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ba5b14c761
When new symbol versions were introduced without SVID compatible error handling the exp2f, log2f and powf symbols were accidentally removed from the ia64 lim.a. The regression was introduced by the commitsf5f0f52651New expf and exp2f version without SVID compat wrapper72d3d28108New symbol version for logf, log2f and powf without SVID compat With WEAK_LIBM_ENTRY(foo), there is a hidden __foo and weak foo symbol definition in both SHARED and !SHARED build. [BZ #23822] * sysdeps/ia64/fpu/e_exp2f.S (exp2f): Use WEAK_LIBM_ENTRY. * sysdeps/ia64/fpu/e_log2f.S (log2f): Likewise. * sysdeps/ia64/fpu/e_exp2f.S (powf): Likewise.
547 lines
14 KiB
ArmAsm
547 lines
14 KiB
ArmAsm
.file "exp2f.s"
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// Copyright (c) 2000 - 2005, 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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// 08/25/00 Initial version
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 09/05/02 Improved performance and accuracy
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// 01/17/03 Fixed to call error support when x=128.0
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// 03/31/05 Reformatted delimiters between data tables
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//
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// API
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//==============================================================
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// float exp2f(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= (K + fh + fl + r), where
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// K is an integer, fh= 0.b1 b2 b3 b4 b5,
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// fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0),
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// and |r|<2^{-11}
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// Th is a table that stores 2^fh (32 entries) rounded to
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// double extended precision (only mantissa is stored)
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// Tl is a table that stores 2^fl (32 entries) rounded to
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// double extended precision (only mantissa is stored)
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//
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// 2^x is approximated as
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// 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2)
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// Note: We use the following trick to speed up conversion from FP to integer:
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//
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// Let x = K + r, where K is an integer, and |r| <= 0.5
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// Let N be the number of significand bits for the FP format used
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// ( N=64 for double-extended, N=53 for double)
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//
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// Then let y = 1.5 * 2^(N-1) + x for RN mode
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// K = y - 1.5 * 2^(N-1)
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// r = x - K
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//
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// If we want to obtain the integer part and the first m fractional bits of x,
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// we can use the same trick, but with a constant of 1.5 * 2^(N-1-m):
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//
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// Let x = K + f + r
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// f = 0.b_1 b_2 ... b_m
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// |r| <= 2^(-m-1)
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//
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// Then let y = 1.5 * 2^(N-1-m) + x for RN mode
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// (K+f) = y - 1.5 * 2^(N-1-m)
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// r = x - K
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// Special values
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//==============================================================
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// exp2(0)= 1
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// exp2(+inf)= inf
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// exp2(-inf)= 0
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//
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// Registers used
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//==============================================================
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// r2-r3, r14-r40
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// f6-f15, f32-f45
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// p6-p8, p12
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//
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GR_TBL_START = r2
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GR_LOG_TBL = r3
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GR_OF_LIMIT = r14
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GR_UF_LIMIT = r15
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GR_EXP_CORR = r16
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GR_F_low = r17
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GR_F_high = r18
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GR_K = r19
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GR_Flow_ADDR = r20
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GR_BIAS = r21
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GR_Fh = r22
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GR_Fh_ADDR = r23
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GR_EXPMAX = r24
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GR_EMIN = r25
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GR_ROUNDVAL = r26
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GR_MASK = r27
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GR_KF0 = r28
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GR_MASK_low = r29
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GR_COEFF_START = r30
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GR_SAVE_B0 = r33
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GR_SAVE_PFS = r34
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GR_SAVE_GP = r35
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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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FR_COEFF1 = f6
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FR_COEFF2 = f7
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FR_R = f9
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FR_KF0 = f12
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FR_UF_LIMIT = f15
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FR_OF_LIMIT = f32
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FR_EXPMIN = f33
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FR_ROUNDVAL = f34
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FR_KF = f35
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FR_2_TO_K = f36
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FR_T_low = f37
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FR_T_high = f38
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FR_P12 = f41
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FR_T_low_K = f42
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FR_T = f44
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FR_P = f45
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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 0xb17217f7d1cf79ab, 0x00003ffe // C_1
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data8 0xf5fdeffc162c7541, 0x00003ffc // C_2
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LOCAL_OBJECT_END(poly_coeffs)
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LOCAL_OBJECT_START(T_table)
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// 2^{0.00000 b6 b7 b8 b9 b10}
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data8 0x8000000000000000, 0x8016302f17467628
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data8 0x802c6436d0e04f50, 0x80429c17d77c18ed
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data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af
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data8 0x80855ad965e88b83, 0x809ba2264dada76a
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data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f
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data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e
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data8 0x810b40a1d81406d4, 0x81219f24a5baa59d
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data8 0x813801881d886f7b, 0x814e67cceb90502c
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data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47
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data8 0x8191b1ea15813bfd, 0x81a827baf7838b78
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data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c
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data8 0x81eba08c8ad4536f, 0x820225f44b55b33b
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data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a
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data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c
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data8 0x8272fb97b2a5894c, 0x828998760d01faf3
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data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906
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//
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// 2^{0.b1 b2 b3 b4 b5}
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data8 0x8000000000000000, 0x82cd8698ac2ba1d7
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data8 0x85aac367cc487b14, 0x88980e8092da8527
