From owner-svn-src-all@FreeBSD.ORG Tue Oct 11 05:17:46 2011 Return-Path: Delivered-To: svn-src-all@freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2001:4f8:fff6::34]) by hub.freebsd.org (Postfix) with ESMTP id 65A171065672; Tue, 11 Oct 2011 05:17:46 +0000 (UTC) (envelope-from das@FreeBSD.org) Received: from svn.freebsd.org (svn.freebsd.org [IPv6:2001:4f8:fff6::2c]) by mx1.freebsd.org (Postfix) with ESMTP id 4B4468FC08; Tue, 11 Oct 2011 05:17:46 +0000 (UTC) Received: from svn.freebsd.org (localhost [127.0.0.1]) by svn.freebsd.org (8.14.4/8.14.4) with ESMTP id p9B5HkJp098720; Tue, 11 Oct 2011 05:17:46 GMT (envelope-from das@svn.freebsd.org) Received: (from das@localhost) by svn.freebsd.org (8.14.4/8.14.4/Submit) id p9B5HkUJ098717; Tue, 11 Oct 2011 05:17:46 GMT (envelope-from das@svn.freebsd.org) Message-Id: <201110110517.p9B5HkUJ098717@svn.freebsd.org> From: David Schultz Date: Tue, 11 Oct 2011 05:17:46 +0000 (UTC) To: src-committers@freebsd.org, svn-src-all@freebsd.org, svn-src-head@freebsd.org X-SVN-Group: head MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Cc: Subject: svn commit: r226245 - head/lib/msun/src X-BeenThere: svn-src-all@freebsd.org X-Mailman-Version: 2.1.5 Precedence: list List-Id: "SVN commit messages for the entire src tree \(except for " user" and " projects" \)" List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Tue, 11 Oct 2011 05:17:46 -0000 Author: das Date: Tue Oct 11 05:17:45 2011 New Revision: 226245 URL: http://svn.freebsd.org/changeset/base/226245 Log: Refactor this code by introducing separate functions to handle the extra-precision add and multiply operations. This simplifies future work but shouldn't result in any functional change. Modified: head/lib/msun/src/s_fma.c head/lib/msun/src/s_fmal.c Modified: head/lib/msun/src/s_fma.c ============================================================================== --- head/lib/msun/src/s_fma.c Tue Oct 11 05:17:26 2011 (r226244) +++ head/lib/msun/src/s_fma.c Tue Oct 11 05:17:45 2011 (r226245) @@ -1,5 +1,5 @@ /*- - * Copyright (c) 2005 David Schultz + * Copyright (c) 2005-2011 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without @@ -32,6 +32,63 @@ __FBSDID("$FreeBSD$"); #include /* + * A struct dd represents a floating-point number with twice the precision + * of a double. We maintain the invariant that "hi" stores the 53 high-order + * bits of the result. + */ +struct dd { + double hi; + double lo; +}; + +/* + * Compute a+b exactly, returning the exact result in a struct dd. We assume + * that both a and b are finite, but make no assumptions about their relative + * magnitudes. + */ +static inline struct dd +dd_add(double a, double b) +{ + struct dd ret; + double s; + + ret.hi = a + b; + s = ret.hi - a; + ret.lo = (a - (ret.hi - s)) + (b - s); + return (ret); +} + +/* + * Compute a*b exactly, returning the exact result in a struct dd. We assume + * that both a and b are normalized, so no underflow or overflow will occur. + * The current rounding mode must be round-to-nearest. + */ +static inline struct dd +dd_mul(double a, double b) +{ + static const double split = 0x1p27 + 1.0; + struct dd ret; + double ha, hb, la, lb, p, q; + + p = a * split; + ha = a - p; + ha += p; + la = a - ha; + + p = b * split; + hb = b - p; + hb += p; + lb = b - hb; + + p = ha * hb; + q = ha * lb + la * hb; + + ret.hi = p + q; + ret.lo = p - ret.hi + q + la * lb; + return (ret); +} + +/* * Fused