2017-04-10 11:32:00 +00:00
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# ieee754 sf routines for FT32
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2017-10-07 00:16:47 +00:00
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/* Copyright (C) 1995-2017 Free Software Foundation, Inc.
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2017-04-10 11:32:00 +00:00
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This file is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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Free Software Foundation; either version 3, or (at your option) any
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later version.
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This file is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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# See http://www.ens-lyon.fr/LIP/Pub/Rapports/PhD/PhD2006/PhD2006-02.pdf
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# for implementation details of all except division which is detailed below
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#
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#ifdef L_fp_tools
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// .global __cmpsf2_
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nan: .long 0x7FFFFFFF # also abs mask
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inf: .long 0x7F800000
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sign_mask: .long 0x80000000
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m_mask: .long 0x007FFFFF
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exp_bias: .long 127
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edge_case: .long 0x00FFFFFF
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smallest_norm: .long 0x00800000 # implicit bit
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high_FF: .long 0xFF000000
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high_uint: .long 0xFFFFFFFF
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ntz_table:
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.byte 32,0,1,12,2,6,0,13,3,0,7,0,0,0,0,14
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.byte 10,4,0,0,8,0,0,25,0,0,0,0,0,21,27,15
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.byte 31,11,5,0,0,0,0,0,9,0,0,24,0,0,20,26
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.byte 30,0,0,0,0,23,0,19,29,0,22,18,28,17,16,0
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#endif
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# Supply a few 'missing' instructions
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# not
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.macro not rd,r1
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xor \rd,\r1,-1
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.endm
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# negate
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.macro neg x
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not \x, \x
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add \x, \x, 1
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.endm
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# set $cc from the result of "ashl reg,dist"
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.macro ashlcc reg,dist
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.long 0x5de04008 | (\reg << 15) | (\dist << 4)
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.endm
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# converts an unsigned number x to a signed rep based on the bits in sign
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# sign should be 0x00000000 or 0xffffffff.
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.macro to_signed x, sign
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add \x,\x,\sign # conditionally decrement x
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xor \x,\x,\sign # conditionally complement x
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.endm
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.macro ld32 r,v
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ldk \r,(\v>>10)
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ldl \r,\r,(\v & 1023)
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.endm
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# calculate trailing zero count in x, also uses scr.
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# Using Seal's algorithm
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.macro ntz x, scr
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not \scr, \x
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add \scr, \scr, 1
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and \x, \x, \scr
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ashl \scr, \x, 4
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add \x, \scr, \x
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ashl \scr, \x, 6
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add \x, \scr, \x
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ashl \scr, \x, 16
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sub \x, \scr, \x
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lshr \x, \x, 26
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ldk \scr, ntz_table
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add \x, \x, \scr
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lpmi.b \x, \x, 0
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.endm
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# calculate leading zero count
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.macro nlz x, scr
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flip \x, \x, 31
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ntz \x, \scr
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.endm
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# Round 26 bit mantissa to nearest
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# | 23 bits frac | G | R | S |
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.macro round m, s1, s2
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ldk \s1,0xc8
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and \s2,\m,7
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lshr \s1,\s1,\s2
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and \s1,\s1,1
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lshr \m,\m,2
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add \m,\m,\s1
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.endm
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# If NZ, set the LSB of reg
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.macro sticky reg
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jmpc z,1f
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or \reg,\reg,1 # set the sticky bit to 1
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1:
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.endm
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##########################################################################
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##########################################################################
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## addition & subtraction
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#if defined(L_subsf3) || defined(L_addsub_sf)
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.global __subsf3
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__subsf3:
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# this is subtraction, so we just change the sign of r1
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lpm $r2,sign_mask
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xor $r1,$r1,$r2
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jmp __addsf3
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#endif
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#if defined(L_addsf3) || defined(L_addsub_sf)
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.global __addsf3
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__addsf3:
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# x in $r0, y in $r1, result z in $r0 --||| 100 instructions +/- |||--
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# unpack e, calc d
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bextu $r2,$r0,(8<<5)|23 # ex in r2
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bextu $r3,$r1,(8<<5)|23 # ey in r3
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sub $r5,$r2,$r3 # d = ex - ey
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# Special values are 0x00 and 0xff in ex and ey.
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# If (ex&ey) != 0 or (xy|ey)=255 then there may be
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# a special value.
