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-rw-r--r--sysdeps/ia64/fpu/s_cbrt.S1224
1 files changed, 651 insertions, 573 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrt.S b/sysdeps/ia64/fpu/s_cbrt.S
index 1e23b6024d..b7a827d1da 100644
--- a/sysdeps/ia64/fpu/s_cbrt.S
+++ b/sysdeps/ia64/fpu/s_cbrt.S
@@ -1,11 +1,10 @@
-.file "cbrt.asm"
+.file "cbrt.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
-//
-// Contributed 2/2/2000 by John Harrison, Cristina Iordache, Ted Kubaska,
-// Bob Norin, Shane Story, and Ping Tak Peter Tang
-// of the Computational Software Lab, Intel Corporation.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -21,27 +20,30 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
-// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
-// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
-// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-//
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
// Intel Corporation is the author of this code, and requests that all
-// problem reports or change requests be submitted to it directly at
-// http://developer.intel.com/opensource.
+// problem reports or change requests be submitted to it directly at
+// http: //www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
-// 2/02/00: Initial version
-// 5/19/00: New version (modified algorithm)
+// 02/02/00 Initial version
+// 05/19/00 New version (modified algorithm)
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 01/28/03 Updated polynomial coefficients (changed to Remez coefficients),
+// to slightly improve accuracy
//
// API
//==============================================================
@@ -53,637 +55,713 @@
//
// Implementation
//
-// cbrt(a) = cbrt(a y) / cbrt(y)
-// = cbrt(1 - (1 - a y)) * 1/cbrt(y)
+// Let y= frcpa(a), where a is the argument
+//
+// cbrt(a)= cbrt(a*y)/cbrt(y) = cbrt(1 - (1-a*y)) * (1/cbrt(y))
+//
+// For all values of y, the 3 possible significands of 1/cbrt(y)
+// are stored in a table (T0) to 64 bits of accuracy. (There are
+// 3 possible significands because the exponent of y modulo 3
+// can be 0, 1, or 2.)
//
-// where y = frcpa(a).
//
-// * cbrt(1 - (1 - a y)) is approximated by a degree-5 polynomial
-//
-// 1 - (1/3)*r - (1/9)*r^2 - (5/81)*r^3 - (10/243)*r^4 - (22/729)*r^5
-//
-// in r = 1 - a y.
+// * cbrt(1 - (1-a*y)) is approximated by a degree-5 polynomial ~
+//
+// ~ 1 - (1/3)*r - (1/9)*r^2 - (5/81)*r^3 - (10/243)*r^4 - (22/729)*r^5
+//
+// in r = 1-a*y.
//
-// * The values 1/cbrt(y) are stored in a table of constants T0
-// to 64 bits of accuracy
//
// The table values are stored for three exponent values and are
// then multiplied by e/3 where e is the exponent of the input number.
