2012-04-17 02:02:27 +00:00
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.file "cbrt.s"
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// Copyright (c) 2000 - 2003, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2000 by the Intel Numerics Group, Intel Corporation
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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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// 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://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 02/02/00 Initial version
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// 05/19/00 New version (modified algorithm)
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 01/28/03 Updated polynomial coefficients (changed to Remez coefficients),
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// to slightly improve accuracy
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//
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// API
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//==============================================================
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// double cbrt(double)
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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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// Let y= frcpa(a), where a is the argument
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//
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// cbrt(a)= cbrt(a*y)/cbrt(y) = cbrt(1 - (1-a*y)) * (1/cbrt(y))
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//
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// For all values of y, the 3 possible significands of 1/cbrt(y)
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// are stored in a table (T0) to 64 bits of accuracy. (There are
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// 3 possible significands because the exponent of y modulo 3
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// can be 0, 1, or 2.)
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//
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//
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// * cbrt(1 - (1-a*y)) is approximated by a degree-5 polynomial ~
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//
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// ~ 1 - (1/3)*r - (1/9)*r^2 - (5/81)*r^3 - (10/243)*r^4 - (22/729)*r^5
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//
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// in r = 1-a*y.
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//
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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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// GR_GP, r23-r26, r28-r30
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// p6, p7, p8, p12
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FR_R = f6
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FR_COEFF1 = f7
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FR_COEFF2 = f9
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FR_COEFF3 = f10
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FR_COEFF4 = f11
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FR_COEFF5 = f12
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FR_R2 = f13
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FR_ARG = f14
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FR_P23 = f15
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FR_P25 = f32
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FR_P15 = f33
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FR_P1 = f34
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FR_P45 = f35
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FR_2EXP = f36
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FR_TMP63 = f37
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GR_GP = r2
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GR_ADDR = r2
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GR_CONST1 = r3
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GR_I1 = r8
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GR_EXP = r9
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GR_ADDR2 = r10
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GR_IT1 = r11
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GR_TMP2 = r11
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GR_EXPON = r15
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GR_TMP1 = r16
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GR_TMP6 = r16
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GR_ITB1 = r17
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GR_TMP3 = r18
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GR_TMP4 = r19
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GR_TMP63 = r19
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GR_TMP5 = r20
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GR_EXP_BY_3 = r20
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GR_CONST4 = r21
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GR_TMP6 = r22
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GR_INDEX = r23
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GR_EBIAS = r24
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GR_SIGNIF = r25
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GR_SIGNIF2 = r25
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GR_TEST = r25
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GR_ARGEXP = r26
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GR_CONST2 = r27
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GR_SIGN = r28
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GR_REM = r29
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GR_CONST3 = r30
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GR_SEXP = r31
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// Data tables
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(poly_coeffs)
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data8 0xaaaaaaaaaaaaaab4, 0x0000bffd // ~ 1/3
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data8 0xbfbc71c71c718e45, 0xbfaf9add3c0bbb43
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data8 0xbfa511edb93dc98d, 0xbf9ee71c45f0dfbc
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LOCAL_OBJECT_END(poly_coeffs)
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// For every entry B in the frcpa table, this table contains
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// the significands of cbrt(1/B), cbrt(2/B), cbrt(4/B).
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// The index to this table is the same as the frcpa index.
