? copysign(result, x)
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: result;
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}
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/* determine if y is an odd int when x < 0
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* yisint = 0 ... y is not an integer
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* yisint = 1 ... y is an odd int
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* yisint = 2 ... y is an even int
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*/
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yisint = 0;
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if (hx < 0) {
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if (iy >= 0x43400000) {
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yisint = 2; /* even integer y */
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} else if (iy >= 0x3ff00000) {
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k = (iy >> 20) - 0x3ff; /* exponent */
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if (k > 20) {
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j = ly >> (52 - k);
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if ((j << (52 - k)) == static_cast<int>(ly)) yisint = 2 - (j & 1);
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} else if (ly == 0) {
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j = iy >> (20 - k);
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if ((j << (20 - k)) == iy) yisint = 2 - (j & 1);
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if (x == 2.0) {
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int y_int = static_cast<int>(y);
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if (y == y_int) {
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return std::ldexp(1.0, y_int);
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}
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}
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}
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/* special value of y */
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if (ly == 0) {
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if (iy == 0x7ff00000) { /* y is +-inf */
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if (((ix - 0x3ff00000) | lx) == 0) {
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return y - y; /* inf**+-1 is NaN */
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} else if (ix >= 0x3ff00000) { /* (|x|>1)**+-inf = inf,0 */
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return (hy >= 0) ? y : zero;
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} else { /* (|x|<1)**-,+inf = inf,0 */
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return (hy < 0) ? -y : zero;
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}
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}
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if (iy == 0x3ff00000) { /* y is +-1 */
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if (hy < 0) {
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return base::Divide(one, x);
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} else {
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return x;
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}
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}
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if (hy == 0x40000000) return x * x; /* y is 2 */
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if (hy == 0x3fe00000) { /* y is 0.5 */
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if (hx >= 0) { /* x >= +0 */
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return sqrt(x);
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}
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}
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}
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ax = fabs(x);
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/* special value of x */
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if (lx == 0) {
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if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
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z = ax; /*x is +-0,+-inf,+-1*/
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if (hy < 0) z = base::Divide(one, z); /* z = (1/|x|) */
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if (hx < 0) {
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if (((ix - 0x3ff00000) | yisint) == 0) {
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/* (-1)**non-int is NaN */
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z = std::numeric_limits<double>::signaling_NaN();
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} else if (yisint == 1) {
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z = -z; /* (x<0)**odd = -(|x|**odd) */
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}
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}
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return z;
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}
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}
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n = (hx >> 31) + 1;
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/* (x<0)**(non-int) is NaN */
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if ((n | yisint) == 0) {
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return std::numeric_limits<double>::signaling_NaN();
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}
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s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
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if ((n | (yisint - 1)) == 0) s = -one; /* (-ve)**(odd int) */
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/* |y| is huge */
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if (iy > 0x41e00000) { /* if |y| > 2**31 */
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if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
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if (ix <= 0x3fefffff) return (hy < 0) ? huge * huge : tiny * tiny;
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if (ix >= 0x3ff00000) return (hy > 0) ? huge * huge : tiny * tiny;
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}
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/* over/underflow if x is not close to one */
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if (ix < 0x3fefffff) return (hy < 0) ? s * huge * huge : s * tiny * tiny;
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if (ix > 0x3ff00000) return (hy > 0) ? s * huge * huge : s * tiny * tiny;
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/* now |1-x| is tiny <= 2**-20, suffice to compute
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log(x) by x-x^2/2+x^3/3-x^4/4 */
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t = ax - one; /* t has 20 trailing zeros */
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w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
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u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
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v = t * ivln2_l - w * ivln2;
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t1 = u + v;
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SET_LOW_WORD(t1, 0);
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t2 = v - (t1 - u);
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} else {
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double ss, s2, s_h, s_l, t_h, t_l;
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n = 0;
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/* take care subnormal number */
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if (ix < 0x00100000) {
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ax *= two53;
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n -= 53;
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GET_HIGH_WORD(ix, ax);
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}
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n += ((ix) >> 20) - 0x3ff;
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j = ix & 0x000fffff;
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/* determine interval */
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ix = j | 0x3ff00000; /* normalize ix */
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if (j <= 0x3988E) {
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k = 0; /* |x|<sqrt(3/2) */
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} else if (j < 0xBB67A) {
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k = 1; /* |x|<sqrt(3) */
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} else {
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k = 0;
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n += 1;
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ix -= 0x00100000;
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}