// This computation is carried out in parallel with the polynomial
// evaluation:
//
-// T = 2^(e/3) * T0
+// T= 2^(e/3) * T0
//===============
-// input = x
-// C = frcpa(x)
-// r = 1 - C * x
+// input= x
+// C= frcpa(x)
+// r= 1 - C * x
//
-// Special values
+// Special values
//==============================================================
// Registers used
//==============================================================
-// f6-f15
-// r2, r23-r26, r28-r30
-// p6,p7,p8,p12
+// f6-f15
+// GR_GP, r23-r26, r28-r30
+// p6, p7, p8, p12
+
+ FR_R = f6
+ FR_COEFF1 = f7
+ FR_COEFF2 = f9
+ FR_COEFF3 = f10
+ FR_COEFF4 = f11
+ FR_COEFF5 = f12
+ FR_R2 = f13
+ FR_ARG = f14
+ FR_P23 = f15
+ FR_P25 = f32
+ FR_P15 = f33
+ FR_P1 = f34
+ FR_P45 = f35
+ FR_2EXP = f36
+ FR_TMP63 = f37
+
+ GR_GP = r2
+ GR_ADDR = r2
+ GR_CONST1 = r3
+ GR_I1 = r8
+ GR_EXP = r9
+ GR_ADDR2 = r10
+ GR_IT1 = r11
+ GR_TMP2 = r11
+ GR_EXPON = r15
+ GR_TMP1 = r16
+ GR_TMP6 = r16
+ GR_ITB1 = r17
+ GR_TMP3 = r18
+ GR_TMP4 = r19
+ GR_TMP63 = r19
+ GR_TMP5 = r20
+ GR_EXP_BY_3 = r20
+ GR_CONST4 = r21
+ GR_TMP6 = r22
+ GR_INDEX = r23
+ GR_EBIAS = r24
+ GR_SIGNIF = r25
+ GR_SIGNIF2 = r25
+ GR_TEST = r25
+ GR_ARGEXP = r26
+ GR_CONST2 = r27
+ GR_SIGN = r28
+ GR_REM = r29
+ GR_CONST3 = r30
+ GR_SEXP = r31
+
+
+
-#include "libm_support.h"
// Data tables
//==============================================================
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
+RODATA
.align 16
-poly_coeffs:
-ASM_TYPE_DIRECTIVE(poly_coeffs,@object)
-data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // 1/3
-data8 0x3fbc71c71c71c71d, 0x3faf9add3c0ca459
-data8 0x3fa511e8d2b3183b, 0x3f9ee7113506ac13
-ASM_SIZE_DIRECTIVE(poly_coeffs)
-
-T_table:
-ASM_TYPE_DIRECTIVE(T_table,@object)
-
-data8 0x80155c748c374836, 0xa160019ed37fb4ae
-data8 0xcb51ddcb9e93095e, 0x8040404b0879f7f9
-data8 0xa1960b5966da4608, 0xcb95f333968ad59b
-data8 0x806b5dce4b405c10, 0xa1cc5dbe6dc2aab4
-data8 0xcbda64292d3ffd97, 0x8096b586974669b1
-data8 0xa202f97995b69c0d, 0xcc1f3184af961596
-data8 0x80bcd273d952a028, 0xa232fe6eb0c0577d
-data8 0xcc5bb1ac954d33e2, 0x80e898c52813f2f3
-data8 0xa26a2582012f6e17, 0xcca12e9831fc6402
-data8 0x81149add67c2d208, 0xa2a197e5d10465cb
-data8 0xcce70a67b64f24ad, 0x813b4e2c856b6e9a
-data8 0xa2d25a532efefbc8, 0xcd24794726477ea5
