Videre

linedance-app/venv/lib/python3.12/site-packages/numba/np/math/cmathimpl.py

@@ -0,0 +1,542 @@
+"""
+Implement the cmath module functions.
+"""
+
+
+import cmath
+import math
+
+from numba.core.imputils import impl_ret_untracked
+from numba.core import types
+from numba.core.typing import signature
+from numba.cpython import mathimpl
+from numba.core.extending import overload
+
+# registry = Registry('cmathimpl')
+# lower = registry.lower
+
+
+def is_nan(builder, z):
+    return builder.fcmp_unordered('uno', z.real, z.imag)
+
+def is_inf(builder, z):
+    return builder.or_(mathimpl.is_inf(builder, z.real),
+                       mathimpl.is_inf(builder, z.imag))
+
+def is_finite(builder, z):
+    return builder.and_(mathimpl.is_finite(builder, z.real),
+                        mathimpl.is_finite(builder, z.imag))
+
+
+# @lower(cmath.isnan, types.Complex)
+def isnan_float_impl(context, builder, sig, args):
+    [typ] = sig.args
+    [value] = args
+    z = context.make_complex(builder, typ, value=value)
+    res = is_nan(builder, z)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+# @lower(cmath.isinf, types.Complex)
+def isinf_float_impl(context, builder, sig, args):
+    [typ] = sig.args
+    [value] = args
+    z = context.make_complex(builder, typ, value=value)
+    res = is_inf(builder, z)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(cmath.isfinite, types.Complex)
+def isfinite_float_impl(context, builder, sig, args):
+    [typ] = sig.args
+    [value] = args
+    z = context.make_complex(builder, typ, value=value)
+    res = is_finite(builder, z)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @overload(cmath.rect)
+def impl_cmath_rect(r, phi):
+    if all([isinstance(typ, types.Float) for typ in [r, phi]]):
+        def impl(r, phi):
+            if not math.isfinite(phi):
+                if not r:
+                    # cmath.rect(0, phi={inf, nan}) = 0
+                    return abs(r)
+                if math.isinf(r):
+                    # cmath.rect(inf, phi={inf, nan}) = inf + j phi
+                    return complex(r, phi)
+            real = math.cos(phi)
+            imag = math.sin(phi)
+            if real == 0. and math.isinf(r):
+                # 0 * inf would return NaN, we want to keep 0 but xor the sign
+                real /= r
+            else:
+                real *= r
+            if imag == 0. and math.isinf(r):
+                # ditto
+                imag /= r
+            else:
+                imag *= r
+            return complex(real, imag)
+        return impl
+
+
+def intrinsic_complex_unary(inner_func):
+    def wrapper(context, builder, sig, args):
+        [typ] = sig.args
+        [value] = args
+        z = context.make_complex(builder, typ, value=value)
+        x = z.real
+        y = z.imag
+        # Same as above: math.isfinite() is unavailable on 2.x so we precompute
+        # its value and pass it to the pure Python implementation.
+        x_is_finite = mathimpl.is_finite(builder, x)
+        y_is_finite = mathimpl.is_finite(builder, y)
+        inner_sig = signature(sig.return_type,
+                              *(typ.underlying_float,) * 2 + (types.boolean,) * 2)
+        res = context.compile_internal(builder, inner_func, inner_sig,
+                                        (x, y, x_is_finite, y_is_finite))
+        return impl_ret_untracked(context, builder, sig, res)
+    return wrapper
+
+
+NAN = float('nan')
+INF = float('inf')
+
+# @lower(cmath.exp, types.Complex)
+@intrinsic_complex_unary
+def exp_impl(x, y, x_is_finite, y_is_finite):
+    """cmath.exp(x + y j)"""
+    if x_is_finite:
+        if y_is_finite:
+            c = math.cos(y)
+            s = math.sin(y)
+            r = math.exp(x)
+            return complex(r * c, r * s)
+        else:
+            return complex(NAN, NAN)
+    elif math.isnan(x):
+        if y:
+            return complex(x, x)  # nan + j nan
+        else:
+            return complex(x, y)  # nan + 0j
+    elif x > 0.0:
+        # x == +inf
+        if y_is_finite:
+            real = math.cos(y)
+            imag = math.sin(y)
+            # Avoid NaNs if math.cos(y) or math.sin(y) == 0
+            # (e.g. cmath.exp(inf + 0j) == inf + 0j)
+            if real != 0:
+                real *= x
+            if imag != 0:
+                imag *= x
+            return complex(real, imag)
+        else:
+            return complex(x, NAN)
+    else:
+        # x == -inf
+        if y_is_finite:
+            r = math.exp(x)
+            c = math.cos(y)
+            s = math.sin(y)
+            return complex(r * c, r * s)
+        else:
+            r = 0
+            return complex(r, r)
+
+# @lower(cmath.log, types.Complex)
+@intrinsic_complex_unary
+def log_impl(x, y, x_is_finite, y_is_finite):
+    """cmath.log(x + y j)"""
+    a = math.log(math.hypot(x, y))
+    b = math.atan2(y, x)
+    return complex(a, b)
+
+
+# @lower(cmath.log, types.Complex, types.Complex)
+def log_base_impl(context, builder, sig, args):
+    """cmath.log(z, base)"""
+    [z, base] = args
+
+    def log_base(z, base):
+        return cmath.log(z) / cmath.log(base)
+
+    res = context.compile_internal(builder, log_base, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+
+# @overload(cmath.log10)
+def impl_cmath_log10(z):
+    if not isinstance(z, types.Complex):
+        return
+
+    LN_10 = 2.302585092994045684
+
+    def log10_impl(z):
+        """cmath.log10(z)"""
+        z = cmath.log(z)
+        # This formula gives better results on +/-inf than cmath.log(z, 10)
+        # See http://bugs.python.org/issue22544
+        return complex(z.real / LN_10, z.imag / LN_10)
+
+    return log10_impl
+
+
+# @overload(cmath.phase)
+def phase_impl(x):
+    """cmath.phase(x + y j)"""
+
+    if not isinstance(x, types.Complex):
+        return
+
+    def impl(x):
+        return math.atan2(x.imag, x.real)
+    return impl
+
+
+# @overload(cmath.polar)
+def polar_impl(x):
+    if not isinstance(x, types.Complex):
+        return
+
+    def impl(x):
+        r, i = x.real, x.imag
+        return math.hypot(r, i), math.atan2(i, r)
+    return impl
+
+
+# @lower(cmath.sqrt, types.Complex)
+def sqrt_impl(context, builder, sig, args):
+    # We risk spurious overflow for components >= FLT_MAX / (1 + sqrt(2)).
+
+    SQRT2 = 1.414213562373095048801688724209698079E0
+    ONE_PLUS_SQRT2 = (1. + SQRT2)
+    theargflt = sig.args[0].underlying_float
+    # Get a type specific maximum value so scaling for overflow is based on that
+    MAX = mathimpl.DBL_MAX if theargflt.bitwidth == 64 else mathimpl.FLT_MAX
+    # THRES will be double precision, should not impact typing as it's just
+    # used for comparison, there *may* be a few values near THRES which
+    # deviate from e.g. NumPy due to rounding that occurs in the computation
+    # of this value in the case of a 32bit argument.
+    THRES = MAX / ONE_PLUS_SQRT2
+
+    def sqrt_impl(z):
+        """cmath.sqrt(z)"""
+        # This is NumPy's algorithm, see npy_csqrt() in npy_math_complex.c.src
+        a = z.real
+        b = z.imag
+        if a == 0.0 and b == 0.0:
+            return complex(abs(b), b)
+        if math.isinf(b):
+            return complex(abs(b), b)
+        if math.isnan(a):
+            return complex(a, a)
+        if math.isinf(a):
+            if a < 0.0:
+                return complex(abs(b - b), math.copysign(a, b))
+            else:
+                return complex(a, math.copysign(b - b, b))
+
+        # The remaining special case (b is NaN) is handled just fine by
+        # the normal code path below.
