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authorDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-28 13:16:40 +0000
committerDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-28 13:16:40 +0000
commit47ab3d4a42e9ab51c465c4322d2ec233f6324e6b (patch)
treea61a0ffd83f4a3def4b36e5c8e99630c559aa723 /src/math/exp_arm64.s
parentInitial commit. (diff)
downloadgolang-1.18-47ab3d4a42e9ab51c465c4322d2ec233f6324e6b.tar.xz
golang-1.18-47ab3d4a42e9ab51c465c4322d2ec233f6324e6b.zip
Adding upstream version 1.18.10.upstream/1.18.10upstream
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'src/math/exp_arm64.s')
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1 files changed, 182 insertions, 0 deletions
diff --git a/src/math/exp_arm64.s b/src/math/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 6.93147180369123816490e-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