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Editing: exp_arm64.s
// 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
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