From patchwork Thu Aug 23 11:06:47 2018 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 8bit X-Patchwork-Submitter: Wilco Dijkstra X-Patchwork-Id: 29025 Received: (qmail 93258 invoked by alias); 23 Aug 2018 11:07:00 -0000 Mailing-List: contact libc-alpha-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Unsubscribe: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: libc-alpha-owner@sourceware.org Delivered-To: mailing list libc-alpha@sourceware.org Received: (qmail 93243 invoked by uid 89); 23 Aug 2018 11:06:59 -0000 Authentication-Results: sourceware.org; auth=none X-Spam-SWARE-Status: No, score=-22.4 required=5.0 tests=BAYES_00, GIT_PATCH_0, GIT_PATCH_1, GIT_PATCH_2, GIT_PATCH_3, KAM_ASCII_DIVIDERS, KAM_LOTSOFHASH, KAM_SHORT, RCVD_IN_DNSWL_NONE, SEM_URI, SEM_URIRED, SPF_HELO_PASS, SPF_PASS autolearn=ham version=3.3.2 spammy= X-HELO: EUR01-VE1-obe.outbound.protection.outlook.com DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=armh.onmicrosoft.com; s=selector1-arm-com; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-SenderADCheck; bh=SAIVlHZysP5M4S2ybe4BuAWgMV/dlnXY6gNuCHb6ivw=; b=I3rbnOHEkKdhGrxuh8Hc7oYu87EHj5KjObCGBAiRjfSB5/mUJon8NyiIQwNlCt8IlrsIY7Qbk5UXzOfV0v7U0mEaHi8A0LMNIAX+4ZuWnO7yNkU9hce8XG2RVx8k43crWuh3xIGd+CH+QBjvkHTUQZ2WpW0xIlM6trlxRZmv3lQ= From: Wilco Dijkstra To: Joseph Myers CC: "libc-alpha@sourceware.org" , nd Subject: Re: [PATCH] Remove unused math files Date: Thu, 23 Aug 2018 11:06:47 +0000 Message-ID: References: , In-Reply-To: authentication-results: spf=none (sender IP is ) smtp.mailfrom=Wilco.Dijkstra@arm.com; received-spf: None (protection.outlook.com: arm.com does not designate permitted sender hosts) MIME-Version: 1.0 Joseph Myers wrote: > This doesn't look like a complete set of such files to remove.  I'd expect > the m68k and ia64 versions of e_rem_pio2.c, e_rem_pio2f.c, k_rem_pio2f.c > to be removed at the same time. Indeed, using find rather than grep shows up some more empty files, including a one in i386. Here is the updated version: Remove empty files due to the sin/cos improvements: k_sinf.c, k_cosf.c, k_cos.c, k_sin.c. After the tanf change s_rem_pio2f.c and k_rem_pio2f.c (and the ia64, m68k and powerpc equivalents) are no longer used, so remove them. All e_rem_pio2.c files were already empty or commented out, so remove them too. Passes buildmanyglibcs (only i686 compiler fails to build). OK for commit? ChangeLog: 2018-08-23 Wilco Dijkstra * math/Makefile: Remove empty files k_sin(f).c, k_cos(f).c. Remove unused files e_rem_pio2(f).c, k_rem_pio2f.c. * sysdeps/i386/fpu/e_rem_pio2.c: Delete file. * sysdeps/ia64/fpu/e_rem_pio2.c: Likewise. * sysdeps/ia64/fpu/e_rem_pio2f.c: Likewise. * sysdeps/ia64/fpu/k_rem_pio2f.c: Likewise. * sysdeps/ieee754/dbl-64/e_rem_pio2.c: Likewise. * sysdeps/ieee754/dbl-64/k_cos.c: Likewise. * sysdeps/ieee754/dbl-64/k_sin.c: Likewise. * sysdeps/ieee754/flt-32/e_rem_pio2f.c: Likewise. * sysdeps/ieee754/flt-32/k_cosf.c: Likewise. * sysdeps/ieee754/flt-32/k_rem_pio2f.c: Likewise. * sysdeps/ieee754/flt-32/k_sinf.c: Likewise. * sysdeps/m68k/m680x0/fpu/e_rem_pio2.c: Likewise * sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c: Likewise * sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c: Likewise * sysdeps/powerpc/fpu/e_rem_pio2f.c: Likewise. * sysdeps/powerpc/fpu/k_rem_pio2f.c: Likewise. diff --git a/math/Makefile b/math/Makefile index 5210430e81d21776b6de37dc12c475fc5841371e..bff726fe81415f3d81227dd843a8221cb0792c1d 100644 --- a/math/Makefile +++ b/math/Makefile @@ -64,9 +64,9 @@ gen-libm-calls = cargF conjF cimagF crealF cabsF s_cacosF \ libm-calls = \ e_acosF e_acoshF e_asinF e_atan2F e_atanhF e_coshF e_expF e_fmodF \ e_hypotF e_j0F e_j1F e_jnF e_lgammaF_r e_logF e_log10F e_powF \ - e_rem_pio2F e_remainderF e_scalbF e_sinhF e_sqrtF e_gammaF_r \ + e_remainderF e_scalbF e_sinhF e_sqrtF e_gammaF_r \ e_ilogbF \ - k_cosF k_sinF k_tanF s_asinhF s_atanF s_cbrtF \ + k_tanF s_asinhF s_atanF s_cbrtF \ s_ceilF s_cosF s_erfF s_expm1F s_fabsF \ s_floorF s_log1pF s_logbF \ s_nextafterF s_nexttowardF s_rintF s_scalblnF \ @@ -119,23 +119,25 @@ test-types-basic = ldouble double float # long double support type-ldouble-suffix := l -type-ldouble-routines := t_sincosl k_sincosl s_iscanonicall +type-ldouble-routines := t_sincosl k_sinl k_cosl k_sincosl s_iscanonicall \ + e_rem_pio2l type-ldouble-yes := ldouble # double support type-double-suffix := type-double-routines := branred doasin dosincos mpa mpatan2 \ - mpatan mpsqrt mptan sincos32 \ - sincostab k_rem_pio2 + k_rem_pio2 mpatan mpsqrt mptan sincos32 \ + sincostab # float support type-float-suffix := f -type-float-routines := k_rem_pio2f math_errf