-data8 0x8167c1dde03de7aa, 0xa30a5bd6e49e4ab8
-data8 0xcd6b096a0b70ee87, 0x818ed973b811135e
-data8 0xa33b9c9b59879e24, 0xcda9177738b15a90
-data8 0x81bbc0c33e13ec98, 0xa3742fca6a3c1f21
-data8 0xcdf05f2247dffab9, 0x81e33e69fbe7504a
-data8 0xa3a5f1273887bf22, 0xce2f0f347f96f906
-data8 0x820aec524e3c23e9, 0xa3d7ef508ff11574
-data8 0xce6e0be0cd551a61, 0x823880f78e70b805
-data8 0xa4115ce30548bc15, 0xceb666b2c347d1de
-data8 0x826097a62a8e5200, 0xa443df0e53df577a
-data8 0xcef609b0cb874f00, 0x8288dfe00e9b5eaf
-data8 0xa4769fa5913c0ec3, 0xcf35fb5447e5c765
-data8 0x82b15a10c5371624, 0xa4a99f303bc7def5
-data8 0xcf763c47ee869f00, 0x82da06a527b18937
-data8 0xa4dcde37779adf4b, 0xcfb6cd3888d71785
-data8 0x8302e60b635ab394, 0xa5105d46152c938a
-data8 0xcff7aed4fbfbb447, 0x832bf8b2feec2f0e
-data8 0xa5441ce89825cb8d, 0xd038e1ce5167e3c6
-data8 0x83553f0ce00e276b, 0xa5781dad3e54d899
-data8 0xd07a66d7bfa0ebba, 0x837eb98b50f8322a
-data8 0xa5ac602406c4e68c, 0xd0bc3ea6b32d1b21
-data8 0x83a270f44c84f699, 0xa5d9601d95c2c0bc
-data8 0xd0f4f0e8f36c1bf8, 0x83cc4d7cfcfac5ca
-data8 0xa60e1e1a2de14745, 0xd1376458e34b037e
-data8 0x83f65f78a8872b4c, 0xa6431f6e3fbd9658
-data8 0xd17a2ca133f78572, 0x8420a75f2f7b53c8
-data8 0xa67864b0d432fda4, 0xd1bd4a80301c5715
-data8 0x844510461ff14209, 0xa6a6444aa0243c0b
-data8 0xd1f71682b2fa4575, 0x846fbd91b930bed2
-data8 0xa6dc094d10f25792, 0xd23ad555f773f059
-data8 0x84947e18234f3294, 0xa70a574cc02bba69
-data8 0xd2752c7039a5bf73, 0x84bf92755825045a
-data8 0xa7409e2af9549084, 0xd2b98ee008c06b59
-data8 0x84e4ac0ee112ba51, 0xa76f5c64ca2cf13b
-data8 0xd2f4735ffd700280, 0x8509ef44b86f20be
-data8 0xa79e4f0babab5dc0, 0xd32f99ed6d9ac0e1
-data8 0x85359d5d91768427, 0xa7d5579ae5164b85
-data8 0xd374f0666c75d51c, 0x855b3bd5b7384357
-data8 0xa804bd3c6fe61cc8, 0xd3b0a7d13618e4a1
-data8 0x858104f0c415f79a, 0xa8345895e5250a5a
-data8 0xd3eca2ea53bcec0c, 0x85a6f90390d29864
-data8 0xa8642a122b44ef0b, 0xd428e23874f13a17
-data8 0x85d3772fcd56a1dd, 0xa89c38ca18f6108b
-data8 0xd46f82fe293bc6d3, 0x85f9c982fcc002f3
-data8 0xa8cc81063b6e87ca, 0xd4ac57e9b7186420
-data8 0x862047e0e7ea554b, 0xa8fd00bfa409285e
-data8 0xd4e972becb04e8b8, 0x8646f2a26f7f5852
-data8 0xa92db8664d5516da, 0xd526d40a7a9b43a3
-data8 0x866dca21754096b5, 0xa95ea86b75cc2c20
-data8 0xd5647c5b73917370, 0x8694ceb8dfd17a37
-data8 0xa98fd141a4992deb, 0xd5a26c4201bd6d13
