114 lines
2.9 KiB
Zig
114 lines
2.9 KiB
Zig
// Special Cases:
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//
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// - atanh(+-1) = +-inf with signal
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// - atanh(x) = nan if |x| > 1 with signal
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// - atanh(nan) = nan
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const math = @import("index.zig");
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const assert = @import("../debug.zig").assert;
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pub fn atanh(x: var) -> @typeOf(x) {
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const T = @typeOf(x);
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switch (T) {
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f32 => @inlineCall(atanh_32, x),
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f64 => @inlineCall(atanh_64, x),
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else => @compileError("atanh not implemented for " ++ @typeName(T)),
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}
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}
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// atanh(x) = log((1 + x) / (1 - x)) / 2 = log1p(2x / (1 - x)) / 2 ~= x + x^3 / 3 + o(x^5)
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fn atanh_32(x: f32) -> f32 {
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const u = @bitCast(u32, x);
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const i = u & 0x7FFFFFFF;
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const s = u >> 31;
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var y = @bitCast(f32, i); // |x|
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if (y == 1.0) {
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return math.copysign(f32, math.inf(f32), x);
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}
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if (u < 0x3F800000 - (1 << 23)) {
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if (u < 0x3F800000 - (32 << 23)) {
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// underflow
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if (u < (1 << 23)) {
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math.forceEval(y * y)
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}
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}
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// |x| < 0.5
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else {
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y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
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}
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} else {
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y = 0.5 * math.log1p(2 * (y / (1 - y)));
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}
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if (s != 0) -y else y
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}
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fn atanh_64(x: f64) -> f64 {
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const u = @bitCast(u64, x);
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const e = (u >> 52) & 0x7FF;
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const s = u >> 63;
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var y = @bitCast(f64, u & (@maxValue(u64) >> 1)); // |x|
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if (y == 1.0) {
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return math.copysign(f64, math.inf(f64), x);
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}
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if (e < 0x3FF - 1) {
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if (e < 0x3FF - 32) {
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// underflow
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if (e == 0) {
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math.forceEval(f32(y));
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}
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}
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// |x| < 0.5
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else {
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y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
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}
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} else {
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y = 0.5 * math.log1p(2 * (y / (1 - y)));
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}
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if (s != 0) -y else y
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}
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test "math.atanh" {
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assert(atanh(f32(0.0)) == atanh_32(0.0));
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assert(atanh(f64(0.0)) == atanh_64(0.0));
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}
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test "math.atanh_32" {
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const epsilon = 0.000001;
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assert(math.approxEq(f32, atanh_32(0.0), 0.0, epsilon));
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assert(math.approxEq(f32, atanh_32(0.2), 0.202733, epsilon));
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assert(math.approxEq(f32, atanh_32(0.8923), 1.433099, epsilon));
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}
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test "math.atanh_64" {
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const epsilon = 0.000001;
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assert(math.approxEq(f64, atanh_64(0.0), 0.0, epsilon));
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assert(math.approxEq(f64, atanh_64(0.2), 0.202733, epsilon));
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assert(math.approxEq(f64, atanh_64(0.8923), 1.433099, epsilon));
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}
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test "math.atanh32.special" {
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assert(math.isPositiveInf(atanh_32(1)));
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assert(math.isNegativeInf(atanh_32(-1)));
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assert(math.isSignalNan(atanh_32(1.5)));
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assert(math.isSignalNan(atanh_32(-1.5)));
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assert(math.isNan(atanh_32(math.nan(f32))));
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}
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test "math.atanh64.special" {
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assert(math.isPositiveInf(atanh_64(1)));
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assert(math.isNegativeInf(atanh_64(-1)));
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assert(math.isSignalNan(atanh_64(1.5)));
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assert(math.isSignalNan(atanh_64(-1.5)));
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assert(math.isNan(atanh_64(math.nan(f64))));
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}
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