2001-02-19 10:09:18 +01:00
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.file "cbrtf.asm"
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2002-07-06 08:36:39 +02:00
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// Copyright (C) 2000, 2001, Intel Corporation
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2001-02-19 10:09:18 +01:00
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Cristina Iordache, Ted Kubaska,
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// Bob Norin, Shane Story, and Ping Tak Peter Tang
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// of the Computational Software Lab, Intel Corporation.
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2002-07-06 08:36:39 +02:00
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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//
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2001-02-19 10:09:18 +01:00
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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//
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// History
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//==============================================================
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// 2/02/00: Initial version
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// 5/18/00: New version (modified algorithm)
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//
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// API
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//==============================================================
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// float cbrtf(float)
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//
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// Overview of operation
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//==============================================================
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// Background
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//
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// Implementation
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//
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// cbrt(a) = cbrt(a y) / cbrt(y)
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// = cbrt(1 - (1 - a y)) * 1/cbrt(y)
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//
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// where y = frcpa(a).
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//
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// * cbrt(1 - (1 - a y)) is approximated by a degree-2 polynomial
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//
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// 1 - (1/3)*r - (1/9)*r^2
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//
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// in r = 1 - a y.
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//
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// * The values 1/cbrt(y) are stored in a table of constants T0
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// to 64 bits of accuracy
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//
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// The table values are stored for three exponent values and are
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// then multiplied by e/3 where e is the exponent of the input number.
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// This computation is carried out in parallel with the polynomial
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// evaluation:
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//
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// T = 2^(e/3) * T0
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//===============
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// input = x
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// C = frcpa(x)
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// r = 1 - C * x
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//
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// Special values
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//==============================================================
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// Registers used
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//==============================================================
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// f6-f15
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// r2, r23-r26, r28-r30
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// p6,p7,p8,p12
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#include "libm_support.h"
