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      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 expm1rodataL22<> + 0(SB)/8, $-1.0
      9 DATA expm1rodataL22<> + 8(SB)/8, $800.0E+00
     10 DATA expm1rodataL22<> + 16(SB)/8, $1.0
     11 DATA expm1rodataL22<> + 24(SB)/8, $-.231904681384629956E-16
     12 DATA expm1rodataL22<> + 32(SB)/8, $0.50000000000000029671E+00
     13 DATA expm1rodataL22<> + 40(SB)/8, $0.16666666666666676570E+00
     14 DATA expm1rodataL22<> + 48(SB)/8, $0.83333333323590973444E-02
     15 DATA expm1rodataL22<> + 56(SB)/8, $0.13889096526400683566E-02
     16 DATA expm1rodataL22<> + 64(SB)/8, $0.41666666661701152924E-01
     17 DATA expm1rodataL22<> + 72(SB)/8, $0.19841562053987360264E-03
     18 DATA expm1rodataL22<> + 80(SB)/8, $-.693147180559945286E+00
     19 DATA expm1rodataL22<> + 88(SB)/8, $0.144269504088896339E+01
     20 DATA expm1rodataL22<> + 96(SB)/8, $704.0E+00
     21 GLOBL expm1rodataL22<> + 0(SB), RODATA, $104
     22 
     23 DATA expm1xmone<> + 0(SB)/8, $0xbff0000000000000
     24 GLOBL expm1xmone<> + 0(SB), RODATA, $8
     25 DATA expm1xinf<> + 0(SB)/8, $0x7ff0000000000000
     26 GLOBL expm1xinf<> + 0(SB), RODATA, $8
     27 DATA expm1x4ff<> + 0(SB)/8, $0x4ff0000000000000
     28 GLOBL expm1x4ff<> + 0(SB), RODATA, $8
     29 DATA expm1x2ff<> + 0(SB)/8, $0x2ff0000000000000
     30 GLOBL expm1x2ff<> + 0(SB), RODATA, $8
     31 DATA expm1xaddexp<> + 0(SB)/8, $0xc2f0000100003ff0
     32 GLOBL expm1xaddexp<> + 0(SB), RODATA, $8
     33 
     34 // Log multipliers table
     35 DATA expm1tab<> + 0(SB)/8, $0.0
     36 DATA expm1tab<> + 8(SB)/8, $-.171540871271399150E-01
     37 DATA expm1tab<> + 16(SB)/8, $-.306597931864376363E-01
     38 DATA expm1tab<> + 24(SB)/8, $-.410200970469965021E-01
     39 DATA expm1tab<> + 32(SB)/8, $-.486343079978231466E-01
     40 DATA expm1tab<> + 40(SB)/8, $-.538226193725835820E-01
     41 DATA expm1tab<> + 48(SB)/8, $-.568439602538111520E-01
     42 DATA expm1tab<> + 56(SB)/8, $-.579091847395528847E-01
     43 DATA expm1tab<> + 64(SB)/8, $-.571909584179366341E-01
     44 DATA expm1tab<> + 72(SB)/8, $-.548312665987204407E-01
     45 DATA expm1tab<> + 80(SB)/8, $-.509471843643441085E-01
     46 DATA expm1tab<> + 88(SB)/8, $-.456353588448863359E-01
     47 DATA expm1tab<> + 96(SB)/8, $-.389755254243262365E-01
     48 DATA expm1tab<> + 104(SB)/8, $-.310332908285244231E-01
     49 DATA expm1tab<> + 112(SB)/8, $-.218623539150173528E-01
     50 DATA expm1tab<> + 120(SB)/8, $-.115062908917949451E-01
     51 GLOBL expm1tab<> + 0(SB), RODATA, $128
     52 
     53 // Expm1 returns e**x - 1, the base-e exponential of x minus 1.
     54 // It is more accurate than Exp(x) - 1 when x is near zero.
     55 //
     56 // Special cases are:
     57 //      Expm1(+Inf) = +Inf
     58 //      Expm1(-Inf) = -1
     59 //      Expm1(NaN) = NaN
     60 // Very large values overflow to -1 or +Inf.
     61 // The algorithm used is minimax polynomial approximation using a table of
     62 // polynomial coefficients determined with a Remez exchange algorithm.
