Nyaaori/rockbox
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity
rockbox/firmware/target/arm/support-arm.S
Andrew Mahone 950b2dfa2c Clarify comments in ARMv6 divider regarding special-case handling of large (high bit set) numerators. 
git-svn-id: svn://svn.rockbox.org/rockbox/trunk@24783 a1c6a512-1295-4272-9138-f99709370657
2010-02-20 06:29:23 +00:00

705 lines
20 KiB
ArmAsm
Raw Blame History

/***************************************************************************
* __________ __ ___.
* Open \______ \ ____ ____ | | _\_ |__ _______ ___
* Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ /
* Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < <
* Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \
* \/ \/ \/ \/ \/
* $Id$
*
* Copyright (C) 2008 by Jens Arnold
* Copyright (C) 2009 by Andrew Mahone
*
* Optimised replacements for libgcc functions
*
* Based on: libgcc routines for ARM cpu, additional algorithms from ARM System
* Developer's Guide
* Division routines, written by Richard Earnshaw, (rearnsha@armltd.co.uk)
* Copyright 1995, 1996, 1998, 1999, 2000, 2003, 2004, 2005
* Free Software Foundation, Inc.
*
* This program 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 2
* of the License, or (at your option) any later version.
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
* KIND, either express or implied.
*
****************************************************************************/
#include <config.h>
.macro ARM_SDIV32_PRE numerator, divisor, sign
/* sign[31] = divisor sign */
ands \sign, \divisor, #1<<31
rsbeq \divisor, \divisor, #0
/* sign[31] = result sign, sign[0:30], C = numerator sign */
eors \sign, \sign, \numerator, asr #32
rsbcs \numerator, \numerator, #0
.endm
.macro ARM_SDIV32_POST quotient, remainder, sign
movs \sign, \sign, lsl #1
.ifnc "", "\quotient"
rsbcs \quotient, \quotient, #0
.endif
.ifnc "", "\remainder"
rsbmi \remainder, \remainder, #0
.endif
.endm
#if ARM_ARCH < 5
.macro ARMV4_UDIV32_BODY numerator, divisor, quotient, remainder, tmp, bits, div0label, return
.ifnc "", "\div0label"
rsbs \divisor, \divisor, #0
beq \div0label
.else
rsb \divisor, \divisor, #0
.endif
/* This SWAR divider requires a numerator less than 1<<31, because it must
be able to shift the remainder left at each step without shifting out
topmost bit. Since a shift might be needed for the aligned remainder to
exceed the divisor, the topmost bit must be unset at the start to avoid
this overflow case. The original numerator is saved so that the result
can be corrected after the reduced division completes. */
cmn \numerator, \divisor
.ifc "", "\quotient"
.ifc "\numerator", "\remainder"
.if \return
bxcc lr
.else
b 99f
.endif
.else
bcc 20f
.endif
.else
bcc 20f
.endif
movs \tmp, \numerator
movmi \numerator, \numerator, lsr #1
mov \bits, #30
.set shift, 16
.rept 5
cmn \divisor, \numerator, lsr #shift
subcs \bits, \bits, #shift
movcs \divisor, \divisor, lsl #shift
.set shift, shift >> 1
.endr
adds \numerator, \numerator, \divisor
subcc \numerator, \numerator, \divisor
add pc, pc, \bits, lsl #3
nop
.rept 30
adcs \numerator, \divisor, \numerator, lsl #1
subcc \numerator, \numerator, \divisor
.endr
adc \numerator, \numerator, \numerator
movs \tmp, \tmp, asr #1
rsb \bits, \bits, #31
bmi 10f
.ifc "", "\quotient"
mov \remainder, \numerator, lsr \bits
.else
.ifc "", "\remainder"
mov \divisor, \numerator, lsr \bits
eor \quotient, \numerator, \divisor, lsl \bits
.else
mov \remainder, \numerator, lsr \bits
eor \quotient, \numerator, \remainder, lsl \bits
