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      1 // Copyright 2016 The Go Authors. All rights reserved.
      2 // Use of this source code is governed by a BSD-style
      3 // license that can be found in the LICENSE file.
      4 
      5 #include "textflag.h"
      6 
      7 // Various constants
      8 DATA sincosxnan<>+0(SB)/8, $0x7ff8000000000000
      9 GLOBL sincosxnan<>+0(SB), RODATA, $8
     10 DATA sincosxlim<>+0(SB)/8, $0x432921fb54442d19
     11 GLOBL sincosxlim<>+0(SB), RODATA, $8
     12 DATA sincosxadd<>+0(SB)/8, $0xc338000000000000
     13 GLOBL sincosxadd<>+0(SB), RODATA, $8
     14 DATA sincosxpi2l<>+0(SB)/8, $0.108285667392191389e-31
     15 GLOBL sincosxpi2l<>+0(SB), RODATA, $8
     16 DATA sincosxpi2m<>+0(SB)/8, $0.612323399573676480e-16
     17 GLOBL sincosxpi2m<>+0(SB), RODATA, $8
     18 DATA sincosxpi2h<>+0(SB)/8, $0.157079632679489656e+01
     19 GLOBL sincosxpi2h<>+0(SB), RODATA, $8
     20 DATA sincosrpi2<>+0(SB)/8, $0.636619772367581341e+00
     21 GLOBL sincosrpi2<>+0(SB), RODATA, $8
     22 
     23 // Minimax polynomial approximations
     24 DATA sincosc0<>+0(SB)/8, $0.100000000000000000E+01
     25 GLOBL sincosc0<>+0(SB), RODATA, $8
     26 DATA sincosc1<>+0(SB)/8, $-.499999999999999833E+00
     27 GLOBL sincosc1<>+0(SB), RODATA, $8
     28 DATA sincosc2<>+0(SB)/8, $0.416666666666625843E-01
     29 GLOBL sincosc2<>+0(SB), RODATA, $8
     30 DATA sincosc3<>+0(SB)/8, $-.138888888885498984E-02
     31 GLOBL sincosc3<>+0(SB), RODATA, $8
     32 DATA sincosc4<>+0(SB)/8, $0.248015871681607202E-04
     33 GLOBL sincosc4<>+0(SB), RODATA, $8
     34 DATA sincosc5<>+0(SB)/8, $-.275572911309937875E-06
     35 GLOBL sincosc5<>+0(SB), RODATA, $8
     36 DATA sincosc6<>+0(SB)/8, $0.208735047247632818E-08
     37 GLOBL sincosc6<>+0(SB), RODATA, $8
     38 DATA sincosc7<>+0(SB)/8, $-.112753632738365317E-10
     39 GLOBL sincosc7<>+0(SB), RODATA, $8
     40 DATA sincoss0<>+0(SB)/8, $0.100000000000000000E+01
     41 GLOBL sincoss0<>+0(SB), RODATA, $8
     42 DATA sincoss1<>+0(SB)/8, $-.166666666666666657E+00
     43 GLOBL sincoss1<>+0(SB), RODATA, $8
     44 DATA sincoss2<>+0(SB)/8, $0.833333333333309209E-02
     45 GLOBL sincoss2<>+0(SB), RODATA, $8
     46 DATA sincoss3<>+0(SB)/8, $-.198412698410701448E-03
     47 GLOBL sincoss3<>+0(SB), RODATA, $8
     48 DATA sincoss4<>+0(SB)/8, $0.275573191453906794E-05
     49 GLOBL sincoss4<>+0(SB), RODATA, $8
     50 DATA sincoss5<>+0(SB)/8, $-.250520918387633290E-07
     51 GLOBL sincoss5<>+0(SB), RODATA, $8
     52 DATA sincoss6<>+0(SB)/8, $0.160571285514715856E-09
     53 GLOBL sincoss6<>+0(SB), RODATA, $8
     54 DATA sincoss7<>+0(SB)/8, $-.753213484933210972E-12
     55 GLOBL sincoss7<>+0(SB), RODATA, $8
     56 
     57 // Sin returns the sine of the radian argument x.
     58 //
     59 // Special cases are:
     60 //      Sin(0) = 0
     61 //      Sin(Inf) = NaN
     62 //      Sin(NaN) = NaN
     63 // The algorithm used is minimax polynomial approximation.
     64 // with coefficients determined with a Remez exchange algorithm.
