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548 lines
15 KiB
ArmAsm
548 lines
15 KiB
ArmAsm
.file "log2f.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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// 09/11/00 Initial version
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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//
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// API
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//==============================================================
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// float log2f(float)
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//
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// Overview of operation
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//==============================================================
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// Background
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//
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// Implementation
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//
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// Let x = 2^l * m, where m=1.b1 b2 ... b8 b9 ... b52
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// y=frcpa(m), r=m*y-1, f=b1 b2 .. b8 (table index)
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// j=0 if f<128; j=1 if f>=128
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// T is a table that stores log2(1/y) (in entries 1..255) rounded to
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// double extended precision; f is used as an index; T[255]=0
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//
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// If f=0 and b9=0, r is set to 2^{-8}* 0.b9 b10 ... b52 = m-1 (fractional part of m),
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// and 0 is used instead of T[0]
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// (polynomial evaluation only, for m=1+r, 0<=r<2^{-9})
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// If f=255, r is set to (m-2)/2 (T[255]=0, and only polynomial evaluation is used
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// for m=2(1-r'), 0<=r'<2^{-9})
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//
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// log2f(x) is approximated as
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// (l-j) + T[f] + (c1*r+c2*r^2+...+c6*r^6), if f>0
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//
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// Special values
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//==============================================================
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// log2f(0)=-inf, raises Divide by Zero
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// log2f(+inf)=inf
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// log2f(x)=NaN, raises Invalid if x<0
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//
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// Registers used
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//==============================================================
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// f6-f14
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// r2-r3, r23-r30
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// p6,p7,p8,p12
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//
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GR_SAVE_B0 = r33
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GR_SAVE_PFS = r34
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GR_SAVE_GP = r35 // This reg. can safely be used
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GR_SAVE_SP = r36
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GR_Parameter_X = r37
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GR_Parameter_Y = r38
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GR_Parameter_RESULT = r39
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GR_Parameter_TAG = r40
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FR_X = f10
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FR_Y = f1
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FR_RESULT = f8
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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 0x3fdec709dc3a03fd, 0xbfd71547652b82fe //C_3 and C_4
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data8 0xb8aa3b295c17f0bc, 0x00003fff // C_1
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data8 0xb8aa3b295c17f0bc, 0x0000bffe // C_2
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LOCAL_OBJECT_END(poly_coeffs)
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LOCAL_OBJECT_START(T_table)
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data8 0x3f671b0ea42e5fda, 0x3f815cfe8eaec830
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data8 0x3f8cfee70c5ce5dc, 0x3f94564a62192834
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data8 0x3f997723ace35766, 0x3f9f5923c69b54a1
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data8 0x3fa2a094a085d693, 0x3fa538941776b01e
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data8 0x3fa8324c9b914bc7, 0x3faacf54ce07d7e9
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data8 0x3fadced958dadc12, 0x3fb0387efbca869e
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data8 0x3fb18ac6067479c0, 0x3fb30edd3e13530d
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data8 0x3fb463c15936464e, 0x3fb5b9e13c3fa21d
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data8 0x3fb7113f3259e07a, 0x3fb869dd8d1b2035
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data8 0x3fb9c3bea49d3214, 0x3fbb1ee4d7961701
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data8 0x3fbc7b528b70f1c5, 0x3fbdd90a2c676ed4
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data8 0x3fbf05d4976c2028, 0x3fc032fbbaee6d65
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data8 0x3fc0e3b5a9f3284a, 0x3fc195195c7d125b
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data8 0x3fc22dadc2ab3497, 0x3fc2e050231df57d
