Index: src/base/ieee754.cc |
diff --git a/src/base/ieee754.cc b/src/base/ieee754.cc |
new file mode 100644 |
index 0000000000000000000000000000000000000000..59d83f0dae1f907ae228b7728955c8db7e03eeab |
--- /dev/null |
+++ b/src/base/ieee754.cc |
@@ -0,0 +1,197 @@ |
+// The following is adapted from fdlibm (http://www.netlib.org/fdlibm). |
+// |
+// ==================================================== |
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
+// |
+// Developed at SunSoft, a Sun Microsystems, Inc. business. |
+// Permission to use, copy, modify, and distribute this |
+// software is freely granted, provided that this notice |
+// is preserved. |
+// ==================================================== |
+// |
+// The original source code covered by the above license above has been |
+// modified significantly by Google Inc. |
+// Copyright 2016 the V8 project authors. All rights reserved. |
+ |
+#include "src/base/ieee754.h" |
+ |
+#include <limits> |
+ |
+#include "src/base/build_config.h" |
+#include "src/base/macros.h" |
+ |
+namespace v8 { |
+namespace base { |
+namespace ieee754 { |
+ |
+namespace { |
+ |
+union Float64 { |
+ double v; |
+ uint64_t w; |
+ struct { |
+#if V8_TARGET_LITTLE_ENDIAN |
+ uint32_t lw; |
+ uint32_t hw; |
+#else |
+ uint32_t hw; |
+ uint32_t lw; |
+#endif |
+ } words; |
+}; |
+ |
+// Extract the less significant 32-bit word from a double. |
+V8_INLINE uint32_t extractLowWord32(double v) { |
+ Float64 f; |
+ f.v = v; |
+ return f.words.lw; |
+} |
+ |
+// Extract the most significant 32-bit word from a double. |
+V8_INLINE uint32_t extractHighWord32(double v) { |
+ Float64 f; |
+ f.v = v; |
+ return f.words.hw; |
+} |
+ |
+// Insert the most significant 32-bit word into a double. |
+V8_INLINE double insertHighWord32(double v, uint32_t hw) { |
+ Float64 f; |
+ f.v = v; |
+ f.words.hw = hw; |
+ return f.v; |
+} |
+ |
+double const kLn2Hi = 6.93147180369123816490e-01; // 3fe62e42 fee00000 |
+double const kLn2Lo = 1.90821492927058770002e-10; // 3dea39ef 35793c76 |
+double const kTwo54 = 1.80143985094819840000e+16; // 43500000 00000000 |
+double const kLg1 = 6.666666666666735130e-01; // 3FE55555 55555593 |
+double const kLg2 = 3.999999999940941908e-01; // 3FD99999 9997FA04 |
+double const kLg3 = 2.857142874366239149e-01; // 3FD24924 94229359 |
+double const kLg4 = 2.222219843214978396e-01; // 3FCC71C5 1D8E78AF |
+double const kLg5 = 1.818357216161805012e-01; // 3FC74664 96CB03DE |
+double const kLg6 = 1.531383769920937332e-01; // 3FC39A09 D078C69F |
+double const kLg7 = 1.479819860511658591e-01; // 3FC2F112 DF3E5244 |
+ |
+} // namespace |
+ |
+/* log(x) |
+ * Return the logrithm of x |
+ * |
+ * Method : |
+ * 1. Argument Reduction: find k and f such that |
+ * x = 2^k * (1+f), |
+ * where sqrt(2)/2 < 1+f < sqrt(2) . |
+ * |
+ * 2. Approximation of log(1+f). |
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) |
+ * = 2s + 2/3 s**3 + 2/5 s**5 + ....., |
+ * = 2s + s*R |
+ * We use a special Reme algorithm on [0,0.1716] to generate |
+ * a polynomial of degree 14 to approximate R The maximum error |
+ * of this polynomial approximation is bounded by 2**-58.45. In |