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// Data tables
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//==============================================================
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#ifdef _LIBC
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.rodata
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#else
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.data
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#endif
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.align 16
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poly_coeffs:
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ASM_TYPE_DIRECTIVE(poly_coeffs,@object)
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data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // 1/3
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data8 0xe38e38e38e38e38e, 0x00003ffb // 1/9
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ASM_SIZE_DIRECTIVE(poly_coeffs)
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T_table:
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ASM_TYPE_DIRECTIVE(T_table,@object)
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data8 0x80155c748c374836, 0xa160019ed37fb4ae
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data8 0xa6dc094d10f25792, 0xd23ad555f773f059
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data8 0x8753ec4a92d16c5e, 0xaa809b9c60d1890b
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data8 0xd6d1ccc1fc4ef4b7, 0x877bff3aca19f6b4
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data8 0xf7cddf140aedf1d8, 0x9c3ed09216e9ca02
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|
data8 0xc4db5941007aa853, 0xf806291bacb7f7a9
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data8 0x9c568656c0423def, 0xc4f938aec206291a
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data8 0xf82bcc43b92eafef, 0x9c7a320af242ce60
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|
data8 0xc52629e899dfd622, 0xf8646bf0defb759e
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|
data8 0x9c920bf7a8c01dc2, 0xc54436e44043b965
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|
data8 0xf88a487dfc3ff5f7, 0x9ca9f475d98b159c
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data8 0xc562563abf9ea07f, 0xf8b03c2b46cdc17f
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|
data8 0x9ccdeca60e80b5f8, 0xc58fa7d1dc42921c
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|
data8 0xf8e95541c152ae7a, 0x9ce5f9d4653d4902
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|
data8 0xc5adf561b91e110a, 0xf90f832c2700c160
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|
data8 0x9cfe15cb38bfdd8e, 0xc5cc5591bdbd82fa
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data8 0xf935c88e0c7f419b, 0x9d225b983f6c1f96
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data8 0xc5fa08f1ff20593c, 0xf96f5cd84fd86873
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data8 0x9d3a9cca32261ed7, 0xc618980a79ce6862
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data8 0xf995dd53ebdd9d6d, 0x9d52ecfccebe1768
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data8 0xc6373a09e34b50fa, 0xf9bc75a034436a41
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data8 0x9d77818d95b82f86, 0xc66550a6e0baaf35
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data8 0xf9f686f26d5518de, 0x9d8ff7893fa4706c
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data8 0xc6842241926342c9, 0xfa1d5b39b910a8c5
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data8 0x9da87cbef36f2a5e, 0xc6a3070b7c93bb9e
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data8 0xfa4447acc4ecbfd2, 0x9dcd6140b4a35aeb
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data8 0xc6d18260bb84081b, 0xfa7ed7e51e6fdfb4
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data8 0x9de60cd06dc6e2d4, 0xc6f0977c9416828b
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data8 0xfaa601394d49a1a0, 0x9dfec7d4cc43b76f
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data8 0xc70fc0117c641630, 0xfacd431644ce0e40
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data8 0x9e17925ec9fccc4a, 0xc72efc34d7e615be
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data8 0xfaf49d96f7a75909, 0x9e3cdf6db57dc075
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data8 0xc75dfb441594141e, 0xfb2fd3c65e562fd5
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data8 0x9e55d110b63637a8, 0xc77d68aa019bda4c
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data8 0xfb576c5762024805, 0x9e6ed27594550d2e
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data8 0xc79ce9ea478dbc4f, 0xfb7f1debc22c4040
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data8 0x9e87e3adc385d393, 0xc7bc7f1ae453219d