     65 
     66 TEXT sinAsm(SB),NOSPLIT,$0-16
     67 	FMOVD   x+0(FP), F0
     68 	//special case Sin(0) = 0
     69 	FMOVD   $(0.0), F1
     70 	FCMPU   F0, F1
     71 	BEQ     sinIsZero
     72 	WORD    $0xB3120000     //ltdbr %f0,%f0
     73 	BLTU    L17
     74 	FMOVD   F0, F5
     75 L2:
     76 	MOVD    $sincoss7<>+0(SB), R1
     77 	FMOVD   0(R1), F4
     78 	MOVD    $sincoss6<>+0(SB), R1
     79 	FMOVD   0(R1), F1
     80 	MOVD    $sincoss5<>+0(SB), R1
     81 	VLEG    $0, 0(R1), V18
     82 	MOVD    $sincoss4<>+0(SB), R1
     83 	FMOVD   0(R1), F6
     84 	MOVD    $sincoss2<>+0(SB), R1
     85 	VLEG    $0, 0(R1), V16
     86 	MOVD    $sincoss3<>+0(SB), R1
     87 	FMOVD   0(R1), F7
     88 	MOVD    $sincoss1<>+0(SB), R1
     89 	FMOVD   0(R1), F3
     90 	MOVD    $sincoss0<>+0(SB), R1
     91 	FMOVD   0(R1), F2
     92 	WFCHDBS V2, V5, V2
     93 	BEQ     L18
     94 	MOVD    $sincosrpi2<>+0(SB), R1
     95 	FMOVD   0(R1), F3
     96 	MOVD    $sincosxadd<>+0(SB), R1
     97 	FMOVD   0(R1), F2
     98 	WFMSDB  V0, V3, V2, V3
     99 	FMOVD   0(R1), F6
    100 	FADD    F3, F6
    101 	MOVD    $sincosxpi2h<>+0(SB), R1
    102 	FMOVD   0(R1), F2
    103 	FMSUB   F2, F6, F0
    104 	MOVD    $sincosxpi2m<>+0(SB), R1
    105 	FMOVD   0(R1), F4
    106 	FMADD   F4, F6, F0
    107 	MOVD    $sincosxpi2l<>+0(SB), R1
    108 	WFMDB   V0, V0, V1
    109 	FMOVD   0(R1), F7
    110 	WFMDB   V1, V1, V2
    111 	LGDR    F3, R1
    112 	MOVD    $sincosxlim<>+0(SB), R2
    113 	TMLL	R1, $1
    114 	BEQ     L6
    115 	FMOVD   0(R2), F0
    116 	WFCHDBS V0, V5, V0
    117 	BNE     L14
    118 	MOVD    $sincosc7<>+0(SB), R2
    119 	FMOVD   0(R2), F0
    120 	MOVD    $sincosc6<>+0(SB), R2
    121 	FMOVD   0(R2), F4
    122 	MOVD    $sincosc5<>+0(SB), R2
    123 	WFMADB  V1, V0, V4, V0
    124 	FMOVD   0(R2), F6
    125 	MOVD    $sincosc4<>+0(SB), R2
    126 	WFMADB  V1, V0, V6, V0
    127 	FMOVD   0(R2), F4
    128 	MOVD    $sincosc2<>+0(SB), R2
    129 	FMOVD   0(R2), F6
    130 	WFMADB  V2, V4, V6, V4
    131 	MOVD    $sincosc3<>+0(SB), R2
    132 	FMOVD   0(R2), F3
    133 	MOVD    $sincosc1<>+0(SB), R2
    134 	WFMADB  V2, V0, V3, V0
    135 	FMOVD   0(R2), F6
    136 	WFMADB  V1, V4, V6, V4
    137 	TMLL	R1, $2
    138 	WFMADB  V2, V0, V4, V0
    139 	MOVD    $sincosc0<>+0(SB), R1
    140 	FMOVD   0(R1), F2
    141 	WFMADB  V1, V0, V2, V0
    142 	BNE     L15
    143 	FMOVD   F0, ret+8(FP)
    144 	RET
    145 
    146 L6:
    147 	FMOVD   0(R2), F4
    148 	WFCHDBS V4, V5, V4
    149 	BNE     L14
    150 	MOVD    $sincoss7<>+0(SB), R2
    151 	FMOVD   0(R2), F4
    152 	MOVD    $sincoss6<>+0(SB), R2
    153 	FMOVD   0(R2), F3
    154 	MOVD    $sincoss5<>+0(SB), R2
    155 	WFMADB  V1, V4, V3, V4
    156 	WFMADB  V6, V7, V0, V6
    157 	FMOVD   0(R2), F0