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tst $r2,$r3
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jmpc nz,1f
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jmp slow
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1: or $r4,$r2,$r3
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cmp $r4,255
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jmpc nz,no_special_vals
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slow:
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# Check for early exit
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cmp $r2,0
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jmpc z,test_if_not_255
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cmp $r3,0
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jmpc nz,no_early_exit
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test_if_not_255:
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cmp $r2,255
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jmpc z,no_early_exit
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cmp $r3,255
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jmpc z,no_early_exit
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or $r6,$r2,$r3
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cmp $r6,0
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jmpc nz,was_not_zero
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and $r0,$r0,$r1
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lpm $r1,sign_mask
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and $r0,$r0,$r1
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return
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was_not_zero:
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cmp $r2,0
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jmpc nz,ret_x
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move $r0,$r1
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return
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ret_x:
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return
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no_early_exit:
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# setup to test for special values
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sub $r6,$r2,1
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and $r6,$r6,0xFE
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sub $r7,$r3,1
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and $r7,$r7,0xFE
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# test for special values
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cmp $r6,$r7
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jmpc gte,ex_spec_is_gte
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move $r6,$r7
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ex_spec_is_gte:
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cmp $r6,0xFE
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jmpc nz,no_special_vals
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cmp $r5,0
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jmpc ns,d_gte_0
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cmp $r3,0xFF
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jmpc z,ret_y
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cmp $r2,0
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jmpc z,ret_y
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ret_y:
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move $r0,$r1
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return
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d_gte_0:
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cmp $r5,0
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jmpc z,d_is_0
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cmp $r2,0xFF
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jmpc z,ret_x
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cmp $r3,0
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jmpc z,ret_x
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d_is_0:
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cmp $r2,0xFF
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jmpc nz,no_special_vals
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ashl $r6,$r0,9 # clear all except x frac
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ashl $r7,$r1,9 # clear all except y frac
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or $r6,$r6,$r7
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cmp $r6,0
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jmpc nz,ret_nan
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lshr $r4,$r0,31 # sx in r4
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lshr $r5,$r1,31 # sy in r4
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cmp $r4,$r5
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jmpc nz,ret_nan
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return
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ret_nan:
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lpm $r0,nan
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return
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no_special_vals:
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ldk $r8,(1<<10)|(9<<5)|26 # setup implicit bit and mask for e
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#----------------------
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ashr $r4,$r0,31 # sx in r4
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ashl $r0,$r0,3 # shift mx 3 for GRS bits
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bins $r0,$r0,$r8 # clear sx, ex and add implicit bit mx
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# change mx to signed mantissa
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to_signed $r0,$r4
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#----------------------
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ashr $r4,$r1,31 # sy in r4
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ashl $r1,$r1,3 # shift my 3 for GRS bits
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bins $r1,$r1,$r8 # clear sy, ey and add implicit bit my
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# change my to signed mantissa
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to_signed $r1,$r4
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#----------------------
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# test if we swap ms based on d sign
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cmp $r5,0
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jmpc gte,noswap
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# swap mx & my
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xor $r0,$r0,$r1
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xor $r1,$r0,$r1
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xor $r0,$r0,$r1
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# d positive means that ex>=ey, so ez = ex
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# d negative means that ey>ex, so ez = ey