.endif
.endif
.ifne \return
bx lr
.else
b 99f
.endif
10:
mov \tmp, \numerator, lsr \bits
eor \numerator, \numerator, \tmp, lsl \bits
sub \bits, \bits, #1
adc \tmp, \tmp, \tmp
adds \tmp, \tmp, \divisor, asr \bits
.ifnc "", "\quotient"
adc \quotient, \numerator, \numerator
.endif
.ifnc "", "\remainder"
subcc \remainder, \tmp, \divisor, asr \bits
movcs \remainder, \tmp
.endif
.ifne \return
bx lr
.else
b 99f
.endif
20:
.ifnc "", "\remainder"
.ifnc "\remainder", "\numerator"
mov \remainder, \numerator
.endif
.endif
.ifnc "", "\quotient"
mov \quotient, #0
.endif
.ifne \return
bx lr
.else
99:
.endif
.endm
.macro ARMV4_SDIV32_BODY numerator, divisor, quotient, remainder, bits, sign, div0label, return
/* When this is wrapped for signed division, the wrapper code will handle
inverting the divisor, and also the zero divisor test. */
ARM_SDIV32_PRE \numerator, \divisor, \sign
.ifnc "", "\div0label"
tst \divisor, \divisor
beq \div0label
.endif
/* This SWAR divider requires a numerator less than 1<<31, because it must
be able to shift the remainder left at each step without shifting out
topmost bit. With signed inputs, whose absolute value may not exceed
1<<31,this may be accomplished simply by subtracting the divisor before
beginning division, and adding 1 to the quotient. */
adds \numerator, \numerator, \divisor
bcc 20f
mov \bits, #30
.set shift, 16
.rept 5
cmn \divisor, \numerator, lsr #shift
subcs \bits, \bits, #shift
movcs \divisor, \divisor, lsl #shift
.set shift, shift >> 1
.endr
adds \numerator, \numerator, \divisor
subcc \numerator, \numerator, \divisor
add pc, pc, \bits, lsl #3
nop
.rept 30
adcs \numerator, \divisor, \numerator, lsl #1
subcc \numerator, \numerator, \divisor
.endr
rsb \bits, \bits, #31
adc \numerator, \numerator, \numerator
.ifc "", "\quotient"
mov \remainder, \numerator, lsr \bits
.else
.ifc "", "\remainder"
mov \divisor, \numerator, lsr \bits
add \numerator, \numerator, #1
sub \quotient, \numerator, \divisor, lsl \bits
.else
mov \remainder, \numerator, lsr \bits
add \numerator, \numerator, #1
sub \quotient, \numerator, \remainder, lsl \bits
.endif
.endif
.ifne \return
ARM_SDIV32_POST \quotient, \remainder, \sign
bx lr
.else
b 99f
.endif
20:
.ifnc "", "\remainder"
sub \remainder, \numerator, \divisor
.endif
.ifnc "", "\quotient"
mov \quotient, #0
.endif
.ifne \return
ARM_SDIV32_POST "", \remainder, \sign
bx lr
.else
99:
ARM_SDIV32_POST \quotient, \remainder, \sign
.endif
.endm
#else
.macro ARMV5_UDIV32_BODY numerator, divisor, quotient, remainder, bits, inv, neg, div0label, return
cmp \numerator, \divisor
clz \bits, \divisor
bcc 30f
mov \inv, \divisor, lsl \bits
add \neg, pc, \inv, lsr #25
/* Test whether divisor is 2^N */
cmp \inv, #1<<31
/* Load approximate reciprocal */
ldrhib \inv, [\neg, #.L_udiv_est_table-.-64]
bls 20f
subs \bits, \bits, #7
rsb \neg, \divisor, #0
/* Scale approximate reciprocal, or else branch to large-divisor path */
movpl \divisor, \inv, lsl \bits
bmi 10f
/* Newton-Raphson iteration to improve reciprocal accuracy */
mul \inv, \divisor, \neg
smlawt \divisor, \divisor, \inv, \divisor
mul \inv, \divisor, \neg
/* Complete N-R math and produce approximate quotient. Use smmla/smmul on
ARMv6. */
#if ARM_ARCH >= 6
tst \numerator, \numerator
smmla \divisor, \divisor, \inv, \divisor
/* Branch to large-numerator handler, or else use smmul if sign bit is not
set. This wins on average with random numerators, and should be no
slower than using umull for small numerator, even if prediction fails.