    158 	MOVD    $sincoss4<>+0(SB), R2
    159 	FMADD   F4, F1, F0
    160 	FMOVD   0(R2), F3
    161 	MOVD    $sincoss2<>+0(SB), R2
    162 	FMOVD   0(R2), F4
    163 	MOVD    $sincoss3<>+0(SB), R2
    164 	WFMADB  V2, V3, V4, V3
    165 	FMOVD   0(R2), F4
    166 	MOVD    $sincoss1<>+0(SB), R2
    167 	WFMADB  V2, V0, V4, V0
    168 	FMOVD   0(R2), F4
    169 	WFMADB  V1, V3, V4, V3
    170 	FNEG    F6, F4
    171 	WFMADB  V2, V0, V3, V2
    172 	WFMDB   V4, V1, V0
    173 	TMLL	R1, $2
    174 	WFMSDB  V0, V2, V6, V0
    175 	BNE     L15
    176 	FMOVD   F0, ret+8(FP)
    177 	RET
    178 
    179 L14:
    180 	MOVD    $sincosxnan<>+0(SB), R1
    181 	FMOVD   0(R1), F0
    182 	FMOVD   F0, ret+8(FP)
    183 	RET
    184 
    185 L18:
    186 	WFMDB   V0, V0, V2
    187 	WFMADB  V2, V4, V1, V4
    188 	WFMDB   V2, V2, V1
    189 	WFMADB  V2, V4, V18, V4
    190 	WFMADB  V1, V6, V16, V6
    191 	WFMADB  V1, V4, V7, V4
    192 	WFMADB  V2, V6, V3, V6
    193 	FMUL    F0, F2
    194 	WFMADB  V1, V4, V6, V4
    195 	FMADD   F4, F2, F0
    196 	FMOVD   F0, ret+8(FP)
    197 	RET
    198 
    199 L17:
    200 	FNEG    F0, F5
    201 	BR      L2
    202 L15:
    203 	FNEG    F0, F0
    204 	FMOVD   F0, ret+8(FP)
    205 	RET
    206 
    207 
    208 sinIsZero:
    209 	FMOVD   F0, ret+8(FP)
    210 	RET
    211 
    212 // Cos returns the cosine of the radian argument.
    213 //
    214 // Special cases are:
    215 //      Cos(Inf) = NaN
    216 //      Cos(NaN) = NaN
    217 // The algorithm used is minimax polynomial approximation.
    218 // with coefficients determined with a Remez exchange algorithm.
    219 
    220 TEXT cosAsm(SB),NOSPLIT,$0-16
    221 	FMOVD   x+0(FP), F0
    222 	WORD    $0xB3120000     //ltdbr %f0,%f0
    223 	BLTU    L35
    224 	FMOVD   F0, F1
    225 L21:
    226 	MOVD    $sincosc7<>+0(SB), R1
    227 	FMOVD   0(R1), F4
    228 	MOVD    $sincosc6<>+0(SB), R1
    229 	VLEG    $0, 0(R1), V20
    230 	MOVD    $sincosc5<>+0(SB), R1
    231 	VLEG    $0, 0(R1), V18
    232 	MOVD    $sincosc4<>+0(SB), R1
    233 	FMOVD   0(R1), F6
    234 	MOVD    $sincosc2<>+0(SB), R1
    235 	VLEG    $0, 0(R1), V16
    236 	MOVD    $sincosc3<>+0(SB), R1
    237 	FMOVD   0(R1), F7
    238 	MOVD    $sincosc1<>+0(SB), R1
    239 	FMOVD   0(R1), F5
    240 	MOVD    $sincosrpi2<>+0(SB), R1
    241 	FMOVD   0(R1), F2
    242 	MOVD    $sincosxadd<>+0(SB), R1
    243 	FMOVD   0(R1), F3
    244 	MOVD    $sincoss0<>+0(SB), R1
    245 	WFMSDB  V0, V2, V3, V2
    246 	FMOVD   0(R1), F3
    247 	WFCHDBS V3, V1, V3
    248 	LGDR    F2, R1
    249 	BEQ     L36
    250 	MOVD    $sincosxadd<>+0(SB), R2
    251 	FMOVD   0(R2), F4
    252 	FADD    F2, F4
    253 	MOVD    $sincosxpi2h<>+0(SB), R2
    254 	FMOVD   0(R2), F2
    255 	WFMSDB  V4, V2, V0, V2
    256 	MOVD    $sincosxpi2m<>+0(SB), R2
