mirror of
https://github.com/ziglang/zig.git
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4c16f9a3c3
This covers the majority of the functions as covered by the C99 specification for a math library. Code is adapted primarily from musl libc, with the pow and standard trigonometric functions adapted from the Go stdlib. Changes: - Remove assert expose in index and import as needed. - Add float log function and merge with existing base 2 integer implementation. See https://github.com/tiehuis/zig-fmath. See #374.
86 lines
2.1 KiB
Zig
86 lines
2.1 KiB
Zig
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(atanhf, x),
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f64 => @inlineCall(atanhd, 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 atanhf(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 (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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// avoid overflow
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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 atanhd(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 (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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// avoid overflow
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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 "atanh" {
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assert(atanh(f32(0.0)) == atanhf(0.0));
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assert(atanh(f64(0.0)) == atanhd(0.0));
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}
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test "atanhf" {
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const epsilon = 0.000001;
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assert(math.approxEq(f32, atanhf(0.0), 0.0, epsilon));
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assert(math.approxEq(f32, atanhf(0.2), 0.202733, epsilon));
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assert(math.approxEq(f32, atanhf(0.8923), 1.433099, epsilon));
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}
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test "atanhd" {
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const epsilon = 0.000001;
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assert(math.approxEq(f64, atanhd(0.0), 0.0, epsilon));
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assert(math.approxEq(f64, atanhd(0.2), 0.202733, epsilon));
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assert(math.approxEq(f64, atanhd(0.8923), 1.433099, epsilon));
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}
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