/* Copyright (C) 2011-2015 Free Software Foundation, Inc. Contributed by Embecosm on behalf of Adapteva, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ #include "../epiphany-asm.h" .section _fast_div_text,"a",@progbits; .balign 8; _fast_div_table: .word 0x007fffff// mantissa mask .word 0x40257ebb// hold constant a = 2.58586 .word 0x3f000000// hold constant 126 shifted to bits [30:23] .word 0xc0ba2e88// hold constant b = -5.81818 .word 0x4087c1e8// hold constant c = 4.24242 .word 0x40000000// to hold constant 2 for Newton-Raphson iterations .global SYM(__fast_recipsf2) FUNC(__fast_recipsf2) SYM(__fast_recipsf2): //################### //# input operands: //################### // Divisor //R0 // Function address (used with negative offsets to read _fast_div_table) //R1 /* Scratch registers: two single (TMP0/TMP5) and two pairs. */ #define P0L TMP1 #define P0H TMP2 #define P1L TMP3 #define P1H TMP4 //######################################### //# Constants to be used in the algorithm //######################################### ldrd P0L , [ R1 , -3 ] ldrd P1L , [ R1 , -2 ] //############################################################################# //# The Algorithm //# //# Operation: C=A/B //# stage 1 - find the reciprocal 1/B according to the following scheme: //# B = (2^E)*m (1<m<2, E=e-127) //# 1/B = 1/((2^E)*m) = 1/((2^(E+1))*m1) (0.5<m1<1) //# = (2^-(E+1))*(1/m1) = (2^E1)*(1/m1) //# //# Now we can find the new exponent: //# e1 = E1+127 = -E-1+127 = -e+127-1+127 = 253-e ** //# 1/m1 alreadt has the exponent 127, so we have to add 126-e. //# the exponent might underflow, which we can detect as a sign change. //# Since the architeture uses flush-to-zero for subnormals, we can //# give the result 0. then. //# //# The 1/m1 term with 0.5<m1<1 is approximated with the Chebyshev polynomial //# 1/m1 = 2.58586*(m1^2) - 5.81818*m1 + 4.24242 //# //# Next step is to use two iterations of Newton-Raphson algorithm to complete //# the reciprocal calculation. //# //# Final result is achieved by multiplying A with 1/B //############################################################################# // R0 exponent and sign "replacement" into TMP0 AND TMP0,R0,P0L ; ORR TMP0,TMP0,P1L SUB TMP5,R0,TMP0 // R0 sign/exponent extraction into TMP5 // Calculate new mantissa FMADD P1H,TMP0,P0H ; // Calculate new exponent offset 126 - "old exponent" SUB P1L,P1L,TMP5 ldrd P0L , [ R1 , -1 ] FMADD P0L,TMP0,P1H ; eor P1H,r0,P1L // check for overflow (N-BIT). blt .Lret_0 // P0L exponent and sign "replacement" sub P0L,P0L,TMP5 // Newton-Raphson iteration #1 MOV TMP0,P0H ; FMSUB P0H,R0,P0L ; FMUL P0L,P0H,P0L ; // Newton-Raphson iteration #2 FMSUB TMP0,R0,P0L ; FMUL R0,TMP0,P0L ; jr lr .Lret_0:ldrd P0L , [ R1 , -3 ] lsr TMP0,r0,31 ; extract sign lsl TMP0,TMP0,31 add P0L,P0L,r0 ; check for NaN input eor P0L,P0L,r0 movgte r0,TMP0 jr lr // Quotient calculation is expected by the caller: FMUL quotient,divident,R0 ; ENDFUNC(__fast_recipsf2)