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move $r2,$r3
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# |d|
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neg $r5
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noswap:
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# now $r2 = ez = max(ex,ey)
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cmp $r5,26 # max necessary alignment shift is 26
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jmpc lt,under_26
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ldk $r5,26
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under_26:
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ldk $r7,-1
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ashl $r7,$r7,$r5 # create inverse of mask for test of S bit value in discarded my
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not $r7,$r7
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tst $r1,$r7 # determine value of sticky bit
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# shift my >> |d|
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ashr $r1,$r1,$r5
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sticky $r1
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# add ms
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add $r0,$r0,$r1
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# $r4 = sign(mx), mx = |mx|
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ashr $r4,$r0,31
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xor $r0,$r0,$r4
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sub $r0,$r0,$r4
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# realign mantissa using leading zero count
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flip $r7,$r0,31
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ntz $r7,$r8
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ashl $r0,$r0,$r7
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btst $r0,(6<<5)|0 # test low bits for sticky again
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lshr $r0,$r0,6
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sticky $r0
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# update exponent
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add $r2,$r2,5
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sub $r2,$r2,$r7
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# Round to nearest
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round $r0,$r7,$r6
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# detect_exp_update
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lshr $r6,$r0,24
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|
|
|
add $r2,$r2,$r6
|
|
|
|
|
|
|
|
|
|
|
|
# final tests
|
|
|
|
|
|
# mz == 0? if so, we just bail with a +0
|
|
|
|
|
|
cmp $r0,0
|
|
|
|
|
|
jmpc nz,msum_not_zero
|
|
|
|
|
|
ldk $r0,0
|
|
|
|
|
|
return
|
|
|
|
|
|
msum_not_zero:
|
|
|
|
|
|
# Combined check that (1 <= ez <= 254)
|
|
|
|
|
|
sub $r3,$r2,1
|
|
|
|
|
|
cmp $r3,254
|
|
|
|
|
|
jmpc b,no_special_ret
|
|
|
|
|
|
# underflow?
|
|
|
|
|
|
cmp $r2,0
|
|
|
|
|
|
jmpc gt,no_under
|
|
|
|
|
|
ldk $r0,0
|
|
|
|
|
|
jmp pack_sz
|
|
|
|
|
|
no_under:
|
|
|
|
|
|
# overflow?
|
|
|
|
|
|
cmp $r2,255
|
|
|
|
|
|
jmpc lt,no_special_ret
|
|
|
|
|
|
ldk $r0,0x7F8
|
|
|
|
|
|
ashl $r0,$r0,20
|
|
|
|
|
|
jmp pack_sz
|
|
|
|
|
|
no_special_ret:
|
|
|
|
|
|
# Pack ez
|
|
|
|
|
|
ldl $r2,$r2,(8<<5)|23
|
|
|
|
|
|
bins $r0,$r0,$r2 # width = 8, pos = 23 pack ez
|
|
|
|
|
|
# Pack sz
|
|
|
|
|
|
pack_sz:
|
|
|
|
|
|
ldl $r4,$r4,(1<<5)|31
|
|
|
|
|
|
bins $r0,$r0,$r4 # width = 1, pos = 31 set sz to sy
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
## multiplication
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_mulsf3
|
|
|
|
|
|
.global __mulsf3
|
|
|
|
|
|
__mulsf3:
|
|
|
|
|
|
# x in $r0, y in $r1, result z in $r0 --||| 61 instructions +/- |||--
|
|
|
|
|
|
|
|
|
|
|
|
# unpack e
|
|
|
|
|
|
bextu $r2,$r0,(8<<5)|23 # ex in r2
|
|
|
|
|
|
bextu $r3,$r1,(8<<5)|23 # ey in r3
|
|
|
|
|
|
# calc result sign
|
|
|
|
|
|
xor $r4,$r0,$r1
|
|
|
|
|
|
lpm $r5,sign_mask
|
|
|
|
|
|
and $r4,$r4,$r5 # sz in r4
|
|
|
|
|
|
|
|
|
|
|
|
# unpack m add implicit bit
|
|
|
|
|
|
ldk $r5,(1<<10)|(9<<5)|23 # setup implicit bit and mask for e
|
|
|
|
|
|
#----------------------
|
|
|
|
|
|
bins $r0,$r0,$r5 # clear sx, ex and add implicit bit mx
|
|
|
|
|
|
|
|
|
|
|
|
sub $r6,$r2,1
|
|
|
|
|
|
cmp $r6,254
|
|
|
|
|
|
jmpc b,1f
|
|
|
|
|
|
jmp slow_mul
|
|
|
|
|
|
1: sub $r6,$r3,1
|
|
|
|
|
|
cmp $r6,254
|
|
|
|
|
|
jmpc b,no_special_vals_mul
|
|
|
|
|
|
|
|
|
|
|
|
slow_mul:
|
|
|
|
|
|
# Check for early exit
|
|
|
|
|
|
cmp $r2,0
|
|
|
|
|
|
jmpc z,op_is_zero
|
|
|
|
|
|
cmp $r3,0
|
|
|
|
|
|
jmpc nz,no_early_exit_mul
|
|
|
|
|
|
op_is_zero:
|
|
|
|
|
|
cmp $r2,255
|
|
|
|
|
|
jmpc z,no_early_exit_mul
|
|
|
|
|
|
cmp $r3,255
|
|
|
|
|
|
jmpc z,no_early_exit_mul
|
|
|
|
|
|
move $r0,$r4
|
|
|
|
|
|
return
|
|
|
|
|
|
no_early_exit_mul:
|
|
|
|
|
|
# setup to test for special values
|
|
|
|
|
|
sub $r6,$r2,1
|
|
|
|
|
|
and $r6,$r6,0xFE
|
|
|
|
|
|
sub $r7,$r3,1
|
|
|
|
|
|
and $r7,$r7,0xFE
|
|
|
|
|
|
# test for special values
|
|
|
|
|
|
cmp $r6,$r7
|
|
|
|
|
|
jmpc gte,ex_spec_is_gte_ey_mul
|
|
|
|
|
|
move $r6,$r7
|
|
|
|
|
|
ex_spec_is_gte_ey_mul:
|
|
|
|
|
|
cmp $r6,0xFE
|
|
|
|
|
|
jmpc nz,no_special_vals_mul
|
|
|
|
|
|
cmp $r2,0xFF
|
|
|
|
|
|
jmpc nz,ex_not_FF_mul
|
|
|
|
|
|
ashl $r6,$r0,9
|
|
|
|
|
|
cmp $r6,0
|
|
|
|
|
|
jmpc nz,ret_nan
|
|
|
|
|
|
cmp $r3,0
|
|
|
|
|
|
jmpc z,ret_nan
|
|
|
|
|
|
ashl $r6,$r1,1
|
|
|
|
|
|
lpm $r7,high_FF
|
|
|
|
|
|
cmp $r6,$r7
|
|
|
|
|
|
jmpc a,ret_nan
|
|
|
|
|
|
cmp $r6,0
|
|
|
|
|
|
jmpc z,ret_nan
|
|
|
|
|
|
# infinity
|
|
|
|
|
|
lpm $r0,inf
|
|
|
|
|
|
or $r0,$r0,$r4
|
|
|
|
|
|
return
|
|
|
|
|
|
ex_not_FF_mul:
|
|
|
|
|
|
cmp $r2,0
|
|
|
|
|
|
jmpc nz,no_nan_mul
|
|
|
|
|
|
cmp $r3,0xFF
|
|
|
|
|
|
jmpc nz,no_nan_mul
|
|
|
|
|
|
jmp ret_nan
|
|
|
|
|
|
no_nan_mul:
|
|
|
|
|
|
lpm $r0,nan
|
|
|
|
|
|
and $r0,$r0,$r1
|
|
|
|
|
|
or $r0,$r0,$r4
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
|
|
ret_nan:
|
|
|
|
|
|
lpm $r0,nan
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
|
|
no_special_vals_mul:
|
|
|
|
|
|
bins $r1,$r1,$r5 # clear sy, ey and add implicit bit my
|
|
|
|
|
|
# calc ez
|
|
|
|
|
|
add $r3,$r2,$r3
|
|
|
|
|
|
sub $r3,$r3,127 # ez in r3
|
|
|
|
|
|
|
|
|
|
|
|
# (r1,r2) = R0 * R1
|
|
|
|
|
|
mul $r2,$r0,$r1
|
|
|
|
|
|
muluh $r1,$r0,$r1
|
|
|
|
|
|
|
|
|
|
|
|
btst $r1,(1<<5)|15 # XXX use jmpx
|
|
|
|
|
|
jmpc z,mul_z0
|
|
|
|
|
|
|
|
|
|
|
|
# mz is 1X.XX...X
|
|
|
|
|
|
# 48-bit product is in (r1,r2). The low 22 bits of r2
|
|
|
|
|
|
# are discarded.
|
|
|
|
|
|
lshr $r0,$r2,22
|
|
|
|
|
|
ashl $r1,$r1,10
|
|
|
|
|
|
or $r0,$r0,$r1 # r0 = (r1,r2) >> 22
|
|
|
|
|
|
ashlcc 2,10
|
|
|
|
|
|
sticky $r0
|
|
|
|
|
|
add $r3,$r3,1 # bump exponent
|
|
|
|
|
|
|
|
|
|
|
|
# Round to nearest
|
|
|
|
|
|
round $r0, $r1, $r2
|
|
|
|
|
|
lshr $r6,$r0,24
|
|
|
|
|
|
add $r3,$r3,$r6
|
|
|
|
|
|
|
|
|
|
|
|
sub $r6,$r3,1
|
|
|
|
|
|
cmp $r6,254
|
|
|
|
|
|
jmpc b,no_special_ret_mul
|
|
|
|
|
|
|
|
|
|
|
|
special_ret_mul:
