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exp_arm64.s
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exp_arm64.s
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// Copyright 2017 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
#define Ln2Hi 6.9313812256e-01
#define Ln2Lo 9.0580006145e-06
#define Log2e 1.4426950216e+00
#define Overflow 7.097827e+02
#define Underflow -7.451332e+02
#define Overflow2 1.024000e+03
#define Underflow2 -1.0740e+03
#define NearZero 0x317fffff // 2**-28
#define PosInf 0x7f800000
#define FracMask 0x07fffff
#define C1 0x34000000 // 2**-23
#define P1 1.6666667163e-01 // 0x3FC55555; 0x55555555
#define P2 -2.7777778450e-03 // 0xBF66C16C; 0x16BEBD93
#define P3 6.6137559770e-05 // 0x3F11566A; 0xAF25DE2C
#define P4 -1.6533901999e-06 // 0xBEBBBD41; 0xC5D26BF1
#define P5 4.1381369442e-08 // 0x3E663769; 0x72BEA4D0
// Exp returns e**x, the base-e exponential of x.
// This is an assembly implementation of the method used for function Exp in file exp.go.
//
// func Exp(x float32) float32
TEXT ·Exp(SB),$0-16
FMOVS x+0(FP), F0 // F0 = x
FCMPS F0, F0
BNE isNaN // x = NaN, return NaN
FMOVS $Overflow, F1
FCMPS F1, F0
BGT overflow // x > Overflow, return PosInf
FMOVS $Underflow, F1
FCMPS F1, F0
BLT underflow // x < Underflow, return 0
MOVW $NearZero, R0
FMOVS R0, F2
FABSS F0, F3
FMOVS $1.0, F1 // F1 = 1.0
FCMPS F2, F3
BLT nearzero // fabs(x) < NearZero, return 1 + x
// argument reduction, x = k*ln2 + r, |r| <= 0.5*ln2
// computed as r = hi - lo for extra precision.
FMOVS $Log2e, F2
FMOVS $0.5, F3
FNMSUBS F0, F3, F2, F4 // Log2e*x - 0.5
FMADDS F0, F3, F2, F3 // Log2e*x + 0.5
FCMPS $0.0, F0
FCSELS LT, F4, F3, F3 // F3 = k
FCVTZSS F3, R1 // R1 = int(k)
SCVTFS R1, F3 // F3 = float32(int(k))
FMOVS $Ln2Hi, F4 // F4 = Ln2Hi
FMOVS $Ln2Lo, F5 // F5 = Ln2Lo
FMSUBS F3, F0, F4, F4 // F4 = hi = x - float32(int(k))*Ln2Hi
FMULS F3, F5 // F5 = lo = float32(int(k)) * Ln2Lo
FSUBS F5, F4, F6 // F6 = r = hi - lo
FMULS F6, F6, F7 // F7 = t = r * r
// compute y
FMOVS $P5, F8 // F8 = P5
FMOVS $P4, F9 // F9 = P4
FMADDS F7, F9, F8, F13 // P4+t*P5
FMOVS $P3, F10 // F10 = P3
FMADDS F7, F10, F13, F13 // P3+t*(P4+t*P5)
FMOVS $P2, F11 // F11 = P2
FMADDS F7, F11, F13, F13 // P2+t*(P3+t*(P4+t*P5))
FMOVS $P1, F12 // F12 = P1
FMADDS F7, F12, F13, F13 // P1+t*(P2+t*(P3+t*(P4+t*P5)))
FMSUBS F7, F6, F13, F13 // F13 = c = r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))))
FMOVS $2.0, F14
FSUBS F13, F14
FMULS F6, F13, F15
FDIVS F14, F15 // F15 = (r*c)/(2-c)
FSUBS F15, F5, F15 // lo-(r*c)/(2-c)
FSUBS F4, F15, F15 // (lo-(r*c)/(2-c))-hi
FSUBS F15, F1, F16 // F16 = y = 1-((lo-(r*c)/(2-c))-hi)
// inline Ldexp(y, k), benefit:
// 1, no parameter pass overhead.