e_exp2f_data e_logf_data \ +type-float-routines := math_errf e_exp2f_data e_logf_data \ e_log2f_data e_powf_log2_data s_sincosf_data # _Float128 support type-float128-suffix := f128 -type-float128-routines := t_sincosf128 k_sincosf128 +type-float128-routines := t_sincosf128 k_sinf128 k_cosf128 k_sincosf128 \ + e_rem_pio2f128 type-float128-yes := float128 # _Float64x may be supported, only as an alias type. diff --git a/sysdeps/i386/fpu/e_rem_pio2.c b/sysdeps/i386/fpu/e_rem_pio2.c deleted file mode 100644 index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000 --- a/sysdeps/i386/fpu/e_rem_pio2.c +++ /dev/null @@ -1,3 +0,0 @@ -/* Empty. This file is only meant to avoid compiling the file with the - same name in the libm-ieee754 directory. The code is not used since - there is an assembler version for all users of this file. */ diff --git a/sysdeps/ia64/fpu/e_rem_pio2.c b/sysdeps/ia64/fpu/e_rem_pio2.c deleted file mode 100644 index 41254ae60a03a2e76edd28d3adcc68e182966cb2..0000000000000000000000000000000000000000 --- a/sysdeps/ia64/fpu/e_rem_pio2.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed. */ diff --git a/sysdeps/ia64/fpu/e_rem_pio2f.c b/sysdeps/ia64/fpu/e_rem_pio2f.c deleted file mode 100644 index 41254ae60a03a2e76edd28d3adcc68e182966cb2..0000000000000000000000000000000000000000 --- a/sysdeps/ia64/fpu/e_rem_pio2f.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed. */ diff --git a/sysdeps/ia64/fpu/k_rem_pio2f.c b/sysdeps/ia64/fpu/k_rem_pio2f.c deleted file mode 100644 index 41254ae60a03a2e76edd28d3adcc68e182966cb2..0000000000000000000000000000000000000000 --- a/sysdeps/ia64/fpu/k_rem_pio2f.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed. */ diff --git a/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/sysdeps/ieee754/dbl-64/e_rem_pio2.c deleted file mode 100644 index 81a3d073d4142f943b9b09c5ee97e8d51e1d75cf..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/dbl-64/e_rem_pio2.c +++ /dev/null @@ -1,193 +0,0 @@ -#ifdef NOT_NEEDED_ANYMORE - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_rem_pio2(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - * use __kernel_rem_pio2() - */ - -#include -#include - -/* - * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi - */ -static const int32_t two_over_pi[] = { -0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, -0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, -0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, -0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, -0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, -0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, -0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, -0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, -0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, -0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, -0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, -}; - -static const int32_t npio2_hw[] = { -0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, -0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, -0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, -0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, -0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, -0x404858EB, 0x404921FB, -}; - -/* - * invpio2: 53 bits of 2/pi - * pio2_1: first 33 bit of pi/2 - * pio2_1t: pi/2 - pio2_1 - * pio2_2: second 33 bit of pi/2 - * pio2_2t: pi/2 - (pio2_1+pio2_2) - * pio2_3: third 33 bit of pi/2 - * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) - */ - -static const double - zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ - two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ - invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ - pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ - pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ - pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ - pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ - pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ - -int32_t -__ieee754_rem_pio2 (double x, double *y) -{ - double z, w, t, r, fn; - double tx[3]; - int32_t e0, i, j, nx, n, ix, hx; - uint32_t low; - - GET_HIGH_WORD (hx, x); /* high word of x */ - ix = hx & 0x7fffffff; - if (ix <= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ - { - y[0] = x; y[1] = 0; return 0; - } - if (ix < 0x4002d97c) /* |x| < 3pi/4, special case with n=+-1 */ - { - if (hx > 0) - { - z = x - pio2_1; - if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ - { - y[0] = z - pio2_1t; - y[1] = (z - y[0]) - pio2_1t; - } - else /* near pi/2, use 33+33+53 bit pi */ - { - z -= pio2_2; - y[0] = z - pio2_2t; - y[1] = (z - y[0]) - pio2_2t; - } - return 1; - } - else /* negative x */ - { - z = x + pio2_1; - if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ - { - y[0] = z + pio2_1t; - y[1] = (z - y[0]) + pio2_1t; - } - else /* near pi/2, use 33+33+53 bit pi */ - { - z += pio2_2; - y[0] = z + pio2_2t; - y[1] = (z - y[0]) + pio2_2t; - } - return -1; - } - } - if (ix <= 0x413921fb) /* |x| ~<= 2^19*(pi/2), medium size */ - { - t = fabs (x); - n = (int32_t) (t * invpio2 + half); - fn = (double) n; - r = t - fn * pio2_1; - w = fn * pio2_1t; /* 1st round good to 85 bit */ - if (n < 32 && ix != npio2_hw[n - 1]) - { - y[0] = r - w; /* quick check no cancellation */ - } - else - { - uint32_t high; - j = ix >> 20; - y[0] = r - w; - GET_HIGH_WORD (high, y[0]); - i = j - ((high >> 20) & 0x7ff); - if (i > 16) /* 2nd iteration needed, good to 118 */ - { - t = r; - w = fn * pio2_2; - r = t - w; - w = fn * pio2_2t - ((t - r) - w); - y[0] = r - w; - GET_HIGH_WORD (high, y[0]); - i = j - ((high >> 20) & 0x7ff); - if (i > 49) /* 3rd iteration need, 151 bits acc */ - { - t = r; /* will cover all possible cases */ - w = fn * pio2_3; - r = t - w; - w = fn * pio2_3t - ((t - r) - w); - y[0] = r - w; - } - } - } - y[1] = (r - y[0]) - w; - if (hx < 0) - { - y[0] = -y[0]; y[1] = -y[1]; return -n; - } - else - return n; - } - /* - * all other (large) arguments - */ - if (ix >= 0x7ff00000) /* x is inf or NaN */ - { - y[0] = y[1] = x - x; return 0; - } - /* set z = scalbn(|x|,ilogb(x)-23) */ - GET_LOW_WORD (low, x); - SET_LOW_WORD (z, low); - e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ - SET_HIGH_WORD (z, ix - ((int32_t) (e0 << 20))); - for (i = 0; i < 2; i++) - { - tx[i] = (double) ((int32_t) (z)); - z = (z - tx[i]) * two24; - } - tx[2] = z; - nx = 3; - while (tx[nx - 1] == zero) - nx--; /* skip zero term */ - n = __kernel_rem_pio2 (tx, y, e0, nx, 2, two_over_pi); - if (hx < 0) - { - y[0] = -y[0]; y[1] = -y[1]; return -n; - } - return n; -} -#endif diff --git a/sysdeps/ieee754/dbl-64/k_cos.c b/sysdeps/ieee754/dbl-64/k_cos.c deleted file mode 100644 index cc5c205a5fc4d7d2a5e9d09961e8710976211e6e..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/dbl-64/k_cos.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed anymore. */ diff --git a/sysdeps/ieee754/dbl-64/k_sin.c b/sysdeps/ieee754/dbl-64/k_sin.c deleted file mode 100644 index cc5c205a5fc4d7d2a5e9d09961e8710976211e6e..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/dbl-64/k_sin.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed anymore. */ diff --git a/sysdeps/ieee754/flt-32/e_rem_pio2f.c b/sysdeps/ieee754/flt-32/e_rem_pio2f.c deleted file mode 100644 index bd871a26c2e0bfdb59b937c1151c73bb167988b6..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/flt-32/e_rem_pio2f.c +++ /dev/null @@ -1,179 +0,0 @@ -/* e_rem_pio2f.c -- float version of e_rem_pio2.c - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $"; -#endif - -/* __ieee754_rem_pio2f(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - * use __kernel_rem_pio2f() - */ - -#include -#include - -/* - * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi - */ -static const int32_t two_over_pi[] = { -0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, -0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, -0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, -0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, -0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, -0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, -0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, -0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, -0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, -0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, -0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, -0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, -0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, -0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, -0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, -0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, -0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, -0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, -0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, -0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, -0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, -0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, -}; - -/* This array is like the one in e_rem_pio2.c, but the numbers are - single precision and the last 8 bits are forced to 0. */ -static const int32_t