""" 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. """ if config.USE_LEGACY_TYPE_SYSTEM: f_restype = types.int64 if int_restype else None else: f_restype = types.np_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') 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)