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We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
768 lines
29 KiB
ArmAsm
768 lines
29 KiB
ArmAsm
.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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//
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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 0x8f385c95d696b817, 0xb47233773b84d425
|
|
data8 0xe3590bd86a0d30f9, 0x8f59dc43edd930f3
|
|
data8 0xb49c6825430fe730, 0xe38e38e38e38e38e
|
|
data8 0x8f7b7b5f5ffad1c4, 0xb4c6c46bcdb27dcf
|
|
data8 0xe3c397d1e6db7839, 0x8f9d3a1bea165f38
|
|
data8 0xb4f1488c0b35d26f, 0xe3f928f5953feb9e
|
|
data8 0x8fbf18adc34b66da, 0xb51bf4c7c51f0168
|
|
data8 0xe42eeca17c62886c, 0x8fe117499e356095
|
|
data8 0xb546c9616087ab9c, 0xe464e32943446305
|
|
data8 0x90033624aa685f8d, 0xb571c69bdffd9a70
|
|
data8 0xe49b0ce15747a8a2, 0x9025757495f36b86
|
|
data8 0xb59cecbae56984c3, 0xe4d16a1eee94e9d4
|
|
data8 0x903f3a5dcc091203, 0xb5bd64512bb14bb7
|
|
data8 0xe4fa52107353f67d, 0x9061b2fceb2bdbab
|
|
data8 0xb5e8d2a4bf5ba416, 0xe5310a471f4d2dc3
|
|
data8 0x90844ca7211032a7, 0xb6146a9a1bc47819
|
|
data8 0xe567f6f1c2b9c224, 0x90a7079403e6a15d
|
|
data8 0xb6402c7749d621c0, 0xe59f18689a9e4c9a
|
|
data8 0x90c9e3fbafd63799, 0xb66c1882fb435ea2
|
|
data8 0xe5d66f04b8a68ecf, 0x90ece216c8a16ee4
|
|
data8 0xb6982f048c999a56, 0xe60dfb2005c192e9
|
|
data8 0x9110021e7b516f0a, 0xb6c47044075b4142
|
|
data8 0xe645bd1544c7ea51, 0x912a708a39be9075
|
|
data8 0xb6e5bd6bfd02bafd, 0xe66fb21b505b20a0
|
|
data8 0x914dcc7b31146370, 0xb7124a2736ff8ef2
|
|
data8 0xe6a7d32af4a7c59a, 0x91714af8cfe984d5
|
|
data8 0xb73f026a01e94177, 0xe6e02b129c6a5ae4
|
|
data8 0x918c00a6f3795e97, 0xb760a959f1d0a7a7
|
|
data8 0xe70a9136a7403039, 0x91afbc299ed0295d
|
|
data8 0xb78dae7e06868ab0, 0xe74349fb2d92a589
|
|
data8 0x91d39add3e958db0, 0xb7badff8ad9e4e02
|
|
data8 0xe77c3a9c86ed7d42, 0x91ee9920a8974d92
|
|
data8 0xb7dce25b8e17ae9f, 0xe7a713f88151518a
|
|
data8 0x9212b5fcac537c19, 0xb80a6226904045e2
|
|
data8 0xe7e067453317ed2b, 0x9236f6b256923fcf
|
|
data8 0xb8380f1cafd73c1c, 0xe819f37a81871bb5
|
|
data8 0x92523ee6f90dcfc3, 0xb85a6ea8e321b4d8
|
|
data8 0xe8454236bfaeca14, 0x9276bef031e6eb79
|
|
data8 0xb8886b684ae7d2fa, 0xe87f32f24c3fc90e
|
|
data8 0x929236ec237a24ad, 0xb8ab0726fa00cf5d
|
|
data8 0xe8aacd8688892ba6, 0x92b6f70b7efe9dc3
|
|
data8 0xb8d954a4d13b7cb1, 0xe8e523fd32f606f7
|
|
data8 0x92d29f61eec7dc2b, 0xb8fc2d4f6cd9f04a
|
|
data8 0xe9110b5311407927, 0x92f7a05d5b8ba92f
|
|
data8 0xb92acc851476b1ab, 0xe94bc8bf0c108fa3
|
|
data8 0x931379a403be5c16, 0xb94de2d841a184c2
|
|
data8 0xe977fdc439c2ca3c, 0x9338bc44de2e3f34
|
|
data8 0xb97cd4c36c92693c, 0xe9b3236528fc349e
|
|
data8 0x9354c71412c69486, 0xb9a0297f172665e3
|
|