npio2_hw[] = { -0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, -0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, -0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, -0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, -0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, -0x4242c700, 0x42490f00 -}; - -/* - * invpio2: 24 bits of 2/pi - * pio2_1: first 17 bit of pi/2 - * pio2_1t: pi/2 - pio2_1 - * pio2_2: second 17 bit of pi/2 - * pio2_2t: pi/2 - (pio2_1+pio2_2) - * pio2_3: third 17 bit of pi/2 - * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) - */ - -static const float -zero = 0.0000000000e+00, /* 0x00000000 */ -half = 5.0000000000e-01, /* 0x3f000000 */ -two8 = 2.5600000000e+02, /* 0x43800000 */ -invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ -pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ -pio2_1t = 1.0804334124e-05, /* 0x37354443 */ -pio2_2 = 1.0804273188e-05, /* 0x37354400 */ -pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ -pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ -pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ - -int32_t __ieee754_rem_pio2f(float x, float *y) -{ - float z,w,t,r,fn; - float tx[3]; - int32_t e0,i,j,nx,n,ix,hx; - - GET_FLOAT_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ - {y[0] = x; y[1] = 0; return 0;} - if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ - if(hx>0) { - z = x - pio2_1; - if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */ - y[0] = z - pio2_1t; - y[1] = (z-y[0])-pio2_1t; - } else { /* near pi/2, use 24+24+24 bit pi */ - z -= pio2_2; - y[0] = z - pio2_2t; - y[1] = (z-y[0])-pio2_2t; - } - return 1; - } else { /* negative x */ - z = x + pio2_1; - if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */ - y[0] = z + pio2_1t; - y[1] = (z-y[0])+pio2_1t; - } else { /* near pi/2, use 24+24+24 bit pi */ - z += pio2_2; - y[0] = z + pio2_2t; - y[1] = (z-y[0])+pio2_2t; - } - return -1; - } - } - if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ - t = fabsf(x); - n = (int32_t) (t*invpio2+half); - fn = (float)n; - r = t-fn*pio2_1; - w = fn*pio2_1t; /* 1st round good to 40 bit */ - if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) { - y[0] = r-w; /* quick check no cancellation */ - } else { - uint32_t high; - j = ix>>23; - y[0] = r-w; - GET_FLOAT_WORD(high,y[0]); - i = j-((high>>23)&0xff); - if(i>8) { /* 2nd iteration needed, good to 57 */ - t = r; - w = fn*pio2_2; - r = t-w; - w = fn*pio2_2t-((t-r)-w); - y[0] = r-w; - GET_FLOAT_WORD(high,y[0]); - i = j-((high>>23)&0xff); - if(i>25) { /* 3rd iteration need, 74 bits acc */ - t = r; /* will cover all possible cases */ - w = fn*pio2_3; - r = t-w; - w = fn*pio2_3t-((t-r)-w); - y[0] = r-w; - } - } - } - y[1] = (r-y[0])-w; - if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} - else return n; - } - /* - * all other (large) arguments - */ - if(ix>=0x7f800000) { /* x is inf or NaN */ - y[0]=y[1]=x-x; return 0; - } - /* set z = scalbn(|x|,ilogb(x)-7) */ - e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ - SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); - for(i=0;i<2;i++) { - tx[i] = (float)((int32_t)(z)); - z = (z-tx[i])*two8; - } - tx[2] = z; - nx = 3; - while(tx[nx-1]==zero) nx--; /* skip zero term */ - n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); - if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} - return n; -} diff --git a/sysdeps/ieee754/flt-32/k_cosf.c b/sysdeps/ieee754/flt-32/k_cosf.c deleted file mode 100644 index 1cc8931700702e65d29a6e2af287175d23c6b182..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/flt-32/k_cosf.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed. */ diff --git a/sysdeps/ieee754/flt-32/k_rem_pio2f.c b/sysdeps/ieee754/flt-32/k_rem_pio2f.c deleted file mode 100644 index ea4915b765b3e19d7c3a6e40e75fb3d8a93d1700..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/flt-32/k_rem_pio2f.c +++ /dev/null @@ -1,219 +0,0 @@ -/* k_rem_pio2f.c -- float version of k_rem_pio2.c - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $"; -#endif - -#include -#include -#include -#include - -/* In the float version, the input parameter x contains 8 bit - integers, not 24 bit integers. 