-data8 0x86bc00c49e9307e8, 0xa9c1335cae7446ba
-data8 0xd5e0a45015350a7e, 0x86dccd74fce79610
-data8 0xa9ea8686f556f645, 0xd614b539c6194104
-data8 0x870453c845acf90f, 0xaa1c52d17906bb19
-data8 0xd6537310e224283f, 0x872c089a1e90342c
-data8 0xaa4e59b046dab887, 0xd6927ab62244c917
-data8 0x8753ec4a92d16c5e, 0xaa809b9c60d1890b
-data8 0xd6d1ccc1fc4ef4b7, 0x877bff3aca19f6b4
-data8 0xaab319102f3f9b33, 0xd71169cea98fdded
-data8 0x879d88b6fe1c324c, 0xaadd5a18c1e21274
-data8 0xd746a66a5bc9f6d9, 0x87c5f346dbf98c3a
-data8 0xab1045f2ac31bdf5, 0xd786ce8f0fae5317
-data8 0x87e7c653efacef2c, 0xab3ae3ab2df7231e
-data8 0xd7bc7ff214c4e75a, 0x881089d4e73ffefc
-data8 0xab6e3f945d1e96fc, 0xd7fd35467a517ed1
-data8 0x88397e6a366f2a8a, 0xaba1d953a08fa94e
-data8 0xd83e38838648d815, 0x885bc559e5e1c081
-data8 0xabcd090db7ef4c3f, 0xd874a1db598b8951
-data8 0x887e2ee392bb7a93, 0xabf864602d7c323d
-data8 0xd8ab42205b80edaf, 0x88a7a8587e404257
-data8 0xac2ca5886ccf9b57, 0xd8ed1849d202f965
-data8 0x88ca5eda67594784, 0xac5861d4aa441f0f
-data8 0xd92432bd5a173685, 0x88f4356166bd590e
-data8 0xac8d183fe3a2fbed, 0xd9669ca45b03c23e
-data8 0x89173a0acf5ce026, 0xacb93703ff51571e
-data8 0xd99e3327cf89574e, 0x893a62a098b6a57b
-data8 0xace5830ad0c3f14b, 0xd9d602b19b100466
-data8 0x895daf637236ae2c, 0xad11fca5d78b3ff2
-data8 0xda0e0ba86c096841, 0x89883b9d1c2fa9c5
-data8 0xad4797fddf91a798, 0xda5195fcdb1c3dce
-data8 0x89abd8dd374a5d7b, 0xad747701e559ebcb
-data8 0xda8a1eb87a491f6c, 0x89cf9b1dcd197fa0
-data8 0xada184a47e9c7613, 0xdac2e230b91c3f84
-data8 0x89f382a258ea79de, 0xadcec13ab0dda8ff
-data8 0xdafbe0d0b66aea30, 0x8a178faf06648f29
-data8 0xadfc2d1a5fd21ba8, 0xdb351b04a8fafced
-data8 0x8a3bc288b3e1d18a, 0xae29c89a5053c33a
-data8 0xdb6e9139e33cdd8e, 0x8a601b74f4d1f835
-data8 0xae5794122b638df9, 0xdba843ded7151ea1
-data8 0x8a849aba14274764, 0xae858fda8137ae0a
-data8 0xdbe2336319b61fc8, 0x8aa9409f16cdbc9b
-data8 0xaeb3bc4ccc56d3d1, 0xdc1c60376789fa68
-data8 0x8ace0d6bbe2cb316, 0xaee219c374c09920
-data8 0xdc56cacda82d0cd5, 0x8af301688ab33558
-data8 0xaf10a899d3235fe7, 0xdc917398f2797814
-data8 0x8b181cdebe6f3206, 0xaf3f692c341fe8b4
-data8 0xdccc5b0d90a3e628, 0x8b3d60185fafcb7c
-data8 0xaf6e5bd7db9ae6c2, 0xdd0781a10469f0f2
-data8 0x8b62cb603bb2fad0, 0xaf9d80fb081cd91b
-data8 0xdd42e7ca0b52838f, 0x8b80d7d6bc4104de