*/
bmi 40f
smmul \inv, \numerator, \divisor
#else
/* ARMv5e lacks smmul, so always uses umull. */
mov \bits, #0
smlal \bits, \divisor, \inv, \divisor
umull \bits, \inv, \numerator, \divisor
#endif
/* Calculate remainder and correct result. */
add \numerator, \numerator, \neg
.ifnc "", "\remainder"
mla \remainder, \inv, \neg, \numerator
.ifnc "", "\quotient"
mov \quotient, \inv
cmn \remainder, \neg
subcs \remainder, \remainder, \neg
addpl \remainder, \remainder, \neg, lsl #1
addcc \quotient, \quotient, #1
addpl \quotient, \quotient, #2
.else
cmn \remainder, \neg
subcs \remainder, \remainder, \neg
addpl \remainder, \remainder, \neg, lsl #1
.endif
.else
mla \divisor, \inv, \neg, \numerator
mov \quotient, \inv
cmn \divisor, \neg
addcc \quotient, \quotient, #1
addpl \quotient, \quotient, #2
.endif
.if \return
bx lr
.else
b 99f
.endif
10:
/* Very large divisors can be handled without further improving the
reciprocal. First the reciprocal must be reduced to ensure that it
underestimates the correct value. */
rsb \bits, \bits, #0
sub \inv, \inv, #4
mov \divisor, \inv, lsr \bits
/* Calculate approximate quotient and remainder */
umull \bits, \inv, \numerator, \divisor
/* Correct quotient and remainder */
.ifnc "", "\remainder"
mla \remainder, \inv, \neg, \numerator
.ifnc "", "\quotient"
mov \quotient, \inv
cmn \neg, \remainder, lsr #1
addcs \remainder, \remainder, \neg, lsl #1
addcs \quotient, \quotient, #2
cmn \neg, \remainder
addcs \remainder, \remainder, \neg
addcs \quotient, \quotient, #1
.else
cmn \neg, \remainder, lsr #1
addcs \remainder, \remainder, \neg, lsl #1
cmn \neg, \remainder
addcs \remainder, \remainder, \neg
.endif
.else
mla \divisor, \inv, \neg, \numerator
mov \quotient, \inv
cmn \neg, \divisor, lsr #1
addcs \divisor, \divisor, \neg, lsl #1
addcs \quotient, \quotient, #2
cmn \neg, \divisor
addcs \quotient, \quotient, #1
.endif
.if \return
bx lr
.else
b 99f
.endif
20:
/* Handle division by powers of two by shifting right. Mod is handled
by using divisor-1 as a bitmask. */
.ifnc "", "\remainder"
.ifnc "", "\div0label"
bne \div0label
.endif
.ifnc "", "\quotient"
sub \divisor, \divisor, #1
rsb \bits, \bits, #31
and \remainder, \numerator, \divisor
mov \quotient, \numerator, lsr \bits
.else
sub \divisor, \divisor, #1
and \remainder, \numerator, \divisor
.endif
.else
rsb \bits, \bits, #31
.ifnc "", "\div0label"
bne \div0label
.endif
mov \quotient, \numerator, lsr \bits
.endif
.if \return
bx lr
.else
b 99f
.endif
30:
/* Handle numerator < divisor - quotient is zero, remainder is numerator,
which must be restored to its original value on ARMv6. */
.ifnc "", "\remainder"
mov \remainder, \numerator
.endif
.ifnc "", "\quotient"
mov \quotient, #0
.endif
.if \return
bx lr
.endif
#if ARM_ARCH >= 6
40:
/* Handle large (sign bit set) numerators. Works exactly as the ARMv5e code
above 10:. */
umull \bits, \inv, \numerator, \divisor
