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https://github.com/golang/go
synced 2024-11-22 01:44:40 -07:00
math: Pow special cases (signed zero, IEEE 754-2008)
Also added more tests for acosh, hypot, log, log10, log2 in all_test.go. R=rsc CC=golang-dev https://golang.org/cl/1417041
This commit is contained in:
Charles L. Dorian
Russ Cox
parent
6372bbbf3e
commit
3d4c97b82c
@ -627,26 +627,28 @@ var acosSC = []float64{
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var vfacoshSC = []float64{
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Inf(-1),
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0.5,
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1,
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Inf(1),
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NaN(),
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}
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var acoshSC = []float64{
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NaN(),
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NaN(),
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0,
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Inf(1),
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NaN(),
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}
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var vfasinSC = []float64{
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-Pi,
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Pi,
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NaN(),
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}
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var asinSC = []float64{
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NaN(),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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NaN(),
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NaN(),
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@ -654,14 +656,14 @@ var asinSC = []float64{
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var vfasinhSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var asinhSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -669,14 +671,14 @@ var asinhSC = []float64{
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var vfatanSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var atanSC = []float64{
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-Pi / 2,
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Pi / 2,
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NaN(),
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@ -686,7 +688,7 @@ var vfatanhSC = []float64{
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Inf(-1),
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-Pi,
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-1,
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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1,
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Pi,
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@ -697,7 +699,7 @@ var atanhSC = []float64{
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NaN(),
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NaN(),
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -715,16 +717,16 @@ var vfatan2SC = [][2]float64{
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[2]float64{-Pi, 0},
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[2]float64{-Pi, Inf(1)},
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[2]float64{-Pi, NaN()},
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[2]float64{-1 / Inf(1), Inf(-1)}, // -0, -Inf
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[2]float64{-1 / Inf(1), -Pi}, // -0, -Pi
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[2]float64{-1 / Inf(1), -1 / Inf(1)}, // -0, -0
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[2]float64{-1 / Inf(1), 0}, // -0, +0
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[2]float64{-1 / Inf(1), +Pi}, // -0, +Pi
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[2]float64{-1 / Inf(1), Inf(1)}, // -0, +Inf
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[2]float64{-1 / Inf(1), NaN()}, // -0, NaN
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[2]float64{Copysign(0, -1), Inf(-1)},
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[2]float64{Copysign(0, -1), -Pi},
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[2]float64{Copysign(0, -1), Copysign(0, -1)},
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[2]float64{Copysign(0, -1), 0},
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[2]float64{Copysign(0, -1), +Pi},
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[2]float64{Copysign(0, -1), Inf(1)},
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[2]float64{Copysign(0, -1), NaN()},
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[2]float64{0, Inf(-1)},
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[2]float64{0, -Pi},
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[2]float64{0, -1 / Inf(1)}, // +0, -0
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[2]float64{0, Copysign(0, -1)},
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[2]float64{0, 0},
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[2]float64{0, +Pi},
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[2]float64{0, Inf(1)},
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@ -750,14 +752,14 @@ var atan2SC = []float64{
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NaN(), // atan2(-Inf, NaN)
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-Pi, // atan2(-Pi, -Inf)
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-Pi / 2, // atan2(-Pi, +0)
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-1 / Inf(1), // -0 = atan2(-Pi, Inf)
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Copysign(0, -1), // atan2(-Pi, Inf)
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NaN(), // atan2(-Pi, NaN)
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-Pi, // atan2(-0, -Inf)
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-Pi, // atan2(-0, -Pi)
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-Pi, // atan2(-0, -0)
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-1 / Inf(1), // atan2(-0, +0)
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-1 / Inf(1), // atan2(-0, +Pi)
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-1 / Inf(1), // atan2(-0, +Inf)
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Copysign(0, -1), // atan2(-0, +0)
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Copysign(0, -1), // atan2(-0, +Pi)
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Copysign(0, -1), // atan2(-0, +Inf)
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NaN(), // atan2(-0, NaN)