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LOCAL_OBJECT_START(T_table)
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data8 0x80155c748c374836, 0xa160019ed37fb4ae
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data8 0xcb51ddcb9e93095e, 0x8040404b0879f7f9
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data8 0xa1960b5966da4608, 0xcb95f333968ad59b
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data8 0x806b5dce4b405c10, 0xa1cc5dbe6dc2aab4
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data8 0xcbda64292d3ffd97, 0x8096b586974669b1
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data8 0xa202f97995b69c0d, 0xcc1f3184af961596
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data8 0x80bcd273d952a028, 0xa232fe6eb0c0577d
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data8 0xcc5bb1ac954d33e2, 0x80e898c52813f2f3
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data8 0xa26a2582012f6e17, 0xcca12e9831fc6402
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data8 0x81149add67c2d208, 0xa2a197e5d10465cb
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data8 0xcce70a67b64f24ad, 0x813b4e2c856b6e9a
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data8 0xa2d25a532efefbc8, 0xcd24794726477ea5
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data8 0x8167c1dde03de7aa, 0xa30a5bd6e49e4ab8
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data8 0xcd6b096a0b70ee87, 0x818ed973b811135e
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data8 0xa33b9c9b59879e24, 0xcda9177738b15a90
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data8 0x81bbc0c33e13ec98, 0xa3742fca6a3c1f21
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data8 0xcdf05f2247dffab9, 0x81e33e69fbe7504a
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data8 0xa3a5f1273887bf22, 0xce2f0f347f96f906
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data8 0x820aec524e3c23e9, 0xa3d7ef508ff11574
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data8 0xce6e0be0cd551a61, 0x823880f78e70b805
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data8 0xa4115ce30548bc15, 0xceb666b2c347d1de
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data8 0x826097a62a8e5200, 0xa443df0e53df577a
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data8 0xcef609b0cb874f00, 0x8288dfe00e9b5eaf
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data8 0xa4769fa5913c0ec3, 0xcf35fb5447e5c765
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data8 0x82b15a10c5371624, 0xa4a99f303bc7def5
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data8 0xcf763c47ee869f00, 0x82da06a527b18937
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data8 0xa4dcde37779adf4b, 0xcfb6cd3888d71785
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data8 0x8302e60b635ab394, 0xa5105d46152c938a
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data8 0xcff7aed4fbfbb447, 0x832bf8b2feec2f0e
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data8 0xa5441ce89825cb8d, 0xd038e1ce5167e3c6
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data8 0x83553f0ce00e276b, 0xa5781dad3e54d899
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data8 0xd07a66d7bfa0ebba, 0x837eb98b50f8322a
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data8 0xa5ac602406c4e68c, 0xd0bc3ea6b32d1b21