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data8 0xfba6e89f32d0190a, 0x9ead9b54b37a1055
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data8 0xc7ec0476e15e141a, 0xfbe2c803a0894893
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data8 0x9ec6d46a3d7de215, 0xc80bcbe16f1d540f
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data8 0xfc0ad1ff0ed9ecf0, 0x9ee01d9108be3154
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data8 0xc82ba78a5d349735, 0xfc32f57bdfbcbe7f
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data8 0x9ef976db07288d04, 0xc84b978847a06b87
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data8 0xfc5b32968f99b21c, 0x9f12e05a4759ec25
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data8 0xc86b9bf1ee817bc6, 0xfc83896bc861ab08
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data8 0x9f2c5a20f4da6668, 0xc88bb4de3667cdf4
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data8 0xfcabfa1861ed4815, 0x9f52af78ed1733ca
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data8 0xc8bc00e7fe9e23a3, 0xfce8d3cea7d3163e
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data8 0x9f6c52426a39d003, 0xc8dc4d7ff2d25232
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data8 0xfd118595143ee273, 0x9f860593d42fd7f3
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data8 0xc8fcaeebcb40eb47, 0xfd3a519943d4865a
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data8 0x9f9fc97fdb96bd51, 0xc91d25431426a663
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data8 0xfd6337f8e1ae5a4b, 0x9fb99e194f4a7037
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data8 0xc93db09d7fdb2949, 0xfd8c38d1c8e927eb
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data8 0x9fd383731ca51db9, 0xc95e5112e721582a
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data8 0xfdb5544205095a53, 0x9fed79a04fbf9423
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data8 0xc97f06bb49787677, 0xfdde8a67d2613531
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data8 0xa00780b413b24ee8, 0xc99fd1aecd6e1b06
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data8 0xfe07db619e781611, 0xa02eab2c4474b0cd
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data8 0xc9d12a3e27bb1625, 0xfe460768d80bf758
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data8 0xa048dcd51ccfd142, 0xc9f22ad82ba3d5f0
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data8 0xfe6f9bfb06cd32f6, 0xa0631fa894b11b8d
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data8 0xca134113105e67b2, 0xfe994bcd3d14fcc2
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data8 0xa07d73ba65e680af, 0xca346d07b045a876
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|
data8 0xfec316fecaf3f2ab, 0xa097d91e6aaf71b0
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|
data8 0xca55aecf0e94bb88, 0xfeecfdaf33fadb80
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data8 0xa0b24fe89e02602f, 0xca77068257be9bab
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|
data8 0xff16fffe2fa8fad6, 0xa0ccd82d1bd2f68b
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|
data8 0xca98743ae1c693a8, 0xff411e0ba9db886d
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|
data8 0xa0e77200215909e6, 0xcab9f8122c99a101
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data8 0xff6b57f7c33e4e9a, 0xa1021d760d584855
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|
data8 0xcadb9221e268c3b5, 0xff95ade2d1bd7358
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|
data8 0xa11cdaa36068a57d, 0xcafd4283d8043dfd
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|
data8 0xffc01fed60f86fb5, 0xa137a99cbd3f880b
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|
data8 0xcb1f09520d37c6fb, 0xffeaae3832b63956
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|
ASM_SIZE_DIRECTIVE(T_table)
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.align 32
|
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|
.global cbrtf#
|
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.section .text
|
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.proc cbrtf#
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.align 32
|
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|
cbrtf:
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{ .mfi
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getf.sig r28=f8
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|
// will continue only for normal/denormal numbers
|
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|
(p0) fclass.nm.unc p12,p7 = f8, 0x1b
|
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|
// r2 = pointer to C_1,C_2 followed by T_table
|
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|
|
addl r2 = @ltoff(poly_coeffs), gp
|
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|
|
}
|