multiply-add: Compute x * y + z with a single rounding error. * * We use scaling to avoid overflow/underflow, along with the @@ -52,10 +109,10 @@ __FBSDID("$FreeBSD$"); double fma(double x, double y, double z) { - static const double split = 0x1p27 + 1.0; double xs, ys, zs; - double c, cc, hx, hy, p, q, tx, ty; - double r, rr, s; + struct dd xy, r, r2; + double p; + double s; int oround; int ex, ey, ez; int spread; @@ -95,29 +152,29 @@ fma(double x, double y, double z) if (x > 0.0 ^ y < 0.0 ^ z < 0.0) return (x * y); feholdexcept(&env); - r = x * y; + s = x * y; if (!fetestexcept(FE_INEXACT)) - r = nextafter(r, 0); + s = nextafter(s, 0); feupdateenv(&env); - return (r); + return (s); case FE_DOWNWARD: if (z > 0.0) return (x * y); feholdexcept(&env); - r = x * y; + s = x * y; if (!fetestexcept(FE_INEXACT)) - r = nextafter(r, -INFINITY); + s = nextafter(s, -INFINITY); feupdateenv(&env); - return (r); + return (s); default: /* FE_UPWARD */ if (z < 0.0) return (x * y); feholdexcept(&env); - r = x * y; + s = x * y; if (!fetestexcept(FE_INEXACT)) - r = nextafter(r, INFINITY); + s = nextafter(s, INFINITY); feupdateenv(&env); - return (r); + return (s); } } if (spread < -DBL_MANT_DIG) { @@ -145,50 +202,29 @@ fma(double x, double y, double z) } } - /* - * Use Dekker's algorithm to perform the multiplication and - * subsequent addition in twice the machine precision. - * Arrange so that x * y = c + cc, and x * y + z = r + rr. - */ fesetround(FE_TONEAREST); - p = xs * split; - hx = xs - p; - hx += p; - tx = xs - hx; - - p = ys * split; - hy = ys - p; - hy += p; - ty = ys - hy; - - p = hx * hy; - q = hx * ty + tx * hy; - c = p + q; - cc = p - c + q + tx * ty; - + xy = dd_mul(xs, ys); zs = ldexp(zs, -spread); - r = c + zs; - s = r - c; - rr = (c - (r - s)) + (zs - s) + cc; + r = dd_add(xy.hi, zs); + r.lo += xy.lo; spread = ex + ey; - if (spread + ilogb(r) > -1023) { + if (spread + ilogb(r.hi) > -1023) { fesetround(oround); - r = r + rr; + r.hi = r.hi + r.lo; } else { /* * The result is subnormal, so we round before scaling to * avoid double rounding. */ - p = ldexp(copysign(0x1p-1022, r), -spread); - c = r + p; - s = c - r; - cc = (r - (c - s)) + (p - s) + rr; + p = ldexp(copysign(0x1p-1022, r.hi), -spread); + r2 = dd_add(r.hi, p); + r2.lo += r.lo; fesetround(oround); - r = (c + cc) - p; + r.hi = (r2.hi + r2.lo) - p; } - return (ldexp(r, spread)); + return (ldexp(r.hi, spread)); } #else /* LDBL_MANT_DIG == 113 */ /* Modified: head/lib/msun/src/s_fmal.c ============================================================================== --- head/lib/msun/src/s_fmal.c Tue Oct 11 05:17:26 2011 (r226244) +++ head/lib/msun/src/s_fmal.c Tue Oct 11 05:17:45 2011 (r226245) @@ -1,5 +1,5 @@ /*- - * Copyright (c) 2005 David Schultz + * Copyright (c) 2005-2011 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without @@ -32,6 +32,67 @@ __FBSDID("$FreeBSD$"); #include /* + * A struct dd represents a floating-point number with twice the precision + * of a long double. We maintain the invariant that "hi" stores the high-order + * bits of the result. + */ +struct dd { + long double hi; + long double lo; +}; + +/* + * Compute a+b exactly, returning the exact result in a struct dd. We assume + * that both a and b are finite, but make no assumptions about their relative + * magnitudes. + */ +static inline struct dd +dd_add(long double a, long double b) +{ + struct dd ret; + long double s; + + ret.hi = a + b; + s = ret.hi - a; + ret.lo = (a - (ret.hi - s)) + (b - s); + return (ret); +} + +/* + * Compute a*b exactly, returning the exact result in a struct dd. We assume + * that both a and b are normalized, so no underflow or overflow will occur. + * The current rounding mode must be round-to-nearest. + */ +static inline struct dd +dd_mul(long double a, long double b) +{ +#if LDBL_MANT_DIG == 64 + static const long double split = 0x1p32L + 1.0; +#elif LDBL_MANT_DIG == 113 + static const long double split = 0x1p57L + 1.0; +#endif + struct dd ret; + long double ha, hb, la, lb, p, q; + + p = a * split; + ha = a - p; + ha += p; + la = a - ha; + + p = b * split; + hb = b - p; + hb += p; + lb = b - hb; + + p = ha * hb; + q = ha * lb + la * hb; + + ret.hi = p + q; + ret.lo = p - ret.hi + q + la * lb; + return (ret); +} + +/* * Fused multiply-add: Compute x * y + z with a single rounding error. * * We use scaling to avoid overflow/underflow, along with the @@ -43,14 +104,10 @@ __FBSDID("$FreeBSD$"); long double fmal(long double x, long double y, long double z) { -#if LDBL_MANT_DIG == 64 - static const long double split = 0x1p32L + 1.0; -#elif LDBL_MANT_DIG == 113 - static const long double split = 0x1p57L + 1.0; -#endif long double xs, ys, zs; - long double c, cc, hx, hy, p, q, tx, ty; - long double r, rr, s; + struct dd xy, r, r2; + long double p; + long double s; int oround; int ex, ey, ez; int spread; @@ -90,29 +147,29 @@ fmal(long double x, long double y, long if (x > 0.0 ^ y < 0.0 ^ z < 0.0) return (x * y); feholdexcept(&env); - r = x * y; + s = x * y; if (!fetestexcept(FE_INEXACT)) - r = nextafterl(r, 0); + s = nextafterl(s, 0); feupdateenv(&env); - return (r); + return (s); case FE_DOWNWARD: if (z > 0.0) return (x * y); feholdexcept(&env); - r = x * y; + s = x * y; if (!fetestexcept(FE_INEXACT)) - r = nextafterl(r, -INFINITY); + s = nextafterl(s, -INFINITY); feupdateenv(&env); - return (r); + return (s); default: /* FE_UPWARD */ if (z < 0.0) return (x * y); feholdexcept(&env); - r = x * y; + s = x * y; if (!fetestexcept(FE_INEXACT)) - r = nextafterl(r, INFINITY); + s = nextafterl(s, INFINITY); feupdateenv(&env); - return (r); + return (s); } } if (spread < -LDBL_MANT_DIG) { @@ -140,48 +197,27 @@ fmal(long double x, long double y, long } } - /* - * Use Dekker's algorithm to perform the multiplication and - * subsequent addition in twice the machine precision. - * Arrange so that x * y = c + cc, and x * y + z = r + rr. - */ fesetround(FE_TONEAREST); - p = xs * split; - hx = xs - p; - hx += p; - tx = xs - hx; - - p = ys * split; - hy = ys - p; - hy += p; - ty = ys - hy; - - p = hx * hy; - q = hx * ty + tx * hy; - c = p + q; - cc = p - c + q + tx * ty; - + xy = dd_mul(xs, ys); zs = ldexpl(zs, -spread); - r = c + zs; - s = r - c; - rr = (c - (r - s)) + (zs - s) + cc; + r = dd_add(xy.hi, zs); + r.lo += xy.lo; spread = ex + ey; - if (spread + ilogbl(r) > -16383) { + if (spread + ilogbl(r.hi) > -16383) { fesetround(oround); - r = r + rr; + r.hi = r.hi + r.lo; } else { /* * The result is subnormal, so we round before scaling to * avoid double rounding. */ - p = ldexpl(copysignl(0x1p-16382L, r), -spread); - c = r + p; - s = c - r; - cc = (r - (c - s)) + (p - s) + rr; + p = ldexpl(copysignl(0x1p-16382L, r.hi), -spread); + r2 = dd_add(r.hi, p); + r2.lo += r.lo; fesetround(oround); - r = (c + cc) - p; + r.hi = (r2.hi + r2.lo) - p; } - return (ldexpl(r, spread)); + return (ldexpl(r.hi, spread)); }