113 bit precision is not supported. */ - -static const int init_jk[] = {4,7,9}; /* initial value for jk */ - -static const float PIo2[] = { - 1.5703125000e+00, /* 0x3fc90000 */ - 4.5776367188e-04, /* 0x39f00000 */ - 2.5987625122e-05, /* 0x37da0000 */ - 7.5437128544e-08, /* 0x33a20000 */ - 6.0026650317e-11, /* 0x2e840000 */ - 7.3896444519e-13, /* 0x2b500000 */ - 5.3845816694e-15, /* 0x27c20000 */ - 5.6378512969e-18, /* 0x22d00000 */ - 8.3009228831e-20, /* 0x1fc40000 */ - 3.2756352257e-22, /* 0x1bc60000 */ - 6.3331015649e-25, /* 0x17440000 */ -}; - -static const float -zero = 0.0, -one = 1.0, -two8 = 2.5600000000e+02, /* 0x43800000 */ -twon8 = 3.9062500000e-03; /* 0x3b800000 */ - -int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) -{ - int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; - float z,fw,f[20],fq[20],q[20]; - - /* initialize jk*/ - jk = init_jk[prec]; - jp = jk; - - /* determine jx,jv,q0, note that 3>q0 */ - jx = nx-1; - jv = (e0-3)/8; if(jv<0) jv=0; - q0 = e0-8*(jv+1); - - /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ - j = jv-jx; m = jx+jk; - for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; - - /* compute q[0],q[1],...q[jk] */ - for (i=0;i<=jk;i++) { - for(j=0,fw=0.0;j<=jx;j++) - fw += x[j]*f[jx+i-j]; - q[i] = fw; - } - - jz = jk; -recompute: - /* distill q[] into iq[] reversingly */ - for(i=0,j=jz,z=q[jz];j>0;i++,j--) { - fw = (float)((int32_t)(twon8* z)); - iq[i] = (int32_t)(z-two8*fw); - z = q[j-1]+fw; - } - - /* compute n */ - z = __scalbnf(z,q0); /* actual value of z */ - z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */ - n = (int32_t) z; - z -= (float)n; - ih = 0; - if(q0>0) { /* need iq[jz-1] to determine n */ - i = (iq[jz-1]>>(8-q0)); n += i; - iq[jz-1] -= i<<(8-q0); - ih = iq[jz-1]>>(7-q0); - } - else if(q0==0) ih = iq[jz-1]>>7; - else if(z>=(float)0.5) ih=2; - - if(ih>0) { /* q > 0.5 */ - n += 1; carry = 0; - for(i=0;i0) { /* rare case: chance is 1 in 12 */ - switch(q0) { - case 1: - iq[jz-1] &= 0x7f; break; - case 2: - iq[jz-1] &= 0x3f; break; - } - } - if(ih==2) { - z = one - z; - if(carry!=0) z -= __scalbnf(one,q0); - } - } - - /* check if recomputation is needed */ - if(z==zero) { - j = 0; - for (i=jz-1;i>=jk;i--) j |= iq[i]; - if(j==0) { /* need recomputation */ - /* On s390x gcc 6.1 -O3 produces the warning "array subscript is - below array bounds [-Werror=array-bounds]". Only - __ieee754_rem_pio2f calls __kernel_rem_pio2f for normal - numbers and |x| ~> 2^7*(pi/2). Thus x can't be zero and - ipio2 is not zero, too. Thus not all iq[] values can't be - zero. */ - DIAG_PUSH_NEEDS_COMMENT; - DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds"); - for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ - DIAG_POP_NEEDS_COMMENT; - - for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ - f[jx+i] = (float) ipio2[jv+i]; - for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; - q[i] = fw; - } - jz += k; - goto recompute; - } - } - - /* chop off zero terms */ - if(z==(float)0.0) { - jz -= 1; q0 -= 8; - while(iq[jz]==0) { jz--; q0-=8;} - } else { /* break z into 8-bit if necessary */ - z = __scalbnf(z,-q0); - if(z>=two8) { - fw = (float)((int32_t)(twon8*z)); - iq[jz] = (int32_t)(z-two8*fw); - jz += 1; q0 += 8; - iq[jz] = (int32_t) fw; - } else iq[jz] = (int32_t) z ; - } - - /* convert integer "bit" chunk to floating-point value */ - fw = __scalbnf(one,q0); - for(i=jz;i>=0;i--) { - q[i] = fw*(float)iq[i]; fw*=twon8; - } - - /* compute PIo2[0,...,jp]*q[jz,...,0] */ - for(i=jz;i>=0;i--) { - for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; - fq[jz-i] = fw; - } - - /* compress fq[] into y[] */ - switch(prec) { - case 0: - fw = 0.0; - for (i=jz;i>=0;i--) fw += fq[i]; - y[0] = (ih==0)? fw: -fw; - break; - case 1: - case 2:; - float fv = 0.0; - for (i=jz;i>=0;i--) fv = math_narrow_eval (fv + fq[i]); - y[0] = (ih==0)? fv: -fv; - /* GCC mainline (to be GCC 9), as of 2018-05-22 on - i686, warns that fq[0] may be used uninitialized. - This is not possible because jz is always - nonnegative when the above loop initializing fq is - executed, because the result is never zero to full - precision (this function is not called for zero - arguments). */ - DIAG_PUSH_NEEDS_COMMENT; - DIAG_IGNORE_NEEDS_COMMENT (9, "-Wmaybe-uninitialized"); - fv = math_narrow_eval (fq[0]-fv); - DIAG_POP_NEEDS_COMMENT; - for (i=1;i<=jz;i++) fv = math_narrow_eval (fv + fq[i]); - y[1] = (ih==0)? fv: -fv; - break; - case 3: /* painful */ - for (i=jz;i>0;i--) { - float fv = math_narrow_eval (fq[i-1]+fq[i]); - fq[i] += fq[i-1]-fv; - fq[i-1] = fv; - } - for (i=jz;i>1;i--) { - float fv = math_narrow_eval (fq[i-1]+fq[i]); - fq[i] += fq[i-1]-fv; - fq[i-1] = fv; - } - for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; - if(ih==0) { - y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; - } else { - y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; - } - } - return n&7; -} diff --git a/sysdeps/ieee754/flt-32/k_sinf.c b/sysdeps/ieee754/flt-32/k_sinf.c deleted file mode 100644 index 1cc8931700702e65d29a6e2af287175d23c6b182..0000000000000000000000000000000000000000 --- a/sysdeps/ieee754/flt-32/k_sinf.c +++ /dev/null @@ -1 +0,0 @@ -/* Not needed. */ diff --git