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      1 /*
      2  * Copyright (C) 2005 The Android Open Source Project
      3  *
      4  * Licensed under the Apache License, Version 2.0 (the "License");
      5  * you may not use this file except in compliance with the License.
      6  * You may obtain a copy of the License at
      7  *
      8  *      http://www.apache.org/licenses/LICENSE-2.0
      9  *
     10  * Unless required by applicable law or agreed to in writing, software
     11  * distributed under the License is distributed on an "AS IS" BASIS,
     12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     13  * See the License for the specific language governing permissions and
     14  * limitations under the License.
     15  */
     16 
     17 #ifndef ANDROID_GGL_FIXED_H
     18 #define ANDROID_GGL_FIXED_H
     19 
     20 #include <math.h>
     21 #include <pixelflinger/pixelflinger.h>
     22 
     23 // ----------------------------------------------------------------------------
     24 
     25 #define CONST           __attribute__((const))
     26 #define ALWAYS_INLINE   __attribute__((always_inline))
     27 
     28 const GGLfixed FIXED_BITS = 16;
     29 const GGLfixed FIXED_EPSILON  = 1;
     30 const GGLfixed FIXED_ONE  = 1L<<FIXED_BITS;
     31 const GGLfixed FIXED_HALF = 1L<<(FIXED_BITS-1);
     32 const GGLfixed FIXED_MIN  = 0x80000000L;
     33 const GGLfixed FIXED_MAX  = 0x7FFFFFFFL;
     34 
     35 inline GGLfixed gglIntToFixed(GGLfixed i)       ALWAYS_INLINE ;
     36 inline GGLfixed gglFixedToIntRound(GGLfixed f)  ALWAYS_INLINE ;
     37 inline GGLfixed gglFixedToIntFloor(GGLfixed f)  ALWAYS_INLINE ;
     38 inline GGLfixed gglFixedToIntCeil(GGLfixed f)   ALWAYS_INLINE ;
     39 inline GGLfixed gglFracx(GGLfixed v)            ALWAYS_INLINE ;
     40 inline GGLfixed gglFloorx(GGLfixed v)           ALWAYS_INLINE ;
     41 inline GGLfixed gglCeilx(GGLfixed v)            ALWAYS_INLINE ;
     42 inline GGLfixed gglCenterx(GGLfixed v)          ALWAYS_INLINE ;
     43 inline GGLfixed gglRoundx(GGLfixed v)           ALWAYS_INLINE ;
     44 
     45 GGLfixed gglIntToFixed(GGLfixed i) {
     46     return i<<FIXED_BITS;
     47 }
     48 GGLfixed gglFixedToIntRound(GGLfixed f) {
     49     return (f + FIXED_HALF)>>FIXED_BITS;
     50 }
     51 GGLfixed gglFixedToIntFloor(GGLfixed f) {
     52     return f>>FIXED_BITS;
     53 }
     54 GGLfixed gglFixedToIntCeil(GGLfixed f) {
     55     return (f + ((1<<FIXED_BITS) - 1))>>FIXED_BITS;
     56 }
     57 
     58 GGLfixed gglFracx(GGLfixed v) {
     59     return v & ((1<<FIXED_BITS)-1);
     60 }
     61 GGLfixed gglFloorx(GGLfixed v) {
     62     return gglFixedToIntFloor(v)<<FIXED_BITS;
     63 }
     64 GGLfixed gglCeilx(GGLfixed v) {
     65     return gglFixedToIntCeil(v)<<FIXED_BITS;
     66 }
     67 GGLfixed gglCenterx(GGLfixed v) {
     68     return gglFloorx(v + FIXED_HALF) | FIXED_HALF;
     69 }
     70 GGLfixed gglRoundx(GGLfixed v) {
     71     return gglFixedToIntRound(v)<<FIXED_BITS;
     72 }
     73 
     74 // conversion from (unsigned) int, short, byte to fixed...
