绋嬪簭11-5 linux/kernel/math/add.c

  1 /*

  2  * linux/kernel/math/add.c

  3  *

  4  * (C) 1991 Linus Torvalds

  5  */

  6

  7 /*

  8  * temporary real addition routine.

  9  *

 10  * NOTE! These aren't exact: they are only 62 bits wide, and don't do

 11  * correct rounding. Fast hack. The reason is that we shift right the

 12  * values by two, in order not to have overflow (1 bit), and to be able

 13  * to move the sign into the mantissa (1 bit). Much simpler algorithms,

 14  * and 62 bits (61 really - no rounding) accuracy is usually enough. The

 15  * only time you should notice anything weird is when adding 64-bit

 16  * integers together. When using doubles (52 bits accuracy), the

 17  * 61-bit accuracy never shows at all.

 18  */

    /*

     * 涓存椂瀹炴暟鍔犳硶瀛愮▼搴忋��

     *

     * 娉ㄦ剰锛� 杩欎簺骞朵笉绮剧‘锛氬畠浠�鍙�鏈�62姣旂壒瀹藉害锛屽苟涓斾笉鑳借繘琛屾�ｇ‘鍦拌垗鍏ユ搷浣溿��

     * 杩欎簺浠呮槸鑽夊氨涔嬩綔銆傚師鍥犳槸涓轰簡涓嶄細婧㈠嚭锛�1姣旂壒锛夛紝鎴戜滑鎶婂�煎彸绉讳簡2浣嶏紝

     * 骞朵笖浣垮緱绗﹀彿浣嶏紙1姣旂壒锛夎兘澶熺Щ鍏ュ熬鏁颁腑銆傝繖鏄�闈炲父绠�鍗曠殑绠楁硶锛岃�屼笖62浣�

     * 锛堝疄闄呬笂鏄�61浣� - 娌℃湁鑸嶅叆锛夌殑绮惧害閫氬父涔熻冻澶熶簡銆傚彧鏈夊綋浣犳妸64浣嶇殑鏁存暟

     * 鐩稿姞鏃舵墠浼氬彂瑙変竴浜涘�囨��鐨勯棶棰樸�傚綋浣跨敤鍙岀簿搴︼紙52姣旂壒绮惧害锛夋暟鎹�鏃讹紝鏄�姘�

     * 杩滀笉鍙�鑳借秴杩�61姣旂壒绮惧害鐨勩��

     */

 19

 20 #include <linux/math_emu.h> // 鍗忓�勭悊鍣ㄥご鏂囦欢銆傚畾涔変复鏃跺疄鏁扮粨鏋勫拰387瀵勫瓨鍣ㄦ搷浣滃畯绛夈��

 21

    // 姹備竴涓�鏁扮殑璐熸暟锛堜簩杩涘埗琛ョ爜锛夎〃绀恒��

    // 鎶婁复鏃跺疄鏁板熬鏁帮紙鏈夋晥鏁帮級鍙栧弽鍚庡啀鍔�1銆�

    // 鍙傛暟a鏄�涓存椂瀹炴暟缁撴瀯銆傚叾涓�a銆�b瀛楁�电粍鍚堟槸瀹炴暟鐨勬湁鏁堟暟銆�

 22 #define NEGINT(a) \

 23 __asm__("notl %0 ; notl %1 ; addl $1,%0 ; adcl $0,%1" \

 24         :"=r" (a->a),"=r" (a->b) \

 25         :"" (a->a),"1" (a->b))

 26

    // 灏炬暟绗﹀彿鍖栥��

    // 鍗虫妸涓存椂瀹炴暟鍙樻崲鎴愭寚鏁板拰鏁存暟琛ㄧず褰㈠紡锛屼互渚夸簬浠跨湡杩愮畻銆傚洜姝ゆ垜浠�杩欓噷绉板叾涓轰豢鐪熸牸寮忋��

 27 static void signify(temp_real * a)

