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-# *****************************************************************
-#
-# The Compcert verified compiler
-#
-# Xavier Leroy, INRIA Paris-Rocquencourt
-#
-# Copyright (c) 2013 Institut National de Recherche en Informatique et
-# en Automatique.
-#
-# Redistribution and use in source and binary forms, with or without
-# modification, are permitted provided that the following conditions are met:
-# * Redistributions of source code must retain the above copyright
-# notice, this list of conditions and the following disclaimer.
-# * Redistributions in binary form must reproduce the above copyright
-# notice, this list of conditions and the following disclaimer in the
-# documentation and/or other materials provided with the distribution.
-# * Neither the name of the <organization> nor the
-# names of its contributors may be used to endorse or promote products
-# derived from this software without specific prior written permission.
-#
-# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
-# HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
-# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
-# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
-# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
-# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-#
-# *********************************************************************
-
-# Helper functions for 64-bit integer arithmetic. PowerPC version.
-
- .text
-
-# Unsigned division and modulus
-
-# This function computes both the quotient and the remainder of two
-# unsigned 64-bit integers.
-
-# Input: numerator N in (r3,r4), divisor D in (r5,r6)
-# Output: quotient Q in (r5,r6), remainder R in (r3,r4)
-# Destroys: all integer caller-save registers
-
- .globl __compcert_i64_udivmod
- .balign 16
-__compcert_i64_udivmod:
- cmplwi r5, 0 # DH == 0 ?
- stwu r1, -32(r1)
- mflr r0
- stw r0, 8(r1)
- stw r31, 12(r1)
- beq 1f
-# The general case
- stw r30, 16(r1)
- stw r29, 20(r1)
- stw r28, 24(r1)
- mr r28, r3 # Save N in (r28, r29)
- mr r29, r4
- mr r30, r5 # Save D in (r30, r31)
- mr r31, r6
- # Scale N and D down, giving N' and D', such that 2^31 <= D' < 2^32
- cntlzw r7, r5 # r7 = leading zeros in DH = 32 - shift amount
- subfic r8, r7, 32 # r8 = shift amount
- slw r0, r3, r7 # N' = N >> shift amount
- srw r3, r3, r8
- srw r4, r4, r8
- or r4, r4, r0
- slw r0, r5, r7 # D' = D >> shift amount
- srw r6, r6, r8
- or r5, r6, r0
- # Divide N' by D' to get an approximate quotient Q
- bl __compcert_i64_udiv6432 # r3 = quotient, r4 = remainder
- mr r6, r3 # low half of quotient Q
- li r5, 0 # high half of quotient is 0
- # Tentative quotient is either correct or one too high
- # Compute Q * D in (r7, r8)
-4: mullw r7, r6, r30 # r7 = Q * DH
- mullw r8, r6, r31 # r8 = low 32 bits of Q * DL
- mulhwu r0, r6, r31 # r0 = high 32 bits of Q * DL
- addc r7, r7, r0
- subfe. r0, r0, r0 # test carry: EQ iff carry
- beq 2f # handle overflow case
- # Compute R = N - Q * D, with borrow
- subfc r4, r8, r29
- subfe r3, r7, r28
- subfe. r0, r0, r0 # test borrow: EQ iff no borrow
- beq 3f # no borrow: N >= Q * D, we are good
- addi r6, r6, -1 # borrow: adjust Q down by 1
- addc r4, r4, r31 # and R up by D
- adde r3, r3, r30
- # Finished
-3: lwz r0, 8(r1)
- mtlr r0
- lwz r31, 12(r1)
- lwz r30, 16(r1)
- lwz r29, 20(r1)
- lwz r28, 24(r1)
- addi r1, r1, 32
- blr
- # Special case when Q * D overflows
-2: addi r6, r6, -1 # adjust Q down by 1
- b 4b # and redo computation and check of remainder
- .balign 16
-# Special case 64 bits divided by 32 bits
-1: cmplwi r3, 0 # NH == 0?