add \numerator, \numerator, \neg
.ifnc "", "\remainder"
mla \remainder, \inv, \neg, \numerator
.ifnc "", "\quotient"
mla \remainder, \inv, \neg, \numerator
mov \quotient, \inv
cmn \remainder, \neg
subcs \remainder, \remainder, \neg
addpl \remainder, \remainder, \neg, lsl #1
addcc \quotient, \quotient, #1
addpl \quotient, \quotient, #2
.else
cmn \remainder, \neg
subcs \remainder, \remainder, \neg
addpl \remainder, \remainder, \neg, lsl #1
.endif
.else
mla \divisor, \inv, \neg, \numerator
mov \quotient, \inv
cmn \divisor, \neg
addcc \quotient, \quotient, #1
addpl \quotient, \quotient, #2
.endif
.if \return
bx lr
.else
b 99f
.endif
#endif
99:
.endm
.macro ARMV5_SDIV32_BODY numerator, divisor, quotient, remainder, bits, inv, neg, sign, div0label, return
/* sign[31] = divisor sign */
ands \sign, \divisor, #1<<31
rsbne \divisor, \divisor, #0
/* sign[31] = result sign, sign[0:30], C = numerator sign */
eors \sign, \sign, \numerator, asr #32
clz \bits, \divisor
rsbcs \numerator, \numerator, #0
/* On ARMv6, subtract divisor before performing division, which ensures
numerator sign bit is clear and smmul may be used in place of umull. The
fixup for the results can be fit entirely into existing delay slots on
the main division paths. It costs 1c in the num<div path if the
the remainder is to be produced in the numerator's register, and 1c in
the power-of-2-divisor path only if producing both remainder and
quotient. */
#if ARM_ARCH >= 6
subs \numerator, \numerator, \divisor
#else
cmp \numerator, \divisor
#endif
movcs \inv, \divisor, lsl \bits
bcc 30f
/* Test whether divisor is 2^N */
cmp \inv, #1<<31
add \inv, pc, \inv, lsr #25
bls 20f
/* Load approximate reciprocal */
ldrb \inv, [\inv, #.L_udiv_est_table-.-64]
subs \bits, \bits, #7
rsb \neg, \divisor, #0
/* Scale approximate reciprocal, or else branch to large-divisor path */
movpl \divisor, \inv, lsl \bits
bmi 10f
/* Newton-Raphson iteration to improve reciprocal accuracy */
mul \inv, \divisor, \neg
smlawt \divisor, \divisor, \inv, \divisor
mul \inv, \divisor, \neg
/* Complete N-R math and produce approximate quotient. Use smmla/smmul on
ARMv6. */
#if ARM_ARCH >= 6
smmla \divisor, \divisor, \inv, \divisor
smmul \inv, \numerator, \divisor
#else
mov \bits, #0
smlal \bits, \divisor, \inv, \divisor
umull \bits, \inv, \numerator, \divisor
#endif
/* Calculate remainder and correct quotient. */
add \numerator, \numerator, \neg
.ifnc "", "\remainder"
mla \remainder, \inv, \neg, \numerator
.ifnc "", "\quotient"
#if ARM_ARCH >= 6
add \quotient, \inv, #1
#else
mov \quotient, \inv
#endif
cmn \remainder, \neg
subcs \remainder, \remainder, \neg
addpl \remainder, \remainder, \neg, lsl #1
addcc \quotient, \quotient, #1
addpl \quotient, \quotient, #2
.else
cmn \remainder, \neg
subcs \remainder, \remainder, \neg
addpl \remainder, \remainder, \neg, lsl #1
.endif
.else
