@@ -4,6 +4,7 @@
# include "gte.h"
# include "gp.h"
# include "tape.h"
# include "math.atom.h"
# endif
ATOM_FILE_DEBUGGER_LINE_MARKER ( gte_atom_c ) ;
@@ -183,60 +184,95 @@ MipsAtomComp_Proc_(ab, {
gte_mv_from_data_r ( fr_mac3 , C2_MAC3 ) ,
} )
FI_ Slice_MipsCode ac_gte_mv_from_data_r_mac123 ( AtomBuilder_R ab
, Reg fr_mac1 , Reg fr_mac2 , Reg fr_mac3 )
FI_ Slice_MipsCode ac_gte_mv_from_data_r_mac123 ( AtomBuilder_R ab , Reg fr_mac1 , Reg fr_mac2 , Reg fr_mac3 )
MipsAtomComp_Proc_ ( ab , {
gte_mv_from_data_r ( fr_mac1 , C2_MAC1 ) ,
gte_mv_from_data_r ( fr_mac2 , C2_MAC2 ) ,
gte_mv_from_data_r ( fr_mac3 , C2_MAC3 ) ,
} )
FI_ Slice_MipsCode ac_gte_mv_from_mac123_v3s4 ( AtomBuilder_R ab , Reg_ ( V3_S4 ) v ) MipsAtomComp_ProcMap_ ( ab , mac_gte_mv_from_data_r_mac123 ( v . x , v . y , v . z ) )
# pragma endregion MACs (Mips Atom Components)
# pragma region Atom Procs
/* ─── Local copy of PSYQ's sqrtbl (1/sqrt lookup table for VectorNormal). ───
* Source : PSYQ 4.7 libgte sqrtbl at 0x800185B4 in hello_camera . elf .
* objdump - s - - start - address = 0x800185B4 - - stop - address = 0x800185F4 hello_camera . elf → 192 entries × 16 - bit signed , in 1.12 fixed - point ( max value 0x1000 = 1.0 ) .
/* Normalize V3_S4 using the PSYQ/libgte reciprocal-sqrt method:
* | v | ² = x ² + y ² + z ²
* LZCR determines the exponent of | v | ² .
* Round that exponent even and shift | v | ² into [ 1 , 4 ) .
* sqrtbl approximates 1 / sqrt ( mantissa ) .
* GPF multiplies v by that reciprocal - sqrt mantissa .
* srav_shift restores the exponent scale .
* Effectively : v_normalized = v * ( 1 / sqrt ( | v | ² ) ) .
*
* ─ ─ ─ Local port of PSYQ ' s sqrtbl ( 1 / sqrt lookup table for VectorNormal ) . ─ ─ ─
* Source : PSYQ 4.7 libgte sqrtbl at 0x800185B4 in hello_camera . elf .
* objdump - s - - start - address = 0x800185B4 - - stop - address = 0x800185F4 hello_camera . elf - > 192 entries x 16 - bit signed , stored in 1.12 fixed point .
* Data is identical to the libgte original ( byte - for - byte verified ) .
*
* ─ ─ ─ Per - entry semantics ( decoded from libgte msc02 VectorNormal ) ─ ─ ─
* Each entry is ` 1 / sqrt ( x ) ` in 1.12 fixed point ( value / 4096 ) .
* The 192 entries span 4 octaves of the input magnitude , with 48 entries per octave :
* Octave 0 ( entries 0 - 47 ) : mantissa in [ 0x8000 , 0x10000 ) output ~ [ 1.000 , 0.707 ]
* Octave 1 ( entries 48 - 95 ) : mantissa in [ 0x10000 , 0x20000 ) output ~ [ 0.707 , 0.500 ]
* Octave 2 ( entries 96 - 143 ) : mantissa in [ 0x20000 , 0x40000 ) output ~ [ 0.500 , 0.354 ]
* Octave 3 ( entries144 - 191 ) : mantissa in [ 0x40000 , 0x80000 ) output ~ [ 0.354 , 0.251 ]
* Within each octave , 8 sub - entries interpolate over the 8 fractional bits of the mantissa
* ( the byte ` ( 0x80 | ( i mod 8 ) ) ` for the lower - byte of the aligned value ) .