-data8 0xafc35ce063eb3787, 0xdd729ad01c69114d
-data8 0x8ba68bf73ac74f39, 0xaff2ddcb5f28f03d
-data8 0xddae749c001fbf5e, 0x8bcc68fb9f9f7335
-data8 0xb022923b148e05c5, 0xddea8f50a51c69b1
-data8 0x8bf26f31c534fca2, 0xb0527a919adbf58b
-data8 0xde26eb69a0f0f111, 0x8c10f86e13a1a1f9
-data8 0xb078f3ab1d701c65, 0xde576480262399bc
-data8 0x8c3749916cc6abb5, 0xb0a93a6870649f31
-data8 0xde943789645933c8, 0x8c5dc4c4f7706032
-data8 0xb0d9b624d62ec856, 0xded14d58139a28af
-data8 0x8c7cac3a8c42e3e0, 0xb100a5f53fb3c8e1
-data8 0xdf025c00bbf2b5c7, 0x8ca373f1b7bf2716
-data8 0xb131821882f5540a, 0xdf3feb44d723a713
-data8 0x8cc29907fb951294, 0xb158bf8e4cb04055
-data8 0xdf715bc16c159be0, 0x8ce9ae4e9492aac8
-data8 0xb189fd69d56b238f, 0xdfaf66240e29cda8
-data8 0x8d0911dddbfdad0e, 0xb1b189958e8108e4
-data8 0xdfe139cbf6e19bdc, 0x8d3075c4f20f04ee
-data8 0xb1e32a8165b09832, 0xe01fc0fe94d9fc52
-data8 0x8d5018a9d4de77d5, 0xb20b0678fc271eec
-data8 0xe051f92ffcc0bd60, 0x8d77cc47dd143515
-data8 0xb23d0bd3f7592b6e, 0xe090feec9c9a06ac
-data8 0x8d97af6352739cb7, 0xb26538b2db8420dc
-data8 0xe0c39d0c9ff862d6, 0x8db7af523167800f
-data8 0xb28d89e339ceca14, 0xe0f668eeb99f188d
-data8 0x8ddfd80bc68c32ff, 0xb2c022ca12e55a16
-data8 0xe1362890eb663139, 0x8e00197e1e7c88fe
-data8 0xb2e8c6852c6b03f1, 0xe1695c7212aecbaa
-data8 0x8e207859f77e20e7, 0xb3118f4eda9fe40f
-data8 0xe19cbf0391bbbbe9, 0x8e40f4ce60c9f8e2
-data8 0xb33a7d6268109ebe, 0xe1d050901c531e85
-data8 0x8e69ba46cf2fde4d, 0xb36ddbc5ea70ec55
-data8 0xe2110903b4f4047a, 0x8e8a7a00bd7ae63e
-data8 0xb3971e9b39264023, 0xe2450559b4d80b6d
-data8 0x8eab57ef1cf2f529, 0xb3c0877ecc18e24a
-data8 0xe27931a231554ef3, 0x8ecc5442cffb1dad
-data8 0xb3ea16ae3a6c905f, 0xe2ad8e2ac3c5b04b
-data8 0x8eed6f2d2a4acbfe, 0xb413cc67aa0e4d2d
-data8 0xe2e21b41b9694cce, 0x8f0ea8dff24441ff
-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
-ASM_SIZE_DIRECTIVE(T_table)
-
-
-
-
-
-
-.align 32
-.global cbrt#
+LOCAL_OBJECT_START(poly_coeffs)
+
+ data8 0xaaaaaaaaaaaaaab4, 0x0000bffd // ~ 1/3
+ data8 0xbfbc71c71c718e45, 0xbfaf9add3c0bbb43
+ data8 0xbfa511edb93dc98d, 0xbf9ee71c45f0dfbc
+LOCAL_OBJECT_END(poly_coeffs)
+
+
+// For every entry B in the frcpa table, this table contains
+// the significands of cbrt(1/B), cbrt(2/B), cbrt(4/B).
+// The index to this table is the same as the frcpa index.