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data8 0x3fc379f79c2b255b, 0x3fc42ddd2ba1b4a9
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data8 0x3fc4c89b9e6807f5, 0x3fc563dc29ffacb2
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data8 0x3fc619a25f5d798d, 0x3fc6b5ffbf367644
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data8 0x3fc752e1f660f8d6, 0x3fc7f049e753e7cf
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data8 0x3fc8a8980abfbd32, 0x3fc94724cca657be
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data8 0x3fc9e63a24971f46, 0x3fca85d8feb202f7
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data8 0x3fcb2602497d5346, 0x3fcbc6b6f5ee1c9b
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data8 0x3fcc67f7f770a67e, 0x3fcceec4b2234fba
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data8 0x3fcd91097ad13982, 0x3fce33dd57f3d335
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data8 0x3fced74146bc7b10, 0x3fcf7b3646fef683
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data8 0x3fd00223a943dc19, 0x3fd054a474bf0eb7
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data8 0x3fd0999d9b9259a1, 0x3fd0eca66d3b2581
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data8 0x3fd13ffa2e85b475, 0x3fd185a444fa0a7b
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data8 0x3fd1cb8312f27eff, 0x3fd21fa1441ce5e8
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data8 0x3fd265f526e603cb, 0x3fd2baa0c34be1ec
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data8 0x3fd3016b45de21ce, 0x3fd3486c38aa29a8
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data8 0x3fd38fa3efaa8262, 0x3fd3e562c0816a02
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data8 0x3fd42d141f53b646, 0x3fd474fd543f222c
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data8 0x3fd4bd1eb680e548, 0x3fd505789e234bd1
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data8 0x3fd54e0b64003b70, 0x3fd596d761c3c1f0
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data8 0x3fd5dfdcf1eeae0e, 0x3fd6291c6fd9329c
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data8 0x3fd6729637b59418, 0x3fd6bc4aa692e0fd
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data8 0x3fd7063a1a5fb4f2, 0x3fd75064f1ed0715
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data8 0x3fd79acb8cf10390, 0x3fd7d67c1e43ae5c
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data8 0x3fd8214f4068afa7, 0x3fd86c5f36dea3dc
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data8 0x3fd8b7ac64dd7f9d, 0x3fd8f4167a0c6f92
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data8 0x3fd93fd2d5e1bf1d, 0x3fd98bcd84296946
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data8 0x3fd9c8c333e6e9a5, 0x3fda152f142981b4
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data8 0x3fda527fd95fd8ff, 0x3fda9f5e3edeb9e6
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data8 0x3fdadd0b2b5755a7, 0x3fdb2a5d6f51ff83
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data8 0x3fdb686799b00be3, 0x3fdbb62f1b887cd8
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data8 0x3fdbf4979f666668, 0x3fdc332a6e8399d4
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data8 0x3fdc819dc2d45fe4, 0x3fdcc0908e19b7bd
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data8 0x3fdcffae611ad12b, 0x3fdd3ef776d43ff4
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data8 0x3fdd8e5002710128, 0x3fddcdfb486cb9a1
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data8 0x3fde0dd294245fe4, 0x3fde4dd622a28840
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data8 0x3fde8e06317114f0, 0x3fdece62fe9a9915
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data8 0x3fdf1f164a15389a, 0x3fdf5fd8a9063e35
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data8 0x3fdfa0c8937e7d5d, 0x3fdfe1e649bb6335
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data8 0x3fe011990641535a, 0x3fe032560e91e59e
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data8 0x3fe0532a5ebcd44a, 0x3fe0741617f5fc28
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data8 0x3fe08cd653f38839, 0x3fe0adeb55c1103b
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data8 0x3fe0cf181d5d1dd0, 0x3fe0f05ccd0aced7
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data8 0x3fe111b9875788ab, 0x3fe1332e6f1bcf73
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data8 0x3fe154bba77c2088, 0x3fe16df59bfa06c1
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data8 0x3fe18fadb6e2d3c2, 0x3fe1b17e849adc26
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data8 0x3fe1caeb6a0de814, 0x3fe1ece7c830eec9
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data8 0x3fe20efd3dae01df, 0x3fe2289de375d901
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data8 0x3fe24adf9b6a6fe0, 0x3fe26d3ad1aebcfc
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data8 0x3fe287100c2771f4, 0x3fe2a9983b3c1b28
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data8 0xbfda78e146f7bef4, 0xbfda33760a7f6051
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data8 0xbfd9ff43476fb5f7, 0xbfd9b97c3c4eec8f
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data8 0xbfd98504431717fc, 0xbfd93ee07535f967
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data8 0xbfd90a228d5712b2, 0xbfd8c3a104cb24f5
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data8 0xbfd88e9c72e0b226, 0xbfd847bc33d8618e
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data8 0xbfd812703988bb69, 0xbfd7dd0569c04bff
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data8 0xbfd7959c202292f1, 0xbfd75fe8d2c5d48f
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data8 0xbfd72a1637cbc183, 0xbfd6e221cd9d0cde
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data8 0xbfd6ac059985503b, 0xbfd675c99ce81f92
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data8 0xbfd63f6db2590482, 0xbfd5f6c138136489
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data8 0xbfd5c01a39fbd688, 0xbfd58952cf519193
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data8 0xbfd5526ad18493ce, 0xbfd51b6219bfe6ea
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data8 0xbfd4d1cdf8b4846f, 0xbfd49a784bcd1b8b