- beq 4f
- divwu r31, r3, r6 # Divide NH by DL, quotient QH in r31
- mullw r0, r31, r6
- subf r3, r0, r3 # NH is remainder of this division
- mr r5, r6
- bl __compcert_i64_udiv6432 # divide NH : NL by DL
- mr r5, r31 # high word of quotient
- mr r6, r3 # low word of quotient
- # r4 contains low word of remainder
- li r3, 0 # high word of remainder = 0
- lwz r0, 8(r1)
- mtlr r0
- lwz r31, 12(r1)
- addi r1, r1, 32
- blr
- .balign 16
-# Special case 32 bits divided by 32 bits
-4: mr r0, r6
- divwu r6, r4, r6 # low word of quotient
- li r5, 0 # high word of quotient is 0
- mullw r0, r6, r0
- subf r4, r0, r4 # low word of remainder
- li r3, 0 # high word of remainder is 0
- addi r1, r1, 32
- blr
-
- .type __compcert_i64_udivmod, @function
- .size __compcert_i64_udivmod, .-__compcert_i64_udivmod
-
-# Auxiliary division function: 64 bit integer divided by 32 bit integer
-# Not exported
-# Input: numerator N in (r3,r4), divisor D in r5
-# Output: quotient Q in r3, remainder R in r4
-# Destroys: all integer caller-save registers
-# Assumes: high word of N is less than D
-
- .balign 16
-__compcert_i64_udiv6432:
-# Algorithm 9.3 from Hacker's Delight, section 9.4
-# Initially: u1 in r3, u0 in r4, v in r5
-# s = __builtin_clz(v);
- cntlzw r6, r5 # s in r6
-# v = v << s;
- slw r5, r5, r6
-# vn1 = v >> 16; # vn1 in r7
- srwi r7, r5, 16
-# vn0 = v & 0xFFFF; # vn0 in r8
- rlwinm r8, r5, 0, 16, 31
-# un32 = (u1 << s) | (u0 >> 32 - s);
- subfic r0, r6, 32
- srw r0, r4, r0
- slw r3, r3, r6 # u1 dies, un32 in r3
- or r3, r3, r0
-# un10 = u0 << s;
- slw r4, r4, r6 # u0 dies, un10 in r4
-# un1 = un10 >> 16;
- srwi r9, r4, 16 # un1 in r9
-# un0 = un10 & 0xFFFF;
- rlwinm r4, r4, 0, 16, 31 # un10 dies, un0 in r4
-# q1 = un32/vn1;
- divwu r10, r3, r7 # q in r10
-# rhat = un32 - q1*vn1;
- mullw r0, r10, r7
- subf r11, r0, r3 # rhat in r11
-# again1:
-1:
-# if (q1 >= b || q1*vn0 > b*rhat + un1) {
- cmplwi r10, 0xFFFF
- bgt 2f
- mullw r0, r10, r8
- slwi r12, r11, 16
- add r12, r12, r9
- cmplw r0, r12
- ble 3f
-2:
-# q1 = q1 - 1;
- addi r10, r10, -1
-# rhat = rhat + vn1;
- add r11, r11, r7
-# if (rhat < b) goto again1;}
- cmplwi r11, 0xFFFF
- ble 1b
-3:
-# un21 = un32*b + un1 - q1*v;
- slwi r0, r3, 16 # un32 dies
- add r9, r0, r9 # un1 dies
- mullw r0, r10, r5
- subf r9, r0, r9 # un21 in r9
-# q0 = un21/vn1;
- divwu r3, r9, r7 # q0 in r3
-# rhat = un21 - q0*vn1;
- mullw r0, r3, r7
- subf r11, r0, r9 # rhat in r11
-# again2:
-4:
-# if (q0 >= b || q0*vn0 > b*rhat + un0) {
- cmplwi r3, 0xFFFF
- bgt 5f
- mullw r0, r3, r8
- slwi r12, r11, 16
- add r12, r12, r4
- cmplw r0, r12
- ble 6f
-5:
-# q0 = q0 - 1;
- addi r3, r3, -1
-# rhat = rhat + vn1;
- add r11, r11, r7
-# if (rhat < b) goto again2;}
- cmplwi r11, 0xFFFF
- ble 4b
-6:
-# remainder = (un21*b + un0 - q0*v) >> s;
- slwi r0, r9, 16
- add r4, r0, r4 # un0 dies, remainder in r4
- mullw r0, r3, r5
- subf r4, r0, r4
- srw r4, r4, r6
-# quotient = q1*b + q0;
- slwi r0, r10, 16
- add r3, r0, r3
- blr
-
- .type __compcert_i64_udiv6432, @function
- .size __compcert_i64_udiv6432,.-__compcert_i64_udiv6432