ld80/s_expl.c:
* Update the evaluation of the polynomial. This allows the removal of the now unused variables t23 and t45. ld128/s_expl.c: * Update the evaluation of the polynomial and the intermediate result t. This update allows several numerical constants to be written as double rather than long double constants. Update the constants as appropriate. Obtained from: bde
This commit is contained in:
Steve Kargl
parent
199b8e343d
commit
31407861b8
@ -41,28 +41,48 @@ __FBSDID("$FreeBSD$");
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#define LOG2_INTERVALS 7
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#define BIAS (LDBL_MAX_EXP - 1)
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static const long double
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huge = 0x1p10000L,
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twom10000 = 0x1p-10000L,
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/* XXX Prevent gcc from erroneously constant folding this: */
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static volatile const long double tiny = 0x1p-10000L;
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static const long double
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INV_L = 1.84664965233787316142070359168242182e+02L,
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L1 = 5.41521234812457272982212595914567508e-03L,
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L2 = -1.02536706388947310094527932552595546e-29L,
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huge = 0x1p10000L,
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/* log(2**16384 - 0.5) rounded towards zero: */
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/* log(2**16384 - 0.5 + 1) rounded towards zero for expm1l() is the same: */
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o_threshold = 11356.523406294143949491931077970763428L,
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twom10000 = 0x1p-10000L,
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/* log(2**(-16381-64-1)) rounded towards zero: */
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u_threshold = -11433.462743336297878837243843452621503L;
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static const double
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/*
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* ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
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* have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
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* bits zero so that multiplication of it by n is exact.
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*/
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INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
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L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
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static const long double
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A2 = 5.00000000000000000000000000000000000e-1L,
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A3 = 1.66666666666666666666666666666666972e-1L,
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A4 = 4.16666666666666666666666666653708268e-2L,
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A5 = 8.33333333333333333333333315069867254e-3L,
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A6 = 1.38888888888888888888996596213795377e-3L,
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A7 = 1.98412698412698412718821436278644414e-4L,
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A8 = 2.48015873015869681884882576649543128e-5L,
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A9 = 2.75573192240103867817876199544468806e-6L,
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A10 = 2.75573236172670046201884000197885520e-7L,
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A11 = 2.50517544183909126492878226167697856e-8L;
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/* 0x1.62e42fefa39ef35793c768000000p-8 */
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L1 = 5.41521234812457272982212595914567508e-3L;
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static const long double
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/*
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* Domain [-0.002708, 0.002708], range ~[-2.4011e-38, 2.4244e-38]:
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* |exp(x) - p(x)| < 2**-124.9
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* (0.002708 is ln2/(2*INTERVALS) rounded up a little).
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*/
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A2 = 0.5,
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A3 = 1.66666666666666666666666666651085500e-1L,
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A4 = 4.16666666666666666666666666425885320e-2L,
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A5 = 8.33333333333333333334522877160175842e-3L,
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A6 = 1.38888888888888888889971139751596836e-3L;
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static const double
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A7 = 1.9841269841269471e-4,
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A8 = 2.4801587301585284e-5,
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A9 = 2.7557324277411234e-6,
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A10 = 2.7557333722375072e-7;
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static const struct {
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long double hi;
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@ -202,7 +222,9 @@ long double
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expl(long double x)
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{
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union IEEEl2bits u, v;
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long double fn, r, r1, r2, q, t, twopk, twopkp10000;
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long double q, r, r1, t, twopk, twopkp10000;
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double dr, fn, r2;
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int k, n, n2;
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uint32_t hx, ix;
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@ -227,8 +249,15 @@ expl(long double x)
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}
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/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
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fn = x * INV_L + 0x1.8p112 - 0x1.8p112;
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/* Use a specialized rint() to get fn. Assume round-to-nearest. */
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/* XXX assume no extra precision for the additions, as for trig fns. */
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/* XXX this set of comments is now quadruplicated. */
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fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52;
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#if defined(HAVE_EFFICIENT_IRINT)
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n = irint(fn);
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#else
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n = (int)fn;
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#endif
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n2 = (unsigned)n % INTERVALS;
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k = n >> LOG2_INTERVALS;
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r1 = x - fn * L1;
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@ -245,11 +274,12 @@ expl(long double x)
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twopkp10000 = v.e;
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}
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r = r1 + r2;
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q = r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + r * (A7 +
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r * (A8 + r * (A9 + r * (A10 + r * A11)))))))));
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/* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
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dr = r;
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q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
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dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
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t = tbl[n2].lo + tbl[n2].hi;
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t = tbl[n2].hi + (tbl[n2].lo + t * (r2 + q + r1));
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t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
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/* Scale by 2**k. */
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if (k >= LDBL_MIN_EXP) {
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@ -235,7 +235,8 @@ long double
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expl(long double x)
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{
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union IEEEl2bits u, v;
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long double fn, q, r, r1, r2, t, t23, t45, twopk, twopkp10000, z;
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long double fn, q, r, r1, r2, t, twopk, twopkp10000;
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long double z;
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int k, n, n2;
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uint16_t hx, ix;
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@ -288,12 +289,9 @@ expl(long double x)
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twopkp10000 = v.e;
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}
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/* Evaluate expl(midpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
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/* Here q = q(r), not q(r1), since r1 is lopped like L1. */
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t45 = r * A5 + A4;
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/* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
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z = r * r;
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t23 = r * A3 + A2;
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q = r2 + z * t23 + z * z * t45 + z * z * z * A6;
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q = r2 + z * (A2 + r * A3) + z * z * (A4 + r * A5) + z * z * z * A6;
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t = (long double)tbl[n2].lo + tbl[n2].hi;
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t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
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