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SET_HIGH_WORD(ax, ix);
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/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
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v = base::Divide(one, ax + bp[k]);
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ss = u * v;
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s_h = ss;
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SET_LOW_WORD(s_h, 0);
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/* t_h=ax+bp[k] High */
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t_h = zero;
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SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
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t_l = ax - (t_h - bp[k]);
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s_l = v * ((u - s_h * t_h) - s_h * t_l);
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/* compute log(ax) */
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s2 = ss * ss;
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r = s2 * s2 *
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(L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
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r += s_l * (s_h + ss);
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s2 = s_h * s_h;
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t_h = 3.0 + s2 + r;
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SET_LOW_WORD(t_h, 0);
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t_l = r - ((t_h - 3.0) - s2);
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/* u+v = ss*(1+...) */
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u = s_h * t_h;
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v = s_l * t_h + t_l * ss;
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/* 2/(3log2)*(ss+...) */
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p_h = u + v;
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SET_LOW_WORD(p_h, 0);
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p_l = v - (p_h - u);
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z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
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z_l = cp_l * p_h + p_l * cp + dp_l[k];
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/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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t = static_cast<double>(n);
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t1 = (((z_h + z_l) + dp_h[k]) + t);
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SET_LOW_WORD(t1, 0);
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t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
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}
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/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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y1 = y;
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SET_LOW_WORD(y1, 0);
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p_l = (y - y1) * t1 + y * t2;
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p_h = y1 * t1;
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z = p_l + p_h;
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EXTRACT_WORDS(j, i, z);
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if (j >= 0x40900000) { /* z >= 1024 */
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if (((j - 0x40900000) | i) != 0) { /* if z > 1024 */
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return s * huge * huge; /* overflow */
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} else {
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if (p_l + ovt > z - p_h) return s * huge * huge; /* overflow */
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}
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} else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
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if (((j - 0xc090cc00) | i) != 0) { /* z < -1075 */
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return s * tiny * tiny; /* underflow */
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} else {
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if (p_l <= z - p_h) return s * tiny * tiny; /* underflow */
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}
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}
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/*
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* compute 2**(p_h+p_l)
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*/
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i = j & 0x7fffffff;
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k = (i >> 20) - 0x3ff;
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n = 0;
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if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
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n = j + (0x00100000 >> (k + 1));
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k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
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t = zero;
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SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
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n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
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if (j < 0) n = -n;
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p_h -= t;
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}
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t = p_l + p_h;
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SET_LOW_WORD(t, 0);
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u = t * lg2_h;
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v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
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z = u + v;
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w = v - (z - u);
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t = z * z;
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t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
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r = base::Divide(z * t1, (t1 - two) - (w + z * w));
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z = one - (r - z);
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GET_HIGH_WORD(j, z);
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j += static_cast<int>(static_cast<uint32_t>(n) << 20);
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if ((j >> 20) <= 0) {
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z = scalbn(z, n); /* subnormal output */
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} else {
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int tmp;
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GET_HIGH_WORD(tmp, z);
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SET_HIGH_WORD(z, tmp + static_cast<int>(static_cast<uint32_t>(n) << 20));
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}
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return s * z;
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#endif
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return std::pow(x, y);
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}
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/*
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25
test/mjsunit/regress/regress-9622.js
Normal file
25
test/mjsunit/regress/regress-9622.js
Normal file
@ -0,0 +1,25 @@
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// Copyright 2019 the V8 project authors. All rights reserved.
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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'use strict';
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assertEquals(0.6840442338072671 ** 2.4, 0.4019777798321958);
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const constants = {
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'0': 1,
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'-1': 0.1,
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'-2': 0.01,
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'-3': 0.001,
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'-4': 0.0001,
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'-5': 0.00001,
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'-6': 0.000001,
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'-7': 0.0000001,
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'-8': 0.00000001,
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'-9': 0.000000001,
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};
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|
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for (let i = 0; i > -10; i -= 1) {
|
||||
assertEquals(10 ** i, constants[i]);
|
||||
assertEquals(10 ** i, 1 / (10 ** -i));
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user