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Pi, // atan2(+0, -Inf)
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Pi, // atan2(+0, -Pi)
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@ -781,14 +783,14 @@ var atan2SC = []float64{
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var vfcbrtSC = []float64{
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Inf(-1),
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-1 / Inf(1),
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var cbrtSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -796,14 +798,14 @@ var cbrtSC = []float64{
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var vfceilSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var ceilSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -833,7 +835,7 @@ var cosSC = []float64{
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var vfcoshSC = []float64{
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Inf(-1),
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-1 / Inf(1),
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -848,14 +850,14 @@ var coshSC = []float64{
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var vferfSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var erfSC = []float64{
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-1,
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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1,
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NaN(),
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@ -885,14 +887,14 @@ var expSC = []float64{
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var vfexpm1SC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var expm1SC = []float64{
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-1,
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-1 / Inf(1),
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -900,7 +902,7 @@ var expm1SC = []float64{
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var vffabsSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -924,10 +926,10 @@ var vffmodSC = [][2]float64{
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[2]float64{-Pi, 0},
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[2]float64{-Pi, Inf(1)},
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[2]float64{-Pi, NaN()},
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[2]float64{-1 / Inf(1), Inf(-1)}, // -0, -Inf
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[2]float64{-1 / Inf(1), 0}, // -0, 0
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[2]float64{-1 / Inf(1), Inf(1)}, // -0, Inf
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[2]float64{-1 / Inf(1), NaN()}, // -0, NaN
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[2]float64{Copysign(0, -1), Inf(-1)},
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[2]float64{Copysign(0, -1), 0},
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[2]float64{Copysign(0, -1), Inf(1)},
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[2]float64{Copysign(0, -1), NaN()},
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[2]float64{0, Inf(-1)},
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[2]float64{0, 0},
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[2]float64{0, Inf(1)},
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@ -960,9 +962,9 @@ var fmodSC = []float64{
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NaN(), // fmod(-Pi, 0)
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-Pi, // fmod(-Pi, +Inf)
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NaN(), // fmod(-Pi, NaN)
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-1 / Inf(1), // -0 = fmod(-0, -Inf)
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Copysign(0, -1), // fmod(-0, -Inf)
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NaN(), // fmod(-0, 0)
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-1 / Inf(1), // -0 = fmod(-0, Inf)
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Copysign(0, -1), // fmod(-0, Inf)
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NaN(), // fmod(-0, NaN)
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0, // fmod(0, -Inf)
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NaN(), // fmod(0, 0)
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@ -988,14 +990,14 @@ var fmodSC = []float64{
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var vffrexpSC = []float64{
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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}
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var frexpSC = []fi{
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fi{Inf(-1), 0},
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fi{-1 / Inf(1), 0}, // -0, 0
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fi{Copysign(0, -1), 0},
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fi{0, 0},
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fi{Inf(1), 0},
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fi{NaN(), 0},
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@ -1004,7 +1006,7 @@ var frexpSC = []fi{
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var vfgammaSC = []float64{
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Inf(-1),
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-3,
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -1023,6 +1025,10 @@ var vfhypotSC = [][2]float64{
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[2]float64{Inf(-1), 0},
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[2]float64{Inf(-1), Inf(1)},
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[2]float64{Inf(-1), NaN()},
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[2]float64{Copysign(0, -1), Copysign(0, -1)},
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[2]float64{Copysign(0, -1), 0},
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[2]float64{0, Copysign(0, -1)},
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[2]float64{0, 0}, // +0, +0
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[2]float64{0, Inf(-1)},
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[2]float64{0, Inf(1)},
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[2]float64{0, NaN()},
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@ -1040,6 +1046,10 @@ var hypotSC = []float64{
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Inf(1),
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Inf(1),
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Inf(1),
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0,
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0,
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0,