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|
{.mfi
|
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|
|
// r29=bias-((2^8-1)/3) -63=0xffff-0x55-0x3f=0xff6b
|
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|
|
mov r29=0xff6b
|
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|
|
// normalize a
|
|
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|
|
fma.s1 f14=f8,f1,f0
|
|
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|
|
nop.i 0;;
|
|
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|
|
}
|
|
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|
|
{.mib
|
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|
|
nop.m 0
|
|
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|
|
(p7) cmp.eq p12,p0=r28,r0
|
|
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|
|
nop.b 0;;
|
|
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|
|
}
|
|
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|
|
{.mfb
|
|
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|
|
// load start address for C_1,C_2 followed by T_table
|
|
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|
|
ld8 r2=[r2]
|
|
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|
|
(p12) fma.s.s0 f8=f8,f1,f0
|
|
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|
|
(p12) br.ret.spnt b0;;
|
|
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|
|
}
|
|
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|
|
{.mmf
|
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|
|
|
// load C_1
|
|
|
|
|
ldfe f7=[r2],16
|
|
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|
|
nop.m 0
|
|
|
|
|
// y=frcpa(a)
|
|
|
|
|
frcpa.s0 f8,p6=f1,f8;;
|
|
|
|
|
}
|
|
|
|
|
{.mmi
|
|
|
|
|
// load C_2
|
|
|
|
|
ldfe f9=[r2],16
|
|
|
|
|
// r28=bias-(2^8-1)
|
|
|
|
|
mov r28=0xff00
|
|
|
|
|
nop.i 0;;
|
|
|
|
|
}
|
|
|
|
|
{.mmi
|
|
|
|
|
// get normalized significand
|
|
|
|
|
getf.sig r23=f14
|
|
|
|
|
// get exponent
|
|
|
|
|
getf.exp r24=f14
|
|
|
|
|
mov r25=0x20000;;
|
|
|
|
|
}
|
|
|
|
|
{.mii
|
|
|
|
|
// get r26=sign
|
|
|
|
|
and r26=r24,r25
|
|
|
|
|
// eliminate leading 1 from r23=1st table index
|
|
|
|
|
shl r23=r23,1
|
|
|
|
|
// eliminate sign from exponent (r25)
|
|
|
|
|
andcm r25=r24,r25;;
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
// subtract bias from r25=exponent
|
|
|
|
|
sub r25=r25,r28
|
|
|
|
|
// r=1-a*y
|
|
|
|
|
(p6) fnma.s1 f6=f8,f14,f1
|
|
|
|
|
// r23=1st table index (y_index8 bits)
|
|
|
|
|
shr.u r23=r23,56;;
|
|
|
|
|
}
|
|
|
|
|
{.mii
|
|
|
|
|
// 1: exponent*=5; // (2^{16}-1)/3=0x5555
|
|
|
|
|
shladd r24=r25,2,r25
|
|
|
|
|
// r23=3*y_index
|
|
|
|
|
shladd r23=r23,1,r23;;
|
|
|
|
|
// r30=(5*expon)*16+5*expon=(0x55)*expon
|
|
|
|
|
shladd r30=r24,4,r24;;
|
|
|
|
|
}
|
|
|
|
|
{.mmi
|
|
|
|
|
// adjust T_table pointer by 1st index
|
|
|
|
|
shladd r2=r23,3,r2;;
|
|
|
|
|
// f10=T[0][y]
|
|
|
|
|
(p6) ldf8 f10=[r2],8
|
|
|
|
|
// r24=(0x5500)*expon
|
|
|
|
|
shl r24=r30,8;;
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
// f11=T[1][y]
|
|
|
|
|
(p6) ldf8 f11=[r2],8
|
|
|
|
|
// P_1=C_1+C_2*r
|
|
|
|
|
(p6) fma.s1 f7=f9,f6,f7
|
|
|
|
|
// r24=(0x5555)*expon
|
|
|
|
|
add r24=r24,r30;;
|
|
|
|
|
}
|
|
|
|
|
{.mmi
|
|
|
|
|
// r24=(0x5556)*expon // 0x5556=(2^{16}+2)/3
|
|
|
|
|
add r24=r24,r25;;
|
|
|
|
|
// f8=T[2][y]
|
|
|
|
|
(p6) ldf8 f8=[r2]
|
|
|
|
|
// r24=floor(expon/3)
|
|
|
|
|
shr r24=r24,16;;
|
|
|
|
|
}
|
|
|
|
|
{.mmi
|
|
|
|
|
nop.m 0
|
|
|
|
|
// r28=3*exponent
|
|
|
|
|
shladd r28=r24,1,r24
|
|
|
|
|
// bias exponent
|
|
|
|
|
add r24=r29,r24;;
|
|
|
|
|
}
|
|
|
|
|
{.mmi
|
|
|
|
|
// get remainder of exponent/3
|
|
|
|
|
sub r25=r25,r28
|
|
|
|
|
// add sign to exponent
|
|
|
|
|
or r24=r24,r26
|
|
|
|
|
nop.i 0;;
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
nop.m 0
|
|
|
|
|
// P_2=-r*P_1
|
|
|
|
|
(p6) fnma.s1 f6=f7,f6,f0
|
|
|
|
|
// remainder=0 ?
|
|
|
|
|
(p6) cmp.eq.unc p7,p8=r0,r25;;
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
// f14=sign*2^{exponent/3}
|
|
|
|
|
(p6) setf.exp f14=r24
|
|
|
|
|
nop.f 0
|
|
|
|
|
// remainder = 1 ?
|
|
|
|
|
(p8) cmp.eq.unc p8,p12=1,r25;;
|
|
|
|
|
}
|
|
|
|
|
.pred.rel "mutex",p7,p8
|
|
|
|
|
{.mfi
|
|
|
|
|
nop.m 0
|
|
|
|
|
// remainder=0 -> use T=f10
|
|
|
|
|
(p7) fma.s1 f8=f10,f6,f10
|
|
|
|
|
nop.i 0
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
nop.m 0
|
|
|
|
|
// remainder =1 -> use f11
|
|
|
|
|
(p8) fma.s1 f8=f11,f6,f11
|
|
|
|
|
nop.i 0;;
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
nop.m 0
|
|
|
|
|
// result=T+T*P_2
|
|
|
|
|
(p12) fma.s.s0 f8=f8,f6,f8
|
|
|
|
|
nop.i 0;;
|
|
|
|
|
}
|
|
|
|
|
{.mfb
|
|
|
|
|
nop.m 0
|
|
|
|
|
// T*=sgn*2^{expon/3}
|
|
|
|
|
(p6) fma.s.s0 f8=f8,f14,f0
|
|
|
|
|
br.ret.sptk b0;;
|
|
|
|
|
}
|
|
|
|
|
.endp cbrtf
|
|
|
|
|
ASM_SIZE_DIRECTIVE(cbrtf)
|