+
+        # Scale to avoid overflow
+        if abs(a) >= THRES or abs(b) >= THRES:
+            a *= 0.25
+            b *= 0.25
+            scale = True
+        else:
+            scale = False
+        # Algorithm 312, CACM vol 10, Oct 1967
+        if a >= 0:
+            t = math.sqrt((a + math.hypot(a, b)) * 0.5)
+            real = t
+            imag = b / (2 * t)
+        else:
+            t = math.sqrt((-a + math.hypot(a, b)) * 0.5)
+            real = abs(b) / (2 * t)
+            imag = math.copysign(t, b)
+        # Rescale
+        if scale:
+            return complex(real * 2, imag)
+        else:
+            return complex(real, imag)
+
+    res = context.compile_internal(builder, sqrt_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+
+# @lower(cmath.cos, types.Complex)
+def cos_impl(context, builder, sig, args):
+    def cos_impl(z):
+        """cmath.cos(z) = cmath.cosh(z j)"""
+        return cmath.cosh(complex(-z.imag, z.real))
+
+    res = context.compile_internal(builder, cos_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+# @overload(cmath.cosh)
+def impl_cmath_cosh(z):
+    if not isinstance(z, types.Complex):
+        return
+
+    def cosh_impl(z):
+        """cmath.cosh(z)"""
+        x = z.real
+        y = z.imag
+        if math.isinf(x):
+            if math.isnan(y):
+                # x = +inf, y = NaN => cmath.cosh(x + y j) = inf + Nan * j
+                real = abs(x)
+                imag = y
+            elif y == 0.0:
+                # x = +inf, y = 0 => cmath.cosh(x + y j) = inf + 0j
+                real = abs(x)
+                imag = y
+            else:
+                real = math.copysign(x, math.cos(y))
+                imag = math.copysign(x, math.sin(y))
+            if x < 0.0:
+                # x = -inf => negate imaginary part of result
+                imag = -imag
+            return complex(real, imag)
+        return complex(math.cos(y) * math.cosh(x),
+                    math.sin(y) * math.sinh(x))
+    return cosh_impl
+
+
+# @lower(cmath.sin, types.Complex)
+def sin_impl(context, builder, sig, args):
+    def sin_impl(z):
+        """cmath.sin(z) = -j * cmath.sinh(z j)"""
+        r = cmath.sinh(complex(-z.imag, z.real))
+        return complex(r.imag, -r.real)
+
+    res = context.compile_internal(builder, sin_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+# @overload(cmath.sinh)
+def impl_cmath_sinh(z):
+    if not isinstance(z, types.Complex):
+        return
+
+    def sinh_impl(z):
+        """cmath.sinh(z)"""
+        x = z.real
+        y = z.imag
+        if math.isinf(x):
+            if math.isnan(y):
+                # x = +/-inf, y = NaN => cmath.sinh(x + y j) = x + NaN * j
+                real = x
+                imag = y
+            else:
+                real = math.cos(y)
+                imag = math.sin(y)
+                if real != 0.:
+                    real *= x
+                if imag != 0.:
+                    imag *= abs(x)
+            return complex(real, imag)
+        return complex(math.cos(y) * math.sinh(x),
+                       math.sin(y) * math.cosh(x))
+    return sinh_impl
+
+
+# @lower(cmath.tan, types.Complex)
+def tan_impl(context, builder, sig, args):
+    def tan_impl(z):
+        """cmath.tan(z) = -j * cmath.tanh(z j)"""
+        r = cmath.tanh(complex(-z.imag, z.real))
+        return complex(r.imag, -r.real)
+
+    res = context.compile_internal(builder, tan_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+
+# @overload(cmath.tanh)
+def impl_cmath_tanh(z):
+    if not isinstance(z, types.Complex):
+        return
+
+    def tanh_impl(z):
+        """cmath.tanh(z)"""
+        x = z.real
+        y = z.imag
+        if math.isinf(x):
+            real = math.copysign(1., x)
+            if math.isinf(y):
+                imag = 0.
+            else:
+                imag = math.copysign(0., math.sin(2. * y))
+            return complex(real, imag)
+        # This is CPython's algorithm (see c_tanh() in cmathmodule.c).
+        # XXX how to force float constants into single precision?