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data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0
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data8 0x91c3d373ab11c336, 0x94f4efa8fef70961
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data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538
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data8 0x9ef5326091a111ad, 0xa27043030c496818
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data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8
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data8 0xad583eea42a14ac6, 0xb123f581d2ac258f
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data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9
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data8 0xbd08a39f580c36be, 0xc12c4cca66709456
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data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2
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data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a
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data8 0xd744fccad69d6af4, 0xdbfbb797daf23755
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data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8
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data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb
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data8 0xf5257d152486cc2c, 0xfa83b2db722a033a
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LOCAL_OBJECT_END(T_table)
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.section .text
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WEAK_LIBM_ENTRY(exp2f)
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{.mfi
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alloc r32= ar.pfs, 1, 4, 4, 0
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// will continue only for non-zero normal/denormal numbers
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fclass.nm p12, p0= f8, 0x1b
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// GR_TBL_START= pointer to C_1...C_2 followed by T_table
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addl GR_TBL_START= @ltoff(poly_coeffs), gp
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}
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{.mlx
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mov GR_OF_LIMIT= 0xffff + 7 // Exponent of overflow limit
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movl GR_ROUNDVAL= 0x5a400000 // 1.5*2^(63-10) (SP)
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}
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;;
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// Form special constant 1.5*2^(63-10) to give integer part and first 10
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// fractional bits of x
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{.mfi
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setf.s FR_ROUNDVAL= GR_ROUNDVAL // Form special constant
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fcmp.lt.s1 p6, p8= f8, f0 // X<0 ?
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nop.i 0
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}
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{.mfb
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ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table
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nop.f 0
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(p12) br.cond.spnt SPECIAL_exp2 // Branch if nan, inf, zero
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}
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;;
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{.mlx
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setf.exp FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit
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movl GR_UF_LIMIT= 0xc3160000 // (-2^7-22) = -150
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}
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;;
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{.mfi
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ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1
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fma.s0 f8= f8, f1, f0 // normalize x
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nop.i 0
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}
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;;
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{.mmi
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ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2
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setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit
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mov GR_EXP_CORR= 0xffff-126
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}
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;;
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{.mfi
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nop.m 0
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fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL // y= x + 1.5*2^(63-10)
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nop.i 0
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}
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;;
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{.mfi
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mov GR_MASK= 1023
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fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f)
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mov GR_MASK_low= 31
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}
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;;
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{.mfi
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getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y)
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fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT // x >= overflow threshold ?
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add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table
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}
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;;
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{.mmi
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and GR_F_low= GR_KF0, GR_MASK_low // f_low
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and GR_F_high= GR_MASK, GR_KF0 // f_high*32
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shr GR_K= GR_KF0, 10 // K
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}
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;;
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{.mmi
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shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low}
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add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63
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shr GR_Fh= GR_F_high, 5 // f_high
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}
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;;
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{.mfi
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setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126}
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fnma.s1 FR_R= FR_KF, f1, f8 // r= x - (K+f)
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shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high}
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}
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{.mlx
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ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low}
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movl GR_EMIN= 0xc2fc0000 // EMIN= -126
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}
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;;
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{.mfi
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ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high}
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(p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ?
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nop.i 0
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}
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;;
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{.mfb
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setf.s FR_EXPMIN= GR_EMIN // FR_EXPMIN= EMIN
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fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
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(p12) br.cond.spnt OUT_RANGE_exp2
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}
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;;
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{.mfi
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nop.m 0
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fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low
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nop.i 0
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}
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;;
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{.mfi
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nop.m 0
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fma.s1 FR_P= FR_R, FR_P12, f0 // P= P12+r
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nop.i 0
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}
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;;
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{.mfi
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nop.m 0
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fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high
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nop.i 0
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}
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;;
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{.mfi
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nop.m 0
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fcmp.lt.s0 p6, p8= f8, FR_EXPMIN // underflow (x<EMIN) ?