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0,
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Inf(1),
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Inf(1),
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NaN(),
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@ -1119,7 +1129,9 @@ var lgammaSC = []fi{
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var vflogSC = []float64{
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Inf(-1),
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-Pi,
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Copysign(0, -1),
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0,
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1,
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Inf(1),
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NaN(),
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}
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@ -1127,6 +1139,8 @@ var logSC = []float64{
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NaN(),
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NaN(),
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Inf(-1),
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Inf(-1),
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0,
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Inf(1),
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NaN(),
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}
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@ -1148,7 +1162,7 @@ var vflog1pSC = []float64{
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Inf(-1),
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-Pi,
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-1,
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -1157,7 +1171,7 @@ var log1pSC = []float64{
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NaN(),
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NaN(),
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Inf(-1),
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-1 / Inf(1), // -0
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Copysign(0, -1),
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0,
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Inf(1),
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NaN(),
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@ -1169,7 +1183,7 @@ var vfmodfSC = []float64{
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NaN(),
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}
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var modfSC = [][2]float64{
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[2]float64{Inf(-1), NaN()}, // [2]float64{-1 / Inf(1), Inf(-1)}, // -0, -Inf
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[2]float64{Inf(-1), NaN()}, // [2]float64{Copysign(0, -1), Inf(-1)},
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[2]float64{Inf(1), NaN()}, // [2]float64{0, Inf(1)},
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[2]float64{NaN(), NaN()},
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}
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@ -1188,6 +1202,7 @@ var nextafterSC = []float64{
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var vfpowSC = [][2]float64{
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[2]float64{Inf(-1), -Pi},
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[2]float64{Inf(-1), -3},
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[2]float64{Inf(-1), Copysign(0, -1)},
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[2]float64{Inf(-1), 0},
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[2]float64{Inf(-1), 1},
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[2]float64{Inf(-1), 3},
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@ -1196,6 +1211,7 @@ var vfpowSC = [][2]float64{
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[2]float64{-Pi, Inf(-1)},
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[2]float64{-Pi, -Pi},
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[2]float64{-Pi, Copysign(0, -1)},
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[2]float64{-Pi, 0},
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[2]float64{-Pi, 1},
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[2]float64{-Pi, Pi},
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@ -1204,16 +1220,24 @@ var vfpowSC = [][2]float64{
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[2]float64{-1, Inf(-1)},
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[2]float64{-1, Inf(1)},
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[2]float64{-1, NaN()},
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[2]float64{-1 / 2, Inf(-1)},
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[2]float64{-1 / 2, Inf(1)},
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[2]float64{-1 / Inf(1), -3}, // -0, -3
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[2]float64{-1 / Inf(1), 3}, // -0, 3
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[2]float64{Copysign(0, -1), Inf(-1)},
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[2]float64{Copysign(0, -1), -Pi},
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[2]float64{Copysign(0, -1), -3},
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[2]float64{Copysign(0, -1), 3},
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[2]float64{Copysign(0, -1), Pi},
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[2]float64{Copysign(0, -1), Inf(1)},
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[2]float64{0, Inf(-1)},
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[2]float64{0, -Pi},
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[2]float64{0, -3},
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[2]float64{0, Copysign(0, -1)},
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[2]float64{0, 0},
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[2]float64{0, 3},
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[2]float64{0, Pi},
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[2]float64{0, Inf(1)},
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[2]float64{0, NaN()},
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[2]float64{1 / 2, Inf(-1)},
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@ -1223,16 +1247,19 @@ var vfpowSC = [][2]float64{
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[2]float64{1, NaN()},
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[2]float64{Pi, Inf(-1)},
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[2]float64{Pi, Copysign(0, -1)},
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[2]float64{Pi, 0},
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[2]float64{Pi, 1},
