1 // Copyright 2017 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 // Minimax polynomial approximation and other constants 8 DATA exprodataL22<> + 0(SB)/8, $800.0E+00 9 DATA exprodataL22<> + 8(SB)/8, $1.0000000000000022e+00 10 DATA exprodataL22<> + 16(SB)/8, $0.500000000000004237e+00 11 DATA exprodataL22<> + 24(SB)/8, $0.166666666630345592e+00 12 DATA exprodataL22<> + 32(SB)/8, $0.138926439368309441e-02 13 DATA exprodataL22<> + 40(SB)/8, $0.833349307718286047e-02 14 DATA exprodataL22<> + 48(SB)/8, $0.416666664838056960e-01 15 DATA exprodataL22<> + 56(SB)/8, $-.231904681384629956E-16 16 DATA exprodataL22<> + 64(SB)/8, $-.693147180559945286E+00 17 DATA exprodataL22<> + 72(SB)/8, $0.144269504088896339E+01 18 DATA exprodataL22<> + 80(SB)/8, $704.0E+00 19 GLOBL exprodataL22<> + 0(SB), RODATA, $88 20 21 DATA expxinf<> + 0(SB)/8, $0x7ff0000000000000 22 GLOBL expxinf<> + 0(SB), RODATA, $8 23 DATA expx4ff<> + 0(SB)/8, $0x4ff0000000000000 24 GLOBL expx4ff<> + 0(SB), RODATA, $8 25 DATA expx2ff<> + 0(SB)/8, $0x2ff0000000000000 26 GLOBL expx2ff<> + 0(SB), RODATA, $8 27 DATA expxaddexp<> + 0(SB)/8, $0xc2f0000100003fef 28 GLOBL expxaddexp<> + 0(SB), RODATA, $8 29 30 // Log multipliers table 31 DATA exptexp<> + 0(SB)/8, $0.442737824274138381E-01 32 DATA exptexp<> + 8(SB)/8, $0.263602189790660309E-01 33 DATA exptexp<> + 16(SB)/8, $0.122565642281703586E-01 34 DATA exptexp<> + 24(SB)/8, $0.143757052860721398E-02 35 DATA exptexp<> + 32(SB)/8, $-.651375034121276075E-02 36 DATA exptexp<> + 40(SB)/8, $-.119317678849450159E-01 37 DATA exptexp<> + 48(SB)/8, $-.150868749549871069E-01 38 DATA exptexp<> + 56(SB)/8, $-.161992609578469234E-01 39 DATA exptexp<> + 64(SB)/8, $-.154492360403337917E-01 40 DATA exptexp<> + 72(SB)/8, $-.129850717389178721E-01 41 DATA exptexp<> + 80(SB)/8, $-.892902649276657891E-02 42 DATA exptexp<> + 88(SB)/8, $-.338202636596794887E-02 43 DATA exptexp<> + 96(SB)/8, $0.357266307045684762E-02 44 DATA exptexp<> + 104(SB)/8, $0.118665304327406698E-01 45 DATA exptexp<> + 112(SB)/8, $0.214434994118118914E-01 46 DATA exptexp<> + 120(SB)/8, $0.322580645161290314E-01 47 GLOBL exptexp<> + 0(SB), RODATA, $128 48 49 // Exp returns e**x, the base-e exponential of x. 50 // 51 // Special cases are: 52 // Exp(+Inf) = +Inf 53 // Exp(NaN) = NaN 54 // Very large values overflow to 0 or +Inf. 55 // Very small values underflow to 1. 56 // The algorithm used is minimax polynomial approximation using a table of 57 // polynomial coefficients determined with a Remez exchange algorithm. 