+        tx = math.tanh(x)
+        ty = math.tan(y)
+        cx = 1. / math.cosh(x)
+        txty = tx * ty
+        denom = 1. + txty * txty
+        return complex(
+            tx * (1. + ty * ty) / denom,
+            ((ty / denom) * cx) * cx)
+
+    return tanh_impl
+
+
+# @lower(cmath.acos, types.Complex)
+def acos_impl(context, builder, sig, args):
+    LN_4 = math.log(4)
+    THRES = mathimpl.FLT_MAX / 4
+
+    def acos_impl(z):
+        """cmath.acos(z)"""
+        # CPython's algorithm (see c_acos() in cmathmodule.c)
+        if abs(z.real) > THRES or abs(z.imag) > THRES:
+            # Avoid unnecessary overflow for large arguments
+            # (also handles infinities gracefully)
+            real = math.atan2(abs(z.imag), z.real)
+            imag = math.copysign(
+                math.log(math.hypot(z.real * 0.5, z.imag * 0.5)) + LN_4,
+                -z.imag)
+            return complex(real, imag)
+        else:
+            s1 = cmath.sqrt(complex(1. - z.real, -z.imag))
+            s2 = cmath.sqrt(complex(1. + z.real, z.imag))
+            real = 2. * math.atan2(s1.real, s2.real)
+            imag = math.asinh(s2.real * s1.imag - s2.imag * s1.real)
+            return complex(real, imag)
+
+    res = context.compile_internal(builder, acos_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+# @overload(cmath.acosh)
+def impl_cmath_acosh(z):
+    if not isinstance(z, types.Complex):
+        return
+
+    LN_4 = math.log(4)
+    THRES = mathimpl.FLT_MAX / 4
+
+    def acosh_impl(z):
+        """cmath.acosh(z)"""
+        # CPython's algorithm (see c_acosh() in cmathmodule.c)
+        if abs(z.real) > THRES or abs(z.imag) > THRES:
+            # Avoid unnecessary overflow for large arguments
+            # (also handles infinities gracefully)
+            real = math.log(math.hypot(z.real * 0.5, z.imag * 0.5)) + LN_4
+            imag = math.atan2(z.imag, z.real)
+            return complex(real, imag)
+        else:
+            s1 = cmath.sqrt(complex(z.real - 1., z.imag))
+            s2 = cmath.sqrt(complex(z.real + 1., z.imag))
+            real = math.asinh(s1.real * s2.real + s1.imag * s2.imag)
+            imag = 2. * math.atan2(s1.imag, s2.real)
+            return complex(real, imag)
+        # Condensed formula (NumPy)
+        #return cmath.log(z + cmath.sqrt(z + 1.) * cmath.sqrt(z - 1.))
+
+    return acosh_impl
+
+
+# @lower(cmath.asinh, types.Complex)
+def asinh_impl(context, builder, sig, args):
+    LN_4 = math.log(4)
+    THRES = mathimpl.FLT_MAX / 4
+
+    def asinh_impl(z):
+        """cmath.asinh(z)"""
+        # CPython's algorithm (see c_asinh() in cmathmodule.c)
+        if abs(z.real) > THRES or abs(z.imag) > THRES:
+            real = math.copysign(
+                math.log(math.hypot(z.real * 0.5, z.imag * 0.5)) + LN_4,
+                z.real)
+            imag = math.atan2(z.imag, abs(z.real))
+            return complex(real, imag)
+        else:
+            s1 = cmath.sqrt(complex(1. + z.imag, -z.real))
+            s2 = cmath.sqrt(complex(1. - z.imag, z.real))
+            real = math.asinh(s1.real * s2.imag - s2.real * s1.imag)
+            imag = math.atan2(z.imag, s1.real * s2.real - s1.imag * s2.imag)
+            return complex(real, imag)
+
+    res = context.compile_internal(builder, asinh_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+# @lower(cmath.asin, types.Complex)
+def asin_impl(context, builder, sig, args):
+    def asin_impl(z):
+        """cmath.asin(z) = -j * cmath.asinh(z j)"""
+        r = cmath.asinh(complex(-z.imag, z.real))
+        return complex(r.imag, -r.real)
+
+    res = context.compile_internal(builder, asin_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+# @lower(cmath.atan, types.Complex)
+def atan_impl(context, builder, sig, args):
+    def atan_impl(z):
+        """cmath.atan(z) = -j * cmath.atanh(z j)"""
+        r = cmath.atanh(complex(-z.imag, z.real))
+        if math.isinf(z.real) and math.isnan(z.imag):
+            # XXX this is odd but necessary
+            return complex(r.imag, r.real)
+        else:
+            return complex(r.imag, -r.real)
+
+    res = context.compile_internal(builder, atan_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)
+
+# @lower(cmath.atanh, types.Complex)
+def atanh_impl(context, builder, sig, args):
+    LN_4 = math.log(4)
+    THRES_LARGE = math.sqrt(mathimpl.FLT_MAX / 4)
+    THRES_SMALL = math.sqrt(mathimpl.FLT_MIN)
+    PI_12 = math.pi / 2
+
+    def atanh_impl(z):
+        """cmath.atanh(z)"""
+        # CPython's algorithm (see c_atanh() in cmathmodule.c)
+        if z.real < 0.:
+            # Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z).
+            negate = True
+            z = -z
+        else:
+            negate = False
+
+        ay = abs(z.imag)
+        if math.isnan(z.real) or z.real > THRES_LARGE or ay > THRES_LARGE:
+            if math.isinf(z.imag):
+                real = math.copysign(0., z.real)
+            elif math.isinf(z.real):
+                real = 0.
+            else:
+                # may be safe from overflow, depending on hypot's implementation...