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[2]float64{Pi, Inf(1)},
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[2]float64{Pi, NaN()},
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[2]float64{Inf(1), -Pi},
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[2]float64{Inf(1), Copysign(0, -1)},
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[2]float64{Inf(1), 0},
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[2]float64{Inf(1), 1},
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[2]float64{Inf(1), Pi},
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[2]float64{Inf(1), NaN()},
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[2]float64{NaN(), -Pi},
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[2]float64{NaN(), Copysign(0, -1)},
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[2]float64{NaN(), 0},
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[2]float64{NaN(), 1},
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[2]float64{NaN(), Pi},
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@ -1240,47 +1267,60 @@ var vfpowSC = [][2]float64{
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}
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var powSC = []float64{
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0, // pow(-Inf, -Pi)
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0, // pow(-Inf, -3)
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1, // pow(-Inf, 0)
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Copysign(0, -1), // pow(-Inf, -3)
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1, // pow(-Inf, -0)
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1, // pow(-Inf, +0)
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Inf(-1), // pow(-Inf, 1)
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Inf(-1), // pow(-Inf, 3)
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Inf(1), // pow(-Inf, Pi)
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NaN(), // pow(-Inf, NaN)
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0, // pow(-Pi, -Inf)
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NaN(), // pow(-Pi, -Pi)
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1, // pow(-Pi, -0)
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1, // pow(-Pi, +0)
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-Pi, // pow(-Pi, 1)
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NaN(), // pow(-Pi, Pi)
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Inf(1), // pow(-Pi, +Inf)
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NaN(), // pow(-Pi, NaN)
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NaN(), // pow(-1, -Inf)
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NaN(), // pow(-1, +Inf)
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1, // pow(-1, -Inf) IEEE 754-2008
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1, // pow(-1, +Inf) IEEE 754-2008
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NaN(), // pow(-1, NaN)
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Inf(1), // pow(-1/2, -Inf)
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0, // pow(-1/2, +Inf)
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Inf(1), // pow(-0, -3)
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0, // pow(-0, 3)
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Inf(1), // pow(-0, -Inf)
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Inf(1), // pow(-0, -Pi)
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Inf(-1), // pow(-0, -3) IEEE 754-2008
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Copysign(0, -1), // pow(-0, 3) IEEE 754-2008
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0, // pow(-0, +Pi)
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0, // pow(-0, +Inf)
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Inf(1), // pow(+0, -Inf)
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Inf(1), // pow(+0, -Pi)
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Inf(1), // pow(+0, -3)
|
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1, // pow(+0, -0)
|
||||
1, // pow(+0, +0)
|
||||
0, // pow(+0, 3)
|
||||
0, // pow(+0, +Pi)
|
||||
0, // pow(+0, +Inf)
|
||||
NaN(), // pow(+0, NaN)
|
||||
Inf(1), // pow(1/2, -Inf)
|
||||
0, // pow(1/2, +Inf)
|
||||
NaN(), // pow(1, -Inf)
|
||||
NaN(), // pow(1, +Inf)
|
||||
NaN(), // pow(1, NaN)
|
||||
1, // pow(1, -Inf) IEEE 754-2008
|
||||
1, // pow(1, +Inf) IEEE 754-2008
|
||||
1, // pow(1, NaN) IEEE 754-2008
|
||||
0, // pow(+Pi, -Inf)
|
||||
1, // pow(+Pi, -0)
|
||||
1, // pow(+Pi, +0)
|
||||
Pi, // pow(+Pi, 1)
|
||||
Inf(1), // pow(+Pi, +Inf)
|
||||
NaN(), // pow(+Pi, NaN)
|
||||
0, // pow(+Inf, -Pi)
|
||||
1, // pow(+Inf, -0)
|
||||
1, // pow(+Inf, +0)
|
||||
Inf(1), // pow(+Inf, 1)
|
||||
Inf(1), // pow(+Inf, Pi)
|
||||
NaN(), // pow(+Inf, NaN)
|
||||
NaN(), // pow(NaN, -Pi)
|
||||
1, // pow(NaN, -0)
|
||||
1, // pow(NaN, +0)
|
||||
NaN(), // pow(NaN, 1)
|
||||
NaN(), // pow(NaN, +Pi)
|
||||
@ -1289,8 +1329,8 @@ var powSC = []float64{
|
||||
|
||||
var vfsignbitSC = []float64{
|
||||
Inf(-1),
|
||||
-1 / Inf(1), // -0
|
||||
1 / Inf(1), // +0
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
}
|
||||
@ -1304,14 +1344,14 @@ var signbitSC = []bool{
|
||||
|
||||
var vfsinSC = []float64{
|
||||
Inf(-1),
|
||||
-1 / Inf(1),
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
}
|
||||
var sinSC = []float64{
|
||||
NaN(),
|
||||
-1 / Inf(1),
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
NaN(),
|
||||
NaN(),
|
||||
@ -1319,14 +1359,14 @@ var sinSC = []float64{
|
||||
|
||||
var vfsinhSC = []float64{
|
||||
Inf(-1),
|
||||
-1 / Inf(1),
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
}
|
||||
var sinhSC = []float64{
|
||||
Inf(-1),
|
||||
-1 / Inf(1),
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
@ -1335,7 +1375,7 @@ var sinhSC = []float64{
|
||||
var vfsqrtSC = []float64{
|
||||
Inf(-1),
|
||||
-Pi,
|
||||
-1 / Inf(1), // -0
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
@ -1343,7 +1383,7 @@ var vfsqrtSC = []float64{
|
||||
var sqrtSC = []float64{
|
||||
NaN(),
|
||||
NaN(),
|
||||
-1 / Inf(1), // -0
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
@ -1351,14 +1391,14 @@ var sqrtSC = []float64{
|
||||
|
||||
var vftanhSC = []float64{
|
||||
Inf(-1),
|
||||
-1 / Inf(1),
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
Inf(1),
|
||||
NaN(),
|
||||
}
|
||||
var tanhSC = []float64{
|
||||
-1,
|
||||
-1 / Inf(1),
|
||||
Copysign(0, -1),
|
||||
0,
|
||||
1,
|
||||
NaN(),
|
||||
|
||||
@ -9,13 +9,37 @@ func isOddInt(x float64) bool {
|
||||
return xf == 0 && int64(xi)&1 == 1
|
||||
}
|
||||
|
||||
// Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
|
||||
// updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".