    257 	FMOVD   0(R2), F0
    258 	WFMADB  V4, V0, V2, V0
    259 	MOVD    $sincosxpi2l<>+0(SB), R2
    260 	WFMDB   V0, V0, V2
    261 	FMOVD   0(R2), F5
    262 	WFMDB   V2, V2, V6
    263 	MOVD    $sincosxlim<>+0(SB), R2
    264 	TMLL	R1, $1
    265 	BNE     L25
    266 	FMOVD   0(R2), F0
    267 	WFCHDBS V0, V1, V0
    268 	BNE     L33
    269 	MOVD    $sincosc7<>+0(SB), R2
    270 	FMOVD   0(R2), F0
    271 	MOVD    $sincosc6<>+0(SB), R2
    272 	FMOVD   0(R2), F4
    273 	MOVD    $sincosc5<>+0(SB), R2
    274 	WFMADB  V2, V0, V4, V0
    275 	FMOVD   0(R2), F1
    276 	MOVD    $sincosc4<>+0(SB), R2
    277 	WFMADB  V2, V0, V1, V0
    278 	FMOVD   0(R2), F4
    279 	MOVD    $sincosc2<>+0(SB), R2
    280 	FMOVD   0(R2), F1
    281 	WFMADB  V6, V4, V1, V4
    282 	MOVD    $sincosc3<>+0(SB), R2
    283 	FMOVD   0(R2), F3
    284 	MOVD    $sincosc1<>+0(SB), R2
    285 	WFMADB  V6, V0, V3, V0
    286 	FMOVD   0(R2), F1
    287 	WFMADB  V2, V4, V1, V4
    288 	TMLL	R1, $2
    289 	WFMADB  V6, V0, V4, V0
    290 	MOVD    $sincosc0<>+0(SB), R1
    291 	FMOVD   0(R1), F4
    292 	WFMADB  V2, V0, V4, V0
    293 	BNE     L34
    294 	FMOVD   F0, ret+8(FP)
    295 	RET
    296 
    297 L25:
    298 	FMOVD   0(R2), F3
    299 	WFCHDBS V3, V1, V1
    300 	BNE     L33
    301 	MOVD    $sincoss7<>+0(SB), R2
    302 	FMOVD   0(R2), F1
    303 	MOVD    $sincoss6<>+0(SB), R2
    304 	FMOVD   0(R2), F3
    305 	MOVD    $sincoss5<>+0(SB), R2
    306 	WFMADB  V2, V1, V3, V1
    307 	FMOVD   0(R2), F3
    308 	MOVD    $sincoss4<>+0(SB), R2
    309 	WFMADB  V2, V1, V3, V1
    310 	FMOVD   0(R2), F3
    311 	MOVD    $sincoss2<>+0(SB), R2
    312 	FMOVD   0(R2), F7
    313 	WFMADB  V6, V3, V7, V3
    314 	MOVD    $sincoss3<>+0(SB), R2
    315 	FMADD   F5, F4, F0
    316 	FMOVD   0(R2), F4
    317 	MOVD    $sincoss1<>+0(SB), R2
    318 	FMADD   F1, F6, F4
    319 	FMOVD   0(R2), F1
    320 	FMADD   F3, F2, F1
    321 	FMUL    F0, F2
    322 	WFMADB  V6, V4, V1, V6
    323 	TMLL	R1, $2
    324 	FMADD   F6, F2, F0
    325 	BNE     L34
    326 	FMOVD   F0, ret+8(FP)
    327 	RET
    328 
    329 L33:
    330 	MOVD    $sincosxnan<>+0(SB), R1
    331 	FMOVD   0(R1), F0
    332 	FMOVD   F0, ret+8(FP)
    333 	RET
    334 
    335 L36:
    336 	FMUL    F0, F0
    337 	MOVD    $sincosc0<>+0(SB), R1
    338 	WFMDB   V0, V0, V1
    339 	WFMADB  V0, V4, V20, V4
    340 	WFMADB  V1, V6, V16, V6
    341 	WFMADB  V0, V4, V18, V4
    342 	WFMADB  V0, V6, V5, V6
    343 	WFMADB  V1, V4, V7, V4
    344 	FMOVD   0(R1), F2
    345 	WFMADB  V1, V4, V6, V4
    346 	WFMADB  V0, V4, V2, V0
    347 	FMOVD   F0, ret+8(FP)
    348 	RET
    349 
    350 L35:
    351 	FNEG    F0, F1
    352 	BR      L21
    353 L34:
    354 	FNEG    F0, F0
    355 	FMOVD   F0, ret+8(FP)
    356 	RET
    357