 28 {

    // 鎶�64浣嶄簩杩涘埗灏炬暟鍙崇Щ2浣嶏紙鍥犳�ゆ寚鏁伴渶瑕佸姞2锛夈�傚洜涓烘寚鏁板瓧娈�exponent鐨勬渶楂樻瘮鐗逛綅鏄�

    // 绗﹀彿浣嶏紝鎵�浠ヨ嫢鎸囨暟鍊煎皬浜庨浂锛岃�存槑璇ユ暟鏄�璐熸暟銆備簬鏄�鍒欐妸灏炬暟鐢ㄨˉ鐮佽〃绀猴紙鍙栬礋锛夈�傜劧鍚庢妸

    // 鎸囨暟鍙栨�ｅ�笺�傛�ゆ椂灏炬暟涓�涓嶄粎鍖呭惈绉昏繃2浣嶇殑鏈夋晥鏁帮紝鑰屼笖杩樺寘鍚�鏁板�肩殑绗﹀彿浣嶃��

    // 30琛屼笂锛�%0 - a->a锛�%1 - a->b銆傛眹缂栨寚浠も��shrdl $2, %1, %0鈥�鎵ц�屽弻绮惧害锛�64浣嶏級鍙崇Щ锛�

    // 鍗虫妸缁勫悎灏炬暟<b,a>鍙崇Щ2浣嶃�傜敱浜庤�ョЩ鍔ㄦ搷浣滀笉浼氭敼鍙�%1锛�a->b锛変腑鐨勫�硷紝鍥犳�よ繕闇�瑕佸崟鐙�

    // 瀵瑰叾鍙崇Щ2浣嶃��

 29         a->exponent += 2;

 30         __asm__("shrdl $2,%1,%0 ; shrl $2,%1"   // 浣跨敤鍙岀簿搴︽寚浠ゆ妸灏炬暟鍙崇Щ2浣嶃��

 31                 :"=r" (a->a),"=r" (a->b)

 32                 :"" (a->a),"1" (a->b));

 33         if (a->exponent < 0)                   // 鏄�璐熸暟锛屽垯灏炬暟鐢ㄨˉ鐮佽〃绀猴紙鍙栬礋鍊硷級銆�

 34                 NEGINT(a);

 35         a->exponent &= 0x7fff;                 // 鍘绘帀绗﹀彿浣嶏紙鑻ユ湁锛夈��

 36 }

 37

    // 灏炬暟闈炵�﹀彿鍖栥��

    // 灏嗕豢鐪熸牸寮忚浆鎹�涓轰复鏃跺疄鏁版牸寮忋�傚嵆鎶婃寚鏁板拰鏁存暟琛ㄧず鐨勫疄鏁拌浆鎹�涓轰复鏃跺疄鏁版牸寮忋��

 38 static void unsignify(temp_real * a)

 39 {

    // 瀵逛簬鍊间负0鐨勬暟涓嶇敤澶勭悊锛岀洿鎺ヨ繑鍥炪�傚惁鍒欙紝鎴戜滑鍏堝�嶄綅涓存椂瀹炴暟鏍煎紡鐨勭�﹀彿浣嶃�傜劧鍚庡垽鏂�

    // 灏炬暟鐨勯珮浣�long瀛楁��a->b鏄�鍚﹀甫鏈夌�﹀彿浣嶃�傝嫢鏈夛紝鍒欏湪 exponent 瀛楁�垫坊鍔犵�﹀彿浣嶏紝鍚屾椂

    // 鎶婂熬鏁扮敤鏃犵�﹀彿鏁板舰寮忚〃绀猴紙鍙栬ˉ锛夈�傛渶鍚庡�瑰熬鏁拌繘琛岃�勬牸鍖栧�勭悊锛屽悓鏃舵寚鏁板�间綔鐩稿簲閫掑噺銆�

    // 鍗虫墽琛屽乏绉绘搷浣滐紝浣垮緱灏炬暟鏈�楂樻湁鏁堜綅涓嶄负0锛堟渶鍚�a->b鍊艰〃鐜颁负璐熷�硷級銆�

 40         if (!(a->a || a->b)) {                 // 鑻ュ�间负0灏辫繑鍥炪��

 41                 a->exponent = 0;

 42                 return;

 43         }

 44         a->exponent &= 0x7fff;                 // 鍘绘帀绗﹀彿浣嶏紙鑻ユ湁锛夈��

 45         if (a->b < 0) {                        // 鏄�璐熸暟锛屽垯灏炬暟鍙栨�ｅ�笺��

 46                 NEGINT(a);

 47                 a->exponent |= 0x8000;         // 涓存椂瀹炴暟娣诲姞缃�绗﹀彿浣嶃��

 48         }

 49         while (a->b >= 0) {

 50                 a->exponent--;                 // 瀵瑰熬鏁拌繘琛岃�勬牸鍖栧�勭悊銆�

 51                 __asm__("addl %0,%0 ; adcl %1,%1"

 52                         :"=r" (a->a),"=r" (a->b)

 53                         :"" (a->a),"1" (a->b));