a/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c b/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c deleted file mode 100644 index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000 --- a/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c +++ /dev/null @@ -1,3 +0,0 @@ -/* Empty. This file is only meant to avoid compiling the file with the - same name in the libm-ieee754 directory. The code is not used since - there is an assembler version for all users of this file. */ diff --git a/sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c b/sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c deleted file mode 100644 index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000 --- a/sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c +++ /dev/null @@ -1,3 +0,0 @@ -/* Empty. This file is only meant to avoid compiling the file with the - same name in the libm-ieee754 directory. The code is not used since - there is an assembler version for all users of this file. */ diff --git a/sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c b/sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c deleted file mode 100644 index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000 --- a/sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c +++ /dev/null @@ -1,3 +0,0 @@ -/* Empty. This file is only meant to avoid compiling the file with the - same name in the libm-ieee754 directory. The code is not used since - there is an assembler version for all users of this file. */ diff --git a/sysdeps/powerpc/fpu/e_rem_pio2f.c b/sysdeps/powerpc/fpu/e_rem_pio2f.c deleted file mode 100644 index 30fd53ee2c4288fdd4fb5923d668d097ecfcb290..0000000000000000000000000000000000000000 --- a/sysdeps/powerpc/fpu/e_rem_pio2f.c +++ /dev/null @@ -1,188 +0,0 @@ -/* e_rem_pio2f.c -- float version of e_rem_pio2.c - Copyright (C) 2011-2018 Free Software Foundation, Inc. - This file is part of the GNU C Library. - Contributed by Adhemerval Zanella , 2011 - - The GNU C Library is free software; you can redistribute it and/or - modify it under the terms of the GNU Library General Public License as - published by the Free Software Foundation; either version 2 of the - License, or (at your option) any later version. - - The GNU C Library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Library General Public License for more details. - - You should have received a copy of the GNU Library General Public - License along with the GNU C Library; see the file COPYING.LIB. If - not, see . */ - -#include - -#include -#include "s_float_bitwise.h" - -/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */ -int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx); - -/* __ieee754_rem_pio2f(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - */ - -static const float npio2_hw[] = { - 1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00, - 7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01, - 1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01, - 2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01, - 2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01, - 3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01, - 3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01, - 4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01 -}; - - -static const float zero = 0.0000000000e+00; -static const float two8 = 2.5600000000e+02; - -static const float half = 5.0000000000e-01; -static const float invpio2 = 6.3661980629e-01; -static const float pio2_1 = 1.5707855225e+00; -static const float pio2_1t = 1.0804334124e-05; -static const float pio2_2 = 1.0804273188e-05; -static const float pio2_2t = 6.0770999344e-11; -static const float pio2_3 = 6.0770943833e-11; -static const float pio2_3t = 6.1232342629e-17; - -static const float pio4 = 7.8539801e-01; -static const float pio3_4 = 2.3561945e+00; -static const float pio2_24b = 1.5707951e+00; -static const float pio2_2e7 = 2.0106054e+02; - - -int32_t -__ieee754_rem_pio2f (float x, float *y) -{ - float ax, z, n, r, w, t, e0; - float tx[3]; - int32_t i, nx; - - ax = __builtin_fabsf (x); - if (ax <= pio4) - { - y[0] = x; - y[1] = 0; - return 0; - } - if (ax < pio3_4) - { - if (x > 0) - { - z = x - pio2_1; - if (!__float_and_test28 (ax, pio2_24b)) - { - y[0] = z - pio2_1t; - y[1] = (z - y[0]) - pio2_1t; - } - else - { - z -= pio2_2; - y[0] = z - pio2_2t; - y[1] = (z - y[0]) - pio2_2t; - } - return 1; - } - else - { - z = x + pio2_1; - if (!