     75 #define GGL_B_TO_X(_x)      GGLfixed( ((int32_t(_x)+1)>>1)<<10 )
     76 #define GGL_S_TO_X(_x)      GGLfixed( ((int32_t(_x)+1)>>1)<<2 )
     77 #define GGL_I_TO_X(_x)      GGLfixed( ((int32_t(_x)>>1)+1)>>14 )
     78 #define GGL_UB_TO_X(_x)     GGLfixed(   uint32_t(_x) +      \
     79                                         (uint32_t(_x)<<8) + \
     80                                         (uint32_t(_x)>>7) )
     81 #define GGL_US_TO_X(_x)     GGLfixed( (_x) + ((_x)>>15) )
     82 #define GGL_UI_TO_X(_x)     GGLfixed( (((_x)>>1)+1)>>15 )
     83 
     84 // ----------------------------------------------------------------------------
     85 
     86 GGLfixed gglPowx(GGLfixed x, GGLfixed y) CONST;
     87 GGLfixed gglSqrtx(GGLfixed a) CONST;
     88 GGLfixed gglSqrtRecipx(GGLfixed x) CONST;
     89 GGLfixed gglFastDivx(GGLfixed n, GGLfixed d) CONST;
     90 int32_t gglMulDivi(int32_t a, int32_t b, int32_t c);
     91 
     92 int32_t gglRecipQNormalized(int32_t x, int* exponent);
     93 int32_t gglRecipQ(GGLfixed x, int q) CONST;
     94 
     95 inline GGLfixed gglRecip(GGLfixed x) CONST;
     96 inline GGLfixed gglRecip(GGLfixed x) {
     97     return gglRecipQ(x, 16);
     98 }
     99 
    100 inline GGLfixed gglRecip28(GGLfixed x) CONST;
    101 int32_t gglRecip28(GGLfixed x) {
    102     return gglRecipQ(x, 28);
    103 }
    104 
    105 // ----------------------------------------------------------------------------
    106 
    107 #if defined(__arm__) && !defined(__thumb__)
    108 
    109 // inline ARM implementations
    110 inline GGLfixed gglMulx(GGLfixed x, GGLfixed y, int shift) CONST;
    111 inline GGLfixed gglMulx(GGLfixed x, GGLfixed y, int shift) {
    112     GGLfixed result, t;
    113     if (__builtin_constant_p(shift)) {
    114     asm("smull  %[lo], %[hi], %[x], %[y]            \n"
    115         "movs   %[lo], %[lo], lsr %[rshift]         \n"
    116         "adc    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
    117         : [lo]"=r"(result), [hi]"=r"(t), [x]"=r"(x)
    118         : "%[x]"(x), [y]"r"(y), [lshift] "I"(32-shift), [rshift] "I"(shift)
    119         : "cc"
    120         );
    121     } else {
    122     asm("smull  %[lo], %[hi], %[x], %[y]            \n"
    123         "movs   %[lo], %[lo], lsr %[rshift]         \n"
    124         "adc    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
    125         : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
    126         : "%[x]"(x), [y]"r"(y), [lshift] "r"(32-shift), [rshift] "r"(shift)
    127         : "cc"
    128         );
    129     }
    130     return result;
    131 }
    132 
    133 inline GGLfixed gglMulAddx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) CONST;
    134 inline GGLfixed gglMulAddx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) {
    135     GGLfixed result, t;
    136     if (__builtin_constant_p(shift)) {
    137     asm("smull  %[lo], %[hi], %[x], %[y]            \n"
    138         "add    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
    139         "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
    140         : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
    141         : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "I"(32-shift), [rshift] "I"(shift)
    142         );
    143     } else {
    144     asm("smull  %[lo], %[hi], %[x], %[y]            \n"
    145         "add    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
    146         "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
    147         : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
    148         : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "r"(32-shift), [rshift] "r"(shift)
    149         );
    150     }
    151     return result;
    152 }
    153 
    154 inline GGLfixed gglMulSubx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) CONST;
    155 inline GGLfixed gglMulSubx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) {
    156     GGLfixed result, t;
    157     if (__builtin_constant_p(shift)) {
    158     asm("smull  %[lo], %[hi], %[x], %[y]            \n"
    159         "rsb    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
    160         "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
    161         : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
    162         : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "I"(32-shift), [rshift] "I"(shift)
    163         );
    164     } else {
    165     asm("smull  %[lo], %[hi], %[x], %[y]            \n"