mla \divisor, \inv, \neg, \numerator
#if ARM_ARCH >= 6
add \quotient, \inv, #1
#else
mov \quotient, \inv
#endif
cmn \divisor, \neg
addcc \quotient, \quotient, #1
addpl \quotient, \quotient, #2
.endif
ARM_SDIV32_POST \quotient, \remainder, \sign
.ifnc "", "\return"
\return
.else
b 99f
.endif
10:
/* Very large divisors can be handled without further improving the
reciprocal. First the reciprocal must be reduced to ensure that it
underestimates the correct value. */
rsb \bits, \bits, #0
sub \inv, \inv, #4
mov \divisor, \inv, lsr \bits
/* Calculate approximate quotient and remainder */
#if ARM_ARCH >= 6
smmul \inv, \numerator, \divisor
#else
umull \bits, \inv, \numerator, \divisor
#endif
/* Correct quotient and remainder */
.ifnc "", "\remainder"
mla \remainder, \inv, \neg, \numerator
.ifnc "", "\quotient"
#if ARM_ARCH >= 6
add \quotient, \inv, #1
#else
mov \quotient, \inv
#endif
cmn \neg, \remainder, lsr #1
addcs \remainder, \remainder, \neg, lsl #1
addcs \quotient, \quotient, #2
cmn \neg, \remainder
addcs \remainder, \remainder, \neg
addcs \quotient, \quotient, #1
.else
cmn \neg, \remainder, lsr #1
addcs \remainder, \remainder, \neg, lsl #1
cmn \neg, \remainder
addcs \remainder, \remainder, \neg
.endif
.else
mla \divisor, \inv, \neg, \numerator
#if ARM_ARCH >= 6
add \quotient, \inv, #1
#else
mov \quotient, \inv
#endif
cmn \neg, \divisor, lsr #1
addcs \divisor, \divisor, \neg, lsl #1
addcs \quotient, \quotient, #2
cmn \neg, \divisor
addcs \quotient, \quotient, #1
.endif
ARM_SDIV32_POST \quotient, \remainder, \sign
.ifnc "", "\return"
\return
.else
b 99f
.endif
20:
/* Handle division by powers of two by shifting right. Mod is handled
by using divisor-1 as a bitmask. */
.ifnc "", "\div0label"
bne \div0label
.endif
.ifnc "", "\remainder"
.ifnc "", "\quotient"
rsb \bits, \bits, #31
#if ARM_ARCH >= 6
add \numerator, \numerator, \divisor
#endif
sub \divisor, \divisor, #1
and \remainder, \numerator, \divisor
mov \quotient, \numerator, lsr \bits
.else
sub \divisor, \divisor, #1
and \remainder, \numerator, \divisor
.endif
.else
rsb \bits, \bits, #31
#if ARM_ARCH >= 6
add \numerator, \numerator, \divisor
#endif
mov \quotient, \numerator, lsr \bits
.endif
ARM_SDIV32_POST \quotient, \remainder, \sign
.ifnc "", "\return"
\return
.else
b 99f
.endif
30:
/* Handle numerator < divisor - quotient is zero, remainder is numerator,
which must be restored to its original value on ARMv6. */
.ifnc "", "\remainder"
#if ARM_ARCH >= 6
add \remainder, \numerator, \divisor
#else
.ifnc "\remainder", "\numerator"
mov \remainder, \numerator
.endif
#endif
.endif
.ifnc "", "\quotient"
mov \quotient, #0
.endif
.ifnc "", "\remainder"
ARM_SDIV32_POST "", \remainder, \sign
.endif
.ifnc "", "\return"
\return
.endif
99:
.endm
#endif
.section .text
__div0_wrap_s:
sub sp, sp, #4
mov r0, #0
b __div0
.size __div0_wrap_s, . - __div0_wrap_s
__div0_wrap:
str lr, [sp, #-4]!