* Sampling the first value of each octave :
* [ 0 ] 0x1000 = 1.0000 ; 1 / sqrt ( 1.0000 )
* [ 48 ] 0x0e4f = 0.8940 ; 1 / sqrt ( 1.2500 )
* [ 96 ] 0x0d10 = 0.8164 ; 1 / sqrt ( 1.5000 )
* [ 144 ] 0x0c0a = 0.7520 ; 1 / sqrt ( 1.7500 )
* And representative sub - entries within octave 0 ( mantissa in [ 0x8000 , 0x8100 ) ) :
* [ 0 ] 0x1000 = 1.0000 ; 1 / sqrt ( 0x8000 )
* [ 1 ] 0x0fe0 = 0.9922 ; 1 / sqrt ( 0x8100 )
* [ 2 ] 0x0fc1 = 0.9846 ; 1 / sqrt ( 0x8200 )
* [ 3 ] 0x0fa3 = 0.9773 ; 1 / sqrt ( 0x8300 )
* [ 4 ] 0x0f85 = 0.9700 ; 1 / sqrt ( 0x8400 )
* [ 5 ] 0x0f68 = 0.9629 ; 1 / sqrt ( 0x8500 )
* [ 6 ] 0x0f4c = 0.9561 ; 1 / sqrt ( 0x8600 )
* [ 7 ] 0x0f30 = 0.9492 ; 1 / sqrt ( 0x8700 )
* ─ ─ ─ Table semantics ─ ─ ─
* For table index i in [ 0 , 192 ) :
* x = 1 + i / 64
* tbl [ i ] = floor ( 4096 / sqrt ( x ) )
* Thus the table uniformly samples 1 / sqrt ( x ) over :
* x in [ 1.0 , 4.0 )
* at steps of 1 / 64 , with the result represented in 1.12 fixed point ( 0x1000 = 1.0 ) .
*
* The algorithm ' s ` addi - 64 / sll 1 / lh ` selects the entry at ` ( aligned - 64 ) * 2 ` for the case where ` aligned ` has its top bit at bit 24.
* After the sllv / srav pair , ` aligned ` always lands in ` [ 0x80 , 0x100 ) `
* ( with top bit at bit 24 → after ` sub $ aligned - 64 ` , the index sits in ` [ 0x40 , 0x80 ) * 2 = [ 0x80 , 0x100 ) ` bytes = entries [ 64 , 128 ) within the sqrtbl ) .
* The earlier 64 entries ( octave 0 ) are reached when the magnitude after shifting puts the top bit below bit 24 ( the ` sllv ` branch ) ,
* and the load upper_halves of the table bracket the input range .
* The later 64 entries ( octaves 2 - 3 ) are the ` srav ` branch when the magnitude ' s top bit is well above bit 24.
* Representative entries :
* [ 0 ] 0x1000 = 1.000000 ; 1 / sqrt ( 1.000000 )
* [ 16 ] 0x0e4f = 0.894287 ; 1 / sqrt ( 1.250000 )
* [ 32 ] 0x0d10 = 0.816406 ; 1 / sqrt ( 1.500000 )
* [ 48 ] 0x0c18 = 0.755859 ; 1 / sqrt ( 1.750000 )
* [ 64 ] 0x0b50 = 0.707031 ; 1 / sqrt ( 2.000000 )
* [ 128 ] 0x093c = 0.577148 ; 1 / sqrt ( 3.000000 )
* [ 191 ] 0x0804 = 0.500977 ; 1 / sqrt ( 3.984375 )
*
* Reproduced verbatim from libgte ( verified against libpsn00b / psxgte / vector . s : 100 - 123 — 24 rows × 8 halfwords , last entry 0x0804 ) .