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data8 0xbfd4630161832547, 0xbfd42b6911cf5465
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data8 0xbfd3f3af3461e1c4, 0xbfd3bbd3a0a1dcfb
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data8 0xbfd383d62dac7ae7, 0xbfd34bb6b2546218
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data8 0xbfd313750520f520, 0xbfd2db10fc4d9aaf
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data8 0xbfd2a28a6dc90387, 0xbfd269e12f346e2c
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data8 0xbfd2311515e2e855, 0xbfd1f825f6d88e13
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data8 0xbfd1bf13a6c9c69f, 0xbfd185ddfa1a7ed0
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data8 0xbfd14c84c4dd6128, 0xbfd11307dad30b76
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data8 0xbfd0d9670f6941fe, 0xbfd09fa235ba2020
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data8 0xbfd0790adbb03009, 0xbfd03f09858c55fb
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data8 0xbfd004e3a7c97cbd, 0xbfcf9532288fcf69
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data8 0xbfcf205339208f27, 0xbfceab2a23a5b83e
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data8 0xbfce5ce55fdd37a5, 0xbfcde73fe3b1480f
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data8 0xbfcd714f44623927, 0xbfccfb1321b8c400
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data8 0xbfccac163c770dc9, 0xbfcc355b67195dd0
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data8 0xbfcbbe540a3f036f, 0xbfcb6ecf175f95e9
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data8 0xbfcaf74751e1be33, 0xbfca7f71fb7bab9d
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data8 0xbfca2f632320b86b, 0xbfc9b70ba539dfae
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data8 0xbfc93e6587910444, 0xbfc8edcae8352b6c
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data8 0xbfc874a0db01a719, 0xbfc7fb27199df16d
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data8 0xbfc7a9fec7d05ddf, 0xbfc72fff456ac70d
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data8 0xbfc6de7d66023dbc, 0xbfc663f6fac91316
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data8 0xbfc6121ac74813cf, 0xbfc5970c478fff4a
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data8 0xbfc51bab907a5c8a, 0xbfc4c93d33151b24
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data8 0xbfc44d527fdadf55, 0xbfc3fa87be0f3a1b
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data8 0xbfc3a797cd35d959, 0xbfc32ae9e278ae1a
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data8 0xbfc2d79c6937efdd, 0xbfc25a619370d9dc
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data8 0xbfc206b5bde2f8b8, 0xbfc188ecbd1d16be
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data8 0xbfc134e1b489062e, 0xbfc0b6894488e95f
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data8 0xbfc0621e2f556b5c, 0xbfc00d8c711a12cc
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data8 0xbfbf1cd21257e18c, 0xbfbe72ec117fa5b2
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data8 0xbfbdc8b7c49a1ddb, 0xbfbcc8d5e467b710
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data8 0xbfbc1ddc9c39c7a1, 0xbfbb7294093cdd0f
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data8 0xbfba7111df348494, 0xbfb9c501cdf75872
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data8 0xbfb918a16e46335b, 0xbfb81579a73e83c6
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data8 0xbfb7684f39f4ff2d, 0xbfb6bad3758efd87
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data8 0xbfb60d060d7e41ac, 0xbfb507b836033bb7
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data8 0xbfb4591d6310d85a, 0xbfb3aa2fdd27f1c3
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data8 0xbfb2faef55ccb372, 0xbfb1f3723b4ae6db
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data8 0xbfb14360d6136ffa, 0xbfb092fb594145c1
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data8 0xbfafc482e8b48a7e, 0xbfae6265ace11ae4
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data8 0xbfacff9e5c4341d0, 0xbfaaea3316095f72
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data8 0xbfa985bfc3495194, 0xbfa820a01ac754cb
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data8 0xbfa6bad3758efd87, 0xbfa554592bb8cd58
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data8 0xbfa3ed3094685a26, 0xbfa2855905ca70f6
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data8 0xbfa11cd1d5133413, 0xbf9dfd78881399f1
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data8 0xbf9b28f618cc85df, 0xbf98530faa3c087b
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data8 0xbf957bc3dddcd7fa, 0xbf92a3115322f9e6
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data8 0xbf8f91ed4eef8370, 0xbf89dae4ec6b8b2e
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data8 0xbf842106b1499209, 0xbf7cc89f97d67594
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data8 0xbf71497accf7e11d, 0x0000000000000000
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LOCAL_OBJECT_END(T_table)
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.section .text
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GLOBAL_LIBM_ENTRY(log2f)
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{ .mfi
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alloc r32=ar.pfs,1,4,4,0
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// y=frcpa(x)
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frcpa.s1 f6,p0=f1,f8
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// will form significand of 1.5 (to test whether the index is 128 or above)
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mov r24=0xc
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}
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{.mfi
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nop.m 0
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// normalize x
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fma.s1 f7=f8,f1,f0
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// r2 = pointer to C_1...C_6 followed by T_table
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addl r2 = @ltoff(poly_coeffs), gp;;
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}
