超低消費電力のARMマイコンLPC812を使ってFMシンセサイザーを作る方法と、その実装に用いられる乗算の最適化について解説します
"3.ϚΠίϯͰ࡞ΔγϯηαΠβʔNaomasa Matsubayashi
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MEMORY {!flash (rx) : ORIGIN = 0x00000000, LENGTH = 16K!ram (rwx) : ORIGIN = 0x10000000, LENGTH = 4K!}!ENTRY(Reset_Handler)!SECTIONS {!.text : {!KEEP(*(.isr_vector))!*(.text*)!KEEP(*(.init))!KEEP(*(.fini))!*crtbegin.o(.ctors)!*crtbegin?.o(.ctors)!*(EXCLUDE_FILE(*crtend?.o *crtend.o) .ctors)!*(SORT(.ctors.*))!*(.ctors)!*crtbegin.o(.dtors)!*crtbegin?.o(.dtors)!*(EXCLUDE_FILE(*crtend?.o *crtend.o) .dtors)!*(SORT(.dtors.*))!*(.dtors)!*(.rodata*)!KEEP(*(.eh_frame*))!} > flash!.ARM.extab : {!*(.ARM.extab* .gnu.linkonce.armextab.*)!} > flash!__exidx_start = .;!.ARM.exidx : {!*(.ARM.exidx* .gnu.linkonce.armexidx.*)!} > flash!__exidx_end = .;!__etext__ = .;!.data : AT(__etext__) {!__data_values__ = LOADADDR(.data);!__data_begin__ = .;!*(vtable)!*(.data*)!3".ͱϑϥογϡϝϞϦͷ։࢝ΞυϨεͱαΠζී௨σʔλγʔτʹॻ͍ͯ͋Δ!ࠓճ͏-1$ͷใҎԼͷ63-͔ΒḷΕΔIUUQXXXOYQMQDDPNMQD@NJDPODPSUFYNMQDldscript
MEMORY {!flash (rx) : ORIGIN = 0x00000000, LENGTH = 16K!ram (rwx) : ORIGIN = 0x10000000, LENGTH = 4K!}!ENTRY(Reset_Handler)!SECTIONS {!.text : {!KEEP(*(.isr_vector))!*(.text*)!KEEP(*(.init))!KEEP(*(.fini))!*crtbegin.o(.ctors)!*crtbegin?.o(.ctors)!*(EXCLUDE_FILE(*crtend?.o *crtend.o) .ctors)!*(SORT(.ctors.*))!*(.ctors)!*crtbegin.o(.dtors)!*crtbegin?.o(.dtors)!*(EXCLUDE_FILE(*crtend?.o *crtend.o) .dtors)!*(SORT(.dtors.*))!*(.dtors)!*(.rodata*)!KEEP(*(.eh_frame*))!} > flash!.ARM.extab : {!*(.ARM.extab* .gnu.linkonce.armextab.*)!} > flash!__exidx_start = .;!.ARM.exidx : {!*(.ARM.exidx* .gnu.linkonce.armexidx.*)!} > flash!__exidx_end = .;!__etext__ = .;!.data : AT(__etext__) {!__data_values__ = LOADADDR(.data);!__data_begin__ = .;!*(vtable)!*(.data*)!. = ALIGN(4);!ϑϥογϡϝϞϦʹ!ׂΓࠐΈϕΫλϚγϯޠॻ͖มΘΒͳ͍σʔλ!Λஔ͘ldscript