data8 0xe9dfa70b745ac1b4, 0x937a4c273907e262
|
|
data8 0xb9cf6f21e36c3924, 0xea1b36268d0eaa38
|
|
data8 0x93968919f6e7975d, 0xb9f3030951267208
|
|
data8 0xea480963fd394197, 0x93bc516fdd4680c9
|
|
data8 0xba229d6a618e7c59, 0xea84034425f27484
|
|
data8 0x93d8c123d9be59b2, 0xba467144459f9855
|
|
data8 0xeab12713138dd1cc, 0x93f546c955e60076
|
|
data8 0xba6a60c3c48f1a4b, 0xeade6db73a5e503b
|
|
data8 0x941b70a65879079f, 0xba9a76056b67ee7a
|
|
data8 0xeb1b0268343b121b, 0x943829f337410591
|
|
data8 0xbabea699563ada6e, 0xeb489b0b2bdb5f14
|
|
data8 0x9454f995765bc4d2, 0xbae2f350b262cc4b
|
|
data8 0xeb765721e85f03d0, 0x947b86b57f5842ed
|
|
data8 0xbb1385a23be24e57, 0xebb389645f222f62
|
|
data8 0x94988aeb23470f86, 0xbb3814975e17c680
|
|
data8 0xebe198f090607e0c, 0x94b5a5dc9695f42a
|
|
data8 0xbb5cc031009bf467, 0xec0fcc9321024509
|
|
data8 0x94d2d7a9170d8b42, 0xbb81889680024764
|
|
data8 0xec3e247da8b82f61, 0x94f9e87dd78bf019
|
|
data8 0xbbb2c0d8703ae95d, 0xec7c27d21321c9f7
|
|
data8 0x95175019a503d89e, 0xbbd7cd09ba3c5463
|
|
data8 0xecaad5278824e453, 0x9534cefa625fcb3a
|
|
data8 0xbbfcf68c4977718f, 0xecd9a76d097d4e77
|
|
data8 0x955265405c491a25, 0xbc223d88cfc88eee
|
|
data8 0xed089ed5dcd99446, 0x9570130c1f9bb857
|
|
data8 0xbc47a2284fee4ff8, 0xed37bb95add09a1c
|
|
data8 0x9597ca4119525184, 0xbc79ac0916ed7b8a
|
|
data8 0xed76c70508f904b6, 0x95b5af6fb5aa4d3c
|
|
data8 0xbc9f5670d1a13030, 0xeda63bb05e7f93c6
|
|
data8 0x95d3ac9273aafd7a, 0xbcc51f068cb95c1d
|
|
data8 0xedd5d661daed2dc4, 0x95f1c1cafdfd3684
|
|
data8 0xbceb05f4b30a9bc0, 0xee05974eef86b903
|
|
data8 0x960fef3b430b8d5f, 0xbd110b6604c7d306
|
|
data8 0xee357ead791fc670, 0x962e350575b409c5
|
|
data8 0xbd372f8598620f19, 0xee658cb3c134a463
|
|
data8 0x964c934c0dfc1708, 0xbd5d727edb6b3c7e
|
|
data8 0xee95c1987f080211, 0x966b0a31c9c6bc7d
|
|
data8 0xbd83d47d937bbc6d, 0xeec61d92d8c4314f
|
|
data8 0x968999d9ad8d264e, 0xbdaa55addf1ae47d
|
|
data8 0xeef6a0da64a014ac, 0x96a8426705198795
|
|
data8 0xbdd0f63c36aa73f0, 0xef274ba72a07c811
|
|
data8 0x96c703fd64445ee5, 0xbdf7b6556d550a15
|
|
data8 0xef581e31a2c91260, 0x96e5dec0a7b4268d
|
|
data8 0xbe1e9626b1ffa96b, 0xef8918b2bc43aec6
|
|
data8 0x9704d2d4f59f79f3, 0xbe4595dd903e5371
|
|
data8 0xefba3b63d89d7cbf, 0x9723e05ebe91b9b0
|
|
data8 0xbe6cb5a7f14bc935, 0xefeb867ecffaa607
|
|
data8 0x97430782be323831, 0xbe93f5b41d047cf7
|
|
data8 0xf01cfa3df1b9c9fa, 0x97624865fc0df8bf
|
|
data8 0xbebb5630bae4c15f, 0xf04e96dc05b43e2d
|
|
data8 0x9781a32dcc640b2a, 0xbee2d74cd30a430c
|
|
data8 0xf0805c944d827454, 0x97a117ffd0f48e46
|
|
data8 0xbf0a7937cf38d981, 0xf0b24ba285c495cb
|
|
data8 0x97c0a701f9d263c9, 0xbf323c217be2bc8c
|
|
data8 0xf0e46442e76f6569, 0x97e0505a8637a036
|
|
data8 0xbf5a203a09342bbb, 0xf116a6b2291d7896
|
|
data8 0x97f57a9fb0b08c6e, 0xbf74cad1c14ebfc4