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{.mfi
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// get significand
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getf.sig r25=f8
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// f8 denormal ?
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fclass.m p8,p10=f8,0x9
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// will form significand of 1.5 (to test whether the index is 128 or above)
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shl r24=r24,60
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}
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{.mfi
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mov r26=0x804
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nop.f 0
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// r23=bias-1
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mov r23=0xfffe;;
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}
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{.mmf
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getf.exp r29=f8
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// load start address for C_1...C_6 followed by T_table
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ld8 r2=[r2]
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// will continue only for positive normal/denormal numbers
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fclass.nm.unc p12,p7 = f8, 0x19 ;;
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}
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.pred.rel "mutex",p8,p10
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{.mfi
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// denormal input, repeat get significand (after normalization)
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(p8) getf.sig r25=f7
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// x=1 ?
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fcmp.eq.s0 p6,p0=f8,f1
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// get T_index
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(p10) shr.u r28=r25,63-8
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}
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{.mfi
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// f12=0.5
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setf.exp f12=r23
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nop.f 0
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// r27=bias
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mov r27=0xffff;;
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}
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{.mfb
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// denormal input, repeat get exponent (after normalization)
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(p8) getf.exp r29=f7
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nop.f 0
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(p12) br.cond.spnt SPECIAL_log2f
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}
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{.mfi
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cmp.geu p12,p0=r25,r24
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nop.f 0
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mov r23=0xff;;
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}
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{.mfi
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add r3=32,r2
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// r=1-x*y
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fms.s1 f6=f6,f8,f1
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// r26=0x80400...0 (threshold for using polynomial approximation)
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shl r26=r26,64-12
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}
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{.mfi
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// load C_3, C_4
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ldfpd f10,f11=[r2],16
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nop.f 0
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// r27=bias-1 (if index >=128, will add exponent+1)
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(p12) mov r27=0xfffe;;
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}
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{.mfi
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// load C_1
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ldfe f14=[r2],32
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// x=1, return 0
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(p6) fma.s.s0 f8=f0,f0,f0
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(p8) shr.u r28=r25,63-8
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}
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{.mib
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// load C_2
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ldfe f13=[r3]
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// r29=exponent-bias
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sub r29=r29,r27
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// x=1, return
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(p6) br.ret.spnt b0;;
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}
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{.mfi
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// get T_index
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and r28=r28,r23
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fmerge.se f7=f1,f7
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// if first 9 bits after leading 1 are all zero, then p8=1
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cmp.ltu p8,p12=r25,r26;;
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}
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{.mfi
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// f8=expon - bias
|
|
setf.sig f8=r29
|
|
nop.f 0
|
|
// get T address
|
|
shladd r2=r28,3,r2
|
|
}
|
|
{.mfi
|
|
// first 8 bits after leading 1 are all ones ?