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data8 0x83a270f44c84f699, 0xa5d9601d95c2c0bc
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data8 0xd0f4f0e8f36c1bf8, 0x83cc4d7cfcfac5ca
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data8 0xa60e1e1a2de14745, 0xd1376458e34b037e
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data8 0x83f65f78a8872b4c, 0xa6431f6e3fbd9658
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data8 0xd17a2ca133f78572, 0x8420a75f2f7b53c8
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data8 0xa67864b0d432fda4, 0xd1bd4a80301c5715
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data8 0x844510461ff14209, 0xa6a6444aa0243c0b
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data8 0xd1f71682b2fa4575, 0x846fbd91b930bed2
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data8 0xa6dc094d10f25792, 0xd23ad555f773f059
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data8 0x84947e18234f3294, 0xa70a574cc02bba69
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data8 0xd2752c7039a5bf73, 0x84bf92755825045a
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data8 0xa7409e2af9549084, 0xd2b98ee008c06b59
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data8 0x84e4ac0ee112ba51, 0xa76f5c64ca2cf13b
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data8 0xd2f4735ffd700280, 0x8509ef44b86f20be
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data8 0xa79e4f0babab5dc0, 0xd32f99ed6d9ac0e1
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data8 0x85359d5d91768427, 0xa7d5579ae5164b85
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data8 0xd374f0666c75d51c, 0x855b3bd5b7384357
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data8 0xa804bd3c6fe61cc8, 0xd3b0a7d13618e4a1
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data8 0x858104f0c415f79a, 0xa8345895e5250a5a
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data8 0xd3eca2ea53bcec0c, 0x85a6f90390d29864
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data8 0xa8642a122b44ef0b, 0xd428e23874f13a17
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data8 0x85d3772fcd56a1dd, 0xa89c38ca18f6108b
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data8 0xd46f82fe293bc6d3, 0x85f9c982fcc002f3
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data8 0xa8cc81063b6e87ca, 0xd4ac57e9b7186420
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data8 0x862047e0e7ea554b, 0xa8fd00bfa409285e
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data8 0xd4e972becb04e8b8, 0x8646f2a26f7f5852
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data8 0xa92db8664d5516da, 0xd526d40a7a9b43a3
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data8 0x866dca21754096b5, 0xa95ea86b75cc2c20
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data8 0xd5647c5b73917370, 0x8694ceb8dfd17a37
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data8 0xa98fd141a4992deb, 0xd5a26c4201bd6d13
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data8 0x86bc00c49e9307e8, 0xa9c1335cae7446ba
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data8 0xd5e0a45015350a7e, 0x86dccd74fce79610
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data8 0xa9ea8686f556f645, 0xd614b539c6194104
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data8 0x870453c845acf90f, 0xaa1c52d17906bb19
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data8 0xd6537310e224283f, 0x872c089a1e90342c
