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https://sourceware.org/git/glibc.git
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ee6189855a
equivalent, but shorter instructions. * sysdeps/unix/sysv/linux/x86_64/sysdep.h: Likewise. * sysdeps/unix/sysv/linux/x86_64/setcontext.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/clone.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/swapcontext.S: Likewise. * sysdeps/unix/x86_64/sysdep.S: Likewise. * sysdeps/x86_64/strchr.S: Likewise. * sysdeps/x86_64/memset.S: Likewise. * sysdeps/x86_64/strcspn.S: Likewise. * sysdeps/x86_64/strcmp.S: Likewise. * sysdeps/x86_64/elf/start.S: Likewise. * sysdeps/x86_64/strspn.S: Likewise. * sysdeps/x86_64/dl-machine.h: Likewise. * sysdeps/x86_64/bsd-_setjmp.S: Likewise. * sysdeps/x86_64/bsd-setjmp.S: Likewise. * sysdeps/x86_64/strtok.S: Likewise.
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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// 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 0xcbda64292d3ffd97, 0x8096b586974669b1
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data8 0xa202f97995b69c0d, 0xcc1f3184af961596
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data8 0x80bcd273d952a028, 0xa232fe6eb0c0577d
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data8 0xcce70a67b64f24ad, 0x813b4e2c856b6e9a
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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 0x820aec524e3c23e9, 0xa3d7ef508ff11574
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data8 0xb43da8e9d163e1af, 0xe316d93615862714
|
|
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)
|