Replace the macro name NUM with INTERVALS. This change provides
compatibility with the INTERVALS macro used in the soon-to-be-commmitted expm1l() and someday-to-be-committed log*l() functions. Add a comment into ld128/s_expl.c noting at gcc issue that was deleted when rewriting ld80/e_expl.c as ld128/s_expl.c. Requested by: bde Approved by: das (mentor)
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Notes:
svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=238784
@ -35,6 +35,7 @@ __FBSDID("$FreeBSD$");
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#define BIAS (LDBL_MAX_EXP - 1)
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/* XXX Prevent gcc from erroneously constant folding this: */
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static volatile const long double twom10000 = 0x1p-10000L, tiny = 0x1p-10000L;
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static const long double
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@ -57,12 +58,12 @@ P9 = 2.75573192240103867817876199544468806e-6L,
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P10 = 2.75573236172670046201884000197885520e-7L,
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P11 = 2.50517544183909126492878226167697856e-8L;
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#define NUM 128
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#define INTERVALS 128
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static const struct {
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long double hi;
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long double lo;
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} s[NUM] = {
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} s[INTERVALS] = {
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0x1p0L, 0x0p0L,
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0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
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0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
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@ -226,8 +227,8 @@ expl(long double x)
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fn = x * INV_L + 0x1.8p112 - 0x1.8p112;
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n = (int)fn;
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n2 = (unsigned)n % NUM; /* Tang's j. */
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k = (n - n2) / NUM;
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n2 = (unsigned)n % INTERVALS; /* Tang's j. */
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k = (n - n2) / INTERVALS;
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r1 = x - fn * L1;
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r2 = -fn * L2;
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@ -36,7 +36,7 @@ __FBSDID("$FreeBSD$");
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* in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15,
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* 144-157 (1989).
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*
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* where the 32 table entries have been expanded to NUM (see below).
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* where the 32 table entries have been expanded to INTERVALS (see below).
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*/
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#include <float.h>
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@ -65,9 +65,9 @@ u_threshold = LD80C(0xb21dfe7f09e2baa9, 13, 1, -11399.4985314888605581L);
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static const double __aligned(64)
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/*
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* ln2/NUM = L1+L2 (hi+lo decomposition for multiplication). L1 must have
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* at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(NUM)) lowest bits zero
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* so that multiplication of it by n is exact.
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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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L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */
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L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */
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@ -75,7 +75,7 @@ INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
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/*
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* Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]:
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* |exp(x) - p(x)| < 2**-77.2
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* (0.002708 is ln2/(2*NUM) rounded up a little).
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* (0.002708 is ln2/(2*INTERVALS) rounded up a little).
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*/
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P2 = 0.5,
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P3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */
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@ -84,16 +84,16 @@ P5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */
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P6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
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/*
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* 2^(i/NUM) for i in [0,NUM] is represented by two values where the
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* first 47 (?!) bits of the significand is stored in hi and the next 53
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* 2^(i/INTERVALS) for i in [0,INTERVALS] is represented by two values where
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* the first 47 (?!) bits of the significand is stored in hi and the next 53
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* bits are in lo.
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*/
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#define NUM 128
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#define INTERVALS 128
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static const struct {
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double hi;
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double lo;
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} s[NUM] __aligned(16) = {
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} s[INTERVALS] __aligned(16) = {
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0x1p+0, 0x0p+0,
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0x1.0163da9fb330p+0, 0x1.ab6c25335719bp-47,
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0x1.02c9a3e77804p+0, 0x1.07737be56527cp-47,
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@ -265,8 +265,8 @@ expl(long double x)
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#else
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n = (int)fn;
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#endif
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n2 = (unsigned)n % NUM; /* Tang's j. */
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k = (n - n2) / NUM;
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n2 = (unsigned)n % INTERVALS; /* Tang's j. */
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k = (n - n2) / INTERVALS;
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r1 = x - fn * L1;
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r2 = -fn * L2;
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