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|
module math
import math.internal
const (
sin_data = [
-0.3295190160663511504173,
0.0025374284671667991990,
0.0006261928782647355874,
-4.6495547521854042157541e-06,
-5.6917531549379706526677e-07,
3.7283335140973803627866e-09,
3.0267376484747473727186e-10,
-1.7400875016436622322022e-12,
-1.0554678305790849834462e-13,
5.3701981409132410797062e-16,
2.5984137983099020336115e-17,
-1.1821555255364833468288e-19,
]
sin_cs = ChebSeries{
c: sin_data
order: 11
a: -1
b: 1
}
cos_data = [
0.165391825637921473505668118136,
-0.00084852883845000173671196530195,
-0.000210086507222940730213625768083,
1.16582269619760204299639757584e-6,
1.43319375856259870334412701165e-7,
-7.4770883429007141617951330184e-10,
-6.0969994944584252706997438007e-11,
2.90748249201909353949854872638e-13,
1.77126739876261435667156490461e-14,
-7.6896421502815579078577263149e-17,
-3.7363121133079412079201377318e-18,
]
cos_cs = ChebSeries{
c: cos_data
order: 10
a: -1
b: 1
}
)
pub fn sin(x f64) f64 {
p1 := 7.85398125648498535156e-1
p2 := 3.77489470793079817668e-8
p3 := 2.69515142907905952645e-15
sgn_x := if x < 0 { -1 } else { 1 }
abs_x := abs(x)
if abs_x < internal.root4_f64_epsilon {
x2 := x * x
return x * (1.0 - x2 / 6.0)
} else {
mut sgn_result := sgn_x
mut y := floor(abs_x / (0.25 * pi))
mut octant := int(y - ldexp(floor(ldexp(y, -3)), 3))
if (octant & 1) == 1 {
octant++
octant &= 7
y += 1.0
}
if octant > 3 {
octant -= 4
sgn_result = -sgn_result
}
z := ((abs_x - y * p1) - y * p2) - y * p3
mut result := 0.0
if octant == 0 {
t := 8.0 * abs(z) / pi - 1.0
sin_cs_val, _ := math.sin_cs.eval_e(t)
result = z * (1.0 + z * z * sin_cs_val)
} else {
t := 8.0 * abs(z) / pi - 1.0
cos_cs_val, _ := math.cos_cs.eval_e(t)
result = 1.0 - 0.5 * z * z * (1.0 - z * z * cos_cs_val)
}
result *= sgn_result
return result
}
}
pub fn cos(x f64) f64 {
p1 := 7.85398125648498535156e-1
p2 := 3.77489470793079817668e-8
p3 := 2.69515142907905952645e-15
abs_x := abs(x)
if abs_x < internal.root4_f64_epsilon {
x2 := x * x
return 1.0 - 0.5 * x2
} else {
mut sgn_result := 1
mut y := floor(abs_x / (0.25 * pi))
mut octant := int(y - ldexp(floor(ldexp(y, -3)), 3))
if (octant & 1) == 1 {
octant++
octant &= 7
y += 1.0
}
if octant > 3 {
octant -= 4
sgn_result = -sgn_result
}
if octant > 1 {
sgn_result = -sgn_result
}
z := ((abs_x - y * p1) - y * p2) - y * p3
mut result := 0.0
if octant == 0 {
t := 8.0 * abs(z) / pi - 1.0
cos_cs_val, _ := math.cos_cs.eval_e(t)
result = 1.0 - 0.5 * z * z * (1.0 - z * z * cos_cs_val)
} else {
t := 8.0 * abs(z) / pi - 1.0
sin_cs_val, _ := math.sin_cs.eval_e(t)
result = z * (1.0 + z * z * sin_cs_val)
}
result *= sgn_result
return result
}
}
// cosf calculates cosine. (float32).
[inline]
pub fn cosf(a f32) f32 {
return f32(cos(a))
}
// sinf calculates sine. (float32)
[inline]
pub fn sinf(a f32) f32 {
return f32(sin(a))
}
pub fn sincos(x f64) (f64, f64) {
p1 := 7.85398125648498535156e-1
p2 := 3.77489470793079817668e-8
p3 := 2.69515142907905952645e-15
sgn_x := if x < 0 { -1 } else { 1 }
abs_x := abs(x)
if abs_x < internal.root4_f64_epsilon {
x2 := x * x
return x * (1.0 - x2 / 6.0), 1.0 - 0.5 * x2
} else {
mut sgn_result_sin := sgn_x
mut sgn_result_cos := 1
mut y := floor(abs_x / (0.25 * pi))
mut octant := int(y - ldexp(floor(ldexp(y, -3)), 3))
if (octant & 1) == 1 {
octant++
octant &= 7
y += 1.0
}
if octant > 3 {
octant -= 4
sgn_result_sin = -sgn_result_sin
sgn_result_cos = -sgn_result_cos
}
sgn_result_cos = if octant > 1 { -sgn_result_cos } else { sgn_result_cos }
z := ((abs_x - y * p1) - y * p2) - y * p3
t := 8.0 * abs(z) / pi - 1.0
sin_cs_val, _ := math.sin_cs.eval_e(t)
cos_cs_val, _ := math.cos_cs.eval_e(t)
mut result_sin := 0.0
mut result_cos := 0.0
if octant == 0 {
result_sin = z * (1.0 + z * z * sin_cs_val)
result_cos = 1.0 - 0.5 * z * z * (1.0 - z * z * cos_cs_val)
} else {
result_sin = 1.0 - 0.5 * z * z * (1.0 - z * z * cos_cs_val)
result_cos = z * (1.0 + z * z * sin_cs_val)
}
result_sin *= sgn_result_sin
result_cos *= sgn_result_cos
return result_sin, result_cos
}
}
|