+                h = math.hypot(z.real * 0.5, z.imag * 0.5)
+                real = z.real/4./h/h
+            imag = -math.copysign(PI_12, -z.imag)
+        elif z.real == 1. and ay < THRES_SMALL:
+            # C99 standard says:  atanh(1+/-0.) should be inf +/- 0j
+            if ay == 0.:
+                real = INF
+                imag = z.imag
+            else:
+                real = -math.log(math.sqrt(ay) /
+                                 math.sqrt(math.hypot(ay, 2.)))
+                imag = math.copysign(math.atan2(2., -ay) / 2, z.imag)
+        else:
+            sqay = ay * ay
+            zr1 = 1 - z.real
+            real = math.log1p(4. * z.real / (zr1 * zr1 + sqay)) * 0.25
+            imag = -math.atan2(-2. * z.imag,
+                               zr1 * (1 + z.real) - sqay) * 0.5
+
+        if math.isnan(z.imag):
+            imag = NAN
+        if negate:
+            return complex(-real, -imag)
+        else:
+            return complex(real, imag)
+
+    res = context.compile_internal(builder, atanh_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig, res)

linedance-app/venv/lib/python3.12/site-packages/numba/np/math/mathimpl.py

@@ -0,0 +1,454 @@
+"""
+Provide math calls that uses intrinsics or libc math functions.
+"""
+
+import math
+import operator
+import sys
+import numpy as np
+
+import llvmlite.ir
+from llvmlite.ir import Constant
+
+from numba.core.imputils import impl_ret_untracked
+from numba.core import types, config, cgutils
+from numba.core.extending import overload
+from numba.core.typing import signature
+from numba.cpython.unsafe.numbers import trailing_zeros
+
+
+# registry = Registry('mathimpl')
+# lower = registry.lower
+
+
+# Helpers, shared with cmathimpl.
+_NP_FLT_FINFO = np.finfo(np.dtype('float32'))
+FLT_MAX = _NP_FLT_FINFO.max
+FLT_MIN = _NP_FLT_FINFO.tiny
+
+_NP_DBL_FINFO = np.finfo(np.dtype('float64'))
+DBL_MAX = _NP_DBL_FINFO.max
+DBL_MIN = _NP_DBL_FINFO.tiny
+
+FLOAT_ABS_MASK = 0x7fffffff
+FLOAT_SIGN_MASK = 0x80000000
+DOUBLE_ABS_MASK = 0x7fffffffffffffff
+DOUBLE_SIGN_MASK = 0x8000000000000000
+
+
+def is_nan(builder, val):
+    """
+    Return a condition testing whether *val* is a NaN.
+    """
+    return builder.fcmp_unordered('uno', val, val)
+
+def is_inf(builder, val):
+    """
+    Return a condition testing whether *val* is an infinite.
+    """
+    pos_inf = Constant(val.type, float("+inf"))
+    neg_inf = Constant(val.type, float("-inf"))
+    isposinf = builder.fcmp_ordered('==', val, pos_inf)
+    isneginf = builder.fcmp_ordered('==', val, neg_inf)
+    return builder.or_(isposinf, isneginf)
+
+def is_finite(builder, val):
+    """
+    Return a condition testing whether *val* is a finite.
+    """
+    # is_finite(x)  <=>  x - x != NaN
+    val_minus_val = builder.fsub(val, val)
+    return builder.fcmp_ordered('ord', val_minus_val, val_minus_val)
+
+def f64_as_int64(builder, val):
+    """
+    Bitcast a double into a 64-bit integer.
+    """
+    assert val.type == llvmlite.ir.DoubleType()
+    return builder.bitcast(val, llvmlite.ir.IntType(64))
+
+def int64_as_f64(builder, val):
+    """
+    Bitcast a 64-bit integer into a double.
+    """
+    assert val.type == llvmlite.ir.IntType(64)
+    return builder.bitcast(val, llvmlite.ir.DoubleType())
+
+def f32_as_int32(builder, val):
+    """
+    Bitcast a float into a 32-bit integer.
+    """
+    assert val.type == llvmlite.ir.FloatType()
+    return builder.bitcast(val, llvmlite.ir.IntType(32))
+
+def int32_as_f32(builder, val):
+    """
+    Bitcast a 32-bit integer into a float.
+    """
+    assert val.type == llvmlite.ir.IntType(32)
+    return builder.bitcast(val, llvmlite.ir.FloatType())
+
+def negate_real(builder, val):
+    """
+    Negate real number *val*, with proper handling of zeros.
+    """
+    # The negative zero forces LLVM to handle signed zeros properly.
+    return builder.fsub(Constant(val.type, -0.0), val)
+
+def call_fp_intrinsic(builder, name, args):
+    """
+    Call a LLVM intrinsic floating-point operation.