    166         "rsb    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
    167         "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
    168         : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
    169         : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "r"(32-shift), [rshift] "r"(shift)
    170         );
    171     }
    172     return result;
    173 }
    174 
    175 inline int64_t gglMulii(int32_t x, int32_t y) CONST;
    176 inline int64_t gglMulii(int32_t x, int32_t y)
    177 {
    178     // 64-bits result: r0=low, r1=high
    179     union {
    180         struct {
    181             int32_t lo;
    182             int32_t hi;
    183         } s;
    184         int64_t res;
    185     };
    186     asm("smull %0, %1, %2, %3   \n"
    187         : "=r"(s.lo), "=&r"(s.hi)
    188         : "%r"(x), "r"(y)
    189         :
    190         );
    191     return res;
    192 }
    193 #elif defined(__mips__)
    194 
    195 /*inline MIPS implementations*/
    196 inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) CONST;
    197 inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) {
    198     GGLfixed result,tmp,tmp1,tmp2;
    199 
    200     if (__builtin_constant_p(shift)) {
    201         if (shift == 0) {
    202             asm ("mult %[a], %[b] \t\n"
    203               "mflo  %[res]   \t\n"
    204             : [res]"=&r"(result),[tmp]"=&r"(tmp)
    205             : [a]"r"(a),[b]"r"(b)
    206             : "%hi","%lo"
    207             );
    208         } else if (shift == 32)
    209         {
    210             asm ("mult %[a], %[b] \t\n"
    211             "li  %[tmp],1\t\n"
    212             "sll  %[tmp],%[tmp],0x1f\t\n"
    213             "mflo %[res]   \t\n"
    214             "addu %[tmp1],%[tmp],%[res] \t\n"
    215             "sltu %[tmp1],%[tmp1],%[tmp]\t\n"   /*obit*/
    216             "sra %[tmp],%[tmp],0x1f \t\n"
    217             "mfhi  %[res]   \t\n"
    218             "addu %[res],%[res],%[tmp]\t\n"
    219             "addu %[res],%[res],%[tmp1]\t\n"
    220             : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1)
    221             : [a]"r"(a),[b]"r"(b),[shift]"I"(shift)
    222             : "%hi","%lo"
    223             );
    224         } else if ((shift >0) && (shift < 32))
    225         {
    226             asm ("mult %[a], %[b] \t\n"
    227             "li  %[tmp],1 \t\n"
    228             "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
    229             "mflo  %[res]   \t\n"
    230             "addu %[tmp1],%[tmp],%[res] \t\n"
    231             "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
    232             "addu  %[res],%[res],%[tmp] \t\n"
    233             "mfhi  %[tmp]   \t\n"
    234             "addu  %[tmp],%[tmp],%[tmp1] \t\n"
    235             "sll   %[tmp],%[tmp],%[lshift] \t\n"
    236             "srl   %[res],%[res],%[rshift]    \t\n"
    237             "or    %[res],%[res],%[tmp] \t\n"
    238             : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    239             : [a]"r"(a),[b]"r"(b),[lshift]"I"(32-shift),[rshift]"I"(shift),[shiftm1]"I"(shift-1)
    240             : "%hi","%lo"
    241             );
    242         } else {
    243             asm ("mult %[a], %[b] \t\n"
    244             "li  %[tmp],1 \t\n"
    245             "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
    246             "mflo  %[res]   \t\n"
    247             "addu %[tmp1],%[tmp],%[res] \t\n"
    248             "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
    249             "sra  %[tmp2],%[tmp],0x1f \t\n"
    250             "addu  %[res],%[res],%[tmp] \t\n"
    251             "mfhi  %[tmp]   \t\n"
    252             "addu  %[tmp],%[tmp],%[tmp2] \t\n"
    253             "addu  %[tmp],%[tmp],%[tmp1] \t\n"            /*tmp=hi*/
    254             "srl   %[tmp2],%[res],%[rshift]    \t\n"
    255             "srav  %[res], %[tmp],%[rshift]\t\n"
    256             "sll   %[tmp],%[tmp],1 \t\n"
    257             "sll   %[tmp],%[tmp],%[norbits] \t\n"
    258             "or    %[tmp],%[tmp],%[tmp2] \t\n"
    259             "movz  %[res],%[tmp],%[bit5] \t\n"
    260             : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    261             : [a]"r"(a),[b]"r"(b),[norbits]"I"(~(shift)),[rshift]"I"(shift),[shiftm1] "I"(shift-1),[bit5]"I"(shift & 0x20)
    262             : "%hi","%lo"
    263             );
    264         }
    265     } else {
    266         asm ("mult %[a], %[b] \t\n"