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data8 0xaa4e59b046dab887, 0xd6927ab62244c917
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data8 0x8753ec4a92d16c5e, 0xaa809b9c60d1890b
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data8 0xd6d1ccc1fc4ef4b7, 0x877bff3aca19f6b4
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data8 0xaab319102f3f9b33, 0xd71169cea98fdded
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data8 0x879d88b6fe1c324c, 0xaadd5a18c1e21274
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data8 0xd746a66a5bc9f6d9, 0x87c5f346dbf98c3a
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data8 0xab1045f2ac31bdf5, 0xd786ce8f0fae5317
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data8 0x87e7c653efacef2c, 0xab3ae3ab2df7231e
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data8 0xd7bc7ff214c4e75a, 0x881089d4e73ffefc
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data8 0xab6e3f945d1e96fc, 0xd7fd35467a517ed1
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data8 0x88397e6a366f2a8a, 0xaba1d953a08fa94e
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data8 0xd83e38838648d815, 0x885bc559e5e1c081
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data8 0xabcd090db7ef4c3f, 0xd874a1db598b8951
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data8 0x887e2ee392bb7a93, 0xabf864602d7c323d
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data8 0xd8ab42205b80edaf, 0x88a7a8587e404257
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data8 0xac2ca5886ccf9b57, 0xd8ed1849d202f965
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data8 0x88ca5eda67594784, 0xac5861d4aa441f0f
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data8 0xd92432bd5a173685, 0x88f4356166bd590e
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data8 0xac8d183fe3a2fbed, 0xd9669ca45b03c23e
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data8 0x89173a0acf5ce026, 0xacb93703ff51571e
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data8 0xd99e3327cf89574e, 0x893a62a098b6a57b
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data8 0xace5830ad0c3f14b, 0xd9d602b19b100466
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data8 0x895daf637236ae2c, 0xad11fca5d78b3ff2
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data8 0xda0e0ba86c096841, 0x89883b9d1c2fa9c5
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data8 0x99d31ca0887f30f9, 0xc1ce9268f31cc734
|
|
|
|
|
data8 0xf42e718b90c8bc16, 0x99f48a669c74c09e
|
|
|
|
|
data8 0xc1f8b0877c1b0c08, 0xf463822a0a3b4b00
|
|
|
|
|
data8 0x9a16154eb445c873, 0xc222f35a87b415ba
|
|
|
|
|
data8 0xf498c1076015faf8, 0x9a2c822ec198d667
|
|
|
|
|
data8 0xc23f3467349e5c88, 0xf4bc5a19a33990b5
|
|
|
|
|
data8 0x9a4e3e080cd91b78, 0xc269b4e40e088c01
|
|
|
|
|
data8 0xf4f1e6a7d6f5425f, 0x9a70177afe52322e
|
|
|
|
|
data8 0xc2945aac24daaf6e, 0xf527a232cf6be334
|
|
|
|
|
data8 0x9a86b8fa94eebe10, 0xc2b0de05e43c1d66
|
|
|
|
|
data8 0xf54b8ecdcda90851, 0x9aa8c42866ae2958
|
|
|
|
|
data8 0xc2dbc275e1229d09, 0xf5819949c7ad87b4
|
|
|
|
|
data8 0x9abf86f9e12fc45e, 0xc2f86fca9d80eeff
|
|
|
|
|
data8 0xf5a5bac9213b48a9, 0x9ae1c462fc05f49d
|
|
|
|
|
data8 0xc323938449a2587e, 0xf5dc1501f324a812
|
|
|
|
|
data8 0x9af8a8dc936b84d0, 0xc3406b40a538ed20
|
|
|
|
|
data8 0xf6006bee86b5589e, 0x9b1b19033be35730
|
|
|
|
|