* */
* ─ ─ ─ How VectorNormal indexes it ─ ─ ─
* Let :
* mag_sq = x * x + y * y + z * z
* lzcr = leading - zero count of mag_sq
* For a non - zero magnitude , libgte first rounds LZCR down to an even number :
* lzcr_even = lzcr & ~ 1
*
* It then shifts mag_sq so that its significant bits land in one of two
* adjacent normalized ranges :
* if lzcr_even > = 24 :
* aligned = mag_sq < < ( lzcr_even - 24 )
* else :
* aligned = mag_sq > > ( 24 - lzcr_even )
*
* Because lzcr_even differs from the true LZCR by at most one bit :
* raw LZCR even - > aligned in [ 0x80 , 0x100 )
* raw LZCR odd - > aligned in [ 0x40 , 0x080 )
* therefore :
* aligned in [ 0x40 , 0x100 )
*
* Dividing this normalized integer by 64 gives exactly the table domain :
* x = aligned / 64
* x in [ 1.0 , 4.0 )
*
* The lookup is therefore :
* index = aligned - 0x40
* byte_offset = index * sizeof ( S2 )
* inv_len = sqrtbl [ index ]
* or equivalently , matching the libgte instructions :
* addi aligned , - 64
* sll aligned , 1
* lh inv_len , sqrtbl + aligned
*
* ─ ─ ─ Why the domain spans [ 1 , 4 ) instead of [ 1 , 2 ) ─ ─ ─
* Square - root scaling depends on the parity of the exponent .
* Rounding LZCR to even absorbs exponent changes in pairs of bits , leaving the lookup mantissa normalized over a factor - of - four interval [ 1 , 4 ) .
*
* The corresponding exponent correction is retained separately as :
* srav_shift = ( 31 - lzcr_even ) > > 1
*
* After GPF multiplies the original vector components by the table ' s reciprocal - square - root coefficient ,
* this shift restores the exponent scale and yields the normalized vector .
*
* Reproduced verbatim from libgte ; also matches PSn00bSDK VectorNormalS _norm_table ( 24 rows x 8 halfwords , final entry 0x0804 ) .
* */
internal S2 const gte_normalize_sqr_tbl [ 192 ] align_ ( 2 ) = {
0x1000 , 0x0fe0 , 0x0fc1 , 0x0fa3 , 0x0f85 , 0x0f68 , 0x0f4c , 0x0f30 ,
0x0f15 , 0x0efb , 0x0ee1 , 0x0ec7 , 0x0eae , 0x0e96 , 0x0e7e , 0x0e66 ,
@@ -269,10 +305,10 @@ typedef Struct_(RegUse_normalize_v3s4) {
union { Reg_ ( V3_S4 ) res , src ; } ;
union { Reg r0 , src_ptr , mac2 ; } ;
union { Reg r1 , dst_ptr ; } ;
union { Reg r2 , dst_offset , mac1 , v_sqr_aligned ; } ;
union { Reg r3 , src_offset , btarget , shift_count , sqrtbl_index ; } ;
union { Reg r2 , dst_offset , mac1 , v_sqr_aligned , sqrtbl_byte_offset ; } ;
union { Reg r3 , src_offset , align_delta , shift_count , sqrtbl_lookup ; } ;
union { Reg r4 , mac3 , v_sqr_sum , srav_shift ; } ;
union { Reg r5 , lzcr , inv_len ; } ;
union { Reg r5 , lzcr_raw , lzcr_even , inv_len ; } ;
} ;
/* ─── Full normalize (all 4 stages inline) ───