+
+LOCAL_OBJECT_START(T_table)
+
+
+ data8 0x80155c748c374836, 0xa160019ed37fb4ae
+ data8 0xcb51ddcb9e93095e, 0x8040404b0879f7f9
+ data8 0xa1960b5966da4608, 0xcb95f333968ad59b
+ data8 0x806b5dce4b405c10, 0xa1cc5dbe6dc2aab4
+ data8 0xcbda64292d3ffd97, 0x8096b586974669b1
+ data8 0xa202f97995b69c0d, 0xcc1f3184af961596
+ data8 0x80bcd273d952a028, 0xa232fe6eb0c0577d
+ data8 0xcc5bb1ac954d33e2, 0x80e898c52813f2f3
+ data8 0xa26a2582012f6e17, 0xcca12e9831fc6402
+ data8 0x81149add67c2d208, 0xa2a197e5d10465cb
+ data8 0xcce70a67b64f24ad, 0x813b4e2c856b6e9a
+ data8 0xa2d25a532efefbc8, 0xcd24794726477ea5
+ data8 0x8167c1dde03de7aa, 0xa30a5bd6e49e4ab8
+ data8 0xcd6b096a0b70ee87, 0x818ed973b811135e
+ data8 0xa33b9c9b59879e24, 0xcda9177738b15a90
+ data8 0x81bbc0c33e13ec98, 0xa3742fca6a3c1f21
+ data8 0xcdf05f2247dffab9, 0x81e33e69fbe7504a
+ data8 0xa3a5f1273887bf22, 0xce2f0f347f96f906
+ data8 0x820aec524e3c23e9, 0xa3d7ef508ff11574
+ data8 0xce6e0be0cd551a61, 0x823880f78e70b805
+ data8 0xa4115ce30548bc15, 0xceb666b2c347d1de
+ data8 0x826097a62a8e5200, 0xa443df0e53df577a
+ data8 0xcef609b0cb874f00, 0x8288dfe00e9b5eaf
+ data8 0xa4769fa5913c0ec3, 0xcf35fb5447e5c765
+ data8 0x82b15a10c5371624, 0xa4a99f303bc7def5
+ data8 0xcf763c47ee869f00, 0x82da06a527b18937
+ data8 0xa4dcde37779adf4b, 0xcfb6cd3888d71785
+ data8 0x8302e60b635ab394, 0xa5105d46152c938a
+ data8 0xcff7aed4fbfbb447, 0x832bf8b2feec2f0e
+ data8 0xa5441ce89825cb8d, 0xd038e1ce5167e3c6
+ data8 0x83553f0ce00e276b, 0xa5781dad3e54d899
+ data8 0xd07a66d7bfa0ebba, 0x837eb98b50f8322a
+ data8 0xa5ac602406c4e68c, 0xd0bc3ea6b32d1b21
+ data8 0x83a270f44c84f699, 0xa5d9601d95c2c0bc
+ data8 0xd0f4f0e8f36c1bf8, 0x83cc4d7cfcfac5ca
+ data8 0xa60e1e1a2de14745, 0xd1376458e34b037e
+ data8 0x83f65f78a8872b4c, 0xa6431f6e3fbd9658
+ data8 0xd17a2ca133f78572, 0x8420a75f2f7b53c8
+ data8 0xa67864b0d432fda4, 0xd1bd4a80301c5715
+ data8 0x844510461ff14209, 0xa6a6444aa0243c0b
+ data8 0xd1f71682b2fa4575, 0x846fbd91b930bed2
+ data8 0xa6dc094d10f25792, 0xd23ad555f773f059
+ data8 0x84947e18234f3294, 0xa70a574cc02bba69
+ data8 0xd2752c7039a5bf73, 0x84bf92755825045a
+ data8 0xa7409e2af9549084, 0xd2b98ee008c06b59
+ data8 0x84e4ac0ee112ba51, 0xa76f5c64ca2cf13b
+ data8 0xd2f4735ffd700280, 0x8509ef44b86f20be
+ data8 0xa79e4f0babab5dc0, 0xd32f99ed6d9ac0e1
+ data8 0x85359d5d91768427, 0xa7d5579ae5164b85
+ data8 0xd374f0666c75d51c, 0x855b3bd5b7384357
+ data8 0xa804bd3c6fe61cc8, 0xd3b0a7d13618e4a1
+ data8 0x858104f0c415f79a, 0xa8345895e5250a5a
+ data8 0xd3eca2ea53bcec0c, 0x85a6f90390d29864
+ data8 0xa8642a122b44ef0b, 0xd428e23874f13a17
+ data8 0x85d3772fcd56a1dd, 0xa89c38ca18f6108b
+ data8 0xd46f82fe293bc6d3, 0x85f9c982fcc002f3
+ data8 0xa8cc81063b6e87ca, 0xd4ac57e9b7186420
