vlib/math: Add a pure V backend for vlib/math (#11267)

vlib/math/sin.v

@@ -0,0 +1,179 @@
+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
+	}
+}