zig/lib/std/math/modf.zig

// SPDX-License-Identifier: MIT
// Copyright (c) 2015-2021 Zig Contributors
// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
// The MIT license requires this copyright notice to be included in all copies
// and substantial portions of the software.
// 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/math/modff.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/modf.c

const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
const maxInt = std.math.maxInt;

fn modf_result(comptime T: type) type {
    return struct {
        fpart: T,
        ipart: T,
    };
}
pub const modf32_result = modf_result(f32);
pub const modf64_result = modf_result(f64);

/// Returns the integer and fractional floating-point numbers that sum to x. The sign of each
/// result is the same as the sign of x.
///
/// Special Cases:
///  - modf(+-inf) = +-inf, nan
///  - modf(nan)   = nan, nan
pub fn modf(x: anytype) modf_result(@TypeOf(x)) {
    const T = @TypeOf(x);
    return switch (T) {
        f32 => modf32(x),
        f64 => modf64(x),
        else => @compileError("modf not implemented for " ++ @typeName(T)),
    };
}

fn modf32(x: f32) modf32_result {
    var result: modf32_result = undefined;

    const u = @bitCast(u32, x);
    const e = @intCast(i32, (u >> 23) & 0xFF) - 0x7F;
    const us = u & 0x80000000;

    // TODO: Shouldn't need this.
    if (math.isInf(x)) {
        result.ipart = x;
        result.fpart = math.nan(f32);
        return result;
    }

    // no fractional part
    if (e >= 23) {
        result.ipart = x;
        if (e == 0x80 and u << 9 != 0) { // nan
            result.fpart = x;
        } else {
            result.fpart = @bitCast(f32, us);
        }
        return result;
    }

    // no integral part
    if (e < 0) {
        result.ipart = @bitCast(f32, us);
        result.fpart = x;
        return result;
    }

    const mask = @as(u32, 0x007FFFFF) >> @intCast(u5, e);
    if (u & mask == 0) {
        result.ipart = x;
        result.fpart = @bitCast(f32, us);
        return result;
    }

    const uf = @bitCast(f32, u & ~mask);
    result.ipart = uf;
    result.fpart = x - uf;
    return result;
}

fn modf64(x: f64) modf64_result {
    var result: modf64_result = undefined;

    const u = @bitCast(u64, x);
    const e = @intCast(i32, (u >> 52) & 0x7FF) - 0x3FF;
    const us = u & (1 << 63);

    if (math.isInf(x)) {
        result.ipart = x;
        result.fpart = math.nan(f64);
        return result;
    }

    // no fractional part
    if (e >= 52) {
        result.ipart = x;
        if (e == 0x400 and u << 12 != 0) { // nan
            result.fpart = x;
        } else {
            result.fpart = @bitCast(f64, us);
        }
        return result;
    }

    // no integral part
    if (e < 0) {
        result.ipart = @bitCast(f64, us);
        result.fpart = x;
        return result;
    }

    const mask = @as(u64, maxInt(u64) >> 12) >> @intCast(u6, e);
    if (u & mask == 0) {
        result.ipart = x;
        result.fpart = @bitCast(f64, us);
        return result;
    }

    const uf = @bitCast(f64, u & ~mask);
    result.ipart = uf;
    result.fpart = x - uf;
    return result;
}

test "math.modf" {
    const a = modf(@as(f32, 1.0));
    const b = modf32(1.0);
    // NOTE: No struct comparison on generic return type function? non-named, makes sense, but still.
    expect(a.ipart == b.ipart and a.fpart == b.fpart);

    const c = modf(@as(f64, 1.0));
    const d = modf64(1.0);
    expect(a.ipart == b.ipart and a.fpart == b.fpart);
}

test "math.modf32" {
    const epsilon = 0.000001;
    var r: modf32_result = undefined;

    r = modf32(1.0);
    expect(math.approxEqAbs(f32, r.ipart, 1.0, epsilon));
    expect(math.approxEqAbs(f32, r.fpart, 0.0, epsilon));

    r = modf32(2.545);
    expect(math.approxEqAbs(f32, r.ipart, 2.0, epsilon));
    expect(math.approxEqAbs(f32, r.fpart, 0.545, epsilon));

    r = modf32(3.978123);
    expect(math.approxEqAbs(f32, r.ipart, 3.0, epsilon));
    expect(math.approxEqAbs(f32, r.fpart, 0.978123, epsilon));

    r = modf32(43874.3);
    expect(math.approxEqAbs(f32, r.ipart, 43874, epsilon));
    expect(math.approxEqAbs(f32, r.fpart, 0.300781, epsilon));

    r = modf32(1234.340780);
    expect(math.approxEqAbs(f32, r.ipart, 1234, epsilon));
    expect(math.approxEqAbs(f32, r.fpart, 0.340820, epsilon));
}

test "math.modf64" {
    const epsilon = 0.000001;
    var r: modf64_result = undefined;

    r = modf64(1.0);
    expect(math.approxEqAbs(f64, r.ipart, 1.0, epsilon));
    expect(math.approxEqAbs(f64, r.fpart, 0.0, epsilon));

    r = modf64(2.545);
    expect(math.approxEqAbs(f64, r.ipart, 2.0, epsilon));
    expect(math.approxEqAbs(f64, r.fpart, 0.545, epsilon));

    r = modf64(3.978123);
    expect(math.approxEqAbs(f64, r.ipart, 3.0, epsilon));
    expect(math.approxEqAbs(f64, r.fpart, 0.978123, epsilon));

    r = modf64(43874.3);
    expect(math.approxEqAbs(f64, r.ipart, 43874, epsilon));
    expect(math.approxEqAbs(f64, r.fpart, 0.3, epsilon));

    r = modf64(1234.340780);
    expect(math.approxEqAbs(f64, r.ipart, 1234, epsilon));
    expect(math.approxEqAbs(f64, r.fpart, 0.340780, epsilon));
}

test "math.modf32.special" {
    var r: modf32_result = undefined;

    r = modf32(math.inf(f32));
    expect(math.isPositiveInf(r.ipart) and math.isNan(r.fpart));

    r = modf32(-math.inf(f32));
    expect(math.isNegativeInf(r.ipart) and math.isNan(r.fpart));

    r = modf32(math.nan(f32));
    expect(math.isNan(r.ipart) and math.isNan(r.fpart));
}

test "math.modf64.special" {
    var r: modf64_result = undefined;

    r = modf64(math.inf(f64));
    expect(math.isPositiveInf(r.ipart) and math.isNan(r.fpart));

    r = modf64(-math.inf(f64));
    expect(math.isNegativeInf(r.ipart) and math.isNan(r.fpart));

    r = modf64(math.nan(f64));
    expect(math.isNan(r.ipart) and math.isNan(r.fpart));
}