|
|
data8 0xf1383fa9e9b5b381, 0x9815503365914a9d
|
|
data8 0xbf9ce6a497a89f78, 0xf16ac84f90083b9b
|
|
data8 0x98354085054fd204, 0xbfc52428bec6e72f
|
|
data8 0xf19d7b686dcb03d7, 0x98554bbbf8a77902
|
|
data8 0xbfed838fddab024b, 0xf1d0593311db1757
|
|
data8 0x987571fffb7f94f6, 0xc016050c0420981a
|
|
data8 0xf20361ee8f1c711e, 0x9895b3791dd03c23
|
|
data8 0xc03ea8cfabddc330, 0xf23695da7de51d3f
|
|
data8 0x98ab43a5fc65d0c8, 0xc059d3cbd65ddbce
|
|
data8 0xf258d095e465cc35, 0x98cbb2d196bd713d
|
|
data8 0xc082b122a3c78c9d, 0xf28c4d0bfc982b34
|
|
data8 0x98ec3d9ec7b6f21a, 0xc0abb1499ae736c4
|
|
data8 0xf2bff55eb3f0ea71, 0x990ce436db5e8344
|
|
data8 0xc0d4d474c3aedaaf, 0xf2f3c9cf9884636e
|
|
data8 0x9922b8218160967a, 0xc0f054ca33eb3437
|
|
data8 0xf31670135ab9cc0f, 0x99438d686f75779d
|
|
data8 0xc119b2c67e600ed0, 0xf34a8e9f0b54cdfb
|
|
data8 0x99647eea131fa20b, 0xc1433453de2033ff
|
|
data8 0xf37ed9fa6b8add3f, 0x997a85045a47c6d0
|
|
data8 0xc15ef3e44e10032d, 0xf3a1cfe884ef6bb6
|
|
data8 0x999ba5f14f8add02, 0xc188b130431d80e6
|
|
data8 0xf3d66689dcc8e8d3, 0x99bce38b5465ecae
|
|
data8 0xc1b2929d6067730e, 0xf40b2ab069d5c96a
|
|
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
|
|
data8 0x9f2c5a20f4da6668, 0xc88bb4de3667cdf4
|
|
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)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.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 ;;
|
|
}
|
|
|
|
{.mmi
|
|
// FR_2EXP = sign*2^{exponent/3}
|
|
setf.exp FR_2EXP = GR_SEXP
|
|
// adjust T_table pointer by 2nd index
|
|
shladd GR_INDEX = GR_REM, 3, GR_ITB1
|
|
// is the argument of the form 2^(3*k) ?
|
|
// get (significand - leading 1) | (exponent mod 3)
|
|
or GR_TEST = GR_REM, GR_SIGNIF2 ;;
|
|
}
|
|
|
|
{.mmi
|
|
// 2^63
|
|
setf.exp FR_TMP63 = GR_TMP63
|
|
// load T
|
|
ldf8 f8 = [ GR_INDEX ]
|
|
// is the argument of the form 2^(3*k) ?
|
|
cmp.eq p14, p0 = GR_TEST, r0 ;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// (c2+c3*r)+r^2*(c4+c5*r)
|
|
fma.s1 FR_P25 = FR_P45, FR_R2, FR_P23
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// c1*r
|
|
fma.s1 FR_P1 = FR_COEFF1, FR_R, f0
|
|
nop.i 0 ;;
|
|
}
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
(p14) fma.d.s0 f8 = FR_2EXP, FR_TMP63, f0
|
|
(p14) br.ret.spnt b0 ;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// P = c1*r+r^2* [ (c2+c3*r)+r^2*(c4+c5*r) ]
|
|
fma.s1 FR_P15 = FR_P25, FR_R2, FR_P1
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// T' = T*(2^exp)
|
|
fma.s1 f8 = f8, FR_2EXP, f0
|
|
nop.i 0 ;;
|
|
}
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// result = T'+T'*P
|
|
fma.d.s0 f8 = f8, FR_P15, f8
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
|
|
GLOBAL_LIBM_END(cbrt)
|
|
libm_alias_double_other (cbrt, cbrt)
|