|
|
|
|
|
|
# When the final exponent <= 0, result is flushed to 0 except
|
|
|
|
|
|
# for the border case 0x00FFFFFF which is promoted to next higher
|
|
|
|
|
|
# FP no., that is, the smallest "normalized" number.
|
|
|
|
|
|
cmp $r3,0
|
|
|
|
|
|
jmpc gt,exp_normal
|
|
|
|
|
|
# Pack ez
|
|
|
|
|
|
ldl $r3,$r3,(8<<5)|23
|
|
|
|
|
|
bins $r0,$r0,$r3 # width = 8, pos = 23 pack ez
|
|
|
|
|
|
lpm $r2,edge_case
|
|
|
|
|
|
cmp $r0,$r2
|
|
|
|
|
|
jmpc nz,no_edge_case
|
|
|
|
|
|
lpm $r0,smallest_norm
|
|
|
|
|
|
jmp pack_sz_mul
|
|
|
|
|
|
no_edge_case:
|
|
|
|
|
|
ldk $r0,0
|
|
|
|
|
|
jmp pack_sz_mul
|
|
|
|
|
|
exp_normal:
|
|
|
|
|
|
# overflow?
|
|
|
|
|
|
cmp $r3,255
|
|
|
|
|
|
jmpc lt,no_special_ret_mul
|
|
|
|
|
|
ldk $r0,0x7F8
|
|
|
|
|
|
ashl $r0,$r0,20
|
|
|
|
|
|
jmp pack_sz_mul
|
|
|
|
|
|
no_special_ret_mul:
|
|
|
|
|
|
# Pack ez
|
|
|
|
|
|
ldl $r3,$r3,(8<<5)|23
|
|
|
|
|
|
bins $r0,$r0,$r3 # width = 8, pos = 23 pack ez
|
|
|
|
|
|
# Pack sz
|
|
|
|
|
|
pack_sz_mul:
|
|
|
|
|
|
or $r0,$r0,$r4
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
|
|
mul_z0:
|
|
|
|
|
|
# mz is 0X.XX...X
|
|
|
|
|
|
# 48-bit product is in (r1,r2). The low 21 bits of r2
|
|
|
|
|
|
# are discarded.
|
|
|
|
|
|
lshr $r0,$r2,21
|
|
|
|
|
|
ashl $r1,$r1,11
|
|
|
|
|
|
or $r0,$r0,$r1 # r0 = (r1,r2) >> 22
|
|
|
|
|
|
ashlcc 2,11
|
|
|
|
|
|
sticky $r0
|
|
|
|
|
|
# Round to nearest
|
|
|
|
|
|
round $r0, $r1, $r2
|
|
|
|
|
|
lshr $r6,$r0,24
|
|
|
|
|
|
add $r3,$r3,$r6
|
|
|
|
|
|
|
|
|
|
|
|
sub $r6,$r3,1
|
|
|
|
|
|
cmp $r6,254
|
|
|
|
|
|
jmpc b,no_special_ret_mul
|
|
|
|
|
|
jmp special_ret_mul
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
## division
|
|
|
|
|
|
|
|
|
|
|
|
## See http://perso.ens-lyon.fr/gilles.villard/BIBLIOGRAPHIE/PDF/arith19.pdf
|
|
|
|
|
|
## for implementation details
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_divsf3
|
|
|
|
|
|
dc_1: .long 0xffffe7d7
|
|
|
|
|
|
dc_2: .long 0xffffffe8
|
|
|
|
|
|
dc_3: .long 0xffbad86f
|
|
|
|
|
|
dc_4: .long 0xfffbece7
|
|
|
|
|
|
dc_5: .long 0xf3672b51
|
|
|
|
|
|
dc_6: .long 0xfd9d3a3e
|
|
|
|
|
|
dc_7: .long 0x9a3c4390
|
|
|
|
|
|
dc_8: .long 0xd4d2ce9b
|
|
|
|
|
|
dc_9: .long 0x1bba92b3
|
|
|
|
|
|
dc_10: .long 0x525a1a8b
|
|
|
|
|
|
dc_11: .long 0x0452b1bf
|
|
|
|
|
|
dc_12: .long 0xFFFFFFC0
|
|
|
|
|
|
spec_val_test: .long 0x7F7FFFFF
|
|
|
|
|
|
|
|
|
|
|
|
.global __divsf3
|
|
|
|
|
|
__divsf3:
|
|
|
|
|
|
push $r13
|
|
|
|
|
|
# x in $r0, y in $r1, result z in $r0 --||| 73 instructions +/- |||-
|
|
|
|
|
|
bextu $r10,$r0,(8<<5)|23 # ex in r2
|
|
|
|
|
|
bextu $r11,$r1,(8<<5)|23 # ey in r3
|
|
|
|
|
|
lpm $r6, m_mask
|
|
|
|
|
|
and $r2, $r0, $r6 # mx
|
|
|
|
|
|
and $r3, $r1, $r6 # my
|
|
|
|
|
|
cmp $r2,$r3
|
|
|
|
|
|
bextu $r2,$r30,(1<<5)|4 # c = Tx >= T;
|
|
|
|
|
|
ashl $r3,$r3,9 # T = X << 9;
|
|
|
|
|
|
lpm $r13, sign_mask
|
|
|
|
|
|
ashl $r4,$r0,8 # X8 = X << 8;
|
|
|
|
|
|
or $r4,$r4,$r13 # Mx = X8 | 0x80000000;
|
|
|
|
|
|
lshr $r5,$r4,$r2 # S = Mx >> c;
|
|
|
|
|
|
# calc D
|
|
|
|
|
|
sub $r2, $r11, $r2
|
|
|
|
|
|
add $r12, $r10, 125
|
|
|
|
|
|
sub $r2, $r12, $r2 # int D = (Ex + 125) - (Ey - c);
|
|
|
|
|
|
# calc result sign
|
|
|
|
|
|
xor $r12,$r0,$r1
|
|
|
|
|
|
and $r12,$r12,$r13 # Sr = ( X ˆ Y ) & 0x80000000;
|
|
|
|
|
|