+ data8 0x862047e0e7ea554b, 0xa8fd00bfa409285e
+ data8 0xd4e972becb04e8b8, 0x8646f2a26f7f5852
+ data8 0xa92db8664d5516da, 0xd526d40a7a9b43a3
+ data8 0x866dca21754096b5, 0xa95ea86b75cc2c20
+ data8 0xd5647c5b73917370, 0x8694ceb8dfd17a37
+ data8 0xa98fd141a4992deb, 0xd5a26c4201bd6d13
+ data8 0x86bc00c49e9307e8, 0xa9c1335cae7446ba
+ data8 0xd5e0a45015350a7e, 0x86dccd74fce79610
+ data8 0xa9ea8686f556f645, 0xd614b539c6194104
+ data8 0x870453c845acf90f, 0xaa1c52d17906bb19
+ data8 0xd6537310e224283f, 0x872c089a1e90342c
+ data8 0xaa4e59b046dab887, 0xd6927ab62244c917
+ data8 0x8753ec4a92d16c5e, 0xaa809b9c60d1890b
+ data8 0xd6d1ccc1fc4ef4b7, 0x877bff3aca19f6b4
+ data8 0xaab319102f3f9b33, 0xd71169cea98fdded
+ data8 0x879d88b6fe1c324c, 0xaadd5a18c1e21274
+ data8 0xd746a66a5bc9f6d9, 0x87c5f346dbf98c3a
+ data8 0xab1045f2ac31bdf5, 0xd786ce8f0fae5317
+ data8 0x87e7c653efacef2c, 0xab3ae3ab2df7231e
+ data8 0xd7bc7ff214c4e75a, 0x881089d4e73ffefc
+ data8 0xab6e3f945d1e96fc, 0xd7fd35467a517ed1
+ data8 0x88397e6a366f2a8a, 0xaba1d953a08fa94e
+ data8 0xd83e38838648d815, 0x885bc559e5e1c081
+ data8 0xabcd090db7ef4c3f, 0xd874a1db598b8951
+ data8 0x887e2ee392bb7a93, 0xabf864602d7c323d
+ data8 0xd8ab42205b80edaf, 0x88a7a8587e404257
+ data8 0xac2ca5886ccf9b57, 0xd8ed1849d202f965
+ data8 0x88ca5eda67594784, 0xac5861d4aa441f0f
+ data8 0xd92432bd5a173685, 0x88f4356166bd590e
+ data8 0xac8d183fe3a2fbed, 0xd9669ca45b03c23e
+ data8 0x89173a0acf5ce026, 0xacb93703ff51571e
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+ 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
-.proc cbrt#
-.align 32
-cbrt:
-
-
-{ .mfi
- // get significand
- getf.sig r23=f8
- // will continue only for normal/denormal numbers
- (p0) fclass.nm.unc p12,p0 = f8, 0x1b
- // r2 = pointer to C_1,...,C_5 followed by T_table
- addl r2 = @ltoff(poly_coeffs), gp
+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 r24=f8
- // normalize a
- fma.s1 f14=f8,f1,f0
- // r29=bias-((2^{12}-1)/3) -63=0xffff-0x555-0x3f=0xfa6b
- mov r29=0xfa6b;;
+ // 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 r25=0x20000
- // r28=2^52
- movl r28=0x8000000000000000;;
-}
-{.mfb
- // load start address for C_1,...,C_5 followed by T_table
- ld8 r3=[r2]
- (p12) fma.d.s0 f8=f8,f1,f0
- (p12) br.ret.spnt b0
+ mov GR_CONST2 = 0x20000
+ // GR_CONST3 = 2^52
+ movl GR_CONST3 = 0x8000000000000000 ;;
}
+
+.pred.rel "mutex", p12, p13
{.mfi
- nop.m 0
- // y=frcpa(a)
- frcpa.s0 f8,p6=f1,f8
- // p7=1 if denormal input
- cmp.gtu p7,p0=r28,r23;;
+ // 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
- (p7) getf.exp r24=f14
- // get normalized significand
- (p7) getf.sig r23=f14
- // r28=bias-(2^{12}-1)
- mov r28=0xf000;;
+ // 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 r26=sign
