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| -rw-r--r-- | src/math/exp_arm64.s | 182 |
1 files changed, 182 insertions, 0 deletions
diff --git a/src/math/exp_arm64.s b/src/math/exp_arm64.s new file mode 100644 index 0000000..19736cb --- /dev/null +++ b/src/math/exp_arm64.s @@ -0,0 +1,182 @@ +// 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 ·Exp(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 ·Exp2(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 |