+    """
+    mod = builder.module
+    intr = mod.declare_intrinsic(name, [a.type for a in args])
+    return builder.call(intr, args)
+
+
+def _unary_int_input_wrapper_impl(wrapped_impl):
+    """
+    Return an implementation factory to convert the single integral input
+    argument to a float64, then defer to the *wrapped_impl*.
+    """
+    def implementer(context, builder, sig, args):
+        val, = args
+        input_type = sig.args[0]
+        fpval = context.cast(builder, val, input_type, types.float64)
+        inner_sig = signature(types.float64, types.float64)
+        res = wrapped_impl(context, builder, inner_sig, (fpval,))
+        return context.cast(builder, res, types.float64, sig.return_type)
+
+    return implementer
+
+def unary_math_int_impl(fn, float_impl):
+    impl = _unary_int_input_wrapper_impl(float_impl)
+    # lower(fn, types.Integer)(impl)
+
+def unary_math_intr(fn, intrcode):
+    """
+    Implement the math function *fn* using the LLVM intrinsic *intrcode*.
+    """
+    # @lower(fn, types.Float)
+    def float_impl(context, builder, sig, args):
+        res = call_fp_intrinsic(builder, intrcode, args)
+        return impl_ret_untracked(context, builder, sig.return_type, res)
+
+    unary_math_int_impl(fn, float_impl)
+    return float_impl
+
+def unary_math_extern(fn, f32extern, f64extern, int_restype=False):
+    """
+    Register implementations of Python function *fn* using the
+    external function named *f32extern* and *f64extern* (for float32
+    and float64 inputs, respectively).
+    If *int_restype* is true, then the function's return value should be
+    integral, otherwise floating-point.
+    """
+    f_restype = types.int64 if int_restype else None
+
+    def float_impl(context, builder, sig, args):
+        """
+        Implement *fn* for a types.Float input.
+        """
+        [val] = args
+        mod = builder.module
+        input_type = sig.args[0]
+        lty = context.get_value_type(input_type)
+        func_name = {
+            types.float32: f32extern,
+            types.float64: f64extern,
+            }[input_type]
+        fnty = llvmlite.ir.FunctionType(lty, [lty])
+        fn = cgutils.insert_pure_function(builder.module, fnty, name=func_name)
+        res = builder.call(fn, (val,))
+        res = context.cast(builder, res, input_type, sig.return_type)
+        return impl_ret_untracked(context, builder, sig.return_type, res)
+
+    # lower(fn, types.Float)(float_impl)
+
+    # Implement wrapper for integer inputs
+    unary_math_int_impl(fn, float_impl)
+
+    return float_impl
+
+
+unary_math_intr(math.fabs, 'llvm.fabs')
+exp_impl = unary_math_intr(math.exp, 'llvm.exp')
+if sys.version_info >= (3, 11):
+    exp2_impl = unary_math_intr(math.exp2, 'llvm.exp2')
+log_impl = unary_math_intr(math.log, 'llvm.log')
+log10_impl = unary_math_intr(math.log10, 'llvm.log10')
+sin_impl = unary_math_intr(math.sin, 'llvm.sin')
+cos_impl = unary_math_intr(math.cos, 'llvm.cos')
+
+log1p_impl = unary_math_extern(math.log1p, "log1pf", "log1p")
+expm1_impl = unary_math_extern(math.expm1, "expm1f", "expm1")
+erf_impl = unary_math_extern(math.erf, "erff", "erf")
+erfc_impl = unary_math_extern(math.erfc, "erfcf", "erfc")
+
+tan_impl = unary_math_extern(math.tan, "tanf", "tan")
+asin_impl = unary_math_extern(math.asin, "asinf", "asin")
+acos_impl = unary_math_extern(math.acos, "acosf", "acos")
+atan_impl = unary_math_extern(math.atan, "atanf", "atan")
+
+asinh_impl = unary_math_extern(math.asinh, "asinhf", "asinh")
+acosh_impl = unary_math_extern(math.acosh, "acoshf", "acosh")
+atanh_impl = unary_math_extern(math.atanh, "atanhf", "atanh")
+sinh_impl = unary_math_extern(math.sinh, "sinhf", "sinh")
+cosh_impl = unary_math_extern(math.cosh, "coshf", "cosh")
+tanh_impl = unary_math_extern(math.tanh, "tanhf", "tanh")
+
+log2_impl = unary_math_extern(math.log2, "log2f", "log2")
+ceil_impl = unary_math_extern(math.ceil, "ceilf", "ceil", True)
+floor_impl = unary_math_extern(math.floor, "floorf", "floor", True)
+
+gamma_impl = unary_math_extern(math.gamma, "numba_gammaf", "numba_gamma") # work-around
+sqrt_impl = unary_math_extern(math.sqrt, "sqrtf", "sqrt")
+trunc_impl = unary_math_extern(math.trunc, "truncf", "trunc", True)