- and r26=r24,r25
- // eliminate leading 1 from r23=1st table index
- shl r23=r23,1
- // eliminate sign from exponent (r25)
- andcm r25=r24,r25;;
+ // 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 r2=32,r3
- // r23=1st table index (y_index,8 bits)
- shr.u r23=r23,56
- nop.b 0
+ 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 f7=[r3],16
- // subtract bias from r25=exponent
- sub r25=r25,r28
- nop.b 0;;
+ // 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 f9,f10=[r3]
- // 1: exponent*=5; // (2^{16}-1)/3=0x5555
- shladd r24=r25,2,r25
- nop.b 0
+ // 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 f11,f12=[r2],16
- // r23=3*y_index
- shladd r23=r23,1,r23
- nop.b 0;;
+ // 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
- // r30=(5*expon)*16+5*expon=(0x55)*expon
- shladd r30=r24,4,r24
- // r=1-a*y
- (p6) fnma.s1 f6=f8,f14,f1
- // adjust T_table pointer by 1st index
- shladd r2=r23,3,r2;;
+ // 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
- nop.m 0
- // r24=(0x5500)*expon
- shl r24=r30,8;;
- // r24=(0x5555)*expon
- add r24=r24,r30;;
+ // 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
- // r24=(0x5556)*expon // 0x5556=(2^{16}+2)/3
- add r24=r24,r25
- nop.i 0;;
- // r24=floor(expon/3)
- shr r24=r24,16;;
+ // 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
- // r28=3*exponent
- shladd r28=r24,1,r24
- // r2=r*r
- (p6) fma.s1 f13=f6,f6,f0
- // bias exponent
- add r24=r29,r24;;
+ // 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 : r25-r28
- sub r25=r25,r28
- // c2+c3*r
- (p6) fma.s1 f9=f10,f6,f9
- // add sign to exponent
- or r24=r24,r26
+ // 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
- nop.m 0
- // c4+c5*r
- (p6) fma.s1 f11=f12,f6,f11
- nop.i 0;;
+ // 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
- // f14=sign*2^{exponent/3}
- (p6) setf.exp f14=r24
- // adjust T_table pointer by 2nd index
- shladd r2=r25,3,r2
- nop.i 0;;
+ // 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
- // load T
- (p6) ldf8 f8=[r2]
- nop.m 0
- nop.i 0;;
+ // 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)
- (p6) fma.s1 f9=f11,f13,f9
- nop.i 0
+ 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
- (p6) fma.s1 f7=f7,f6,f0
- nop.i 0;;
+ 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)]
- (p6) fma.s1 f9=f9,f13,f7
- nop.i 0
+ 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)
- (p6) fma.s1 f8=f8,f14,f0
- nop.i 0;;
+ 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
- (p6) fnma.d.s0 f8=f8,f9,f8
- br.ret.sptk b0;;
+ nop.m 0
+ // result = T'+T'*P
+ fma.d.s0 f8 = f8, FR_P15, f8
+ br.ret.sptk b0 ;;
}
-.endp cbrt
-ASM_SIZE_DIRECTIVE(cbrt)
+
+
+GLOBAL_LIBM_END(cbrt)
generated by cgit v1.2.3 (git 2.39.1) at 2024-04-27 14:44:14 +0000