// 2, skip unnecessary checks for Inf/NaN/Zero
FMOVS F16, R0
ANDS $FracMask, R0, R2 // fraction
LSRW $23, R0, R5 // exponent
ADDS R1, R5 // R1 = int(k)
CMPW $1, R5
BGE normal
ADDS $23, R5 // denormal
MOVW $C1, R8
FMOVS R8, F1 // m = 2**-23
normal:
ORRW R5<<23, R2, R0
FMOVS R0, F0
FMULS F1, F0 // return m * x
FMOVS F0, ret+8(FP)
RET
nearzero:
FADDS F1, F0
isNaN:
FMOVS F0, ret+8(FP)
RET
underflow:
MOVW ZR, ret+8(FP)
RET
overflow:
MOVW $PosInf, R0
MOVW R0, ret+8(FP)
RET
// Exp2 returns 2**x, the base-2 exponential of x.
// This is an assembly implementation of the method used for function Exp2 in file exp.go.
//
// func Exp2(x float32) float32
TEXT ·Exp2(SB),$0-16
FMOVS x+0(FP), F0 // F0 = x
FCMPS F0, F0
BNE isNaN // x = NaN, return NaN
FMOVS $Overflow2, F1
FCMPS F1, F0
BGT overflow // x > Overflow, return PosInf
FMOVS $Underflow2, F1
FCMPS F1, F0
BLT underflow // x < Underflow, return 0
// argument reduction; x = r*lg(e) + k with |r| <= ln(2)/2
// computed as r = hi - lo for extra precision.
FMOVS $0.5, F2
FSUBS F2, F0, F3 // x + 0.5
FADDS F2, F0, F4 // x - 0.5
FCMPS $0.0, F0
FCSELS LT, F3, F4, F3 // F3 = k
FCVTZSS F3, R1 // R1 = int(k)
SCVTFS R1, F3 // F3 = float32(int(k))
FSUBS F3, F0, F3 // t = x - float32(int(k))
FMOVS $Ln2Hi, F4 // F4 = Ln2Hi
FMOVS $Ln2Lo, F5 // F5 = Ln2Lo
FMULS F3, F4 // F4 = hi = t * Ln2Hi
FNMULS F3, F5 // F5 = lo = -t * Ln2Lo
FSUBS F5, F4, F6 // F6 = r = hi - lo
FMULS F6, F6, F7 // F7 = t = r * r
// compute y
FMOVS $P5, F8 // F8 = P5
FMOVS $P4, F9 // F9 = P4
FMADDS F7, F9, F8, F13 // P4+t*P5
FMOVS $P3, F10 // F10 = P3
FMADDS F7, F10, F13, F13 // P3+t*(P4+t*P5)
FMOVS $P2, F11 // F11 = P2
FMADDS F7, F11, F13, F13 // P2+t*(P3+t*(P4+t*P5))
FMOVS $P1, F12 // F12 = P1
FMADDS F7, F12, F13, F13 // P1+t*(P2+t*(P3+t*(P4+t*P5)))
FMSUBS F7, F6, F13, F13 // F13 = c = r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))))
FMOVS $2.0, F14
FSUBS F13, F14
FMULS F6, F13, F15
FDIVS F14, F15 // F15 = (r*c)/(2-c)
FMOVS $1.0, F1 // F1 = 1.0
FSUBS F15, F5, F15 // lo-(r*c)/(2-c)
FSUBS F4, F15, F15 // (lo-(r*c)/(2-c))-hi
FSUBS F15, F1, F16 // F16 = y = 1-((lo-(r*c)/(2-c))-hi)
// inline Ldexp(y, k), benefit:
// 1, no parameter pass overhead.
// 2, skip unnecessary checks for Inf/NaN/Zero
FMOVS F16, R0
ANDS $FracMask, R0, R2 // fraction
LSRW $23, R0, R5 // exponent
ADDS R1, R5 // R1 = int(k)
CMPW $1, R5
BGE normal
ADDS $23, R5 // denormal
MOVW $C1, R8
FMOVS R8, F1 // m = 2**-52
normal:
ORRW R5<<23, R2, R0
FMOVS R0, F0
FMULS F1, F0 // return m * x
isNaN:
FMOVS F0, ret+8(FP)
RET
underflow:
MOVW ZR, ret+8(FP)
RET
overflow:
MOVW $PosInf, R0
MOVW R0, ret+8(FP)
RET