# check early exit
|
|
|
|
|
|
cmp $r10, 0
|
|
|
|
|
|
jmpc nz, no_early_ret_dev
|
|
|
|
|
|
cmp $r11, 0
|
|
|
|
|
|
jmpc z, no_early_ret_dev
|
|
|
|
|
|
cmp $r11, 255
|
|
|
|
|
|
jmpc z, no_early_ret_dev
|
|
|
|
|
|
move $r0, $r12
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
no_early_ret_dev:
|
|
|
|
|
|
# setup to test for special values
|
|
|
|
|
|
sub $r8,$r10,1
|
|
|
|
|
|
and $r8,$r8,0xFE
|
|
|
|
|
|
sub $r9,$r11,1
|
|
|
|
|
|
and $r9,$r9,0xFE
|
|
|
|
|
|
# test for special values
|
|
|
|
|
|
cmp $r8, $r9
|
|
|
|
|
|
jmpc gte, absXm1_gte_absYm1
|
|
|
|
|
|
move $r8, $r9
|
|
|
|
|
|
absXm1_gte_absYm1:
|
|
|
|
|
|
cmp $r8, 0xFE
|
|
|
|
|
|
jmpc nz, no_spec_ret_div
|
|
|
|
|
|
cmp $r10, 0xFF
|
|
|
|
|
|
jmpc nz, ex_not_FF_div
|
|
|
|
|
|
lpm $r6, m_mask
|
|
|
|
|
|
and $r2, $r0, $r6 # mx
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc nz, ret_nan_div
|
|
|
|
|
|
cmp $r11, 0xFF
|
|
|
|
|
|
jmpc z, ret_nan_div
|
|
|
|
|
|
jmp ret_inf_div
|
|
|
|
|
|
ex_not_FF_div:
|
|
|
|
|
|
cmp $r11, 0xFF
|
|
|
|
|
|
jmpc nz, ey_not_FF_div
|
|
|
|
|
|
ashl $r13, $r1, 9
|
|
|
|
|
|
cmp $r13, 0
|
|
|
|
|
|
jmpc nz, ret_nan_div
|
|
|
|
|
|
move $r0, $r12
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
ey_not_FF_div:
|
|
|
|
|
|
or $r10, $r10, $r11
|
|
|
|
|
|
cmp $r10, 0
|
|
|
|
|
|
jmpc z, ret_nan_div
|
|
|
|
|
|
ret_inf_div:
|
|
|
|
|
|
lpm $r6, inf
|
|
|
|
|
|
move $r0, $r6
|
|
|
|
|
|
or $r0, $r0, $r12
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
ret_nan_div:
|
|
|
|
|
|
lpm $r0, nan
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
|
|
no_spec_ret_div:
|
|
|
|
|
|
# check for overflow
|
|
|
|
|
|
ldk $r6, 0xFE
|
|
|
|
|
|
cmp $r2, $r6
|
|
|
|
|
|
jmpc lt, no_overflow_div
|
|
|
|
|
|
lpm $r6, inf
|
|
|
|
|
|
or $r0, $r12, $r6
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
no_overflow_div:
|
|
|
|
|
|
# check for underflow
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc ns, no_underflow_div
|
|
|
|
|
|
xnor $r6, $r6, $r6 # -1
|
|
|
|
|
|
cmp $r2, $r6
|
|
|
|
|
|
jmpc nz, ret_sr_div
|
|
|
|
|
|
ldk $r7, 0xFF
|
|
|
|
|
|
xor $r6, $r6, $r7 # 0xFF ^ -1 = 0xFFFFFF00
|
|
|
|
|
|
cmp $r4, $r6
|
|
|
|
|
|
jmpc nz, ret_sr_div
|
|
|
|
|
|
lpm $r6, sign_mask
|
|
|
|
|
|
cmp $r4, $r6
|
|
|
|
|
|
jmpc nz, ret_sr_div
|
|
|
|
|
|
lshr $r0, $r6, 8
|
|
|
|
|
|
or $r0, $r0, $r12
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
ret_sr_div:
|
|
|
|
|
|
move $r0, $r12
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
no_underflow_div:
|
|
|
|
|
|
lpm $r6, dc_1
|
|
|
|
|
|
muluh $r7, $r3, $r6 # i0 = mul( T , 0xffffe7d7 );
|
|
|
|
|
|
lpm $r6, dc_2
|
|
|
|
|
|
sub $r7, $r6, $r7 # i1 = 0xffffffe8 - i0;
|
|
|
|
|
|
muluh $r7, $r5, $r7 # i2 = mul( S , i1 );
|
|
|
|
|
|
add $r7, $r7, 0x20 # i3 = 0x00000020 + i2;
|
|
|
|
|
|
muluh $r8, $r3, $r3 # i4 = mul( T , T );
|
|
|
|
|
|
muluh $r9, $r5, $r8 # i5 = mul( S , i4 );
|
|
|
|
|
|
lpm $r6, dc_3
|
|
|
|
|
|
muluh $r10, $r3, $r6 # i6 = mul( T , 0xffbad86f );
|
|
|
|
|
|
lpm $r6, dc_4
|
|
|
|
|
|
sub $r10, $r6, $r10 # i7 = 0xfffbece7 - i6;
|
|
|
|
|
|
muluh $r10, $r9, $r10 # i8 = mul( i5 , i7 );
|
|
|
|
|
|
add $r7, $r7, $r10 # i9 = i3 + i8;
|
|
|
|
|
|
muluh $r9, $r8, $r9 # i10 = mul( i4 , i5 );
|
|
|
|
|
|
lpm $r6, dc_5
|
|
|
|
|
|
muluh $r10, $r3, $r6 # i11 = mul( T , 0xf3672b51 );
