SINPI(3)

✨ SINPI(3) ✨

okay so this one is from the Library Functions Manual, and it's all about the half–cycle sine functions sinpi, sinpif, and sinpil 💖 buckle up bestie, it's cuter than regular sine, no cap.

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🌸 NAME 🌸

sinpi, sinpif, sinpil — half–cycle sine functions

🎀 LIBRARY 🎀

Math Library (libm, -lm) — yes you gotta link -lm, that's just the vibe.

🦋 SYNOPSIS 🦋

#include <math.h>

double
sinpi(double x);

float
sinpif(float x);

long double
sinpil(long double x);

three flavours, same energy: double, float, and the long boi long double 💅

💫 DESCRIPTION 💫

so the sinpi(), sinpif(), and sinpil() functions compute the sine of π × x. and — this is the iconic part — they measure angles in half-cycles ✨ like, the whole point is that you hand it x and it's doing the π multiply for you internally. slay.

🔥 RETURN VALUES 🔥

the sinpi(), sinpif(), and sinpil() functions returns sin(π × x) 🫶

⚠️ but listen: if |x| ≥ 2^(p - 1) where p is the floating–point precision of x, then the returned value is ±0 and it has no significance. like, none. zero meaning, literally ±0. don't come for it 😭

👑 SPECIAL VALUES 👑

the glow-up table, keep it in your notes bestie:

• sinpi(±0) — returns ±0. cute, symmetric, we love.
• sinpi(±n) — returns ±0 for positive integers n. periodt.
• sinpi(±∞) — return an NaN and raises an FE_INVALID exception 💀 infinity does not get a sine today.
• sinpi(NaN) — return an NaN and raises an FE_INVALID exception 🙈 NaN in, NaN out, exception served.

🌈 SEE ALSO 🌈

cos(3), cospi(3), fenv(3), math(3), sin(3), tan(3), tanpi(3) — go read the whole friend group iykyk 🧚

💜 AUTHORS 💜

The half–cycle trignometric functions were written by Steven G. Kargl <kargl@FreeBSD.org>. thank you king 👑🫶

⭐ STANDARDS ⭐

These functions conform to , to ISO/IEC TS 18661-4, "Information technology — Programming languages, their environments, and system software interfaces — Floating–point extensions for C" — Part 4: Supplementary functions, and to . 💅 (yes, the blanks are literally in the page, not me being mysterious ✨)

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🍓 and that's the whole page, bestie! this one's from Debian, dated November 16, 2025, and it's SINPI(3) all the way down. go forth and compute your half-cycles 💖🎀