    267         "li  %[tmp],1 \t\n"
    268         "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
    269         "mflo  %[res]   \t\n"
    270         "addu %[tmp1],%[tmp],%[res] \t\n"
    271         "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
    272         "sra  %[tmp2],%[tmp],0x1f \t\n"
    273         "addu  %[res],%[res],%[tmp] \t\n"
    274         "mfhi  %[tmp]   \t\n"
    275         "addu  %[tmp],%[tmp],%[tmp2] \t\n"
    276         "addu  %[tmp],%[tmp],%[tmp1] \t\n"            /*tmp=hi*/
    277         "srl   %[tmp2],%[res],%[rshift]    \t\n"
    278         "srav  %[res], %[tmp],%[rshift]\t\n"
    279         "sll   %[tmp],%[tmp],1 \t\n"
    280         "sll   %[tmp],%[tmp],%[norbits] \t\n"
    281         "or    %[tmp],%[tmp],%[tmp2] \t\n"
    282         "movz  %[res],%[tmp],%[bit5] \t\n"
    283          : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    284          : [a]"r"(a),[b]"r"(b),[norbits]"r"(~(shift)),[rshift] "r"(shift),[shiftm1]"r"(shift-1),[bit5] "r"(shift & 0x20)
    285          : "%hi","%lo"
    286          );
    287         }
    288 
    289         return result;
    290 }
    291 
    292 inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
    293 inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
    294     GGLfixed result,t,tmp1,tmp2;
    295 
    296     if (__builtin_constant_p(shift)) {
    297         if (shift == 0) {
    298                  asm ("mult %[a], %[b] \t\n"
    299                  "mflo  %[lo]   \t\n"
    300                  "addu  %[lo],%[lo],%[c]    \t\n"
    301                  : [lo]"=&r"(result)
    302                  : [a]"r"(a),[b]"r"(b),[c]"r"(c)
    303                  : "%hi","%lo"
    304                  );
    305                 } else if (shift == 32) {
    306                     asm ("mult %[a], %[b] \t\n"
    307                     "mfhi  %[lo]   \t\n"
    308                     "addu  %[lo],%[lo],%[c]    \t\n"
    309                     : [lo]"=&r"(result)
    310                     : [a]"r"(a),[b]"r"(b),[c]"r"(c)
    311                     : "%hi","%lo"
    312                     );
    313                 } else if ((shift>0) && (shift<32)) {
    314                     asm ("mult %[a], %[b] \t\n"
    315                     "mflo  %[res]   \t\n"
    316                     "mfhi  %[t]   \t\n"
    317                     "srl   %[res],%[res],%[rshift]    \t\n"
    318                     "sll   %[t],%[t],%[lshift]     \t\n"
    319                     "or  %[res],%[res],%[t]    \t\n"
    320                     "addu  %[res],%[res],%[c]    \t\n"
    321                     : [res]"=&r"(result),[t]"=&r"(t)
    322                     : [a]"r"(a),[b]"r"(b),[c]"r"(c),[lshift]"I"(32-shift),[rshift]"I"(shift)
    323                     : "%hi","%lo"
    324                     );
    325                 } else {
    326                     asm ("mult %[a], %[b] \t\n"
    327                     "nor %[tmp1],$zero,%[shift]\t\n"
    328                     "mflo  %[res]   \t\n"
    329                     "mfhi  %[t]   \t\n"
    330                     "srl   %[res],%[res],%[shift]    \t\n"
    331                     "sll   %[tmp2],%[t],1     \t\n"
    332                     "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
    333                     "or  %[tmp1],%[tmp2],%[res]    \t\n"
    334                     "srav  %[res],%[t],%[shift]     \t\n"
    335                     "andi %[tmp2],%[shift],0x20\t\n"
    336                     "movz %[res],%[tmp1],%[tmp2]\t\n"
    337                     "addu  %[res],%[res],%[c]    \t\n"
    338                     : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    339                     : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"I"(shift)
    340                     : "%hi","%lo"
    341                     );
    342                 }
    343             } else {
    344                 asm ("mult %[a], %[b] \t\n"
    345                 "nor %[tmp1],$zero,%[shift]\t\n"
    346                 "mflo  %[res]   \t\n"
    347                 "mfhi  %[t]   \t\n"
    348                 "srl   %[res],%[res],%[shift]    \t\n"
    349                 "sll   %[tmp2],%[t],1     \t\n"
    350                 "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
    351                 "or  %[tmp1],%[tmp2],%[res]    \t\n"
    352                 "srav  %[res],%[t],%[shift]     \t\n"
    353                 "andi %[tmp2],%[shift],0x20\t\n"
    354                 "movz %[res],%[tmp1],%[tmp2]\t\n"
    355                 "addu  %[res],%[res],%[c]    \t\n"
