Author: kargl
Date: Mon May 27 20:43:16 2013
New Revision: 251041
URL: http://svnweb.freebsd.org/changeset/base/251041
Log:
* Update polynomial coefficients.
* Use ENTERI/RETURNI to allow the use of FP_PE on i386 target.
Reviewed by: das (and bde a long time ago)
Approved by: das (mentor)
Obtained from: bde (polynomial coefficients)
Modified:
head/lib/msun/ld80/s_exp2l.c
Modified: head/lib/msun/ld80/s_exp2l.c
==============================================================================
--- head/lib/msun/ld80/s_exp2l.c Mon May 27 18:45:45 2013
(r251040)
+++ head/lib/msun/ld80/s_exp2l.c Mon May 27 20:43:16 2013
(r251041)
@@ -36,25 +36,31 @@ __FBSDID("$FreeBSD$");
#include "fpmath.h"
#include "math.h"
+#include "math_private.h"
#define TBLBITS 7
#define TBLSIZE (1 << TBLBITS)
#define BIAS (LDBL_MAX_EXP - 1)
-#define EXPMASK (BIAS + LDBL_MAX_EXP)
static volatile long double
huge = 0x1p10000L,
twom10000 = 0x1p-10000L;
+static const union IEEEl2bits
+P1 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309429e-1L);
+
static const double
- redux = 0x1.8p63 / TBLSIZE,
- P1 = 0x1.62e42fefa39efp-1,
- P2 = 0x1.ebfbdff82c58fp-3,
- P3 = 0x1.c6b08d7049fap-5,
- P4 = 0x1.3b2ab6fba4da5p-7,
- P5 = 0x1.5d8804780a736p-10,
- P6 = 0x1.430918835e33dp-13;
+redux = 0x1.8p63 / TBLSIZE,
+/*
+ * Domain [-0.00390625, 0.00390625], range ~[-1.7079e-23, 1.7079e-23]
+ * |exp(x) - p(x)| < 2**-75.6
+ */
+P2 = 2.4022650695910072e-1, /* 0x1ebfbdff82c58f.0p-55 */
+P3 = 5.5504108664816879e-2, /* 0x1c6b08d7049e1a.0p-57 */
+P4 = 9.6181291055695180e-3, /* 0x13b2ab6fa8321a.0p-59 */
+P5 = 1.3333563089183052e-3, /* 0x15d8806f67f251.0p-62 */
+P6 = 1.5413361552277414e-4; /* 0x1433ddacff3441.0p-65 */
static const double tbl[TBLSIZE * 2] = {
0x1.6a09e667f3bcdp-1, -0x1.bdd3413b2648p-55,
@@ -187,8 +193,8 @@ static const double tbl[TBLSIZE * 2] = {
0x1.68155d44ca973p+0, 0x1.038ae44f74p-57,
};
-/*
- * exp2l(x): compute the base 2 exponential of x
+/*-
+ * Compute the base 2 exponential of x for Intel 80-bit format.
*
* Accuracy: Peak error < 0.511 ulp.
*
@@ -204,7 +210,7 @@ static const double tbl[TBLSIZE * 2] = {
* with |z| <= 2**-(TBLBITS+1).
*
* We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
- * degree-6 minimax polynomial with maximum error under 2**-69.
+ * degree-6 minimax polynomial with maximum error under 2**-75.6.
* The table entries each have 104 bits of accuracy, encoded as
* a pair of double precision values.
*/
@@ -219,30 +225,22 @@ exp2l(long double x)
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
- ix = hx & EXPMASK;
+ ix = hx & 0x7fff;
if (ix >= BIAS + 14) { /* |x| >= 16384 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
- if (u.xbits.man != 1ULL << 63 || (hx & 0x8000) == 0)
- return (x + x); /* x is +Inf or NaN */
- else
- return (0.0); /* x is -Inf */
+ if (hx & 0x8000 && u.xbits.man == 1ULL << 63)
+ return (0.0L); /* x is -Inf */
+ return (x + x); /* x is +Inf, NaN or unsupported */
}
if (x >= 16384)
return (huge * huge); /* overflow */
if (x <= -16446)
return (twom10000 * twom10000); /* underflow */
- } else if (ix <= BIAS - 66) { /* |x| < 0x1p-66 */
- return (1.0 + x);
+ } else if (ix <= BIAS - 66) { /* |x| < 0x1p-65 (includes pseudos) */
+ return (1.0L + x); /* 1 with inexact */
}
-#ifdef __i386__
- /*
- * The default precision on i386 is 53 bits, so long doubles are
- * broken. Call exp2() to get an accurate (double precision) result.
- */
- if (fpgetprec() != FP_PE)
- return (exp2(x));
-#endif
+ ENTERI();
/*
* Reduce x, computing z, i0, and k. The low bits of x + redux
@@ -266,26 +264,25 @@ exp2l(long double x)
z = x - u.e;
v.xbits.man = 1ULL << 63;
if (k >= LDBL_MIN_EXP) {
- v.xbits.expsign = LDBL_MAX_EXP - 1 + k;
+ v.xbits.expsign = BIAS + k;
twopk = v.e;
} else {
- v.xbits.expsign = LDBL_MAX_EXP - 1 + k + 10000;
+ v.xbits.expsign = BIAS + k + 10000;
twopkp10000 = v.e;
}
/* Compute r = exp2l(y) = exp2lt[i0] * p(z). */
long double t_hi = tbl[i0];
long double t_lo = tbl[i0 + 1];
- /* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */
- r = t_lo + (t_hi + t_lo) * z * (P1 + z * (P2 + z * (P3 + z * (P4
+ r = t_lo + (t_hi + t_lo) * z * (P1.e + z * (P2 + z * (P3 + z * (P4
+ z * (P5 + z * P6))))) + t_hi;
/* Scale by 2**k. */
if (k >= LDBL_MIN_EXP) {
if (k == LDBL_MAX_EXP)
- return (r * 2.0 * 0x1p16383L);
- return (r * twopk);
+ RETURNI(r * 2.0 * 0x1p16383L);
+ RETURNI(r * twopk);
} else {
- return (r * twopkp10000 * twom10000);
+ RETURNI(r * twopkp10000 * twom10000);
}
}
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