* Generic 4 - stage GTE normalize ( SQR → sum + LZCR → align + sqrtbl → GPF + srav ) . */
@@ -294,30 +330,30 @@ MipsAtom_Proc_(aa, {
add_u_self ( r . v_sqr_sum , r . mac1 ) ,
add_u_self ( r . v_sqr_sum , r . mac2 ) ,
gte_mv_to_data_r ( r . v_sqr_sum , C2_LZCS ) , GteDelay_ nop2 ,
gte_mv_from_data_r ( r . lzcr , C2_LZCR ) , GteDelay_ nop ,
gte_mv_from_data_r ( r . lzcr_raw , C2_LZCR ) , GteDelay_ nop ,
/* Stage 3: even(LZCR), half-shift, align |v|² to bit 24. */
mac_lzcr_round_even_half_shift ( r . lzcr , r . v_sqr_sum , r . v_sqr_aligned ) ,
add_si ( r . btarget , r . lzcr , - 24 ) ,
branch_lt_zero ( r . btarget , atom_offset ( aligned_done , srav_path ) ) , BdSlot_ nop , /* bltz → srav_path (LZCR < 24 path) */
mac_lzcr_round_even_half_shift ( r . lzcr_raw , r . v_sqr_sum , r . v_sqr_aligned ) ,
add_si ( r . align_delta , r . lzcr_even , - 24 ) ,
branch_lt_zero ( r . align_delta , atom_offset ( aligned_done , srav_path ) ) , BdSlot_ nop , /* bltz → srav_path (LZCR < 24 path) */
jump_rel ( atom_offset ( srav_path , aligned_done ) ) , /* b → aligned_done (LZCR >= 24 path) */
BdSlot_ shift_lleft_var ( r . v_sqr_aligned , r . v_sqr_aligned , r . btarget ) ,
BdSlot_ shift_lleft_var ( r . v_sqr_aligned , r . v_sqr_aligned , r . align_delta ) ,
atom_label ( srav_path )
li_s ( r . shift_count , 24 ) ,
sub_s ( r . shift_count , r . shift_count , r . lzcr ) ,
sub_s ( r . shift_count , r . shift_count , r . lzcr_even ) ,
shift_aright_var ( r . v_sqr_aligned , r . v_sqr_aligned , r . shift_count ) ,
atom_label ( aligned_done )
add_si ( r . v_sqr_aligned , r . v_sqr_aligned , - 64 ) ,
shift_lleft ( r . v_sqr_aligned , r . v_sqr_aligned , 1 ) ,
mac_load_word_imm ( r . sqrtbl_index , & gte_normalize_sqr_tbl ) , add_u_self ( r . sqrtbl_index , r . v_sqr_aligned ) ,
load_half ( r . inv_len , r . sqrtbl_index , 0 ) ,
add_si ( r . sqrtbl_byte_offset , r . v_sqr_aligned , - 64 ) ,
shift_lleft ( r . sqrtbl_byte_offset , r . sqrtbl_byte_offset , 1 ) ,
mac_load_word_imm ( r . sqrtbl_lookup , & gte_normalize_sqr_tbl ) , add_u_self ( r . sqrtbl_lookup , r . sqrtbl_byte_offset ) ,
load_half ( r . inv_len , r . sqrtbl_lookup , 0 ) ,
LdSlot_ nop ,
mac_gte_general_purpose_interopolation ( r . inv_len ,
r . src . x , r . src . y , r . src . z ,
r . res . x , r . res . y , r . res . z ,
GteDelay_ load_word ( R_AtomJmp , R_TapePtr , 0 ) , LdSlot_ // ac_yield: word 1
GteDelay_ add_ui_self ( R_TapePtr , S_ ( MipsCode ) ) // ac_yield: word 2
GteDelay_ add_ui_self ( R_TapePtr , S_ ( MipsCode ) ) // ac_yield: word
) ,
mac_shift_aright_var_v3s4_self ( r . res , r . srav_shift ) ,
mac_store_v3s4 ( r . res , r . dst_ptr , 0 ) ,