+lgamma_impl = unary_math_extern(math.lgamma, "lgammaf", "lgamma")
+
+
+# @lower(math.isnan, types.Float)
+def isnan_float_impl(context, builder, sig, args):
+    [val] = args
+    res = is_nan(builder, val)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+# @lower(math.isnan, types.Integer)
+def isnan_int_impl(context, builder, sig, args):
+    res = cgutils.false_bit
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.isinf, types.Float)
+def isinf_float_impl(context, builder, sig, args):
+    [val] = args
+    res = is_inf(builder, val)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+# @lower(math.isinf, types.Integer)
+def isinf_int_impl(context, builder, sig, args):
+    res = cgutils.false_bit
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.isfinite, types.Float)
+def isfinite_float_impl(context, builder, sig, args):
+    [val] = args
+    res = is_finite(builder, val)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.isfinite, types.Integer)
+def isfinite_int_impl(context, builder, sig, args):
+    res = cgutils.true_bit
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.copysign, types.Float, types.Float)
+def copysign_float_impl(context, builder, sig, args):
+    lty = args[0].type
+    mod = builder.module
+    fn = cgutils.get_or_insert_function(mod, llvmlite.ir.FunctionType(lty, (lty, lty)),
+                                        'llvm.copysign.%s' % lty.intrinsic_name)
+    res = builder.call(fn, args)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# -----------------------------------------------------------------------------
+
+
+# @lower(math.frexp, types.Float)
+def frexp_impl(context, builder, sig, args):
+    val, = args
+    fltty = context.get_data_type(sig.args[0])
+    intty = context.get_data_type(sig.return_type[1])
+    expptr = cgutils.alloca_once(builder, intty, name='exp')
+    fnty = llvmlite.ir.FunctionType(fltty, (fltty, llvmlite.ir.PointerType(intty)))
+    fname = {
+        "float": "numba_frexpf",
+        "double": "numba_frexp",
+        }[str(fltty)]
+    fn = cgutils.get_or_insert_function(builder.module, fnty, fname)
+    res = builder.call(fn, (val, expptr))
+    res = cgutils.make_anonymous_struct(builder, (res, builder.load(expptr)))
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.ldexp, types.Float, types.intc)
+def ldexp_impl(context, builder, sig, args):
+    val, exp = args
+    fltty, intty = map(context.get_data_type, sig.args)
+    fnty = llvmlite.ir.FunctionType(fltty, (fltty, intty))
+    fname = {
+        "float": "numba_ldexpf",
+        "double": "numba_ldexp",
+        }[str(fltty)]
+    fn = cgutils.insert_pure_function(builder.module, fnty, name=fname)
+    res = builder.call(fn, (val, exp))
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# -----------------------------------------------------------------------------
+
+
+# @lower(math.atan2, types.int64, types.int64)
+def atan2_s64_impl(context, builder, sig, args):
+    [y, x] = args
+    y = builder.sitofp(y, llvmlite.ir.DoubleType())
+    x = builder.sitofp(x, llvmlite.ir.DoubleType())
+    fsig = signature(types.float64, types.float64, types.float64)
+    return atan2_float_impl(context, builder, fsig, (y, x))
+
+# @lower(math.atan2, types.uint64, types.uint64)
+def atan2_u64_impl(context, builder, sig, args):
+    [y, x] = args
+    y = builder.uitofp(y, llvmlite.ir.DoubleType())
+    x = builder.uitofp(x, llvmlite.ir.DoubleType())
+    fsig = signature(types.float64, types.float64, types.float64)
+    return atan2_float_impl(context, builder, fsig, (y, x))
+
+# @lower(math.atan2, types.Float, types.Float)
+def atan2_float_impl(context, builder, sig, args):
+    assert len(args) == 2
+    mod = builder.module
+    ty = sig.args[0]
+    lty = context.get_value_type(ty)
+    func_name = {
+        types.float32: "atan2f",
+        types.float64: "atan2"
+        }[ty]
+    fnty = llvmlite.ir.FunctionType(lty, (lty, lty))
+    fn = cgutils.insert_pure_function(builder.module, fnty, name=func_name)
+    res = builder.call(fn, args)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# -----------------------------------------------------------------------------
+
+
+# @lower(math.hypot, types.int64, types.int64)
