Date: Mon, 27 May 2013 20:43:16 +0000 (UTC) From: Steve Kargl <kargl@FreeBSD.org> To: src-committers@freebsd.org, svn-src-all@freebsd.org, svn-src-head@freebsd.org Subject: svn commit: r251041 - head/lib/msun/ld80 Message-ID: <201305272043.r4RKhGV4051036@svn.freebsd.org>
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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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