__float_and_test28 (ax, pio2_24b)) - { - y[0] = z + pio2_1t; - y[1] = (z - y[0]) + pio2_1t; - } - else - { - z += pio2_2; - y[0] = z + pio2_2t; - y[1] = (z - y[0]) + pio2_2t; - } - return -1; - } - } - if (ax <= pio2_2e7) - { - n = __floorf (ax * invpio2 + half); - i = (int32_t) n; - r = ax - n * pio2_1; - w = n * pio2_1t; /* 1st round good to 40 bit */ - if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1])) - { - y[0] = r - w; - } - else - { - float i, j; - j = __float_and8 (ax); - y[0] = r - w; - i = __float_and8 (y[0]); - if (j / i > 256.0 || j / i < 3.9062500e-3) - { /* 2nd iterations needed, good to 57 */ - t = r; - w = n * pio2_2; - r = t - w; - w = n * pio2_2t - ((t - r) - w); - y[0] = r - w; - i = __float_and8 (y[0]); - if (j / i > 33554432 || j / i < 2.9802322e-8) - { /* 3rd iteration needed, 74 bits acc */ - t = r; - w = n * pio2_3; - r = t - w; - w = n * pio2_3t - ((t - r) - w); - y[0] = r - w; - } - } - } - y[1] = (r - y[0]) - w; - if (x < 0) - { - y[0] = -y[0]; - y[1] = -y[1]; - return -i; - } - else - { - return i; - } - } - - /* all other (large) arguments */ - if (isnanf (x) || isinff (x)) - { - y[0] = y[1] = x - x; - return 0; - } - - /* set z = scalbn(|x|,ilogb(x)-7) */ - e0 = __float_and8 (ax / 128.0); - z = ax / e0; - - tx[0] = __floorf (z); - z = (z - tx[0]) * two8; - tx[1] = __floorf (z); - z = (z - tx[1]) * two8; - tx[2] = __floorf (z); - - nx = 3; - while (tx[nx - 1] == zero) - nx--; - - i = __fp_kernel_rem_pio2f (tx, y, e0, nx); - if (x < 0) - { - y[0] = -y[0]; - y[1] = -y[1]; - return -i; - } - return i; -} diff --git a/sysdeps/powerpc/fpu/k_rem_pio2f.c b/sysdeps/powerpc/fpu/k_rem_pio2f.c deleted file mode 100644 index 7e5a08ba5a5f0d535266467f806cc91162d7f886..0000000000000000000000000000000000000000 --- a/sysdeps/powerpc/fpu/k_rem_pio2f.c +++ /dev/null @@ -1,273 +0,0 @@ -/* k_rem_pio2f.c -- float version of e_rem_pio2.c - Copyright (C) 2011-2018 Free Software Foundation, Inc. - This file is part of the GNU C Library. - Contributed by Adhemerval Zanella , 2011 - - The GNU C Library is free software; you can redistribute it and/or - modify it under the terms of the GNU Library General Public License as - published by the Free Software Foundation; either version 2 of the - License, or (at your option) any later version. - - The GNU C Library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Library General Public License for more details. - - You should have received a copy of the GNU Library General Public - License along with the GNU C Library; see the file COPYING.LIB. If - not, see . */ - -#include - -#include -#include "s_float_bitwise.h" - - -static const float two_over_pi[] = { - 1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02, - 7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01, - 2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02, - 2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02, - 2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02, - 6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01, - 2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02, - 2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01, - 1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01, - 6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02, - 6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02, - 9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01, - 2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01, - 1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01, - 2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02, - 4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02, - 2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01, - 1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01, - 5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01, - 1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02, - 1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02, - 1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01, - 3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02, - 2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01, - 2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02, - 9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01, - 1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02, - 3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02, - 7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02, - 1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01, - 1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02, - 2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02, - 6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02, - 1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02, - 1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02, - 3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00, - 