// 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 6.93147180369123816490e-01
#define Ln2Lo 1.90821492927058770002e-10
#define Log2e 1.44269504088896338700e+00
#define Overflow 7.09782712893383973096e+02
#define Underflow -7.45133219101941108420e+02
#define Overflow2 1.0239999999999999e+03
#define Underflow2 -1.0740e+03
#define NearZero 0x3e30000000000000 // 2**-28
#define PosInf 0x7ff0000000000000
#define FracMask 0x000fffffffffffff
#define C1 0x3cb0000000000000 // 2**-52
#define P1 1.66666666666666657415e-01 // 0x3FC55555; 0x55555555
#define P2 -2.77777777770155933842e-03 // 0xBF66C16C; 0x16BEBD93
#define P3 6.61375632143793436117e-05 // 0x3F11566A; 0xAF25DE2C
#define P4 -1.65339022054652515390e-06 // 0xBEBBBD41; 0xC5D26BF1
#define P5 4.13813679705723846039e-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 float64) float64
TEXT ·archExp(SB),$0-16
FMOVD x+0(FP), F0 // F0 = x
FCMPD F0, F0
BNE isNaN // x = NaN, return NaN
FMOVD $Overflow, F1
FCMPD F1, F0
BGT overflow // x > Overflow, return PosInf
FMOVD $Underflow, F1
FCMPD F1, F0
BLT underflow // x < Underflow, return 0
MOVD $NearZero, R0
FMOVD R0, F2
FABSD F0, F3
FMOVD $1.0, F1 // F1 = 1.0
FCMPD 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.
FMOVD $Log2e, F2
FMOVD $0.5, F3
FNMSUBD F0, F3, F2, F4 // Log2e*x - 0.5
FMADDD F0, F3, F2, F3 // Log2e*x + 0.5
FCMPD $0.0, F0
FCSELD LT, F4, F3, F3 // F3 = k
FCVTZSD F3, R1 // R1 = int(k)
SCVTFD R1, F3 // F3 = float64(int(k))
FMOVD $Ln2Hi, F4 // F4 = Ln2Hi
FMOVD $Ln2Lo, F5 // F5 = Ln2Lo
FMSUBD F3, F0, F4, F4 // F4 = hi = x - float64(int(k))*Ln2Hi
FMULD F3, F5 // F5 = lo = float64(int(k)) * Ln2Lo
FSUBD F5, F4, F6 // F6 = r = hi - lo
FMULD F6, F6, F7 // F7 = t = r * r
// compute y
FMOVD $P5, F8 // F8 = P5
FMOVD $P4, F9 // F9 = P4
FMADDD F7, F9, F8, F13 // P4+t*P5
FMOVD $P3, F10 // F10 = P3
FMADDD F7, F10, F13, F13 // P3+t*(P4+t*P5)
FMOVD $P2, F11 // F11 = P2
FMADDD F7, F11, F13, F13 // P2+t*(P3+t*(P4+t*P5))
FMOVD $P1, F12 // F12 = P1
FMADDD F7, F12, F13, F13 // P1+t*(P2+t*(P3+t*(P4+t*P5)))
FMSUBD F7, F6, F13, F13 // F13 = c = r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))))
FMOVD $2.0, F14
FSUBD F13, F14
FMULD F6, F13, F15
FDIVD F14, F15 // F15 = (r*c)/(2-c)
FSUBD F15, F5, F15 // lo-(r*c)/(2-c)
FSUBD F4, F15, F15 // (lo-(r*c)/(2-c))-hi
FSUBD 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
FMOVD F16, R0
AND $FracMask, R0, R2 // fraction
LSR $52, R0, R5 // exponent
ADD R1, R5 // R1 = int(k)
CMP $1, R5
BGE normal
ADD $52, R5 // denormal
MOVD $C1, R8
FMOVD R8, F1 // m = 2**-52
normal:
ORR R5<<52, R2, R0
FMOVD R0, F0
FMULD F1, F0 // return m * x
FMOVD F0, ret+8(FP)
RET
nearzero:
FADDD F1, F0
isNaN:
FMOVD F0, ret+8(FP)
RET
underflow:
MOVD ZR, ret+8(FP)
RET
overflow:
MOVD $PosInf, R0
MOVD 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 float64) float64
TEXT ·archExp2(SB),$0-16
FMOVD x+0(FP), F0 // F0 = x
FCMPD F0, F0
BNE isNaN // x = NaN, return NaN
FMOVD $Overflow2, F1
FCMPD F1, F0
BGT overflow // x > Overflow, return PosInf
FMOVD $Underflow2, F1
FCMPD 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.
FMOVD $0.5, F2
FSUBD F2, F0, F3 // x + 0.5
FADDD F2, F0, F4 // x - 0.5
FCMPD $0.0, F0
FCSELD LT, F3, F4, F3 // F3 = k
FCVTZSD F3, R1 // R1 = int(k)
SCVTFD R1, F3 // F3 = float64(int(k))
FSUBD F3, F0, F3 // t = x - float64(int(k))
FMOVD $Ln2Hi, F4 // F4 = Ln2Hi
FMOVD $Ln2Lo, F5 // F5 = Ln2Lo
FMULD F3, F4 // F4 = hi = t * Ln2Hi
FNMULD F3, F5 // F5 = lo = -t * Ln2Lo
FSUBD F5, F4, F6 // F6 = r = hi - lo
FMULD F6, F6, F7 // F7 = t = r * r
// compute y
FMOVD $P5, F8 // F8 = P5
FMOVD $P4, F9 // F9 = P4
FMADDD F7, F9, F8, F13 // P4+t*P5
FMOVD $P3, F10 // F10 = P3
FMADDD F7, F10, F13, F13 // P3+t*(P4+t*P5)
FMOVD $P2, F11 // F11 = P2
FMADDD F7, F11, F13, F13 // P2+t*(P3+t*(P4+t*P5))
FMOVD $P1, F12 // F12 = P1
FMADDD F7, F12, F13, F13 // P1+t*(P2+t*(P3+t*(P4+t*P5)))
FMSUBD F7, F6, F13, F13 // F13 = c = r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))))
FMOVD $2.0, F14
FSUBD F13, F14
FMULD F6, F13, F15
FDIVD F14, F15 // F15 = (r*c)/(2-c)
FMOVD $1.0, F1 // F1 = 1.0
FSUBD F15, F5, F15 // lo-(r*c)/(2-c)
FSUBD F4, F15, F15 // (lo-(r*c)/(2-c))-hi
FSUBD 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
FMOVD F16, R0
AND $FracMask, R0, R2 // fraction
LSR $52, R0, R5 // exponent
ADD R1, R5 // R1 = int(k)
CMP $1, R5
BGE normal
ADD $52, R5 // denormal
MOVD $C1, R8
FMOVD R8, F1 // m = 2**-52
normal:
ORR R5<<52, R2, R0
FMOVD R0, F0
FMULD F1, F0 // return m * x
isNaN:
FMOVD F0, ret+8(FP)
RET
underflow:
MOVD ZR, ret+8(FP)
RET
overflow:
MOVD $PosInf, R0
MOVD R0, ret+8(FP)
RET