    356                 : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    357                 : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"r"(shift)
    358                 : "%hi","%lo"
    359                 );
    360             }
    361             return result;
    362 }
    363 
    364 inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
    365 inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
    366     GGLfixed result,t,tmp1,tmp2;
    367 
    368     if (__builtin_constant_p(shift)) {
    369         if (shift == 0) {
    370                  asm ("mult %[a], %[b] \t\n"
    371                  "mflo  %[lo]   \t\n"
    372                  "subu  %[lo],%[lo],%[c]    \t\n"
    373                  : [lo]"=&r"(result)
    374                  : [a]"r"(a),[b]"r"(b),[c]"r"(c)
    375                  : "%hi","%lo"
    376                  );
    377                 } else if (shift == 32) {
    378                     asm ("mult %[a], %[b] \t\n"
    379                     "mfhi  %[lo]   \t\n"
    380                     "subu  %[lo],%[lo],%[c]    \t\n"
    381                     : [lo]"=&r"(result)
    382                     : [a]"r"(a),[b]"r"(b),[c]"r"(c)
    383                     : "%hi","%lo"
    384                     );
    385                 } else if ((shift>0) && (shift<32)) {
    386                     asm ("mult %[a], %[b] \t\n"
    387                     "mflo  %[res]   \t\n"
    388                     "mfhi  %[t]   \t\n"
    389                     "srl   %[res],%[res],%[rshift]    \t\n"
    390                     "sll   %[t],%[t],%[lshift]     \t\n"
    391                     "or  %[res],%[res],%[t]    \t\n"
    392                     "subu  %[res],%[res],%[c]    \t\n"
    393                     : [res]"=&r"(result),[t]"=&r"(t)
    394                     : [a]"r"(a),[b]"r"(b),[c]"r"(c),[lshift]"I"(32-shift),[rshift]"I"(shift)
    395                     : "%hi","%lo"
    396                     );
    397                 } else {
    398                     asm ("mult %[a], %[b] \t\n"
    399                     "nor %[tmp1],$zero,%[shift]\t\n"
    400                      "mflo  %[res]   \t\n"
    401                      "mfhi  %[t]   \t\n"
    402                      "srl   %[res],%[res],%[shift]    \t\n"
    403                      "sll   %[tmp2],%[t],1     \t\n"
    404                      "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
    405                      "or  %[tmp1],%[tmp2],%[res]    \t\n"
    406                      "srav  %[res],%[t],%[shift]     \t\n"
    407                      "andi %[tmp2],%[shift],0x20\t\n"
    408                      "movz %[res],%[tmp1],%[tmp2]\t\n"
    409                      "subu  %[res],%[res],%[c]    \t\n"
    410                      : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    411                      : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"I"(shift)
    412                      : "%hi","%lo"
    413                      );
    414                     }
    415                 } else {
    416                 asm ("mult %[a], %[b] \t\n"
    417                 "nor %[tmp1],$zero,%[shift]\t\n"
    418                 "mflo  %[res]   \t\n"
    419                 "mfhi  %[t]   \t\n"
    420                 "srl   %[res],%[res],%[shift]    \t\n"
    421                 "sll   %[tmp2],%[t],1     \t\n"
    422                 "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
    423                 "or  %[tmp1],%[tmp2],%[res]    \t\n"
    424                 "srav  %[res],%[t],%[shift]     \t\n"
    425                 "andi %[tmp2],%[shift],0x20\t\n"
    426                 "movz %[res],%[tmp1],%[tmp2]\t\n"
    427                 "subu  %[res],%[res],%[c]    \t\n"
    428                 : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
    429                 : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"r"(shift)
    430                 : "%hi","%lo"
    431                 );
    432             }
    433     return result;
    434 }
    435 
    436 inline int64_t gglMulii(int32_t x, int32_t y) CONST;
    437 inline int64_t gglMulii(int32_t x, int32_t y) {
    438     union {
    439         struct {
    440 #if defined(__MIPSEL__)
    441             int32_t lo;
    442             int32_t hi;
    443 #elif defined(__MIPSEB__)
    444             int32_t hi;
    445             int32_t lo;
    446 #endif
    447         } s;
    448         int64_t res;
    449     }u;
    450     asm("mult %2, %3 \t\n"