.ARM.exidx : {!*(.ARM.exidx* .gnu.linkonce.armexidx.*)!} > flash!__exidx_end = .;!__etext__ = .;!.data : AT(__etext__) {!__data_values__ = LOADADDR(.data);!__data_begin__ = .;!*(vtable)!*(.data*)!. = ALIGN(4);!PROVIDE_HIDDEN (__preinit_array_start = .);!KEEP(*(.preinit_array))!PROVIDE_HIDDEN (__preinit_array_end = .);!. = ALIGN(4);!PROVIDE_HIDDEN (__init_array_start = .);!KEEP(*(SORT(.init_array.*)))!KEEP(*(.init_array))!PROVIDE_HIDDEN (__init_array_end = .);!. = ALIGN(4);!PROVIDE_HIDDEN (__fini_array_start = .);!KEEP(*(SORT(.fini_array.*)))!KEEP(*(.fini_array))!PROVIDE_HIDDEN (__fini_array_end = .);!. = ALIGN(4);!__data_end__ = .;!} > ram!.bss : {!__bss_begin__ = .;!*(.bss*)!*(COMMON)!__bss_end__ = .;!} > ram!__stack_begin__ = .;!.stack_dummy : {!*(.stack)!} > ram!__stack_end__ = .;!}3".ʹ!WUBCMFॻ͖มΘΔσʔλελοΫ!Λஔ͘ldscript
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ελʔτΞοϓϧʔνϯReset_Handler:!ldr r1, =__etext__!ldr r2, =__data_begin__!ldr r3, =__data_end__!ldr r0, =init_data!blx r0!ldr r0, =init_bss!blx r0!ldr r0, =run_preinit!blx r0!ldr r0, =run_init!blx r0!ldr r0, =SystemInit!blx r0!ldr r0, =main!blx r0!.pool !.size Reset_Handler, . - Reset_Handler
ελʔτΞοϓϧʔνϯReset_Handler:!ldr r1, =__etext__!ldr r2, =__data_begin__!ldr r3, =__data_end__!ldr r0, =init_data!blx r0!ldr r0, =init_bss!blx r0!ldr r0, =run_preinit!blx r0!ldr r0, =run_init!blx r0!ldr r0, =SystemInit!blx r0!ldr r0, =main!blx r0!.pool !.size Reset_Handler, . - Reset_HandlerΞηϯϒϦͰ֨ಆͨ͘͠ͳ͍ͷͰ$Ͱ࣮ͨ͠ॳظԽίʔυʹඈͿ
ελʔτΞοϓϧʔνϯReset_Handler:!ldr r1, =__etext__!ldr r2, =__data_begin__!ldr r3, =__data_end__!ldr r0, =init_data!blx r0!ldr r0, =init_bss!blx r0!ldr r0, =run_preinit!blx r0!ldr r0, =run_init!blx r0!ldr r0, =SystemInit!blx r0!ldr r0, =main!blx r0!.pool !.size Reset_Handler, . - Reset_HandlerσόΠεͷॳظԽCMSISʹ͓·͔ͤ
void run_preinit(void) {!int *cur = &__preinit_array_start;!for( ; cur < &__preinit_array_end; cur++ ) {!void (*f)(void) = (void *)*cur;!(*f)();!}!}!void run_init(void) {!int *cur = &__init_array_start;!for( ; cur < &__init_array_end; cur++ ) {!void (*f)(void) = (void *)*cur;!(*f)();!}!}!void init_data(void) {!unsigned char *src = &__data_values__;!unsigned char *dest = &__data_begin__;!unsigned int len = &__data_end__ - &__data_begin__;!while( len-- ) *dest++ = *src++;!}!void init_bss(void) {!unsigned char *dest = &__bss_begin__;!unsigned int len = &__bss_end__ - &__bss_begin__;!while( len-- ) *dest++ = 0;!}