+ * other words, |
+ * 2 4 6 8 10 12 14 |
+ * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s |
+ * (the values of Lg1 to Lg7 are listed in the program) |
+ * and |
+ * | 2 14 | -58.45 |
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2 |
+ * | | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. |
+ * In order to guarantee error in log below 1ulp, we compute log |
+ * by |
+ * log(1+f) = f - s*(f - R) (if f is not too large) |
+ * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) |
+ * |
+ * 3. Finally, log(x) = k*ln2 + log(1+f). |
+ * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) |
+ * Here ln2 is split into two floating point number: |
+ * ln2_hi + ln2_lo, |
+ * where n*ln2_hi is always exact for |n| < 2000. |
+ * |
+ * Special cases: |
+ * log(x) is NaN with signal if x < 0 (including -INF) ; |
+ * log(+INF) is +INF; log(0) is -INF with signal; |
+ * log(NaN) is that NaN with no signal. |
+ * |
+ * Accuracy: |
+ * according to an error analysis, the error is always less than |
+ * 1 ulp (unit in the last place). |
+ * |
+ * Constants: |
+ * The hexadecimal values are the intended ones for the following |
+ * constants. The decimal values may be used, provided that the |
+ * compiler will convert from decimal to binary accurately enough |
+ * to produce the hexadecimal values shown. |
+ */ |
+double log(double x) { |
+ double hfsq, f, s, z, r, w, t1, t2, dk; |
+ int32_t k = 0, i, j; |
+ int32_t hx = extractHighWord32(x); |
+ uint32_t lx = extractLowWord32(x); |
+ |
+ if (hx < 0x00100000) { /* x < 2**-1022 */ |
+ if (((hx & 0x7fffffff) | lx) == 0) { |
+ return -std::numeric_limits<double>::infinity(); |
+ } |
+ if (hx < 0) { |
+ return std::numeric_limits<double>::quiet_NaN(); |
+ } |
+ k -= 54; |
+ x *= kTwo54; /* subnormal number, scale up x */ |
+ hx = extractHighWord32(x); |
+ } |
+ if (hx >= 0x7ff00000) return x + x; |
+ k += (hx >> 20) - 1023; |
+ hx &= 0x000fffff; |
+ i = (hx + 0x95f64) & 0x100000; |
+ x = insertHighWord32(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ |
+ k += (i >> 20); |
+ f = x - 1.0; |
+ if ((0x000fffff & (2 + hx)) < 3) { /* -2**-20 <= f < 2**-20 */ |
+ if (f == 0.0) { |
+ if (k == 0) { |
+ return 0.0; |
+ } else { |
+ dk = static_cast<double>(k); |
+ return dk * kLn2Hi + dk * kLn2Lo; |
+ } |
+ } |
+ r = f * f * (0.5 - 0.33333333333333333 * f); |
+ if (k == 0) { |
+ return f - r; |
+ } else { |
+ dk = static_cast<double>(k); |
+ return dk * kLn2Hi - ((r - dk * kLn2Lo) - f); |
+ } |
+ } |
+ s = f / (2.0 + f); |
+ dk = static_cast<double>(k); |
+ z = s * s; |
+ i = hx - 0x6147a; |
+ w = z * z; |
+ j = 0x6b851 - hx; |
+ t1 = w * (kLg2 + w * (kLg4 + w * kLg6)); |
+ t2 = z * (kLg1 + w * (kLg3 + w * (kLg5 + w * kLg7))); |
+ i |= j; |
+ r = t2 + t1; |
+ if (i > 0) { |
+ hfsq = 0.5 * f * f; |
+ if (k == 0) { |
+ return f - (hfsq - s * (hfsq + r)); |
+ } else { |
+ return dk * kLn2Hi - ((hfsq - (s * (hfsq + r) + dk * kLn2Lo)) - f); |
+ } |
+ } else { |
+ if (k == 0) { |
+ return f - s * (f - r); |
+ } else { |
+ return dk * kLn2Hi - ((s * (f - r) - dk * kLn2Lo) - f); |
+ } |
+ } |
+} |
+ |
+} // namespace ieee754 |
+} // namespace base |
+} // namespace v8 |