    451         "mfhi %1   \t\n"
    452         "mflo %0   \t\n"
    453         : "=r"(u.s.lo), "=&r"(u.s.hi)
    454         : "%r"(x), "r"(y)
    455 	: "%hi","%lo"
    456         );
    457     return u.res;
    458 }
    459 
    460 #else // ----------------------------------------------------------------------
    461 
    462 inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) CONST;
    463 inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) {
    464     return GGLfixed((int64_t(a)*b + (1<<(shift-1)))>>shift);
    465 }
    466 inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
    467 inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
    468     return GGLfixed((int64_t(a)*b)>>shift) + c;
    469 }
    470 inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
    471 inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
    472     return GGLfixed((int64_t(a)*b)>>shift) - c;
    473 }
    474 inline int64_t gglMulii(int32_t a, int32_t b) CONST;
    475 inline int64_t gglMulii(int32_t a, int32_t b) {
    476     return int64_t(a)*b;
    477 }
    478 
    479 #endif
    480 
    481 // ------------------------------------------------------------------------
    482 
    483 inline GGLfixed gglMulx(GGLfixed a, GGLfixed b) CONST;
    484 inline GGLfixed gglMulx(GGLfixed a, GGLfixed b) {
    485     return gglMulx(a, b, 16);
    486 }
    487 inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c) CONST;
    488 inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c) {
    489     return gglMulAddx(a, b, c, 16);
    490 }
    491 inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c) CONST;
    492 inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c) {
    493     return gglMulSubx(a, b, c, 16);
    494 }
    495 
    496 // ------------------------------------------------------------------------
    497 
    498 inline int32_t gglClz(int32_t x) CONST;
    499 inline int32_t gglClz(int32_t x)
    500 {
    501 #if (defined(__arm__) && !defined(__thumb__)) || defined(__mips__)
    502     return __builtin_clz(x);
    503 #else
    504     if (!x) return 32;
    505     int32_t exp = 31;
    506     if (x & 0xFFFF0000) { exp -=16; x >>= 16; }
    507     if (x & 0x0000ff00) { exp -= 8; x >>= 8; }
    508     if (x & 0x000000f0) { exp -= 4; x >>= 4; }
    509     if (x & 0x0000000c) { exp -= 2; x >>= 2; }
    510     if (x & 0x00000002) { exp -= 1; }
    511     return exp;
    512 #endif
    513 }
    514 
    515 // ------------------------------------------------------------------------
    516 
    517 int32_t gglDivQ(GGLfixed n, GGLfixed d, int32_t i) CONST;
    518 
    519 inline int32_t gglDivQ16(GGLfixed n, GGLfixed d) CONST;
    520 inline int32_t gglDivQ16(GGLfixed n, GGLfixed d) {
    521     return gglDivQ(n, d, 16);
    522 }
    523 
    524 inline int32_t gglDivx(GGLfixed n, GGLfixed d) CONST;
    525 inline int32_t gglDivx(GGLfixed n, GGLfixed d) {
    526     return gglDivQ(n, d, 16);
    527 }
    528 
    529 // ------------------------------------------------------------------------
    530 
    531 inline GGLfixed gglRecipFast(GGLfixed x) CONST;
    532 inline GGLfixed gglRecipFast(GGLfixed x)
    533 {
    534     // This is a really bad approximation of 1/x, but it's also
    535     // very fast. x must be strictly positive.
    536     // if x between [0.5, 1[ , then 1/x = 3-2*x
    537     // (we use 2.30 fixed-point)
    538     const int32_t lz = gglClz(x);
    539     return (0xC0000000 - (x << (lz - 1))) >> (30-lz);
    540 }
    541 
    542 // ------------------------------------------------------------------------
    543 
    544 inline GGLfixed gglClampx(GGLfixed c) CONST;
    545 inline GGLfixed gglClampx(GGLfixed c)
    546 {
    547 #if defined(__thumb__)
    548     // clamp without branches
    549     c &= ~(c>>31);  c = FIXED_ONE - c;
    550     c &= ~(c>>31);  c = FIXED_ONE - c;
    551 #else
    552 #if defined(__arm__)
    553     // I don't know why gcc thinks its smarter than me! The code below
    554     // clamps to zero in one instruction, but gcc won't generate it and
    555     // replace it by a cmp + movlt (it's quite amazing actually).
    556     asm("bic %0, %1, %1, asr #31\n" : "=r"(c) : "r"(c));
    557 #else
    558     c &= ~(c>>31);
    559 #endif
    560     if (c>FIXED_ONE)
    561         c = FIXED_ONE;
    562 #endif
    563     return c;
    564 }
    565 
    566 // ------------------------------------------------------------------------
    567 
    568 #endif // ANDROID_GGL_FIXED_H
    569