From owner-freebsd-numerics@freebsd.org Sun Feb 19 02:41:01 2017 Return-Path: Delivered-To: freebsd-numerics@mailman.ysv.freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2001:1900:2254:206a::19:1]) by mailman.ysv.freebsd.org (Postfix) with ESMTP id BD661CDBD0A for ; Sun, 19 Feb 2017 02:41:01 +0000 (UTC) (envelope-from sgk@troutmask.apl.washington.edu) Received: from troutmask.apl.washington.edu (troutmask.apl.washington.edu [128.95.76.21]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (Client CN "troutmask", Issuer "troutmask" (not verified)) by mx1.freebsd.org (Postfix) with ESMTPS id A411A3C3 for ; Sun, 19 Feb 2017 02:41:01 +0000 (UTC) (envelope-from sgk@troutmask.apl.washington.edu) Received: from troutmask.apl.washington.edu (localhost [127.0.0.1]) by troutmask.apl.washington.edu (8.15.2/8.15.2) with ESMTPS id v1J2f1UR079192 (version=TLSv1.2 cipher=DHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO) for ; Sat, 18 Feb 2017 18:41:01 -0800 (PST) (envelope-from sgk@troutmask.apl.washington.edu) Received: (from sgk@localhost) by troutmask.apl.washington.edu (8.15.2/8.15.2/Submit) id v1J2f1oF079191 for freebsd-numerics@freebsd.org; Sat, 18 Feb 2017 18:41:01 -0800 (PST) (envelope-from sgk) Date: Sat, 18 Feb 2017 18:41:01 -0800 From: Steve Kargl To: freebsd-numerics@freebsd.org Subject: [PATCH] avoid function call overhead in tgammaf Message-ID: <20170219024101.GA79177@troutmask.apl.washington.edu> Reply-To: sgk@troutmask.apl.washington.edu MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.7.2 (2016-11-26) X-BeenThere: freebsd-numerics@freebsd.org X-Mailman-Version: 2.1.23 Precedence: list List-Id: "Discussions of high quality implementation of libm functions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Sun, 19 Feb 2017 02:41:01 -0000 The following patch treats special values (i.e., +-inf, nan) and values outside a limited domain to avoid the function call overhead of tgamma. Anyone with a commit bit is more than welcomed to commit the patch (after of course a review). Index: src/s_tgammaf.c =================================================================== --- src/s_tgammaf.c (revision 1857) +++ src/s_tgammaf.c (working copy) @@ -27,17 +27,59 @@ #include __FBSDID("$FreeBSD: head/lib/msun/src/s_tgammaf.c 176388 2008-02-18 17:27:11Z das $"); -#include +#include "math.h" +#include "math_private.h" /* - * We simply call tgamma() rather than bloating the math library with - * a float-optimized version of it. The reason is that tgammaf() is - * essentially useless, since the function is superexponential and - * floats have very limited range. + * The gamma function is superexponential, which means that floats have + * a very limited domain. Rather than bloating the math library with a + * float-optimized version of tgammaf, we call tgamma() within the limited + * domain of [-underflow,overflow]. However, to avoid function call overhead, + * tgammaf() directly treats special values and values outside the limited + * domain. */ + +static u_int32_t overflow = 0x420c290f; /* 35.0400981 */ +static u_int32_t underflow = 0x421a67d8; /* 38.6014118 */ +static volatile float huge = 1.e30, tiny = 1.e-30; + float tgammaf(float x) { + u_int32_t hx; + int32_t ix, sg; + + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; + sg = hx & 0x80000000; + + if (ix > overflow) { + if (ix >= 0x7f800000) + return (sg ? x / x : x + x); + if (!sg) + return (huge * huge); + } + + if (ix == 0) + return (1 / x); + + if (sg && ix > underflow) { + /* + * tgammaf(x) for integral x returns an NaN, so we implement + * a poor man's rintf(). + */ + volatile float vz; + float y,z; + + y = -x; + + vz = y + 0x1p23F; /* depend on 0 <= y < 0x1p23 */ + z = vz - 0x1p23F; /* rintf(y) for the above range */ + if (z == y) + return ((x - x) / (x - x)); + + return (tiny * tiny); + } return (tgamma(x)); } -- Steve 20161221 https://www.youtube.com/watch?v=IbCHE-hONow