|
|
cmp.eq p10,p0=r23,r28
|
|
// if first 8 bits after leading bit are 0, use polynomial approx. only
|
|
(p8) fms.s1 f6=f7,f1,f1
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
//r26=1
|
|
mov r26=1
|
|
// if first 8 bits after leading 1 are all ones, use polynomial approx. only
|
|
(p10) fms.s1 f6=f7,f12,f1
|
|
nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p12
|
|
{.mmf
|
|
// load T (unless first 9 bits after leading 1 are 0)
|
|
(p12) ldfd f12=[r2]
|
|
nop.m 0
|
|
// set T=0 (if first 9 bits after leading 1 are 0)
|
|
(p8) fma.s1 f12=f0,f0,f0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// P34=C_3+C_4*r
|
|
fma.s1 f10=f11,f6,f10
|
|
// r26=2^{63}
|
|
shl r26=r26,63
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r2=r*r
|
|
fma.s1 f11=f6,f6,f0
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
// significand of x is 1 ?
|
|
cmp.eq p0,p6=r25,r26
|
|
// P12=C_1+C_2*r
|
|
fma.s1 f14=f13,f6,f14
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// normalize additive term (l=exponent of x)
|
|
fcvt.xf f8=f8
|
|
// if significand(x)=1, return exponent (l)
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// add T+l
|
|
(p6) fma.s1 f8=f8,f1,f12
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P14=P12+r2*P34
|
|
(p6) fma.s1 f13=f10,f11,f14
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// result=T+l+r*P14
|
|
(p6) fma.s.s0 f8=f13,f6,f8
|
|
// return
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
|
|
|
SPECIAL_log2f:
|
|
{.mfi
|
|
nop.m 0
|
|
// x=+Infinity ?
|
|
fclass.m p7,p0=f8,0x21
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// x=+/-Zero ?
|
|
fclass.m p8,p0=f8,0x7
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// x=-Infinity, -normal, -denormal ?
|
|
fclass.m p6,p0=f8,0x3a
|
|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
// log2f(+Infinity)=+Infinity
|
|
nop.f 0
|
|
(p7) br.ret.spnt b0;;
|
|
}
|
|
{.mfi
|
|
(p8) mov GR_Parameter_TAG = 172
|
|
// log2f(+/-0)=-infinity, raises Divide by Zero
|
|
// set f8=-0
|
|
(p8) fmerge.ns f8=f0,f8
|
|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
(p8) frcpa.s0 f8,p0=f1,f8
|
|
(p8) br.cond.sptk __libm_error_region;;
|
|
}
|
|
{.mfb
|
|
(p6) mov GR_Parameter_TAG = 173
|
|
// x<0: return NaN, raise Invalid
|
|
(p6) frcpa.s0 f8,p0=f0,f0
|
|
(p6) br.cond.sptk __libm_error_region;;
|
|
}
|
|
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// Remaining cases: NaNs
|
|
fma.s.s0 f8=f8,f1,f0
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
|
GLOBAL_LIBM_END(log2f)
|
|
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
{ .mfi
|
|
add GR_Parameter_Y=-32,sp // Parameter 2 value
|
|
nop.f 0
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp=-64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
};;
|
|
{ .mmi
|
|
stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
|
|
add GR_Parameter_X = 16,sp // Parameter 1 address
|
|
.save b0, GR_SAVE_B0
|
|
mov GR_SAVE_B0=b0 // Save b0
|
|
};;
|
|
.body
|
|
{ .mib
|
|
stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
br.call.sptk b0=__libm_error_support# // Call error handling function
|
|
};;
|
|
{ .mmi
|
|
nop.m 0
|
|
nop.m 0
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
{ .mmi
|
|
ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
.restore sp
|
|
add sp = 64,sp // Restore stack pointer
|
|
mov b0 = GR_SAVE_B0 // Restore return address
|
|
};;
|
|
{ .mib
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
br.ret.sptk b0 // Return
|
|
};;
|
|
|
|
LOCAL_LIBM_END(__libm_error_region)
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|