Implement arcsin and arccos in NumPy. (#1054)

Author: redbopo

integration_tests/CMakeLists.txt

@@ -171,6 +171,7 @@ RUN(NAME elemental_01        LABELS cpython llvm)
 RUN(NAME elemental_02        LABELS cpython llvm)
 RUN(NAME elemental_03        LABELS cpython llvm)
 RUN(NAME elemental_04        LABELS cpython llvm)
+RUN(NAME elemental_06        LABELS cpython llvm)
 RUN(NAME test_random         LABELS cpython llvm)
 RUN(NAME test_os             LABELS cpython llvm)
 RUN(NAME test_builtin        LABELS cpython llvm)

integration_tests/elemental_06.py

@@ -0,0 +1,127 @@
+from ltypes import i32, f32, f64
+from numpy import empty, arcsin, arccos, sin, cos, sqrt
+from math import pi
+
+def verify1d_same(array: f32[:], result: f32[:], size: i32):
+    i: i32
+    eps: f32
+    eps = 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 = 1e-6
+    for i in range(size):
+        assert abs(arcsin(array[i])**2 - 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 - result[i, j]) <= eps
+
+def verify_arccos_1d(array: f32[:], result: f32[:], size: i32):
+    i: i32
+    eps: f32
+    eps = 1e-6
+    for i in range(size):
+        assert abs(arccos(array[i])**2 - 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 - result[i, j]) <= eps
+
+def elemental_arcsin():
+    i: i32
+    j: i32
+    array1d: f32[201] = empty(201)
+    arcsin1d: f32[201] = empty(201)
+    for i in range(201):
+        array1d[i] =  float((i - 100)/100)
+    arcsin1d = arcsin(array1d) ** 2
+    verify_arcsin_1d(array1d, arcsin1d, 201)
+
+    array2d: f64[64, 64] = empty((64, 64))
+    arcsin2d: f64[64, 64] = empty((64, 64))
+    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
+    verify_arcsin_2d(array2d, arcsin2d, 64, 64)
+
+def elemental_arccos():
+    i: i32
+    j: i32
+    array1d: f32[201] = empty(201)
+    arccos1d: f32[201] = empty(201)
+    for i in range(201):
+        array1d[i] =  float((i - 100)/100)
+    arccos1d = arccos(array1d) ** 2
+    verify_arccos_1d(array1d, arccos1d, 201)
+
+    array2d: f64[64, 64] = empty((64, 64))
+    arccos2d: f64[64, 64] = empty((64, 64))
+    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
+    verify_arccos_2d(array2d, arccos2d, 64, 64)
+
+def elemental_trig_identity():
+    i: i32
+    eps: f32
+    eps = 1e-6
+    array1d: f32[201] = empty(201)
+    observed1d: f32[201] = empty(201)
+    for i in range(201):
+        array1d[i] =  float((i - 100)/100)
+
+    observed1d = arcsin(array1d) + arccos(array1d)
+    for i in range(201):
+        assert abs(observed1d[i] - pi / 2) <= eps
+
+def elemental_reverse():
+    i: i32
+    array1d: f32[201] = empty(201)
+    observed1d: f32[201] = empty(201)
+    for i in range(201):
+        array1d[i] =  float((i - 100)/100)
+    observed1d = sin(arcsin(array1d))
+    verify1d_same(observed1d, array1d, 201)
+
+    observed1d = cos(arccos(array1d))
+    verify1d_same(observed1d, array1d, 201)
+
+def elemental_trig_identity_extra():
+    i: i32
+    array1d: f32[201] = empty(201)
+    array_x: f32[201] = empty(201)
+    array_y: f32[201] = empty(201)
+    for i in range(201):
+        array1d[i] =  float((i - 100)/100)
+    array_x = sin(arccos(array1d))
+    array_y = cos(arcsin(array1d))
+    for i in range(201):
+        array1d[i] =  1 - array1d[i] ** 2
+    array1d = sqrt(array1d)
+    verify1d_same(array_x, array_y, 201)
+    verify1d_same(array_x, array1d, 201)
+
+
+elemental_arcsin()
+elemental_arccos()
+elemental_trig_identity()
+elemental_reverse()
+elemental_trig_identity_extra()

src/runtime/lpython_intrinsic_numpy.py

@@ -125,3 +125,43 @@ def log2(x: f64) -> f64:
 @vectorize
 def log2(x: f32) -> f32:
     return _lfortran_slog(x)/_lfortran_slog(2.0)
+
+########## arcsin ##########
+
+@ccall
+def _lfortran_dasin(x: f64) -> f64:
+    pass
+
+@overload
+@vectorize
+def arcsin(x: f64) -> f64:
+    return _lfortran_dasin(x)
+
+@ccall
+def _lfortran_sasin(x: f32) -> f32:
+    pass
+
+@overload
+@vectorize
+def arcsin(x: f32) -> f32:
+    return _lfortran_sasin(x)
+
+########## arccos ##########
+
+@ccall
+def _lfortran_dacos(x: f64) -> f64:
+    pass
+
+@overload
+@vectorize
+def arccos(x: f64) -> f64:
+    return _lfortran_dacos(x)
+
+@ccall
+def _lfortran_sacos(x: f32) -> f32:
+    pass
+
+@overload
+@vectorize
+def arccos(x: f32) -> f32:
+    return _lfortran_sacos(x)

tests/reference/asr-array_01_decl-39cf894.json

@@ -6,7 +6,7 @@
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tests/reference/asr-array_01_decl-39cf894.stdout

@@ -6,7 +6,7 @@
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tests/reference/asr-array_02_decl-e8f6874.json

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tests/reference/asr-array_02_decl-e8f6874.stdout

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tests/reference/asr-elemental_01-b58df26.json

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tests/reference/asr-elemental_01-b58df26.stdout

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