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; |
} |
} |