|
|
|
|
|
|
lpm $r6, dc_6
|
|
|
|
|
|
sub $r10, $r6, $r10 # i12 = 0xfd9d3a3e - i11;
|
|
|
|
|
|
lpm $r6, dc_7
|
|
|
|
|
|
muluh $r11, $r3, $r6 # i13 = mul( T , 0x9a3c4390 );
|
|
|
|
|
|
lpm $r6, dc_8
|
|
|
|
|
|
sub $r11, $r6, $r11 # i14 = 0xd4d2ce9b - i13
|
|
|
|
|
|
muluh $r11, $r8, $r11 # i15 = mul( i4 , i14 );
|
|
|
|
|
|
add $r10, $r10, $r11 # i16 = i12 + i15;
|
|
|
|
|
|
muluh $r10, $r9, $r10 # i17 = mul( i10 , i16 )
|
|
|
|
|
|
add $r7, $r7, $r10 # i18 = i9 + i17;
|
|
|
|
|
|
muluh $r10, $r8, $r8 # i19 = mul( i4 , i4 );
|
|
|
|
|
|
lpm $r6, dc_9
|
|
|
|
|
|
muluh $r11, $r3, $r6 # i20 = mul( T , 0x1bba92b3 );
|
|
|
|
|
|
lpm $r6, dc_10
|
|
|
|
|
|
sub $r11, $r6, $r11 # i21 = 0x525a1a8b - i20;
|
|
|
|
|
|
lpm $r6, dc_11
|
|
|
|
|
|
muluh $r8, $r8, $r6 # i22 = mul( i4 , 0x0452b1bf );
|
|
|
|
|
|
add $r8, $r11, $r8 # i23 = i21 + i22;
|
|
|
|
|
|
muluh $r8, $r10, $r8 # i24 = mul( i19 , i23 );
|
|
|
|
|
|
muluh $r8, $r9, $r8 # i25 = mul( i10 , i24 );
|
|
|
|
|
|
add $r3, $r7, $r8 # V = i18 + i25;
|
|
|
|
|
|
# W = V & 0xFFFFFFC0;
|
|
|
|
|
|
lpm $r6, dc_12
|
|
|
|
|
|
and $r3, $r3, $r6 # W
|
|
|
|
|
|
# round and pack final values
|
|
|
|
|
|
ashl $r0, $r2, 23 # pack D
|
|
|
|
|
|
or $r0, $r0, $r12 # pack Sr
|
|
|
|
|
|
ashl $r12, $r1, 8
|
|
|
|
|
|
or $r12, $r12, $r13 # My
|
|
|
|
|
|
muluh $r10, $r3, $r12
|
|
|
|
|
|
lshr $r11, $r5, 1
|
|
|
|
|
|
cmp $r10, $r11
|
|
|
|
|
|
jmpc gte, div_ret_1
|
|
|
|
|
|
add $r3, $r3, 0x40
|
|
|
|
|
|
div_ret_1:
|
|
|
|
|
|
lshr $r3, $r3, 7
|
|
|
|
|
|
add $r0, $r0, $r3
|
|
|
|
|
|
pop $r13
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
## Negate
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_negsf
|
|
|
|
|
|
.global __negsf
|
|
|
|
|
|
__negsf:
|
|
|
|
|
|
lpm $r1, sign_mask
|
|
|
|
|
|
xor $r0, $r0, $r1
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
## float to int & unsigned int
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_fixsfsi
|
|
|
|
|
|
.global __fixsfsi
|
|
|
|
|
|
__fixsfsi: # 20 instructions
|
|
|
|
|
|
bextu $r1,$r0,(8<<5)|23 # e in r1
|
|
|
|
|
|
lshr $r2,$r0,31 # s in r2
|
|
|
|
|
|
lpm $r3, m_mask
|
|
|
|
|
|
and $r0,$r0,$r3 # m in r0
|
|
|
|
|
|
# test nan
|
|
|
|
|
|
cmp $r1,0xFF
|
|
|
|
|
|
jmpc nz, int_not_nan
|
|
|
|
|
|
cmp $r0,0
|
|
|
|
|
|
jmpc z, int_not_nan
|
|
|
|
|
|
ldk $r0,0
|
|
|
|
|
|
return
|
|
|
|
|
|
int_not_nan:
|
|
|
|
|
|
# test edges
|
|
|
|
|
|
cmp $r1, 127
|
|
|
|
|
|
jmpc gte, int_not_zero # lower limit
|
|
|
|
|
|
ldk $r0,0
|
|
|
|
|
|
return
|
|
|
|
|
|
int_not_zero:
|
|
|
|
|
|
cmp $r1, 158
|
|
|
|
|
|
jmpc lt, int_not_max # upper limit
|
|
|
|
|
|
lpm $r0, nan
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc z, int_positive
|
|
|
|
|
|
xnor $r0, $r0, 0
|
|
|
|
|
|
return
|
|
|
|
|
|
int_not_max:
|
|
|
|
|
|
lpm $r3, smallest_norm
|
|
|
|
|
|
or $r0, $r0, $r3 # set implicit bit
|
|
|
|
|
|
sub $r1, $r1, 150
|
|
|
|
|
|
cmp $r1, 0
|
|
|
|
|
|
jmpc s, shift_right
|
|
|
|
|
|
ashl $r0, $r0, $r1
|
|
|
|
|
|
jmp set_int_sign
|
|
|
|
|
|
shift_right:
|
|
|
|
|
|
xnor $r1, $r1, 0
|
|
|
|
|
|
add $r1, $r1, 1
|
|
|
|
|
|
lshr $r0, $r0, $r1
|
|
|
|
|
|
set_int_sign:
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc z, int_positive
|
|
|
|
|
|
xnor $r0, $r0, 0
|
|
|
|
|
|
add $r0, $r0, 1
|
|
|
|
|
|
int_positive:
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_fixunssfsi
|
|
|
|
|
|
.global __fixunssfsi
|
|
|
|
|
|
__fixunssfsi: # 19 instructions
|
|
|
|
|
|
lshr $r2, $r0, 31 # s in r2
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc z, uint_not_neg
|
|
|
|
|
|
ldk $r0, 0
|
|
|
|
|
|
return
|
|
|
|
|
|
uint_not_neg:
|
|
|
|
|
|
bextu $r1, $r0, (8<<5)|23 # e in r1
|
|
|
|
|
|
sub $r1, $r1, 127
|
|
|
|
|
|
lpm $r3, m_mask
|
|
|
|
|
|
and $r0, $r0, $r3 # m in r0
|
|
|
|
|
|
# test nan
|
|
|
|
|
|
cmp $r1, 0xFF
|
|
|
|
|
|
jmpc nz, uint_not_nan
|
|
|
|
|
|
cmp $r0, 0
|
|
|
|
|
|
jmpc z, uint_not_nan
|
|
|
|
|
|
ldk $r0, 0
|
|
|
|
|
|
return
|
|
|
|
|
|
uint_not_nan:
|
|
|
|
|
|
# test edges
|
|
|
|
|
|
cmp $r1, 0
|
|
|
|
|
|
jmpc ns, uint_not_zero # lower limit
|
|
|
|
|
|
ldk $r0, 0
|
|
|
|
|
|
return
|
|
|
|
|
|
uint_not_zero:
|
|
|
|
|
|
lpm $r3, smallest_norm
|
|
|
|
|
|
or $r0, $r0, $r3 # set implicit bit
|
|
|
|
|
|
cmp $r1, 23
|
|
|
|
|
|
jmpc lt, shift_uint_right
|
|
|
|
|
|
sub $r1, $r1, 23
|
|
|
|
|
|
ashl $r0, $r0, $r1
|
|
|
|
|
|
return
|
|
|
|
|
|
shift_uint_right:
|
|
|
|
|
|
ldk $r3, 23
|
|
|
|
|
|
sub $r1, $r3, $r1
|
|
|
|
|
|
lshr $r0, $r0, $r1
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
## int & unsigned int to float
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.macro i2f x, s1, s2, s3, lbl
|
|
|
|
|
|
move \s1, \x
|
|
|
|
|
|
nlz \s1, \s2
|
|
|
|
|
|
cmp \s1, 8
|
|
|
|
|
|
jmpc s, float_round\lbl
|
|
|
|
|
|
sub \s2, \s1, 8
|
|
|
|
|
|
ashl \x, \x, \s2
|
|
|
|
|
|
jmp float_no_round\lbl
|
|
|
|
|
|
float_round\lbl:
|
|
|
|
|
|
cmp \s1, 6
|
|
|
|
|
|
jmpc s, float_shift_right\lbl
|
|
|
|
|
|
sub \s2, \s1, 6
|
|
|
|
|
|
ashl \x, \x, \s2
|
|
|
|
|
|
jmp float_round_and_pack\lbl
|
|
|
|
|
|
float_shift_right\lbl:
|
|
|
|
|
|
ldk \s2, 6
|
|
|
|
|
|
sub \s2, \s2, \s1
|
|
|
|
|
|
xnor \s3, \s3 ,\s3 # 0xFFFFFFFF
|
|
|
|
|
|
ashl \s3, \s3 ,\s2 # create inverse of mask for test of S bit value in discarded my
|
|
|
|
|
|
xnor \s3, \s3 ,0 # NOT
|
|
|
|
|
|
tst \x, \s3 # determine value of sticky bit
|
|
|
|
|
|
lshr \x, \x, \s2
|
|
|
|
|
|
jmpc z,float_round_and_pack\lbl
|
|
|
|
|
|
or \x, \x, 1 # set the sticky bit to 1
|
|
|
|
|
|
float_round_and_pack\lbl:
|
|
|
|
|
|
bextu \s2, \x, (1<<5)|2 # extract low bit of m
|
|
|
|
|
|
or \x, \x, \s2 # or p into r
|
|
|
|
|
|
add \x, \x, 1
|
|
|
|
|
|
lshr \x, \x, 2
|
|
|
|
|
|
btst \x, (1<<5)|24 # test for carry from round
|
|
|
|
|
|
jmpc z, float_no_round\lbl
|
|
|
|
|
|
sub \s1, \s1, 1 # inc e for carry (actually dec nlz)
|
|
|
|
|
|
lshr \x, \x, 1
|
|
|
|
|
|
float_no_round\lbl:
|
|
|
|
|
|
ldk \s2, 158
|
|
|
|
|
|
sub \s1, \s2, \s1
|
|
|
|
|
|
# Pack e
|
|
|
|
|
|
ldl \s1, \s1, (8<<5)|23
|
|
|
|
|
|
bins \x, \x, \s1
|
|
|
|
|
|
.endm
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_floatsisf
|
|
|
|
|
|
.global __floatsisf
|
|
|
|
|
|
__floatsisf: # 32 instructions
|
|
|
|
|
|
cmp $r0, 0
|
|
|
|
|
|
jmpc nz, float_not_zero
|
|
|
|
|
|
return
|
|
|
|
|
|
float_not_zero:
|
|
|
|
|
|
ashr $r1, $r0, 31 # s in r1
|
|
|
|
|
|
xor $r0, $r0, $r1 # cond neg
|
|
|
|
|
|
sub $r0, $r0, $r1
|
|
|
|
|
|
i2f $r0, $r2, $r3, $r4, 1
|
|
|
|
|
|
ldl $r1, $r1, (1<<5)|31
|
|
|
|
|
|
bins $r0, $r0, $r1
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_floatunsisf
|
|
|
|
|
|