+def hypot_s64_impl(context, builder, sig, args):
+    [x, y] = args
+    y = builder.sitofp(y, llvmlite.ir.DoubleType())
+    x = builder.sitofp(x, llvmlite.ir.DoubleType())
+    fsig = signature(types.float64, types.float64, types.float64)
+    res = hypot_float_impl(context, builder, fsig, (x, y))
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.hypot, types.uint64, types.uint64)
+def hypot_u64_impl(context, builder, sig, args):
+    [x, y] = args
+    y = builder.sitofp(y, llvmlite.ir.DoubleType())
+    x = builder.sitofp(x, llvmlite.ir.DoubleType())
+    fsig = signature(types.float64, types.float64, types.float64)
+    res = hypot_float_impl(context, builder, fsig, (x, y))
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# @lower(math.hypot, types.Float, types.Float)
+def hypot_float_impl(context, builder, sig, args):
+    xty, yty = sig.args
+    assert xty == yty == sig.return_type
+    x, y = args
+
+    # Windows has alternate names for hypot/hypotf, see
+    # https://msdn.microsoft.com/fr-fr/library/a9yb3dbt%28v=vs.80%29.aspx
+    fname = {
+        types.float32: "_hypotf" if sys.platform == 'win32' else "hypotf",
+        types.float64: "_hypot" if sys.platform == 'win32' else "hypot",
+    }[xty]
+    plat_hypot = types.ExternalFunction(fname, sig)
+
+    if sys.platform == 'win32' and config.MACHINE_BITS == 32:
+        inf = xty(float('inf'))
+
+        def hypot_impl(x, y):
+            if math.isinf(x) or math.isinf(y):
+                return inf
+            return plat_hypot(x, y)
+    else:
+        def hypot_impl(x, y):
+            return plat_hypot(x, y)
+
+    res = context.compile_internal(builder, hypot_impl, sig, args)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# -----------------------------------------------------------------------------
+
+# @lower(math.radians, types.Float)
+def radians_float_impl(context, builder, sig, args):
+    [x] = args
+    coef = context.get_constant(sig.return_type, math.pi / 180)
+    res = builder.fmul(x, coef)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+unary_math_int_impl(math.radians, radians_float_impl)
+
+# -----------------------------------------------------------------------------
+
+# @lower(math.degrees, types.Float)
+def degrees_float_impl(context, builder, sig, args):
+    [x] = args
+    coef = context.get_constant(sig.return_type, 180 / math.pi)
+    res = builder.fmul(x, coef)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+unary_math_int_impl(math.degrees, degrees_float_impl)
+
+# -----------------------------------------------------------------------------
+
+# @lower(math.pow, types.Float, types.Float)
+# @lower(math.pow, types.Float, types.Integer)
+def pow_impl(context, builder, sig, args):
+    impl = context.get_function(operator.pow, sig)
+    return impl(builder, args)
+
+# -----------------------------------------------------------------------------
+
+
+def _unsigned(T):
+    """Convert integer to unsigned integer of equivalent width."""
+    pass
+
+@overload(_unsigned)
+def _unsigned_impl(T):
+    if T in types.unsigned_domain:
+        return lambda T: T
+    elif T in types.signed_domain:
+        newT = getattr(types, 'uint{}'.format(T.bitwidth))
+        return lambda T: newT(T)
+
+
+def gcd_impl(context, builder, sig, args):
+    xty, yty = sig.args
+    assert xty == yty == sig.return_type
+    x, y = args
+
+    def gcd(a, b):
+        """
+        Stein's algorithm, heavily cribbed from Julia implementation.
+        """
+        T = type(a)
+        if a == 0: return abs(b)
+        if b == 0: return abs(a)
+        za = trailing_zeros(a)
+        zb = trailing_zeros(b)
+        k = min(za, zb)
+        # Uses np.*_shift instead of operators due to return types
+        u = _unsigned(abs(np.right_shift(a, za)))
+        v = _unsigned(abs(np.right_shift(b, zb)))
+        while u != v:
+            if u > v:
+                u, v = v, u
+            v -= u
+            v = np.right_shift(v, trailing_zeros(v))
+        r = np.left_shift(T(u), k)
+        return r
+
+    res = context.compile_internal(builder, gcd, sig, args)
+    return impl_ret_untracked(context, builder, sig.return_type, res)
+
+
+# lower(math.gcd, types.Integer, types.Integer)(gcd_impl)