 54         }

 55 }

 56

    // 浠跨湡娴�鐐瑰姞娉曟寚浠よ繍绠椼��

    // 涓存椂瀹炴暟鍙傛暟 src1 + src2 猫 result銆�

 57 void fadd(const temp_real * src1, const temp_real * src2, temp_real * result)

 58 {

 59         temp_real a,b;

 60         int x1,x2,shift;

 61

    // 棣栧厛鍙栦袱涓�鏁扮殑鎸囨暟鍊�x1銆�x2锛堝幓鎺夌�﹀彿浣嶏級銆傜劧鍚庤�╁彉閲�a绛変簬鍏朵腑鏈�澶у�硷紝shift涓烘寚鏁�

    // 宸�鍊硷紙鍗崇浉宸�2鐨勫�嶆暟鍊硷級銆�

 62         x1 = src1->exponent & 0x7fff;

 63         x2 = src2->exponent & 0x7fff;

 64         if (x1 > x2) {

 65                 a = *src1;

 66                 b = *src2;

 67                 shift = x1-x2;

 68         } else {

 69                 a = *src2;

 70                 b = *src1;

 71                 shift = x2-x1;

 72         }

    // 鑻ヤ袱鑰呯浉宸�澶�澶э紝澶т簬绛変簬2鐨�64娆℃柟锛屽垯鎴戜滑鍙�浠ュ拷鐣ュ皬鐨勯偅涓�鏁帮紝鍗�b鍊笺�備簬鏄�鐩存帴杩�

    // 鍥�a鍊煎嵆鍙�銆傚惁鍒欙紝鑻ョ浉宸�澶т簬绛変��2鐨�32娆℃柟锛岄偅涔堟垜浠�鍙�浠ュ拷鐣ュ皬鍊�b涓�鐨勪��32浣嶅�笺��

    // 浜庢槸鎴戜滑鎶� b鐨勯珮long瀛楁�靛�� b.b鍙崇Щ32浣嶏紝鍗虫斁鍒�b.a涓�銆傜劧鍚庢妸b鐨勬寚鏁板�肩浉搴斿湴澧�

    // 鍔�32娆℃柟銆傚嵆鎸囨暟宸�鍊煎噺鍘�32銆傝繖鏍疯皟鏁翠箣鍚庯紝鐩稿姞鐨勪袱涓�鏁扮殑灏炬暟鍩烘湰涓婅惤鍦ㄧ浉鍚屽尯鍩熶腑銆�

 73         if (shift >= 64) {

 74                 *result = a;

 75                 return;

 76         }

 77         if (shift >= 32) {

 78                 b.a = b.b;

 79                 b.b = 0;

 80                 shift -= 32;

 81         }

    // 鎺ョ潃鍐嶈繘琛岀粏鑷村湴璋冩暣锛屼互灏嗙浉鍔犱袱鑰呰皟鏁存垚鐩稿悓銆傝皟鏁存柟娉曟槸鎶婂皬鍊�b鐨勫熬鏁板彸绉�shift

    // 鍚勬瘮鐗逛綅銆傝繖鏍蜂袱鑰呯殑鎸囨暟鐩稿悓锛屽�勪簬鍚屼竴涓�鏁伴噺绾т笅銆傛垜浠�灏卞彲浠ュ�瑰熬鏁拌繘琛岀浉鍔犺繍绠椾簡銆�

    // 鐩稿姞涔嬪墠鎴戜滑闇�瑕佸厛鎶婂畠浠�杞�鎹㈡垚浠跨湡杩愮畻鏍煎紡銆傚湪鍔犳硶杩愮畻鍚庡啀鍙樻崲浼氫复鏃跺疄鏁版牸寮忋��

 82         __asm__("shrdl %4,%1,%0 ; shrl %4,%1"              // 鍙岀簿搴︼紙64浣嶏級鍙崇Щ銆�

 83                 :"=r" (b.a),"=r" (b.b)

 84                 :"" (b.a),"1" (b.b),"c" ((char) shift));

 85         signify(&a);                                       // 鍙樻崲鏍煎紡銆�

 86         signify(&b);

 87         __asm__("addl %4,%0 ; adcl %5,%1"                  // 鎵ц�屽姞娉曡繍绠椼��

 88                 :"=r" (a.a),"=r" (a.b)

 89                 :"" (a.a),"1" (a.b),"g" (b.a),"g" (b.b));

 90         unsignify(&a);                                     // 鍐嶅彉鎹�浼氫复鏃跺疄鏁版牸寮忋��

 91         *result = a;

 92 }

 93