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* Rename the polynomial coefficients from P2, P3, ... to A2, A3, ....

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The names now coincide with the name used in PTP Tang's paper.

* Rename the variable from s to tbl to better reflect that
  this is a table, and to be consistent with the naming scheme
  in s_exp2l.c

Reviewed by:	bde (as part of larger diff)
This commit is contained in:
Steve Kargl 2013-06-03 17:36:26 +00:00
parent be6ec55376
commit bb23de67bb
2 changed files with 24 additions and 25 deletions
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30
lib/msun/ld128/s_expl.c
View File

@ -52,21 +52,21 @@ twom10000 = 0x1p-10000L,
u_threshold = -11433.462743336297878837243843452621503L;
static const long double
P2 = 5.00000000000000000000000000000000000e-1L,
P3 = 1.66666666666666666666666666666666972e-1L,
P4 = 4.16666666666666666666666666653708268e-2L,
P5 = 8.33333333333333333333333315069867254e-3L,
P6 = 1.38888888888888888888996596213795377e-3L,
P7 = 1.98412698412698412718821436278644414e-4L,
P8 = 2.48015873015869681884882576649543128e-5L,
P9 = 2.75573192240103867817876199544468806e-6L,
P10 = 2.75573236172670046201884000197885520e-7L,
P11 = 2.50517544183909126492878226167697856e-8L;
A2 = 5.00000000000000000000000000000000000e-1L,
A3 = 1.66666666666666666666666666666666972e-1L,
A4 = 4.16666666666666666666666666653708268e-2L,
A5 = 8.33333333333333333333333315069867254e-3L,
A6 = 1.38888888888888888888996596213795377e-3L,
A7 = 1.98412698412698412718821436278644414e-4L,
A8 = 2.48015873015869681884882576649543128e-5L,
A9 = 2.75573192240103867817876199544468806e-6L,
A10 = 2.75573236172670046201884000197885520e-7L,
A11 = 2.50517544183909126492878226167697856e-8L;
static const struct {
long double hi;
long double lo;
} s[INTERVALS] = {
} tbl[INTERVALS] = {
0x1p0L, 0x0p0L,
0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
@ -245,10 +245,10 @@ expl(long double x)
}
r = r1 + r2;
q = r * r * (P2 + r * (P3 + r * (P4 + r * (P5 + r * (P6 + r * (P7 +
r * (P8 + r * (P9 + r * (P10 + r * P11)))))))));
t = s[n2].lo + s[n2].hi;
t = s[n2].hi + (s[n2].lo + t * (r2 + q + r1));
q = r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + r * (A7 +
r * (A8 + r * (A9 + r * (A10 + r * A11)))))))));
t = tbl[n2].lo + tbl[n2].hi;
t = tbl[n2].hi + (tbl[n2].lo + t * (r2 + q + r1));
/* Scale by 2**k. */
if (k >= LDBL_MIN_EXP) {

19
lib/msun/ld80/s_expl.c
View File

@ -78,11 +78,11 @@ L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */
* |exp(x) - p(x)| < 2**-77.2
* (0.002708 is ln2/(2*INTERVALS) rounded up a little).
*/
P2 = 0.5,
P3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */
P4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */
P5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */
P6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
A2 = 0.5,
A3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */
A4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */
A5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */
A6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
/*
* 2^(i/INTERVALS) for i in [0,INTERVALS] is represented by two values where
@ -96,8 +96,7 @@ P6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
static const struct {
double hi;
double lo;
/* XXX should rename 's'. */
} s[INTERVALS] = {
} tbl[INTERVALS] = {
0x1p+0, 0x0p+0,
0x1.0163da9fb3335p+0, 0x1.b61299ab8cdb7p-54,
0x1.02c9a3e778060p+0, 0x1.dcdef95949ef4p-53,
@ -284,14 +283,14 @@ expl(long double x)
twopkp10000 = v.e;
}
/* Evaluate expl(midpoint[n2] + r1 + r2) = s[n2] * expl(r1 + r2). */
/* Evaluate expl(midpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
/* Here q = q(r), not q(r1), since r1 is lopped like L1. */
t45 = r * P5 + P4;
z = r * r;
t23 = r * P3 + P2;
q = r2 + z * t23 + z * z * t45 + z * z * z * P6;
t = (long double)s[n2].lo + s[n2].hi;
t = s[n2].lo + t * (q + r1) + s[n2].hi;
t = (long double)tbl[n2].lo + tbl[n2].hi;
t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
/* Scale by 2**k. */
if (k >= LDBL_MIN_EXP) {