void run_preinit(void) {!int *cur = &__preinit_array_start;!for( ; cur < &__preinit_array_end; cur++ ) {!void (*f)(void) = (void *)*cur;!(*f)();!}!}!void run_init(void) {!int *cur = &__init_array_start;!for( ; cur < &__init_array_end; cur++ ) {!void (*f)(void) = (void *)*cur;!(*f)();!}!}!void init_data(void) {!unsigned char *src = &__data_values__;!unsigned char *dest = &__data_begin__;!unsigned int len = &__data_end__ - &__data_begin__;!while( len-- ) *dest++ = *src++;!}!void init_bss(void) {!unsigned char *dest = &__bss_begin__;!unsigned int len = &__bss_end__ - &__bss_begin__;!while( len-- ) *dest++ = 0;!}RAMʹஔ͍͓ͯ͘σʔλΛϑϥογϡϝϞϦ͔Βίϐʔ
void run_preinit(void) {!int *cur = &__preinit_array_start;!for( ; cur < &__preinit_array_end; cur++ ) {!void (*f)(void) = (void *)*cur;!(*f)();!}!}!void run_init(void) {!int *cur = &__init_array_start;!for( ; cur < &__init_array_end; cur++ ) {!void (*f)(void) = (void *)*cur;!(*f)();!}!}!void init_data(void) {!unsigned char *src = &__data_values__;!unsigned char *dest = &__data_begin__;!unsigned int len = &__data_end__ - &__data_begin__;!while( len-- ) *dest++ = *src++;!}!void init_bss(void) {!unsigned char *dest = &__bss_begin__;!unsigned int len = &__bss_end__ - &__bss_begin__;!while( len-- ) *dest++ = 0;!}άϩʔόϧΦϒδΣΫτͷίϯετϥΫλͱ͔Λ࣮ߦ
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#include "LPC8xx.h"!extern "C"!__attribute__((interrupt("IRQ")))!void SysTick_Handler(void) {!LPC_GPIO_PORT->NOT0 = ( 1 << 16 );!}!int main() {!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 6);!LPC_GPIO_PORT->DIR0 |= ( 1 << 16 );!SysTick_Config( 6000000 );!while( 1 );!}
#include "LPC8xx.h"!extern "C"!__attribute__((interrupt("IRQ")))!void SysTick_Handler(void) {!LPC_GPIO_PORT->NOT0 = ( 1 << 16 );!}!int main() {!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 6);!LPC_GPIO_PORT->DIR0 |= ( 1 << 16 );!SysTick_Config( 6000000 );!while( 1 );!}SysTickλΠϚʔͷׂΓࠐΈ͕ൃੜͨ͠Β൪ͷGPIOͷΛస@@BUUSJCVUF@@ JOUFSSVQU l*32zͱ͜ΕΛࢦఆ͓ͯ͘͠ͱHDDׂ͕ΓࠐΈΤϯτϦϧʔνϯΛ͚ͯ͘ΕΔ
#include "LPC8xx.h"!extern "C"!__attribute__((interrupt("IRQ")))!void SysTick_Handler(void) {!LPC_GPIO_PORT->NOT0 = ( 1 << 16 );!}!int main() {!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 6);!LPC_GPIO_PORT->DIR0 |= ( 1 << 16 );!SysTick_Config( 6000000 );!while( 1 );!}GPIOͷΫϩοΫΛ༗ޮʹͯ͠൪Λग़ྗϞʔυʹΓସ͑SysTick͕6,000,000Χϯτ͢ΔʹSysTickׂΓࠐΈΛൃੜͤ͞ΔΑ͏ʹ͢Δ