|
||||
|
||||
// Pow returns x**y, the base-x exponential of y.
|
||||
//
|
||||
// Special cases are (in order):
|
||||
// Pow(x, ±0) = 1 for any x
|
||||
// Pow(1, y) = 1 for any y
|
||||
// Pow(x, 1) = x for any x
|
||||
// Pow(NaN, y) = NaN
|
||||
// Pow(x, NaN) = NaN
|
||||
// Pow(±0, y) = ±Inf for y an odd integer < 0
|
||||
// Pow(±0, -Inf) = +Inf
|
||||
// Pow(±0, +Inf) = +0
|
||||
// Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
|
||||
// Pow(±0, y) = ±0 for y an odd integer > 0
|
||||
// Pow(±0, y) = +0 for finite y > 0 and not an odd integer
|
||||
// Pow(-1, ±Inf) = 1
|
||||
// Pow(x, +Inf) = +Inf for |x| > 1
|
||||
// Pow(x, -Inf) = +0 for |x| > 1
|
||||
// Pow(x, +Inf) = +0 for |x| < 1
|
||||
// Pow(x, -Inf) = +Inf for |x| < 1
|
||||
// Pow(+Inf, y) = +Inf for y > 0
|
||||
// Pow(+Inf, y) = +0 for y < 0
|
||||
// Pow(-Inf, y) = Pow(-0, -y)
|
||||
// Pow(x, y) = NaN for finite x < 0 and finite non-integer y
|
||||
func Pow(x, y float64) float64 {
|
||||
// TODO: maybe ±0.
|
||||
// TODO(rsc): Remove manual inlining of IsNaN, IsInf
|
||||
// when compiler does it for us
|
||||
switch {
|
||||
case y == 0:
|
||||
case y == 0 || x == 1:
|
||||
return 1
|
||||
case y == 1:
|
||||
return x
|
||||
@ -28,43 +52,34 @@ func Pow(x, y float64) float64 {
|
||||
case x == 0:
|
||||
switch {
|
||||
case y < 0:
|
||||
if isOddInt(y) {
|
||||
return Copysign(Inf(1), x)
|
||||
}
|
||||
return Inf(1)
|
||||
case y > 0:
|
||||
if isOddInt(y) {
|
||||
return x
|
||||
}
|
||||
return 0
|
||||
}
|
||||
case y > MaxFloat64 || y < -MaxFloat64: // IsInf(y, 0):
|
||||
switch {
|
||||
case Fabs(x) == 1:
|
||||
return NaN()
|
||||
case Fabs(x) < 1:
|
||||
switch {
|
||||
case IsInf(y, -1):
|
||||
return Inf(1)
|
||||
case IsInf(y, 1):
|
||||
case x == -1:
|
||||
return 1
|
||||
case (Fabs(x) < 1) == IsInf(y, 1):
|
||||
return 0
|
||||
}
|
||||
case Fabs(x) > 1:
|
||||
switch {
|
||||
case IsInf(y, -1):
|
||||
return 0
|
||||
case IsInf(y, 1):
|
||||
default:
|
||||
return Inf(1)
|
||||
}
|
||||
}
|
||||
case x > MaxFloat64 || x < -MaxFloat64: // IsInf(x, 0):
|
||||
if IsInf(x, -1) {
|
||||
return Pow(1/x, -y) // Pow(-0, -y)
|
||||
}
|
||||
switch {
|
||||
case y < 0:
|
||||
return 0
|
||||
case y > 0:
|
||||
switch {
|
||||
case IsInf(x, -1):
|
||||
if isOddInt(y) {
|
||||
return Inf(-1)
|
||||
}
|
||||
return Inf(1)
|
||||
case IsInf(x, 1):
|
||||
return Inf(1)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user