86 lines
2.8 KiB
Zig
86 lines
2.8 KiB
Zig
// SPDX-License-Identifier: MIT
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// Copyright (c) 2015-2020 Zig Contributors
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// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
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// The MIT license requires this copyright notice to be included in all copies
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// and substantial portions of the software.
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// Ported from musl, which is licensed under the MIT license:
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// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
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//
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// https://git.musl-libc.org/cgit/musl/tree/src/complex/__cexpf.c
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// https://git.musl-libc.org/cgit/musl/tree/src/complex/__cexp.c
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const std = @import("../../std.zig");
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const debug = std.debug;
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const math = std.math;
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const cmath = math.complex;
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const Complex = cmath.Complex;
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/// Returns exp(z) scaled to avoid overflow.
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pub fn ldexp_cexp(z: anytype, expt: i32) @TypeOf(z) {
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const T = @TypeOf(z.re);
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return switch (T) {
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f32 => ldexp_cexp32(z, expt),
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f64 => ldexp_cexp64(z, expt),
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else => unreachable,
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};
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}
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fn frexp_exp32(x: f32, expt: *i32) f32 {
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const k = 235; // reduction constant
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const kln2 = 162.88958740; // k * ln2
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const exp_x = math.exp(x - kln2);
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const hx = @bitCast(u32, exp_x);
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// TODO zig should allow this cast implicitly because it should know the value is in range
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expt.* = @intCast(i32, hx >> 23) - (0x7f + 127) + k;
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return @bitCast(f32, (hx & 0x7fffff) | ((0x7f + 127) << 23));
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}
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fn ldexp_cexp32(z: Complex(f32), expt: i32) Complex(f32) {
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var ex_expt: i32 = undefined;
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const exp_x = frexp_exp32(z.re, &ex_expt);
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const exptf = expt + ex_expt;
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const half_expt1 = @divTrunc(exptf, 2);
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const scale1 = @bitCast(f32, (0x7f + half_expt1) << 23);
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const half_expt2 = exptf - half_expt1;
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const scale2 = @bitCast(f32, (0x7f + half_expt2) << 23);
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return Complex(f32).new(math.cos(z.im) * exp_x * scale1 * scale2, math.sin(z.im) * exp_x * scale1 * scale2);
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}
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fn frexp_exp64(x: f64, expt: *i32) f64 {
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const k = 1799; // reduction constant
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const kln2 = 1246.97177782734161156; // k * ln2
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const exp_x = math.exp(x - kln2);
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const fx = @bitCast(u64, x);
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const hx = @intCast(u32, fx >> 32);
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const lx = @truncate(u32, fx);
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expt.* = @intCast(i32, hx >> 20) - (0x3ff + 1023) + k;
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const high_word = (hx & 0xfffff) | ((0x3ff + 1023) << 20);
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return @bitCast(f64, (@as(u64, high_word) << 32) | lx);
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}
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fn ldexp_cexp64(z: Complex(f64), expt: i32) Complex(f64) {
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var ex_expt: i32 = undefined;
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const exp_x = frexp_exp64(z.re, &ex_expt);
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const exptf = @as(i64, expt + ex_expt);
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const half_expt1 = @divTrunc(exptf, 2);
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const scale1 = @bitCast(f64, (0x3ff + half_expt1) << 20);
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const half_expt2 = exptf - half_expt1;
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const scale2 = @bitCast(f64, (0x3ff + half_expt2) << 20);
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return Complex(f64).new(
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math.cos(z.im) * exp_x * scale1 * scale2,
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math.sin(z.im) * exp_x * scale1 * scale2,
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);
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}
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