8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01, - 2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02, - 2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01, - 1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01, - 1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01, - 9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00, - 1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01, - 2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01, - 1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02, - 7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01, - 6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01, - 2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02, - 9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02, - 1.40000000e+02, 1.07000000e+02 -}; - - -static const float PIo2[] = { - 1.5703125000e+00, /* 0x3fc90000 */ - 4.5776367188e-04, /* 0x39f00000 */ - 2.5987625122e-05, /* 0x37da0000 */ - 7.5437128544e-08, /* 0x33a20000 */ - 6.0026650317e-11, /* 0x2e840000 */ - 7.3896444519e-13, /* 0x2b500000 */ - 5.3845816694e-15, /* 0x27c20000 */ - 5.6378512969e-18, /* 0x22d00000 */ - 8.3009228831e-20, /* 0x1fc40000 */ - 3.2756352257e-22, /* 0x1bc60000 */ - 6.3331015649e-25, /* 0x17440000 */ -}; - - -static const float zero = 0.0000000000e+00; -static const float one = 1.0000000000; -static const float twon8 = 3.9062500000e-03; -static const float two8 = 2.5600000000e+02; - - -int32_t -__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx) -{ - int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp; - float z, fw, f[20], fq[20], q[20]; - - /* initialize jk */ - jp = jk = 9; - - /* determine jx,jv,q0, note that 3>q0 */ - jx = nx - 1; - exp = __float_get_exp (e0) - 127; - jv = (exp - 3) / 8; - if (jv < 0) - jv = 0; - q0 = exp - 8 * (jv + 1); - - /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */ - j = jv - jx; - m = jx + jk; - for (i = 0; i <= m; i++, j++) - f[i] = (j < 0) ? zero : two_over_pi[j]; - - /* compute q[0],q[1],...q[jk] */ - for (i = 0; i <= jk; i++) - { - for (j = 0, fw = 0.0; j <= jx; j++) - fw += x[j] * f[jx + i - j]; - q[i] = fw; - } - - jz = jk; -recompute: - /* distill q[] into iq[] reversingly */ - for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) - { - fw = __truncf (twon8 * z); - iq[i] = (int32_t) (z - two8 * fw); - z = q[j - 1] + fw; - } - - /* compute n */ - z = __scalbnf (z, q0); /* actual value of z */ - z -= 8.0 * __floorf (z * 0.125); /* trim off integer >= 8 */ - n = (int32_t) z; - z -= __truncf (z); - ih = 0; - if (q0 > 0) - { /* need iq[jz-1] to determine n */ - i = (iq[jz - 1] >> (8 - q0)); - n += i; - iq[jz - 1] -= i << (8 - q0); - ih = iq[jz - 1] >> (7 - q0); - } - else if (q0 == 0) - ih = iq[jz - 1] >> 7; - else if (z >= 0.5) - ih = 2; - - if (ih > 0) - { /* q > 0.5 */ - n += 1; - carry = 0; - for (i = 0; i < jz; i++) - { /* compute 1-q */ - j = iq[i]; - if (carry == 0) - { - if (j != 0) - { - carry = 1; - iq[i] = 0x100 - j; - } - } - else - iq[i] = 0xff - j; - } - if (q0 > 0) - { /* rare case: chance is 1 in 12 */ - switch (q0) - { - case 1: - iq[jz - 1] &= 0x7f; - break; - case 2: - iq[jz - 1] &= 0x3f; - break; - } - } - if (ih == 2) - { - z = one - z; - if (carry != 0) - z -= __scalbnf (one, q0); - } - } - - /* check if recomputation is needed */ - if (z == zero) - { - j = 0; - for (i = jz - 1; i >= jk; i--) - j |= iq[i]; - if (j == 0) - { /* need recomputation */ - for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */ - - for (i = jz + 1; i <= jz + k; i++) - { /* add q[jz+1] to q[jz+k] */ - f[jx + i] = two_over_pi[jv + i]; - for (j = 0, fw = 0.0; j <= jx; j++) - fw += x[j] * f[jx + i - j]; - q[i] = fw; - } - jz += k; - goto recompute; - } - } - - /* chop off zero terms */ - if (z == 0.0) - { - jz -= 1; - q0 -= 8; - while (iq[jz] == 0) - { - jz--; - q0 -= 8; - } - } - else - { /* break z into 8-bit if necessary */ - z = __scalbnf (z, -q0); - if (z >= two8) - { - fw = __truncf (twon8 * z); - iq[jz] = (int32_t) (z - two8 * fw); - jz += 1; - q0 += 8; - iq[jz] = (int32_t) fw; - } - else - iq[jz] = (int32_t) z; - } - - /* convert integer "bit" chunk to floating-point value */ - fw = __scalbnf (one, q0); - for (i = jz; i >= 0; i--) - { - q[i] = fw * (float) iq[i]; - fw *= twon8; - } - - /* compute PIo2[0,...,jp]*q[jz,...,0] */ - for (i = jz; i >= 0; i--) - { - for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) - fw += PIo2[k] * q[i + k]; - fq[jz - i] = fw; - } - - /* compress fq[] into y[] */ - fw = 0.0; - for (i = jz; i >= 0; i--) - fw += fq[i]; - y[0] = (ih == 0) ? fw : -fw; - fw = fq[0] - fw; - for (i = 1; i <= jz; i++) - fw += fq[i]; - y[1] = (ih == 0) ? fw : -fw; - - return n & 7; -}