     63 
     64 TEXT	expm1Asm(SB), NOSPLIT, $0-16
     65 	FMOVD	x+0(FP), F0
     66 	MOVD	$expm1rodataL22<>+0(SB), R5
     67 	WORD	$0xB3120000	//ltdbr	%f0,%f0
     68 	BLTU	L20
     69 	FMOVD	F0, F2
     70 L2:
     71 	WORD	$0xED205060	//cdb	%f2,.L23-.L22(%r5)
     72 	BYTE	$0x00
     73 	BYTE	$0x19
     74 	BGE	L16
     75 	BVS	L16
     76 	WFCEDBS	V2, V2, V2
     77 	BVS	LEXITTAGexpm1
     78 	MOVD	$expm1xaddexp<>+0(SB), R1
     79 	FMOVD	88(R5), F1
     80 	FMOVD	0(R1), F2
     81 	WFMSDB	V0, V1, V2, V1
     82 	FMOVD	80(R5), F6
     83 	WFADB	V1, V2, V4
     84 	FMOVD	72(R5), F2
     85 	FMADD	F6, F4, F0
     86 	FMOVD	64(R5), F3
     87 	FMOVD	56(R5), F6
     88 	FMOVD	48(R5), F5
     89 	FMADD	F2, F0, F6
     90 	WFMADB	V0, V5, V3, V5
     91 	WFMDB	V0, V0, V2
     92 	WORD	$0xB3CD0011	//lgdr	%r1,%f1
     93 	WFMADB	V6, V2, V5, V6
     94 	FMOVD	40(R5), F3
     95 	FMOVD	32(R5), F5
     96 	WFMADB	V0, V3, V5, V3
     97 	FMOVD	24(R5), F5
     98 	WFMADB	V2, V6, V3, V2
     99 	FMADD	F5, F4, F0
    100 	FMOVD	16(R5), F6
    101 	WFMADB	V0, V2, V6, V2
    102 	WORD	$0xEC3139BC	//risbg	%r3,%r1,57,128+60,3
    103 	BYTE	$0x03
    104 	BYTE	$0x55
    105 	WORD	$0xB3130022	//lcdbr	%f2,%f2
    106 	MOVD	$expm1tab<>+0(SB), R2
    107 	WORD	$0x68432000	//ld	%f4,0(%r3,%r2)
    108 	FMADD	F4, F0, F0
    109 	SLD	$48, R1, R2
    110 	WFMSDB	V2, V0, V4, V0
    111 	WORD	$0xB3C10042	//ldgr	%f4,%r2
    112 	WORD	$0xB3130000	//lcdbr	%f0,%f0
    113 	FSUB	F4, F6
    114 	WFMSDB	V0, V4, V6, V0
    115 	FMOVD	F0, ret+8(FP)
    116 	RET
    117 L16:
    118 	WFCEDBS	V2, V2, V4
    119 	BVS	LEXITTAGexpm1
    120 	WORD	$0xED205008	//cdb	%f2,.L34-.L22(%r5)
    121 	BYTE	$0x00
    122 	BYTE	$0x19
    123 	BLT	L6
    124 	WFCEDBS	V2, V0, V0
    125 	BVS	L7
    126 	MOVD	$expm1xinf<>+0(SB), R1
    127 	FMOVD	0(R1), F0
    128 	FMOVD	F0, ret+8(FP)
    129 	RET
    130 L20:
    131 	WORD	$0xB3130020	//lcdbr	%f2,%f0
    132 	BR	L2
    133 L6:
    134 	MOVD	$expm1xaddexp<>+0(SB), R1
    135 	FMOVD	88(R5), F5
    136 	FMOVD	0(R1), F4
    137 	WFMSDB	V0, V5, V4, V5
    138 	FMOVD	80(R5), F3
    139 	WFADB	V5, V4, V1
    140 	VLEG	$0, 48(R5), V16
    141 	WFMADB	V1, V3, V0, V3
    142 	FMOVD	56(R5), F4
    143 	FMOVD	64(R5), F7
    144 	FMOVD	72(R5), F6
    145 	WFMADB	V3, V16, V7, V16
    146 	WFMADB	V3, V6, V4, V6
    147 	WFMDB	V3, V3, V4
    148 	MOVD	$expm1tab<>+0(SB), R2
    149 	WFMADB	V6, V4, V16, V6
    150 	VLEG	$0, 32(R5), V16
    151 	FMOVD	40(R5), F7
    152 	WFMADB	V3, V7, V16, V7
    153 	VLEG	$0, 24(R5), V16
    154 	WFMADB	V4, V6, V7, V4
    155 	WFMADB	V1, V16, V3, V1
    156 	FMOVD	16(R5), F6
    157 	FMADD	F4, F1, F6
    158 	WORD	$0xB3CD0015	//lgdr	%r1,%f5
    159 	WORD	$0xB3130066	//lcdbr	%f6,%f6
    160 	WORD	$0xEC3139BC	//risbg	%r3,%r1,57,128+60,3
    161 	BYTE	$0x03
    162 	BYTE	$0x55
    163 	WORD	$0x68432000	//ld	%f4,0(%r3,%r2)
    164 	FMADD	F4, F1, F1
    165 	MOVD	$0x4086000000000000, R2
    166 	FMSUB	F1, F6, F4
    167 	WORD	$0xB3130044	//lcdbr	%f4,%f4
    168 	WFCHDBS	V2, V0, V0
    169 	BEQ	L21
    170 	ADDW	$0xF000, R1
    171 	WORD	$0xEC21000F	//risbgn	%r2,%r1,64-64+0,64-64+0+16-1,64-0-16
    172 	BYTE	$0x30
    173 	BYTE	$0x59
    174 	WORD	$0xB3C10002	//ldgr	%f0,%r2
    175 	FMADD	F0, F4, F0
    176 	MOVD	$expm1x4ff<>+0(SB), R3
    177 	FMOVD	0(R5), F4
    178 	FMOVD	0(R3), F2
    179 	WFMADB	V2, V0, V4, V0
    180 	FMOVD	F0, ret+8(FP)
    181 	RET
    182 L7:
    183 	MOVD	$expm1xmone<>+0(SB), R1
    184 	FMOVD	0(R1), F0
    185 	FMOVD	F0, ret+8(FP)
    186 	RET
    187 L21:
    188 	ADDW	$0x1000, R1
    189 	WORD	$0xEC21000F	//risbgn	%r2,%r1,64-64+0,64-64+0+16-1,64-0-16
    190 	BYTE	$0x30
    191 	BYTE	$0x59
    192 	WORD	$0xB3C10002	//ldgr	%f0,%r2
    193 	FMADD	F0, F4, F0
    194 	MOVD	$expm1x2ff<>+0(SB), R3
    195 	FMOVD	0(R5), F4
    196 	FMOVD	0(R3), F2
    197 	WFMADB	V2, V0, V4, V0
    198 	FMOVD	F0, ret+8(FP)
    199 	RET
    200 LEXITTAGexpm1:
    201 	FMOVD	F0, ret+8(FP)
    202 	RET
    203