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// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/complex/__cexpf.c
// https://git.musl-libc.org/cgit/musl/tree/src/complex/__cexp.c
const std = @import("../../std.zig");
const debug = std.debug;
const math = std.math;
const testing = std.testing;
const cmath = math.complex;
const Complex = cmath.Complex;
/// Returns exp(z) scaled to avoid overflow.
pub fn ldexp_cexp(z: anytype, expt: i32) @TypeOf(z) {
const T = @TypeOf(z.re);
return switch (T) {
f32 => ldexp_cexp32(z, expt),
f64 => ldexp_cexp64(z, expt),
else => unreachable,
};
}
fn frexp_exp32(x: f32, expt: *i32) f32 {
const k = 235; // reduction constant
const kln2 = 162.88958740; // k * ln2
const exp_x = @exp(x - kln2);
const hx = @as(u32, @bitCast(exp_x));
// TODO zig should allow this cast implicitly because it should know the value is in range
expt.* = @as(i32, @intCast(hx >> 23)) - (0x7f + 127) + k;
return @as(f32, @bitCast((hx & 0x7fffff) | ((0x7f + 127) << 23)));
}
fn ldexp_cexp32(z: Complex(f32), expt: i32) Complex(f32) {
var ex_expt: i32 = undefined;
const exp_x = frexp_exp32(z.re, &ex_expt);
const exptf = expt + ex_expt;
const half_expt1 = @divTrunc(exptf, 2);
const scale1 = @as(f32, @bitCast((0x7f + half_expt1) << 23));
const half_expt2 = exptf - half_expt1;
const scale2 = @as(f32, @bitCast((0x7f + half_expt2) << 23));
return Complex(f32).init(
@cos(z.im) * exp_x * scale1 * scale2,
@sin(z.im) * exp_x * scale1 * scale2,
);
}
fn frexp_exp64(x: f64, expt: *i32) f64 {
const k = 1799; // reduction constant
const kln2 = 1246.97177782734161156; // k * ln2
const exp_x = @exp(x - kln2);
const fx = @as(u64, @bitCast(exp_x));
const hx = @as(u32, @intCast(fx >> 32));
const lx = @as(u32, @truncate(fx));
expt.* = @as(i32, @intCast(hx >> 20)) - (0x3ff + 1023) + k;
const high_word = (hx & 0xfffff) | ((0x3ff + 1023) << 20);
return @as(f64, @bitCast((@as(u64, high_word) << 32) | lx));
}
fn ldexp_cexp64(z: Complex(f64), expt: i32) Complex(f64) {
var ex_expt: i32 = undefined;
const exp_x = frexp_exp64(z.re, &ex_expt);
const exptf = @as(i64, expt + ex_expt);
const half_expt1 = @divTrunc(exptf, 2);
const scale1 = @as(f64, @bitCast((0x3ff + half_expt1) << (20 + 32)));
const half_expt2 = exptf - half_expt1;
const scale2 = @as(f64, @bitCast((0x3ff + half_expt2) << (20 + 32)));
return Complex(f64).init(
@cos(z.im) * exp_x * scale1 * scale2,
@sin(z.im) * exp_x * scale1 * scale2,
);
}
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