data8 0xc36bcee8211d15e0, 0xf63716b2fa067fa4
|
|
|
|
|
data8 0x9b3da7daf04c2892, 0xc397593adf2ba366
|
|
|
|
|
data8 0xf66df22fb6132b9c, 0x9b54c2e4c8a9012b
|
|
|
|
|
data8 0xc3b475b6206155d5, 0xf6929fb98225deb1
|
|
|
|
|
data8 0x9b77854e6c661200, 0xc3e0410243b97383
|
|
|
|
|
data8 0xf6c9cd13021e3fea, 0x9b8ec2e678d56d2f
|
|
|
|
|
data8 0xc3fd890709833d37, 0xf6eeb177472cedae
|
|
|
|
|
data8 0x9ba60e6a5ca133b6, 0xc41ae295f7e7fa06
|
|
|
|
|
data8 0xf713abf4cb0b3afb, 0x9bc919ea66a151a4
|
|
|
|
|
data8 0xc44709f7bb8a4dd2, 0xf74b4d5333684ef1
|
|
|
|
|
data8 0x9be0887c09ef82bb, 0xc4648fb0e0bec4c1
|
|
|
|
|
data8 0xf7707f75a72f8e94, 0x9c03c8d5fffc3503
|
|
|
|
|
data8 0xc490f9a94695ba14, 0xf7a874b97927af44
|
|
|
|
|
data8 0x9c1b5ad21a81cbb9, 0xc4aeac0173b7d390
|
|
|
|
|
data8 0xf7cddf140aedf1d8, 0x9c3ed09216e9ca02
|
|
|
|
|
data8 0xc4db5941007aa853, 0xf806291bacb7f7a9
|
|
|
|
|
data8 0x9c568656c0423def, 0xc4f938aec206291a
|
|
|
|
|
data8 0xf82bcc43b92eafef, 0x9c7a320af242ce60
|
|
|
|
|
data8 0xc52629e899dfd622, 0xf8646bf0defb759e
|
|
|
|
|
data8 0x9c920bf7a8c01dc2, 0xc54436e44043b965
|
|
|
|
|
data8 0xf88a487dfc3ff5f7, 0x9ca9f475d98b159c
|
|
|
|
|
data8 0xc562563abf9ea07f, 0xf8b03c2b46cdc17f
|
|
|
|
|
data8 0x9ccdeca60e80b5f8, 0xc58fa7d1dc42921c
|
|
|
|
|
data8 0xf8e95541c152ae7a, 0x9ce5f9d4653d4902
|
|
|
|
|
data8 0xc5adf561b91e110a, 0xf90f832c2700c160
|
|
|
|
|
data8 0x9cfe15cb38bfdd8e, 0xc5cc5591bdbd82fa
|
|
|
|
|
data8 0xf935c88e0c7f419b, 0x9d225b983f6c1f96
|
|
|
|
|
data8 0xc5fa08f1ff20593c, 0xf96f5cd84fd86873
|
|
|
|
|
data8 0x9d3a9cca32261ed7, 0xc618980a79ce6862
|
|
|
|
|
data8 0xf995dd53ebdd9d6d, 0x9d52ecfccebe1768
|
|
|
|
|
data8 0xc6373a09e34b50fa, 0xf9bc75a034436a41
|
|
|
|
|
data8 0x9d77818d95b82f86, 0xc66550a6e0baaf35
|
|
|
|
|
data8 0xf9f686f26d5518de, 0x9d8ff7893fa4706c
|
|
|
|
|
data8 0xc6842241926342c9, 0xfa1d5b39b910a8c5
|
|
|
|
|
data8 0x9da87cbef36f2a5e, 0xc6a3070b7c93bb9e
|
|
|
|
|
data8 0xfa4447acc4ecbfd2, 0x9dcd6140b4a35aeb
|
|
|
|
|
data8 0xc6d18260bb84081b, 0xfa7ed7e51e6fdfb4
|
|
|
|
|
data8 0x9de60cd06dc6e2d4, 0xc6f0977c9416828b
|
|
|
|
|
data8 0xfaa601394d49a1a0, 0x9dfec7d4cc43b76f
|
|
|
|
|
data8 0xc70fc0117c641630, 0xfacd431644ce0e40
|
|
|
|
|
data8 0x9e17925ec9fccc4a, 0xc72efc34d7e615be
|
|
|
|
|
data8 0xfaf49d96f7a75909, 0x9e3cdf6db57dc075
|
|
|
|
|
data8 0xc75dfb441594141e, 0xfb2fd3c65e562fd5
|
|
|
|
|
data8 0x9e55d110b63637a8, 0xc77d68aa019bda4c
|
|
|
|
|
data8 0xfb576c5762024805, 0x9e6ed27594550d2e
|
|
|
|
|
data8 0xc79ce9ea478dbc4f, 0xfb7f1debc22c4040
|
|
|
|
|
data8 0x9e87e3adc385d393, 0xc7bc7f1ae453219d
|
|
|
|
|
data8 0xfba6e89f32d0190a, 0x9ead9b54b37a1055
|
|
|
|
|
data8 0xc7ec0476e15e141a, 0xfbe2c803a0894893
|
|
|
|
|
data8 0x9ec6d46a3d7de215, 0xc80bcbe16f1d540f
|
|
|
|
|
data8 0xfc0ad1ff0ed9ecf0, 0x9ee01d9108be3154
|
|
|
|
|
data8 0xc82ba78a5d349735, 0xfc32f57bdfbcbe7f
|
|
|
|
|
data8 0x9ef976db07288d04, 0xc84b978847a06b87
|
|
|
|
|
data8 0xfc5b32968f99b21c, 0x9f12e05a4759ec25
|
|
|
|
|
data8 0xc86b9bf1ee817bc6, 0xfc83896bc861ab08
|
|
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|
|
data8 0x9f2c5a20f4da6668, 0xc88bb4de3667cdf4
|
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|
|
data8 0xfcabfa1861ed4815, 0x9f52af78ed1733ca
|
|
|
|
|
data8 0xc8bc00e7fe9e23a3, 0xfce8d3cea7d3163e
|
|
|
|
|
data8 0x9f6c52426a39d003, 0xc8dc4d7ff2d25232
|
|
|
|
|
data8 0xfd118595143ee273, 0x9f860593d42fd7f3