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nop.i 0
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}
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;;
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{.mfb
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nop.m 0
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fma.s.s0 f8= FR_P, FR_T, FR_T // result= T+T*P
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(p8) br.ret.sptk b0 // return
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}
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;;
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{.mfb
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(p6) mov GR_Parameter_TAG= 164
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nop.f 0
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(p6) br.cond.sptk __libm_error_region
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}
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;;
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SPECIAL_exp2:
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{.mfi
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nop.m 0
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fclass.m p6, p0= f8, 0x22 // x= -Infinity ?
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nop.i 0
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}
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;;
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{.mfi
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nop.m 0
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fclass.m p7, p0= f8, 0x21 // x= +Infinity ?
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nop.i 0
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}
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;;
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{.mfi
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nop.m 0
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fclass.m p8, p0= f8, 0x7 // x= +/-Zero ?
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nop.i 0
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}
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{.mfb
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nop.m 0
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(p6) mov f8= f0 // exp2(-Infinity)= 0
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(p6) br.ret.spnt b0
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}
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;;
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{.mfb
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nop.m 0
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nop.f 0
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(p7) br.ret.spnt b0 // exp2(+Infinity)= +Infinity
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}
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;;
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{.mfb
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nop.m 0
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(p8) mov f8= f1 // exp2(+/-0)= 1
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(p8) br.ret.spnt b0
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}
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;;
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{.mfb
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nop.m 0
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fma.s.s0 f8= f8, f1, f0 // Remaining cases: NaNs
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br.ret.sptk b0
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}
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;;
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OUT_RANGE_exp2:
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// overflow: p8= 1
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{.mii
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(p8) mov GR_EXPMAX= 0x1fffe
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nop.i 0
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nop.i 0
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}
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;;
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{.mmb
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(p8) mov GR_Parameter_TAG= 163
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(p8) setf.exp FR_R= GR_EXPMAX
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nop.b 999
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}
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;;
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{.mfi
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nop.m 999
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(p8) fma.s.s0 f8= FR_R, FR_R, f0 // Create overflow
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nop.i 999
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}
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// underflow: p6= 1
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{.mii
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(p6) mov GR_Parameter_TAG= 164
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(p6) mov GR_EXPMAX= 1
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nop.i 0
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}
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;;
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{.mmb
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nop.m 0
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(p6) setf.exp FR_R= GR_EXPMAX
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nop.b 999
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}
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;;
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{.mfb
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nop.m 999
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(p6) fma.s.s0 f8= FR_R, FR_R, f0 // Create underflow
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nop.b 0
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}
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;;
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WEAK_LIBM_END(exp2f)
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libm_alias_float_other (__exp2, exp2)
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#ifdef SHARED
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.symver exp2f,exp2f@@GLIBC_2.27
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.weak __exp2f_compat
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.set __exp2f_compat,__exp2f
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.symver __exp2f_compat,exp2f@GLIBC_2.2
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#endif
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LOCAL_LIBM_ENTRY(__libm_error_region)
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.prologue
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{.mfi
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add GR_Parameter_Y= -32, sp // Parameter 2 value
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nop.f 0
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.save ar.pfs, GR_SAVE_PFS
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mov GR_SAVE_PFS= ar.pfs // Save ar.pfs
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}
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{.mfi
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.fframe 64
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add sp= -64, sp // Create new stack
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nop.f 0
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mov GR_SAVE_GP= gp // Save gp
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}
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;;
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{.mmi
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stfs [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack
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add GR_Parameter_X= 16, sp // Parameter 1 address
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.save b0, GR_SAVE_B0
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mov GR_SAVE_B0= b0 // Save b0
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}
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;;
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.body
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{.mib
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stfs [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack
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add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address
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nop.b 0
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}
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{.mib
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stfs [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack
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add GR_Parameter_Y= -16, GR_Parameter_Y
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br.call.sptk b0= __libm_error_support# // Call error handling function
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}
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;;
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{.mmi
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add GR_Parameter_RESULT= 48, sp
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nop.m 0
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nop.i 0
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}
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;;
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{.mmi
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ldfs f8= [ GR_Parameter_RESULT ] // Get return result off stack
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.restore sp
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add sp= 64, sp // Restore stack pointer
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mov b0= GR_SAVE_B0 // Restore return address
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}
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;;
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{.mib
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mov gp= GR_SAVE_GP // Restore gp
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mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs
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br.ret.sptk b0 // Return
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}
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;;
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LOCAL_LIBM_END(__libm_error_region)
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.type __libm_error_support#, @function
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.global __libm_error_support#
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