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Unified Diff: src/base/ieee754.cc

Issue 2070813002: Revert of [builtins] Introduce proper Float64Exp operator. (Closed) Base URL: https://chromium.googlesource.com/v8/v8.git@master
Patch Set: Created 4 years, 6 months ago
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Index: src/base/ieee754.cc
diff --git a/src/base/ieee754.cc b/src/base/ieee754.cc
index e642b6327a9b29360db3c09ebc0235b15b3c9f0e..4d11bdafe8b89e26a737a3c332f39fc7d6b45b0f 100644
--- a/src/base/ieee754.cc
+++ b/src/base/ieee754.cc
@@ -389,152 +389,6 @@
return pi - (z - pi_lo); /* atan(+,-) */
default: /* case 3 */
return (z - pi_lo) - pi; /* atan(-,-) */
- }
-}
-
-/* exp(x)
- * Returns the exponential of x.
- *
- * Method
- * 1. Argument reduction:
- * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
- * Given x, find r and integer k such that
- *
- * x = k*ln2 + r, |r| <= 0.5*ln2.
- *
- * Here r will be represented as r = hi-lo for better
- * accuracy.
- *
- * 2. Approximation of exp(r) by a special rational function on
- * the interval [0,0.34658]:
- * Write
- * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
- * We use a special Remes algorithm on [0,0.34658] to generate
- * a polynomial of degree 5 to approximate R. The maximum error
- * of this polynomial approximation is bounded by 2**-59. In
- * other words,
- * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
- * (where z=r*r, and the values of P1 to P5 are listed below)
- * and
- * | 5 | -59
- * | 2.0+P1*z+...+P5*z - R(z) | <= 2
- * | |
- * The computation of exp(r) thus becomes
- * 2*r
- * exp(r) = 1 + -------
- * R - r
- * r*R1(r)
- * = 1 + r + ----------- (for better accuracy)
- * 2 - R1(r)
- * where
- * 2 4 10
- * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
- *
- * 3. Scale back to obtain exp(x):
- * From step 1, we have
- * exp(x) = 2^k * exp(r)
- *
- * Special cases:
- * exp(INF) is INF, exp(NaN) is NaN;
- * exp(-INF) is 0, and
- * for finite argument, only exp(0)=1 is exact.
- *
- * Accuracy:
- * according to an error analysis, the error is always less than
- * 1 ulp (unit in the last place).
- *
- * Misc. info.
- * For IEEE double
- * if x > 7.09782712893383973096e+02 then exp(x) overflow
- * if x < -7.45133219101941108420e+02 then exp(x) underflow
- *
- * 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 exp(double x) {
- static const double
- one = 1.0,
- halF[2] = {0.5, -0.5},
- o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
- u_threshold = -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
- ln2HI[2] = {6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
- -6.93147180369123816490e-01}, /* 0xbfe62e42, 0xfee00000 */
- ln2LO[2] = {1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
- -1.90821492927058770002e-10}, /* 0xbdea39ef, 0x35793c76 */
- invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
- P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
- P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
- P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
- P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
- P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
-
- static volatile double
- huge = 1.0e+300,
- twom1000 = 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
- two1023 = 8.988465674311579539e307; /* 0x1p1023 */
-
- double y, hi = 0.0, lo = 0.0, c, t, twopk;
- int32_t k = 0, xsb;
- u_int32_t hx;
-
- GET_HIGH_WORD(hx, x);
- xsb = (hx >> 31) & 1; /* sign bit of x */
- hx &= 0x7fffffff; /* high word of |x| */
-
- /* filter out non-finite argument */
- if (hx >= 0x40862E42) { /* if |x|>=709.78... */
- if (hx >= 0x7ff00000) {
- u_int32_t lx;
- GET_LOW_WORD(lx, x);
- if (((hx & 0xfffff) | lx) != 0)
- return x + x; /* NaN */
- else
- return (xsb == 0) ? x : 0.0; /* exp(+-inf)={inf,0} */
- }
- if (x > o_threshold) return huge * huge; /* overflow */
- if (x < u_threshold) return twom1000 * twom1000; /* underflow */
- }
-
- /* argument reduction */
- if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
- if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
- hi = x - ln2HI[xsb];
- lo = ln2LO[xsb];
- k = 1 - xsb - xsb;
- } else {
- k = static_cast<int>(invln2 * x + halF[xsb]);
- t = k;
- hi = x - t * ln2HI[0]; /* t*ln2HI is exact here */
- lo = t * ln2LO[0];
- }
- STRICT_ASSIGN(double, x, hi - lo);
- } else if (hx < 0x3e300000) { /* when |x|<2**-28 */
- if (huge + x > one) return one + x; /* trigger inexact */
- } else {
- k = 0;
- }
-
- /* x is now in primary range */
- t = x * x;
- if (k >= -1021) {
- INSERT_WORDS(twopk, 0x3ff00000 + (k << 20), 0);
- } else {
- INSERT_WORDS(twopk, 0x3ff00000 + ((k + 1000) << 20), 0);
- }
- c = x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
- if (k == 0) {
- return one - ((x * c) / (c - 2.0) - x);
- } else {
- y = one - ((lo - (x * c) / (2.0 - c)) - hi);
- }
- if (k >= -1021) {
- if (k == 1024) return y * 2.0 * two1023;
- return y * twopk;
- } else {
- return y * twopk * twom1000;
}
}
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