58 59 TEXT expAsm(SB), NOSPLIT, $0-16 60 FMOVD x+0(FP), F0 61 MOVD $exprodataL22<>+0(SB), R5 62 WORD $0xB3120000 //ltdbr %f0,%f0 63 BLTU L20 64 FMOVD F0, F2 65 L2: 66 WORD $0xED205050 //cdb %f2,.L23-.L22(%r5) 67 BYTE $0x00 68 BYTE $0x19 69 BGE L16 70 BVS L16 71 WFCEDBS V2, V2, V2 72 BVS LEXITTAGexp 73 MOVD $expxaddexp<>+0(SB), R1 74 FMOVD 72(R5), F6 75 FMOVD 0(R1), F2 76 WFMSDB V0, V6, V2, V6 77 FMOVD 64(R5), F4 78 FADD F6, F2 79 FMOVD 56(R5), F1 80 FMADD F4, F2, F0 81 FMOVD 48(R5), F3 82 WFMADB V2, V1, V0, V2 83 FMOVD 40(R5), F1 84 FMOVD 32(R5), F4 85 FMUL F0, F0 86 WFMADB V2, V4, V1, V4 87 WORD $0xB3CD0016 //lgdr %r1,%f6 88 FMOVD 24(R5), F1 89 WFMADB V2, V3, V1, V3 90 FMOVD 16(R5), F1 91 WFMADB V0, V4, V3, V4 92 FMOVD 8(R5), F3 93 WFMADB V2, V1, V3, V1 94 WORD $0xEC3139BC //risbg %r3,%r1,57,128+60,3 95 BYTE $0x03 96 BYTE $0x55 97 WFMADB V0, V4, V1, V0 98 MOVD $exptexp<>+0(SB), R2 99 WORD $0x68432000 //ld %f4,0(%r3,%r2) 100 FMADD F4, F2, F2 101 SLD $48, R1, R2 102 WFMADB V2, V0, V4, V2 103 WORD $0xB3C10002 //ldgr %f0,%r2 104 FMADD F0, F2, F0 105 FMOVD F0, ret+8(FP) 106 RET 107 L16: 108 WFCEDBS V2, V2, V4 109 BVS LEXITTAGexp 110 WORD $0xED205000 //cdb %f2,.L33-.L22(%r5) 111 BYTE $0x00 112 BYTE $0x19 113 BLT L6 114 WFCEDBS V2, V0, V0 115 BVS L13 116 MOVD $expxinf<>+0(SB), R1 117 FMOVD 0(R1), F0 118 FMOVD F0, ret+8(FP) 119 RET 120 L20: 121 WORD $0xB3130020 //lcdbr %f2,%f0 122 BR L2 123 L6: 124 MOVD $expxaddexp<>+0(SB), R1 125 FMOVD 72(R5), F3 126 FMOVD 0(R1), F4 127 WFMSDB V0, V3, V4, V3 128 FMOVD 64(R5), F6 129 FADD F3, F4 130 FMOVD 56(R5), F5 131 WFMADB V4, V6, V0, V6 132 FMOVD 32(R5), F1 133 WFMADB V4, V5, V6, V4 134 FMOVD 40(R5), F5 135 FMUL F6, F6 136 WFMADB V4, V1, V5, V1 137 FMOVD 48(R5), F7 138 WORD $0xB3CD0013 //lgdr %r1,%f3 139 FMOVD 24(R5), F5 140 WFMADB V4, V7, V5, V7 141 FMOVD 16(R5), F5 142 WFMADB V6, V1, V7, V1 143 FMOVD 8(R5), F7 144 WFMADB V4, V5, V7, V5 145 WORD $0xEC3139BC //risbg %r3,%r1,57,128+60,3 146 BYTE $0x03 147 BYTE $0x55 148 WFMADB V6, V1, V5, V6 149 MOVD $exptexp<>+0(SB), R2 150 WFCHDBS V2, V0, V0 151 WORD $0x68132000 //ld %f1,0(%r3,%r2) 152 FMADD F1, F4, F4 153 MOVD $0x4086000000000000, R2 154 WFMADB V4, V6, V1, V4 155 BEQ L21 156 ADDW $0xF000, R1 157 WORD $0xEC21000F //risbgn %r2,%r1,64-64+0,64-64+0+16-1,64-0-16 158 BYTE $0x30 159 BYTE $0x59 160 WORD $0xB3C10002 //ldgr %f0,%r2 161 FMADD F0, F4, F0 162 MOVD $expx4ff<>+0(SB), R3 163 FMOVD 0(R3), F2 164 FMUL F2, F0 165 FMOVD F0, ret+8(FP) 166 RET 167 L13: 168 FMOVD $0, F0 169 FMOVD F0, ret+8(FP) 170 RET 171 L21: 172 ADDW $0x1000, R1 173 WORD $0xEC21000F //risbgn %r2,%r1,64-64+0,64-64+0+16-1,64-0-16 174 BYTE $0x30 175 BYTE $0x59 176 WORD $0xB3C10002 //ldgr %f0,%r2 177 FMADD F0, F4, F0 178 MOVD $expx2ff<>+0(SB), R3 179 FMOVD 0(R3), F2 180 FMUL F2, F0 181 FMOVD F0, ret+8(FP) 182 RET 183 LEXITTAGexp: 184 FMOVD F0, ret+8(FP) 185 RET 186