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void init_dac() {!NVIC_DisableIRQ( (IRQn_Type)( SPI0_IRQn ) );!NVIC_SetPriority(SPI0_IRQn, 0); !do {!NVIC_ClearPendingIRQ(SPI0_IRQn); !} while(NVIC_GetPendingIRQ(SPI0_IRQn) != 0);!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 11);!LPC_SPI0->DLY = 4;!LPC_SPI0->DIV = 2;!LPC_SPI0->TXCTRL = (16-1)<<24 | 1<<22 | ( 1 << 20 );!LPC_SPI0->CFG = (1<<5)|(1<<4)|(1<<2);!switch_matrix::bind_SPI0_SSEL_IO( 8 ); !switch_matrix::bind_SPI0_SCK_IO( 9 );!switch_matrix::bind_SPI0_MOSI_IO( 1 );!LPC_SPI0->INTENSET = 0x0;!NVIC_EnableIRQ( (IRQn_Type)( SPI0_IRQn ) );!LPC_SPI0->TXDAT = 2048 | ( 1 << 13 )|( 1 << 12 );!}!void set_dac( uint16_t value ) {!value &= 4095;!LPC_SPI0->TXDAT = value | ( 1 << 13 )|( 1 << 12 );!}
void init_dac() {!NVIC_DisableIRQ( (IRQn_Type)( SPI0_IRQn ) );!NVIC_SetPriority(SPI0_IRQn, 0); !do {!NVIC_ClearPendingIRQ(SPI0_IRQn); !} while(NVIC_GetPendingIRQ(SPI0_IRQn) != 0);!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 11);!LPC_SPI0->DLY = 4;!LPC_SPI0->DIV = 2;!LPC_SPI0->TXCTRL = (16-1)<<24 | 1<<22 | ( 1 << 20 );!LPC_SPI0->CFG = (1<<5)|(1<<4)|(1<<2);!switch_matrix::bind_SPI0_SSEL_IO( 8 ); !switch_matrix::bind_SPI0_SCK_IO( 9 );!switch_matrix::bind_SPI0_MOSI_IO( 1 );!LPC_SPI0->INTENSET = 0x0;!NVIC_EnableIRQ( (IRQn_Type)( SPI0_IRQn ) );!LPC_SPI0->TXDAT = 2048 | ( 1 << 13 )|( 1 << 12 );!}!void set_dac( uint16_t value ) {!value &= 4095;!LPC_SPI0->TXDAT = value | ( 1 << 13 )|( 1 << 12 );!}LPC812ͷSPIҰʹ16bit·ͰૹΕΔMCP4821 ࠓճͬͨDAC16bitૹΔຖʹग़ྗ͕ߋ৽͞ΕΔૹ৴ྃ࣌ͷׂΓࠐΈ͕ཁΒͳ͍ૹ৴όοϑΝཁΒͳ͍ͬͨͶ
void init_system_clock() {!LPC_SYSCON->SYSAHBCLKDIV = 2;!LPC_SYSCON->SYSPLLCTRL = 0x24;!}!int main() {!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 6);!LPC_SYSCON->SYSAHBCLKCTRL |= (1 << 18);!LPC_GPIO_PORT->DIR0 |= ( 1 << 8 );!LPC_GPIO_PORT->DIR0 |= ( 1 << 9 );!LPC_GPIO_PORT->DIR0 |= ( 1 << 1 );!init_system_clock();!init_dac();!SysTick_Config( 1875*2 );!while( 1 );!}$16ͷΫϩοΫΛ.)[ʹͯ͠SysTickΛ8kHzʹઃఆ
