libgcc/config/epiphany/ieee-754/fast_div.S

   1 /* Copyright (C) 2011-2016 Free Software Foundation, Inc.
   2    Contributed by Embecosm on behalf of Adapteva, Inc.
   3
   4 This file is part of GCC.
   5
   6 GCC is free software; you can redistribute it and/or modify it under
   7 the terms of the GNU General Public License as published by the Free
   8 Software Foundation; either version 3, or (at your option) any later
   9 version.
  10
  11 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  12 WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14 for more details.
  15
  16 Under Section 7 of GPL version 3, you are granted additional
  17 permissions described in the GCC Runtime Library Exception, version
  18 3.1, as published by the Free Software Foundation.
  19
  20 You should have received a copy of the GNU General Public License and
  21 a copy of the GCC Runtime Library Exception along with this program;
  22 see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  23 <http://www.gnu.org/licenses/>.  */
  24
  25 #include "../epiphany-asm.h"
  26
  27 .section _fast_div_text,"a",@progbits;
  28   .balign 8;
  29 _fast_div_table:
  30 .word 0x007fffff//   mantissa mask
  31 .word 0x40257ebb//   hold constant a = 2.58586
  32
  33 .word 0x3f000000//   hold constant 126 shifted to bits [30:23]
  34 .word 0xc0ba2e88//   hold constant b = -5.81818
  35
  36 .word 0x4087c1e8//   hold constant c = 4.24242
  37 .word 0x40000000//  to hold constant 2 for Newton-Raphson iterations
  38
  39  .global SYM(__fast_recipsf2)
  40  FUNC(__fast_recipsf2)
  41 SYM(__fast_recipsf2):
  42
  43 //###################
  44 //# input operands:
  45 //###################
  46 // Divisor
  47 //R0
  48 // Function address (used with negative offsets to read _fast_div_table)
  49 //R1
  50 /* Scratch registers:  two single (TMP0/TMP5) and two pairs.  */
  51 #define P0L TMP1
  52 #define P0H TMP2
  53 #define P1L TMP3
  54 #define P1H TMP4
  55
  56 //#########################################
  57 //# Constants to be used in the algorithm
  58 //#########################################
  59 ldrd P0L , [ R1 , -3 ]
  60
  61 ldrd P1L , [ R1 , -2 ]
  62
  63
  64
  65 //#############################################################################
  66 //#                       The Algorithm
  67 //#
  68 //# Operation: C=A/B
  69 //# stage 1 - find the reciprocal 1/B according to the following scheme:
  70 //#  B = (2^E)*m                                (1<m<2, E=e-127)
  71 //#  1/B = 1/((2^E)*m) = 1/((2^(E+1))*m1)          (0.5<m1<1)
  72 //#      = (2^-(E+1))*(1/m1) = (2^E1)*(1/m1)
  73 //#
  74 //# Now we can find the new exponent:
  75 //# e1 = E1+127 = -E-1+127 = -e+127-1+127 = 253-e **
  76 //# 1/m1 alreadt has the exponent 127, so we have to add 126-e.
  77 //# the exponent might underflow, which we can detect as a sign change.
  78 //# Since the architeture uses flush-to-zero for subnormals, we can
  79 //# give the result 0. then.
  80 //#
  81 //# The 1/m1 term with 0.5<m1<1 is approximated with the Chebyshev polynomial
  82 //# 1/m1 = 2.58586*(m1^2) - 5.81818*m1 + 4.24242
  83 //#
  84 //# Next step is to use two iterations of Newton-Raphson algorithm to complete
  85 //# the reciprocal calculation.
  86 //#
  87 //# Final result is achieved by multiplying A with 1/B
  88 //#############################################################################
  89
  90
  91
  92 // R0 exponent and sign "replacement" into TMP0
  93 AND TMP0,R0,P0L          ;
  94 ORR TMP0,TMP0,P1L
  95 SUB TMP5,R0,TMP0 // R0 sign/exponent extraction into TMP5
  96 // Calculate new mantissa
  97 FMADD P1H,TMP0,P0H               ;
  98                 // Calculate new exponent offset 126 - "old exponent"
  99                 SUB P1L,P1L,TMP5
 100         ldrd P0L , [ R1 , -1 ]
 101 FMADD P0L,TMP0,P1H               ;
 102                 eor P1H,r0,P1L // check for overflow (N-BIT).
 103                 blt .Lret_0
 104 // P0L exponent and sign "replacement"
 105 sub P0L,P0L,TMP5
 106
 107 // Newton-Raphson iteration #1
 108 MOV TMP0,P0H             ;
 109 FMSUB P0H,R0,P0L         ;
 110 FMUL  P0L,P0H,P0L        ;
 111 // Newton-Raphson iteration #2
 112 FMSUB TMP0,R0,P0L       ;
 113 FMUL  R0,TMP0,P0L                ;
 114 jr lr
 115 .Lret_0:ldrd P0L , [ R1 , -3 ]
 116         lsr TMP0,r0,31 ; extract sign
 117         lsl TMP0,TMP0,31
 118         add P0L,P0L,r0 ; check for NaN input
 119         eor P0L,P0L,r0
 120         movgte r0,TMP0
 121         jr lr
 122 // Quotient calculation is expected by the caller: FMUL quotient,divident,R0
 123         ;
 124         ENDFUNC(__fast_recipsf2)