mov r0, #0
b __div0
.size __div0_wrap, . - __div0_wrap
#ifndef __ARM_EABI__
.global __divsi3
.type __divsi3,%function
.global __udivsi3
.type __udivsi3,%function
.global __udivsi3
.type __udivsi3,%function
#else
/* The div+mod averagess a fraction of a cycle worse for signed values, and
slightly better for unsigned, so just alias div to divmod. */
.global __aeabi_uidivmod
.type __aeabi_uidivmod,%function
.global __aeabi_uidiv
.type __aeabi_uidiv,%function
.set __aeabi_uidiv,__aeabi_uidivmod
.global __aeabi_idivmod
.type __aeabi_idivmod,%function
.global __aeabi_idiv
.type __aeabi_idiv,%function
.set __aeabi_idiv,__aeabi_idivmod
#endif
#if ARM_ARCH < 5
.global __clzsi2
.type __clzsi2, %function
__clzsi2:
orr r0, r0, r0, lsr #8
orr r0, r0, r0, lsr #4
orr r0, r0, r0, lsr #2
orr r0, r0, r0, lsr #1
bic r0, r0, r0, lsr #16
rsb r0, r0, r0, lsl #14
rsb r0, r0, r0, lsl #11
rsb r0, r0, r0, lsl #9
ldrb r0, [pc, r0, lsr #26]
bx lr
.byte 32, 20, 19, 0, 0, 18, 0, 7, 10, 17, 0, 0, 14, 0, 6, 0
.byte 0, 9, 0, 16, 0, 0, 1, 26, 0, 13, 0, 0, 24, 5, 0, 0
.byte 0, 21, 0, 8, 11, 0, 15, 0, 0, 0, 0, 2, 27, 0, 25, 0
.byte 22, 0, 12, 0, 0, 3, 28, 0, 23, 0, 4, 29, 0, 0, 30, 31
.size __clzsi2, .-__clzsi2
#ifndef __ARM_EABI__
__udivsi3:
ARMV4_UDIV32_BODY r0, r1, r0, "", r2, r3, __div0_wrap, 1
.size __udivsi3, . - __udivsi3
__divsi3:
ARMV4_SDIV32_BODY r0, r1, r0, "", r2, r3, __div0_wrap, 1
.size __divsi3, . - __divsi3
#else
__aeabi_uidivmod:
ARMV4_UDIV32_BODY r0, r1, r0, r1, r2, r3, __div0_wrap, 1
.size __aeabi_uidivmod, . - __aeabi_uidivmo
__aeabi_idivmod:
ARMV4_SDIV32_BODY r0, r1, r0, r1, r2, r3, __div0_wrap, 1
.size __aeabi_idivmod, . - __aeabi_idivmod
#endif
#else
#ifndef __ARM_EABI__
__udivsi3:
ARMV5_UDIV32_BODY r0, r1, r0, "", r2, r3, ip, __div0_wrap, 1
.size __udivsi3, . - __udivsi3
__divsi3:
str lr, [sp, #-4]
ARMV5_SDIV32_BODY r0, r1, r0, "", r2, lr, ip, r3, __div0_wrap_s, "ldr pc, [sp, #-4]"
.size __divsi3, . - __divsi3
#else
__aeabi_uidivmod:
ARMV5_UDIV32_BODY r0, r1, r0, r1, r2, r3, ip, __div0_wrap, 1
.size __aeabi_uidivmod, . - __aeabi_uidivmo
__aeabi_idivmod:
str lr, [sp, #-4]
ARMV5_SDIV32_BODY r0, r1, r0, r1, r2, lr, ip, r3, __div0_wrap_s, "ldr pc, [sp, #-4]"
.size __aeabi_idivmod, . - __aeabi_idivmod
#endif
.L_udiv_est_table:
.byte 0xff, 0xfc, 0xf8, 0xf4, 0xf0, 0xed, 0xea, 0xe6
.byte 0xe3, 0xe0, 0xdd, 0xda, 0xd7, 0xd4, 0xd2, 0xcf
.byte 0xcc, 0xca, 0xc7, 0xc5, 0xc3, 0xc0, 0xbe, 0xbc
.byte 0xba, 0xb8, 0xb6, 0xb4, 0xb2, 0xb0, 0xae, 0xac
.byte 0xaa, 0xa8, 0xa7, 0xa5, 0xa3, 0xa2, 0xa0, 0x9f
.byte 0x9d, 0x9c, 0x9a, 0x99, 0x97, 0x96, 0x94, 0x93
.byte 0x92, 0x90, 0x8f, 0x8e, 0x8d, 0x8c, 0x8a, 0x89
.byte 0x88, 0x87, 0x86, 0x85, 0x84, 0x83, 0x82, 0x81
#endif
Reference in a new issue View git blame Copy permalink