|
|
|
|
|
data8 0xc8fcaeebcb40eb47, 0xfd3a519943d4865a
|
|
|
|
|
data8 0x9f9fc97fdb96bd51, 0xc91d25431426a663
|
|
|
|
|
data8 0xfd6337f8e1ae5a4b, 0x9fb99e194f4a7037
|
|
|
|
|
data8 0xc93db09d7fdb2949, 0xfd8c38d1c8e927eb
|
|
|
|
|
data8 0x9fd383731ca51db9, 0xc95e5112e721582a
|
|
|
|
|
data8 0xfdb5544205095a53, 0x9fed79a04fbf9423
|
|
|
|
|
data8 0xc97f06bb49787677, 0xfdde8a67d2613531
|
|
|
|
|
data8 0xa00780b413b24ee8, 0xc99fd1aecd6e1b06
|
|
|
|
|
data8 0xfe07db619e781611, 0xa02eab2c4474b0cd
|
|
|
|
|
data8 0xc9d12a3e27bb1625, 0xfe460768d80bf758
|
|
|
|
|
data8 0xa048dcd51ccfd142, 0xc9f22ad82ba3d5f0
|
|
|
|
|
data8 0xfe6f9bfb06cd32f6, 0xa0631fa894b11b8d
|
|
|
|
|
data8 0xca134113105e67b2, 0xfe994bcd3d14fcc2
|
|
|
|
|
data8 0xa07d73ba65e680af, 0xca346d07b045a876
|
|
|
|
|
data8 0xfec316fecaf3f2ab, 0xa097d91e6aaf71b0
|
|
|
|
|
data8 0xca55aecf0e94bb88, 0xfeecfdaf33fadb80
|
|
|
|
|
data8 0xa0b24fe89e02602f, 0xca77068257be9bab
|
|
|
|
|
data8 0xff16fffe2fa8fad6, 0xa0ccd82d1bd2f68b
|
|
|
|
|
data8 0xca98743ae1c693a8, 0xff411e0ba9db886d
|
|
|
|
|
data8 0xa0e77200215909e6, 0xcab9f8122c99a101
|
|
|
|
|
data8 0xff6b57f7c33e4e9a, 0xa1021d760d584855
|
|
|
|
|
data8 0xcadb9221e268c3b5, 0xff95ade2d1bd7358
|
|
|
|
|
data8 0xa11cdaa36068a57d, 0xcafd4283d8043dfd
|
|
|
|
|
data8 0xffc01fed60f86fb5, 0xa137a99cbd3f880b
|
|
|
|
|
data8 0xcb1f09520d37c6fb, 0xffeaae3832b63956
|
|
|
|
|
LOCAL_OBJECT_END(T_table)
|
|
|
|
|
|
|
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|
|
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|
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|
.section .text
|
|
|
|
|
GLOBAL_LIBM_ENTRY(cbrt)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
{.mfi
|
|
|
|
|
// get significand
|
|
|
|
|
getf.sig GR_SIGNIF = f8
|
|
|
|
|
// normalize a
|
|
|
|
|
fma.s1 FR_ARG = f8, f1, f0
|
|
|
|
|
// GR_GP = pointer to C_1,..., C_5 followed by T_table
|
|
|
|
|
addl GR_GP = @ltoff(poly_coeffs), gp ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mfi
|
|
|
|
|
// get exponent
|
|
|
|
|
getf.exp GR_ARGEXP = f8
|
|
|
|
|
// will continue only for normal/denormal numbers
|
|
|
|
|
fclass.m.unc p12, p13 = f8, 0x1e7
|
|
|
|
|
// GR_CONST4 = bias-((2^{12}-1)/3)-63 = 0xffff-0x555-0x3f = 0xfa6b
|
|
|
|
|
mov GR_CONST4 = 0xfa6b ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mlx
|
|
|
|
|
mov GR_CONST2 = 0x20000
|
|
|
|
|
// GR_CONST3 = 2^52
|
|
|
|
|
movl GR_CONST3 = 0x8000000000000000 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
.pred.rel "mutex", p12, p13
|
|
|
|
|
{.mfi
|
|
|
|
|
// load start address for C_1,..., C_5 followed by T_table
|
|
|
|
|
ld8 GR_ADDR = [ GR_GP ]
|
|
|
|
|
// y = frcpa(a)
|
|
|
|
|
(p13) frcpa.s0 f8, p0 = f1, f8
|
|
|
|
|
// p7 = 1 if denormal input
|
|
|
|
|
cmp.gtu p7, p0 = GR_CONST3, GR_SIGNIF
|
|
|
|
|
}
|
|
|
|
|
{.mfb
|
|
|
|
|
nop.m 0
|
|
|
|
|
// if argument is 0, +/-Infinity, NaN, or NaTVal, then return
|
|
|
|
|
(p12) fma.d.s0 f8 = f8, f1, f0
|
|
|
|
|
(p12) br.ret.spnt b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mmi
|
|
|
|
|
// get exponent (for denormal input)
|
|
|
|
|
(p7) getf.exp GR_ARGEXP = FR_ARG
|
|
|
|
|
// get normalized significand (for denormal input)
|
|
|
|
|
(p7) getf.sig GR_SIGNIF = FR_ARG
|
|
|
|
|
// GR_CONST1 = bias-(2^{12}-1)
|
|
|
|
|
mov GR_CONST1 = 0xf000 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mii