uint16_t step = 0;!!extern "C"!__attribute__((interrupt("IRQ")))!void SysTick_Handler(void) {!set_dac( step << 5 );!++step;!}SysTickׂΓࠐΈ͕ൃੜͨ͠ΒΧϯλͷΛDACʹૹΔ͜ΕͰϊίΪϦ͕ग़Δͣ
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CJUͱCJUΛֻ͚ͯ݁ՌΛCJUͰಘΔ໋ྩNVMM
inline constexpr self_type operator*(!const self_type &y!) const {!return self_type(!(!static_cast< double_type >( base ) *!static_cast< double_type >( y.base )!) >> Shift::value, raw()!);!}NVMM͕ΘΕΔ͜ͱΛظͯ͠ࢉΛ͜Μͳ෩ʹ࣮͍ͯͨ͠
…!00001374 <__aeabi_lmul>:!1374: 469c mov ip, r3!1376: 0403 lsls r3, r0, #16!1378: b5f0 push {r4, r5, r6, r7, lr}!137a: 0c1b lsrs r3, r3, #16!137c: 0417 lsls r7, r2, #16!137e: 0c3f lsrs r7, r7, #16!1380: 0c15 lsrs r5, r2, #16!1382: 1c1e adds r6, r3, #0!1384: 1c04 adds r4, r0, #0!1386: 0c00 lsrs r0, r0, #16!1388: 437e muls r6, r7!138a: 436b muls r3, r5!138c: 4347 muls r7, r0!138e: 4345 muls r5, r0!1390: 18fb adds r3, r7, r3!1392: 0c30 lsrs r0, r6, #16!1394: 1818 adds r0, r3, r0!1396: 4287 cmp r7, r0!1398: d902 bls.n 13a0 <__aeabi_lmul+0x2c>!139a: 2380 movs r3, #128 ; 0x80!ݱ࣮
1392: 0c30 lsrs r0, r6, #16!1394: 1818 adds r0, r3, r0!1396: 4287 cmp r7, r0!1398: d902 bls.n 13a0 <__aeabi_lmul+0x2c>!139a: 2380 movs r3, #128 ; 0x80!139c: 025b lsls r3, r3, #9!139e: 18ed adds r5, r5, r3!13a0: 0c03 lsrs r3, r0, #16!13a2: 18ed adds r5, r5, r3!13a4: 4663 mov r3, ip!13a6: 435c muls r4, r3!13a8: 434a muls r2, r1!13aa: 0436 lsls r6, r6, #16!13ac: 0c36 lsrs r6, r6, #16!13ae: 18a1 adds r1, r4, r2!13b0: 0400 lsls r0, r0, #16!13b2: 1980 adds r0, r0, r6!13b4: 1949 adds r1, r1, r5!13b6: bdf0 pop {r4, r5, r6, r7, pc}!…ݱ࣮mullΘΕ͍ͯͳ͍
ARM໋ྩʹରԠ͍ͯ͠ͳ͍5IVNC '16ͷΈ5IVNC '16ͷΈ5IVNCͷΈ5IVNCͷҰ෦͚ͩ5IVNCͷҰ෦͚ͩ5IVNCͷҰ෦͚ͩCortex-M7Cortex-M4Cortex-M3Cortex-M1Cortex-M0+CortexM05IVNCͱ"3.ϓϩηοαͷ͏ͭͷ໋ྩηοτɻ໋ྩ͕ՄมͰ"3.໋ྩηοτΑΓϚγϯޠ͕খ͘͞ͳΔɻҰ෦ͱ
NPWNPWXNPWUBEEBEDBESTVCTCDSTCNVMNMBNMTTNVMMVNVMMTNMBMVNMBMTEJWVEJWTTBUVTBUDNQDNOBOEFPSPSSPSOCJDNWOUTUUFRMTMMTSBTSSPSSSYDM[MESMESIMESCMESTIMESTCMESUMESIUMESCUMESTIUMESTCUMESEMENTUSTUSITUSCTUSTITUSTCTUSUTUSIUTUSCUTUSTIUTUSTCUTUSETUNQVTIQPQMESFYMESFYIMESFYCTUSFYTUSFYITUSFYCDMSFYCCMCYCMYDC[DC[OUCCUCITWDJUDQTJEDQTJFNSTNTSCLQUTYUITYUCVYUIVYUCVCGYTCGYCGDCGJSFWSFWSFWTISCJUTFWXFGXGJOPQJTCENCETCM7/M4/M3ҠಈՃࢉݮࢉࢉআࢉԋࢉൺֱཧԋࢉγϑτϩʔυετΞελοΫૢ࡞ηϚϑΥذঢ়ଶมߋܕͷ֦ுϏοτϑΟʔϧυϏοτྻసώϯτόϦΞARMv7m
