1// Copyright 2010 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#define HSqrt2 7.07106781186547524401e-01 // sqrt(2)/2
8#define Ln2Hi  6.93147180369123816490e-01 // 0x3fe62e42fee00000
9#define Ln2Lo  1.90821492927058770002e-10 // 0x3dea39ef35793c76
10#define L1     6.666666666666735130e-01   // 0x3FE5555555555593
11#define L2     3.999999999940941908e-01   // 0x3FD999999997FA04
12#define L3     2.857142874366239149e-01   // 0x3FD2492494229359
13#define L4     2.222219843214978396e-01   // 0x3FCC71C51D8E78AF
14#define L5     1.818357216161805012e-01   // 0x3FC7466496CB03DE
15#define L6     1.531383769920937332e-01   // 0x3FC39A09D078C69F
16#define L7     1.479819860511658591e-01   // 0x3FC2F112DF3E5244
17#define NaN    0x7FF8000000000001
18#define NegInf 0xFFF0000000000000
19#define PosInf 0x7FF0000000000000
20
21// func Log(x float64) float64
22TEXT ·archLog(SB),NOSPLIT,$0
23	// test bits for special cases
24	MOVQ    x+0(FP), BX
25	MOVQ    $~(1<<63), AX // sign bit mask
26	ANDQ    BX, AX
27	JEQ     isZero
28	MOVQ    $0, AX
29	CMPQ    AX, BX
30	JGT     isNegative
31	MOVQ    $PosInf, AX
32	CMPQ    AX, BX
33	JLE     isInfOrNaN
34	// f1, ki := math.Frexp(x); k := float64(ki)
35	MOVQ    BX, X0
36	MOVQ    $0x000FFFFFFFFFFFFF, AX
37	MOVQ    AX, X2
38	ANDPD   X0, X2
39	MOVSD   $0.5, X0 // 0x3FE0000000000000
40	ORPD    X0, X2 // X2= f1
41	SHRQ    $52, BX
42	ANDL    $0x7FF, BX
43	SUBL    $0x3FE, BX
44	XORPS   X1, X1 // break dependency for CVTSL2SD
45	CVTSL2SD BX, X1 // x1= k, x2= f1
46	// if f1 < math.Sqrt2/2 { k -= 1; f1 *= 2 }
47	MOVSD   $HSqrt2, X0 // x0= 0.7071, x1= k, x2= f1
48	CMPSD   X2, X0, 5 // cmpnlt; x0= 0 or ^0, x1= k, x2 = f1
49	MOVSD   $1.0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 1
50	ANDPD   X0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 0 or 1
51	SUBSD   X3, X1 // x0= 0 or ^0, x1= k, x2 = f1, x3= 0 or 1
52	MOVSD   $1.0, X0 // x0= 1, x1= k, x2= f1, x3= 0 or 1
53	ADDSD   X0, X3 // x0= 1, x1= k, x2= f1, x3= 1 or 2
54	MULSD   X3, X2 // x0= 1, x1= k, x2= f1
55	// f := f1 - 1
56	SUBSD   X0, X2 // x1= k, x2= f
57	// s := f / (2 + f)
58	MOVSD   $2.0, X0
59	ADDSD   X2, X0
60	MOVAPD  X2, X3
61	DIVSD   X0, X3 // x1=k, x2= f, x3= s
62	// s2 := s * s
63	MOVAPD  X3, X4 // x1= k, x2= f, x3= s
64	MULSD   X4, X4 // x1= k, x2= f, x3= s, x4= s2
65	// s4 := s2 * s2
66	MOVAPD  X4, X5 // x1= k, x2= f, x3= s, x4= s2
67	MULSD   X5, X5 // x1= k, x2= f, x3= s, x4= s2, x5= s4
68	// t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))
69	MOVSD   $L7, X6
70	MULSD   X5, X6
71	ADDSD   $L5, X6
72	MULSD   X5, X6
73	ADDSD   $L3, X6
74	MULSD   X5, X6
75	ADDSD   $L1, X6
76	MULSD   X6, X4 // x1= k, x2= f, x3= s, x4= t1, x5= s4
77	// t2 := s4 * (L2 + s4*(L4+s4*L6))
78	MOVSD   $L6, X6
79	MULSD   X5, X6
80	ADDSD   $L4, X6
81	MULSD   X5, X6
82	ADDSD   $L2, X6
83	MULSD   X6, X5 // x1= k, x2= f, x3= s, x4= t1, x5= t2
84	// R := t1 + t2
85	ADDSD   X5, X4 // x1= k, x2= f, x3= s, x4= R
86	// hfsq := 0.5 * f * f
87	MOVSD   $0.5, X0
88	MULSD   X2, X0
89	MULSD   X2, X0 // x0= hfsq, x1= k, x2= f, x3= s, x4= R
90	// return k*Ln2Hi - ((hfsq - (s*(hfsq+R) + k*Ln2Lo)) - f)
91	ADDSD   X0, X4 // x0= hfsq, x1= k, x2= f, x3= s, x4= hfsq+R
92	MULSD   X4, X3 // x0= hfsq, x1= k, x2= f, x3= s*(hfsq+R)
93	MOVSD   $Ln2Lo, X4
94	MULSD   X1, X4 // x4= k*Ln2Lo
95	ADDSD   X4, X3 // x0= hfsq, x1= k, x2= f, x3= s*(hfsq+R)+k*Ln2Lo
96	SUBSD   X3, X0 // x0= hfsq-(s*(hfsq+R)+k*Ln2Lo), x1= k, x2= f
97	SUBSD   X2, X0 // x0= (hfsq-(s*(hfsq+R)+k*Ln2Lo))-f, x1= k
98	MULSD   $Ln2Hi, X1 // x0= (hfsq-(s*(hfsq+R)+k*Ln2Lo))-f, x1= k*Ln2Hi
99	SUBSD   X0, X1 // x1= k*Ln2Hi-((hfsq-(s*(hfsq+R)+k*Ln2Lo))-f)
100  	MOVSD   X1, ret+8(FP)
101	RET
102isInfOrNaN:
103	MOVQ    BX, ret+8(FP) // +Inf or NaN, return x
104	RET
105isNegative:
106	MOVQ    $NaN, AX
107	MOVQ    AX, ret+8(FP) // return NaN
108	RET
109isZero:
110	MOVQ    $NegInf, AX
111	MOVQ    AX, ret+8(FP) // return -Inf
112	RET
113