|
|
|
|
|
// get GR_SIGN = sign
|
|
|
|
|
and GR_SIGN = GR_ARGEXP, GR_CONST2
|
|
|
|
|
// eliminate leading 1 from GR_I1 = 1st table index
|
|
|
|
|
shl GR_I1 = GR_SIGNIF, 1
|
|
|
|
|
// eliminate sign from exponent
|
|
|
|
|
andcm GR_EXP = GR_ARGEXP, GR_CONST2 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mib
|
|
|
|
|
add GR_ADDR2 = 32, GR_ADDR
|
|
|
|
|
// GR_IT1 = 1st table index (y_index, 8 bits)
|
|
|
|
|
shr.u GR_IT1 = GR_I1, 56
|
|
|
|
|
nop.b 0
|
|
|
|
|
}
|
|
|
|
|
{.mib
|
|
|
|
|
// load C_1
|
|
|
|
|
ldfe FR_COEFF1 = [ GR_ADDR ], 16
|
|
|
|
|
// subtract bias from GR_EXPON = exponent
|
|
|
|
|
sub GR_EXPON = GR_EXP, GR_CONST1
|
|
|
|
|
nop.b 0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mib
|
|
|
|
|
// load C_2, C_3
|
|
|
|
|
ldfpd FR_COEFF2, FR_COEFF3 = [ GR_ADDR ]
|
|
|
|
|
// 1: exponent* = 5; // (2^{16}-1)/3 = 0x5555
|
|
|
|
|
shladd GR_TMP1 = GR_EXPON, 2, GR_EXPON
|
|
|
|
|
nop.b 0
|
|
|
|
|
}
|
|
|
|
|
{.mib
|
|
|
|
|
// load C_4, C_5
|
|
|
|
|
ldfpd FR_COEFF4, FR_COEFF5 = [ GR_ADDR2 ], 16
|
|
|
|
|
// GR_TMP2 = 3*y_index
|
|
|
|
|
shladd GR_TMP2 = GR_IT1, 1, GR_IT1
|
|
|
|
|
nop.b 0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mfi
|
|
|
|
|
// GR_TMP6 = (5*expon)*16+5*expon = (0x55)*expon
|
|
|
|
|
shladd GR_TMP6 = GR_TMP1, 4, GR_TMP1
|
|
|
|
|
// r = 1-a*y
|
|
|
|
|
fnma.s1 FR_R = f8, FR_ARG, f1
|
|
|
|
|
// adjust T_table pointer by 1st index
|
|
|
|
|
shladd GR_ITB1 = GR_TMP2, 3, GR_ADDR2 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mii
|
|
|
|
|
// eliminate leading 1 from significand
|
|
|
|
|
add GR_SIGNIF2 = GR_SIGNIF, GR_SIGNIF
|
|
|
|
|
// GR_TMP3 = (0x5500)*expon
|
|
|
|
|
shl GR_TMP3 = GR_TMP6, 8 ;;
|
|
|
|
|
// GR_TMP4 = (0x5555)*expon
|
|
|
|
|
add GR_TMP4 = GR_TMP3, GR_TMP6 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mii
|
|
|
|
|
// GR_TMP5 = (0x5556)*expon // 0x5556 = (2^{16}+2)/3
|
|
|
|
|
add GR_TMP5 = GR_TMP4, GR_EXPON
|
|
|
|
|
nop.i 0 ;;
|
|
|
|
|
// GR_EXP_BY_3 = floor(expon/3)
|
|
|
|
|
shr GR_EXP_BY_3 = GR_TMP5, 16 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mfi
|
|
|
|
|
// GR_TMP6 = 3*exponent
|
|
|
|
|
shladd GR_TMP6 = GR_EXP_BY_3, 1, GR_EXP_BY_3
|
|
|
|
|
// r*r
|
|
|
|
|
fma.s1 FR_R2 = FR_R, FR_R, f0
|
|
|
|
|
// bias exponent
|
|
|
|
|
add GR_EBIAS = GR_CONST4, GR_EXP_BY_3 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{.mfi
|
|
|
|
|
// get remainder of exponent/3
|
|
|
|
|
sub GR_REM = GR_EXPON, GR_TMP6
|
|
|
|
|
// c2+c3*r
|
|
|
|
|
fma.s1 FR_P23 = FR_COEFF3, FR_R, FR_COEFF2
|
|
|
|
|
nop.i 0
|
|
|
|
|
}
|
|
|
|
|
{.mfi
|
|
|
|
|
// add sign to exponent
|
|
|
|
|
or GR_SEXP = GR_EBIAS, GR_SIGN
|
|
|
|
|
// c4+c5*r
|
|
|
|
|
fma.s1 FR_P45 = FR_COEFF5, FR_R, FR_COEFF4
|
|
|
|
|
mov GR_TMP63 = 63+0xffff ;;
|
|
|
|
|
}
|
|
|
|
|
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|
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{.mmi
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// FR_2EXP = sign*2^{exponent/3}
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setf.exp FR_2EXP = GR_SEXP
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// adjust T_table pointer by 2nd index
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shladd GR_INDEX = GR_REM, 3, GR_ITB1
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// is the argument of the form 2^(3*k) ?