NPWNPWXNPWUBEEBEDBESTVCTCDSTCNVMNMBNMTTNVMMVNVMMTNMBMVNMBMTEJWVEJWTTBUVTBUDNQDNOBOEFPSPSSPSOCJDNWOUTUUFRMTMMTSBTSSPSSSYDM[MESMESIMESCMESTIMESTCMESUMESIUMESCUMESTIUMESTCUMESEMENTUSTUSITUSCTUSTITUSTCTUSUTUSIUTUSCUTUSTIUTUSTCUTUSETUNQVTIQPQMESFYMESFYIMESFYCTUSFYTUSFYITUSFYCDMSFYCCMCYCMYDC[DC[OUCCUCITWDJUDQTJEDQTJFNSTNTSCLQUTYUITYUCVYUIVYUCVCGYTCGYCGDCGJSFWSFWSFWTISCJUTFWXFGXGJZFJMEOPQJTCENCETCҠಈՃࢉݮࢉࢉআࢉԋࢉൺֱཧԋࢉγϑτϩʔυετΞελοΫૢ࡞ηϚϑΥذঢ়ଶมߋܕͷ֦ுϏοτϑΟʔϧυϏοτྻసώϯτόϦΞM1/M0+/M0ARMv6m
M1/M0+/M0NPWNPWXNPWUBEEBEDBESTVCTCDSTCNVMNMBNMTTNVMMVNVMMTNMBMVNMBMTEJWVEJWTTBUVTBUDNQDNOBOEFPSPSSPSOCJDNWOUTUUFRMTMMTSBTSSPSSSYDM[MESMESIMESCMESTIMESTCMESUMESIUMESCUMESTIUMESTCUMESEMENTUSTUSITUSCTUSTITUSTCTUSUTUSIUTUSCUTUSTIUTUSTCUTUSETUNQVTIQPQMESFYMESFYIMESFYCTUSFYTUSFYITUSFYCDMSFYCCMCYCMYDC[DC[OUCCUCITWDJUDQTJEDQTJFNSTNTSCLQUTYUITYUCVYUIVYUCVCGYTCGYCGDCGJSFWSFWSFWTISCJUTFWXFGXGJZFJMEOPQJTCENCETCҠಈՃࢉݮࢉࢉআࢉԋࢉൺֱཧԋࢉγϑτϩʔυετΞελοΫૢ࡞ηϚϑΥذঢ়ଶมߋܕͷ֦ுϏοτϑΟʔϧυϏοτྻసώϯτόϦΞARMv6mNVMM٘ਜ਼ʹͳͬͨͷͩNVMNMBNMTTNVMMVNVMMTNMBMVNMBM
NVMMແ͠ͰͲ͏ͬͯ݁Ռ͕CJUͷࢉΛ͢Δ͔a ba*d b*d* c da*c b*c((a*c)<<32)+((a*d+b*c)<<16)+b*dBCDEͦΕͧΕCJUචࢉͷཁྖͰCJUͮͭܭࢉ͍ͯ͘͠
a ba*d b*d* c da*c b*c((a*c)<<32)+((a*d+b*c)<<16)+b*dαϯϓϧຖʹ͜ΜͳܭࢉΛԿ͍ͯͨ͠Βؒʹ߹Θͳ͍
CJUͷࢉΛճආͤΑ
݁Ռ͕໌Β͔ͳ߹CJU͔ΒCJU໌Β͔ͳͷͰCJU͔ΒCJU·Ͱ͕ཉ͍͜͠ͷܭࢉNVM໋ྩͰͰ͖Δ0000.FFFF!0000.FFFF00000000.FFFE0001*
݁Ռ͕໌Β͔ͳ߹࣮'.ԻݯͷܭࢉதʹݱΕΔࢉͷଟ͘ʹ͜Ε͕ΓཱͭADSRFMมௐԻྔͷ࣌ؒมԽ࠷େ྆ลڞʹͷ߹ͷΈҙ͢ΕNVMͰ0,
࣮'.ԻݯͷܭࢉதʹݱΕΔࢉͷຆͲʹ͜Ε͕ΓཱͭϛΩαʔJMJMJMJMJ J J JM M M Mೖྗ'.ΦϖϨʔλͷग़ྗͳͷͰ࠷େॏΈશ෦͋Θͤͯ࠷େ྆ลڞʹͷ߹ͷΈҙ͢ΕNVMͰ0,݁Ռ͕໌Β͔ͳ߹
ݻఆখͱͷࢉFFFF.FFFF!FFFFFFFEFFFF.0001*݁ՌΛͰಘΔʹCJU͔ΒCJU·Ͱ͕ཉ͍͜͠ͷܭࢉNVM໋ྩͰͰ͖Δ
ʜ ʜϒϩοΫͷதͰԿ൪ͷαϯϓϧ͔Ͱද͞ΕΔαϯϓϧͷΠϯσοΫεͱ࣌ࠁͷؔઢܗUGTTT UGTTT࣌ࠁߦྻ
࣌ࠁߦྻαϯϓϧͷΠϯσοΫεͱ࣌ࠁͷؔઢܗYͷߦྻͰදݱग़དྷΔUαϯϓϧͷ࣌ࠁJαϯϓϧͷΠϯσοΫεGT1$.ͷपTT͜ͷϒϩοΫͷ࠶ੜ͕࢝·Δ࣌ࠁ
τʔϯ࣮࣌ؒࡍͷ࣌ࠁʹରͯ͠ԻͷपഒͰਐߦ͢ΔΫϩοΫτʔϯ࣌ؒͷখ෦͚ͩΛऔΓग़͢ͱҙਤͨ͠पͱҐ૬ͷϊίΪϦʹͳΔ
τʔϯߦྻ࣌ࠁͱτʔϯΫϩοΫͷؔઢܗͳͷͰYͷߦྻͰදݱͰ͖Δ͜ͷࢉখಉ͔࢜ͭ݁Ռͷઈର͕Ҏ্ʹͳΔUαϯϓϧͷ࣌ࠁɺUUαϯϓϧͷτʔϯ࣌ࠁGUϊʔτͷपɺTUϊʔτͷҐ૬
͜ͷ෦͕ࣄલʹٻ·͍ͬͯΕΠϯσοΫεͳͷͰτʔϯΫϩοΫߴͳࢉͰٻ·Δτʔϯߦྻ࣌ࠁͱτʔϯΫϩοΫͷؔઢܗͳͷͰYͷߦྻͰදݱͰ͖Δ
ϒϩοΫͷ։࢝࣌ࠁ͕ϒϩοΫຖʹมΘΔͷͰϒϩοΫຖʹ࣌ࠁߦྻͱτʔϯߦྻͷੵΛٻΊΔߦྻͷੵͷܭࢉʹ͍ࢉ͕ೖΔ͕ϒϩοΫʹ͖ͭճͷ͍ࢉͰαϯϓϧ୯Ґͷ͍ࢉΛճආग़དྷΔ
݁Ռ
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·ͱΊখ͞ͳARMʹେ͖ͳັྗ͕ൿΊΒΕ͍ͯΔ
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