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elemental_06.py
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elemental_06.py
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from lpython import i32, f32, f64
from numpy import empty, arcsin, arccos, sin, cos, sqrt, arctan, tan, degrees, radians, hypot, float32, float64
from math import pi
def verify1d_same(array: f32[:], result: f32[:], size: i32):
i: i32
eps: f32
eps = f32(1e-6)
for i in range(size):
assert abs(array[i] - result[i]) <= eps
def verify_arcsin_1d(array: f32[:], result: f32[:], size: i32):
i: i32
eps: f32
eps = f32(1e-6)
for i in range(size):
assert abs(arcsin(array[i])**f32(2.0) - result[i]) <= eps
def verify_arcsin_2d(array: f64[:, :], result: f64[:, :], size1:i32, size2:i32):
i: i32
j: i32
eps: f64
eps = 1e-12
for i in range(size1):
for j in range(size2):
assert abs(arcsin(array[i, j])**2.0 - result[i, j]) <= eps
def verify_arccos_1d(array: f32[:], result: f32[:], size: i32):
i: i32
eps: f32
eps = f32(1e-6)
for i in range(size):
assert abs(arccos(array[i])**f32(2.0) - result[i]) <= eps
def verify_arccos_2d(array: f64[:, :], result: f64[:, :], size1:i32, size2:i32):
i: i32
j: i32
eps: f64
eps = 1e-12
for i in range(size1):
for j in range(size2):
assert abs(arccos(array[i, j])**2.0 - result[i, j]) <= eps
def verify_arctan_1d(array: f32[:], result: f32[:], size: i32):
i: i32
eps: f32
eps = f32(1e-6)
for i in range(size):
assert abs(arctan(array[i])**f32(2.0) - result[i]) <= eps
def verify_arctan_2d(array: f64[:, :], result: f64[:, :], size1:i32, size2:i32):
i: i32
j: i32
eps: f64
eps = 1e-12
for i in range(size1):
for j in range(size2):
assert abs(arctan(array[i, j])**2.0 - result[i, j]) <= eps
def verify_hypot_2d(array1: f64[:, :], array2: f64[:, :], result: f64[:, :], size1:i32, size2:i32):
i: i32
j: i32
eps: f64
eps = 1e-12
for i in range(size1):
for j in range(size2):
assert abs(hypot(array1[i, j], array2[i, j]) - result[i, j]) <= eps
def elemental_arcsin():
i: i32
j: i32
array1d: f32[201] = empty(201, dtype=float32)
arcsin1d: f32[201] = empty(201, dtype=float32)
for i in range(201):
array1d[i] = f32((i - 100)/100)
arcsin1d = arcsin(array1d) ** f32(2.0)
verify_arcsin_1d(array1d, arcsin1d, 201)
array2d: f64[64, 64] = empty((64, 64), dtype=float64)
arcsin2d: f64[64, 64] = empty((64, 64), dtype=float64)
for i in range(64):
for j in range(64): # 2048 = 64 * 32
array2d[i,j]= float((i * 64 + j - 2048 )/2048)
arcsin2d = arcsin(array2d) ** 2.0
verify_arcsin_2d(array2d, arcsin2d, 64, 64)
def elemental_arccos():
i: i32
j: i32
array1d: f32[201] = empty(201, dtype=float32)
arccos1d: f32[201] = empty(201, dtype=float32)
for i in range(201):
array1d[i] = f32((i - 100)/100)
arccos1d = arccos(array1d) ** f32(2.0)
verify_arccos_1d(array1d, arccos1d, 201)
array2d: f64[64, 64] = empty((64, 64), dtype=float64)
arccos2d: f64[64, 64] = empty((64, 64), dtype=float64)
for i in range(64):
for j in range(64): # 2048 = 64 * 32
array2d[i,j]= float((i * 64 + j - 2048 )/2048)
arccos2d = arccos(array2d) ** 2.0
verify_arccos_2d(array2d, arccos2d, 64, 64)
def elemental_arctan():
i: i32
j: i32
eps: f32
eps = f32(1e-6)
array1d: f32[201] = empty(201, dtype=float32)
array1d_rec: f32[201] = empty(201, dtype=float32)
arctan1d: f32[201] = empty(201, dtype=float32)
for i in range(201):
array1d[i] = f32(i - 100)
arctan1d = arctan(array1d) ** f32(2.0)
verify_arctan_1d(array1d, arctan1d, 201)
for i in range(201):
array1d[i] = f32(i + 1)
array1d_rec[i] = f32(1.0/f64(i+1))
arctan1d = arctan(array1d) + arctan(array1d_rec)
for i in range(201):
assert abs(arctan1d[i] - f32(f64(pi) / 2.0)) <= eps
array2d: f64[64, 64] = empty((64, 64), dtype=float64)
arctan2d: f64[64, 64] = empty((64, 64), dtype=float64)