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// get (significand - leading 1) | (exponent mod 3)
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or GR_TEST = GR_REM, GR_SIGNIF2 ;;
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}
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{.mmi
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// 2^63
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setf.exp FR_TMP63 = GR_TMP63
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// load T
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ldf8 f8 = [ GR_INDEX ]
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// is the argument of the form 2^(3*k) ?
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cmp.eq p14, p0 = GR_TEST, r0 ;;
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}
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{.mfi
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nop.m 0
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// (c2+c3*r)+r^2*(c4+c5*r)
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fma.s1 FR_P25 = FR_P45, FR_R2, FR_P23
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nop.i 0
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}
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{.mfi
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nop.m 0
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// c1*r
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fma.s1 FR_P1 = FR_COEFF1, FR_R, f0
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nop.i 0 ;;
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}
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{.mfb
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nop.m 0
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(p14) fma.d.s0 f8 = FR_2EXP, FR_TMP63, f0
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(p14) br.ret.spnt b0 ;;
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}
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{.mfi
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nop.m 0
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// P = c1*r+r^2* [ (c2+c3*r)+r^2*(c4+c5*r) ]
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fma.s1 FR_P15 = FR_P25, FR_R2, FR_P1
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nop.i 0
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}
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{.mfi
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nop.m 0
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// T' = T*(2^exp)
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fma.s1 f8 = f8, FR_2EXP, f0
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nop.i 0 ;;
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}
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{.mfb
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nop.m 0
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// result = T'+T'*P
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fma.d.s0 f8 = f8, FR_P15, f8
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br.ret.sptk b0 ;;
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}
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GLOBAL_LIBM_END(cbrt)
|
2017-11-29 01:23:23 +00:00
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libm_alias_double_other (cbrt, cbrt)
|