.global __floatunsisf
|
|
|
|
|
|
__floatunsisf: # 26 instructions
|
|
|
|
|
|
cmp $r0, 0
|
|
|
|
|
|
jmpc nz, float_not_zero2
|
|
|
|
|
|
return
|
|
|
|
|
|
float_not_zero2:
|
|
|
|
|
|
i2f $r0, $r1, $r2, $r3, 2
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
##########################################################################
|
|
|
|
|
|
## float compare
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
__cmpsf2_:
|
|
|
|
|
|
# calc abs vals
|
|
|
|
|
|
lpm $r3, nan # also abs mask
|
|
|
|
|
|
and $r2, $r0, $r3
|
|
|
|
|
|
and $r3, $r1, $r3
|
|
|
|
|
|
# test if either abs is nan
|
|
|
|
|
|
lpm $r4, inf
|
|
|
|
|
|
cmp $r2, $r4
|
|
|
|
|
|
jmpc gt, cmp_is_gt
|
|
|
|
|
|
cmp $r3, $r4
|
|
|
|
|
|
jmpc gt, cmp_is_gt
|
|
|
|
|
|
# test if both are 0
|
|
|
|
|
|
or $r2, $r2, $r3
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc z, cmp_is_eq
|
|
|
|
|
|
# test if eq
|
|
|
|
|
|
cmp $r0, $r1
|
|
|
|
|
|
jmpc z, cmp_is_eq
|
|
|
|
|
|
# -- if either is pos
|
|
|
|
|
|
and $r2, $r0, $r1
|
|
|
|
|
|
cmp $r2, 0
|
|
|
|
|
|
jmpc s, cmp_both_neg
|
|
|
|
|
|
cmp $r0, $r1
|
|
|
|
|
|
jmpc gt, cmp_is_gt
|
|
|
|
|
|
# r0 < r1
|
|
|
|
|
|
lpm $r0, high_uint
|
|
|
|
|
|
return
|
|
|
|
|
|
cmp_both_neg:
|
|
|
|
|
|
cmp $r0, $r1
|
|
|
|
|
|
jmpc lt, cmp_is_gt
|
|
|
|
|
|
# r0 < r1
|
|
|
|
|
|
lpm $r0, high_uint
|
|
|
|
|
|
return
|
|
|
|
|
|
cmp_is_gt:
|
|
|
|
|
|
ldk $r0, 1
|
|
|
|
|
|
return
|
|
|
|
|
|
cmp_is_eq:
|
|
|
|
|
|
ldk $r0, 0
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_udivsi3
|
|
|
|
|
|
.global __udivsi3
|
|
|
|
|
|
__udivsi3:
|
|
|
|
|
|
# $r0 is dividend
|
|
|
|
|
|
# $r1 is divisor
|
|
|
|
|
|
ldk $r2,0
|
|
|
|
|
|
push $r28
|
|
|
|
|
|
ldk $r28,-32
|
|
|
|
|
|
0:
|
|
|
|
|
|
lshr $r3,$r0,31 # Shift $r2:$r0 left one
|
|
|
|
|
|
ashl $r0,$r0,1
|
|
|
|
|
|
ashl $r2,$r2,1
|
|
|
|
|
|
or $r2,$r2,$r3
|
|
|
|
|
|
cmp $r2,$r1
|
|
|
|
|
|
jmpc b,1f
|
|
|
|
|
|
2:
|
|
|
|
|
|
sub $r2,$r2,$r1
|
|
|
|
|
|
add $r0,$r0,1
|
|
|
|
|
|
1:
|
|
|
|
|
|
add $r28,$r28,1
|
|
|
|
|
|
jmpx 31,$r28,1,0b
|
|
|
|
|
|
pop $r28
|
|
|
|
|
|
# $r0: quotient
|
|
|
|
|
|
# $r2: remainder
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_umodsi3
|
|
|
|
|
|
.global __umodsi3
|
|
|
|
|
|
__umodsi3:
|
|
|
|
|
|
call __udivsi3
|
|
|
|
|
|
move $r0,$r2
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_divsi3
|
|
|
|
|
|
.global __divsi3
|
|
|
|
|
|
__divsi3:
|
|
|
|
|
|
xor $r5,$r0,$r1 # $r5 is sign of result
|
|
|
|
|
|
ashr $r2,$r0,31 # $r0 = abs($r0)
|
|
|
|
|
|
xor $r0,$r0,$r2
|
|
|
|
|
|
sub $r0,$r0,$r2
|
|
|
|
|
|
ashr $r2,$r1,31 # $r1 = abs($r1)
|
|
|
|
|
|
xor $r1,$r1,$r2
|
|
|
|
|
|
sub $r1,$r1,$r2
|
|
|
|
|
|
call __udivsi3
|
|
|
|
|
|
ashr $r5,$r5,31
|
|
|
|
|
|
xor $r0,$r0,$r5
|
|
|
|
|
|
sub $r0,$r0,$r5
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
|
|
#ifdef L_modsi3
|
|
|
|
|
|
.global __modsi3
|
|
|
|
|
|
__modsi3:
|
|
|
|
|
|
move $r5,$r0 # $r5 is sign of result
|
|
|
|
|
|
ashr $r2,$r0,31 # $r0 = abs($r0)
|
|
|
|
|
|
xor $r0,$r0,$r2
|
|
|
|
|
|
sub $r0,$r0,$r2
|
|
|
|
|
|
ashr $r2,$r1,31 # $r1 = abs($r1)
|
|
|
|
|
|
xor $r1,$r1,$r2
|
|
|
|
|
|
sub $r1,$r1,$r2
|
|
|
|
|
|
call __umodsi3
|
|
|
|
|
|
ashr $r5,$r5,31
|
|
|
|
|
|
xor $r0,$r0,$r5
|
|
|
|
|
|
sub $r0,$r0,$r5
|
|
|
|
|
|
return
|
|
|
|
|
|
#endif
|