for i in range(64):
for j in range(64):
array2d[i,j]= float(64*i + j - 2048)
arctan2d = arctan(array2d) ** 2.0
verify_arctan_2d(array2d, arctan2d, 64, 64)
def elemental_trig_identity():
i: i32
eps: f32
eps = f32(1e-6)
array1d: f32[201] = empty(201, dtype=float32)
observed1d: f32[201] = empty(201, dtype=float32)
for i in range(201):
array1d[i] = f32((i - 100)/100)
observed1d = arcsin(array1d) + arccos(array1d)
for i in range(201):
assert abs(observed1d[i] - f32(pi / 2.0)) <= eps
def elemental_reverse():
i: i32
array1d: f32[201] = empty(201, dtype=float32)
observed1d: f32[201] = empty(201, dtype=float32)
for i in range(201):
array1d[i] = f32((i - 100)/100)
observed1d = sin(arcsin(array1d))
verify1d_same(observed1d, array1d, 201)
observed1d = cos(arccos(array1d))
verify1d_same(observed1d, array1d, 201)
observed1d = tan(arctan(array1d))
verify1d_same(observed1d, array1d, 201)
observed1d = degrees(radians(array1d))
verify1d_same(observed1d, array1d, 201)
def elemental_trig_identity_extra():
i: i32
array1d: f32[201] = empty(201, dtype=float32)
array_x: f32[201] = empty(201, dtype=float32)
array_y: f32[201] = empty(201, dtype=float32)
for i in range(201):
array1d[i] = f32((i - 100)/100)
array_x = sin(arccos(array1d))
array_y = cos(arcsin(array1d))
for i in range(201):
array1d[i] = f32(1.0) - array1d[i] ** f32(2.0)
array1d = sqrt(array1d)
verify1d_same(array_x, array_y, 201)
verify1d_same(array_x, array1d, 201)
def elemental_degrees():
i: i32
j: i32
eps_32: f32
eps_64: f64
eps_32 = f32(1e-6)
eps_64 = 1e-12
array1d: f32[200] = empty(200, dtype=float32)
degrees1d: f32[200] = empty(200, dtype=float32)
for i in range(200):
array1d[i] = f32(i)
degrees1d = sin(degrees(array1d))
for i in range(200):
assert abs(degrees1d[i] - sin(degrees(array1d[i]))) <= eps_32
array2d: f64[64, 64] = empty((64, 64), dtype=float64)
degrees2d: f64[64, 64] = empty((64, 64), dtype=float64)
for i in range(64):
for j in range(64):
array2d[i,j]= float(i*64+j)
degrees2d = sin(degrees(array2d))
for i in range(64):
for j in range(64):
assert abs(degrees2d[i, j] - sin(degrees(array2d[i, j]))) <= eps_64
def elemental_radians():
i: i32
j: i32
eps_32: f32
eps_64: f64
eps_32 = f32(1e-6)
eps_64 = 1e-12
array1d: f32[200] = empty(200, dtype=float32)
radians1d: f32[200] = empty(200, dtype=float32)
for i in range(200):
array1d[i] = f32(i)
radians1d = cos(radians(array1d))
for i in range(200):
assert abs(radians1d[i] - cos(radians(array1d[i]))) <= eps_32
array2d: f64[64, 64] = empty((64, 64), dtype=float64)
radians2d: f64[64, 64] = empty((64, 64), dtype=float64)
for i in range(64):
for j in range(64):
array2d[i,j]= float(i*64+j)
radians2d = cos(radians(array2d))
for i in range(64):
for j in range(64):
assert abs(radians2d[i, j] - cos(radians(array2d[i, j]))) <= eps_64
def elemental_hypot():
i: i32
j: i32
eps_32: f32
eps_32 = f32(1e-6)
hypot1d: f32[200] = empty(200, dtype=float32)
array1d1: f32[200] = empty(200, dtype=float32)
array1d2: f32[200] = empty(200, dtype=float32)
for i in range(200):
array1d1[i] = f32(i)
array1d2[i] = f32(i+10)
hypot1d = hypot(array1d1, array1d2)
for i in range(200):
assert abs(hypot1d[i] - hypot(array1d1[i], array1d2[i])) <= eps_32
array2d1: f64[64, 64] = empty((64, 64), dtype=float64)
array2d2: f64[64, 64] = empty((64, 64), dtype=float64)
hypot2d: f64[64, 64] = empty((64, 64), dtype=float64)
for i in range(64):
for j in range(64):
array2d1[i,j]= float(i * j)
array2d2[i,j]= float(64*i + j - 2048)
hypot2d = hypot(array2d1, array2d2)
verify_hypot_2d(array2d1, array2d2, hypot2d, 64, 64)
elemental_arcsin()
elemental_arccos()
elemental_arctan()
elemental_degrees()
elemental_radians()
elemental_trig_identity()
elemental_reverse()
elemental_trig_identity_extra()
elemental_hypot()