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// origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
//
// Optimized by Bruce D. Evans. */
use super::rem_pio2_large;
// #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
// #define EPS DBL_EPSILON
const EPS: f64 = 2.2204460492503131e-16;
// #elif FLT_EVAL_METHOD==2
// #define EPS LDBL_EPSILON
// #endif
// TODO: Support FLT_EVAL_METHOD?
const TO_INT: f64 = 1.5 / EPS;
/// 53 bits of 2/pi
const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
/// first 33 bits of pi/2
const PIO2_1: f64 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
/// pi/2 - PIO2_1
const PIO2_1T: f64 = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
/// second 33 bits of pi/2
const PIO2_2: f64 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
/// pi/2 - (PIO2_1+PIO2_2)
const PIO2_2T: f64 = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
/// third 33 bits of pi/2
const PIO2_3: f64 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
/// pi/2 - (PIO2_1+PIO2_2+PIO2_3)
const PIO2_3T: f64 = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
// return the remainder of x rem pi/2 in y[0]+y[1]
// use rem_pio2_large() for large x
//
// caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub(crate) fn rem_pio2(x: f64) -> (i32, f64, f64) {
let x1p24 = f64::from_bits(0x4170000000000000);
let sign = (f64::to_bits(x) >> 63) as i32;
let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
fn medium(x: f64, ix: u32) -> (i32, f64, f64) {
/* rint(x/(pi/2)), Assume round-to-nearest. */
let tmp = x * INV_PIO2 + TO_INT;
// force rounding of tmp to it's storage format on x87 to avoid
// excess precision issues.
#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
let tmp = force_eval!(tmp);
let f_n = tmp - TO_INT;
let n = f_n as i32;
let mut r = x - f_n * PIO2_1;
let mut w = f_n * PIO2_1T; /* 1st round, good to 85 bits */
let mut y0 = r - w;
let ui = f64::to_bits(y0);
let ey = (ui >> 52) as i32 & 0x7ff;
let ex = (ix >> 20) as i32;
if ex - ey > 16 {
/* 2nd round, good to 118 bits */
let t = r;
w = f_n * PIO2_2;
r = t - w;
w = f_n * PIO2_2T - ((t - r) - w);
y0 = r - w;
let ey = (f64::to_bits(y0) >> 52) as i32 & 0x7ff;
if ex - ey > 49 {
/* 3rd round, good to 151 bits, covers all cases */
let t = r;
w = f_n * PIO2_3;
r = t - w;
w = f_n * PIO2_3T - ((t - r) - w);
y0 = r - w;
}
}
let y1 = (r - y0) - w;
(n, y0, y1)
}
if ix <= 0x400f6a7a {
/* |x| ~<= 5pi/4 */
if (ix & 0xfffff) == 0x921fb {
/* |x| ~= pi/2 or 2pi/2 */
return medium(x, ix); /* cancellation -- use medium case */
}
if ix <= 0x4002d97c {
/* |x| ~<= 3pi/4 */
if sign == 0 {
let z = x - PIO2_1; /* one round good to 85 bits */
let y0 = z - PIO2_1T;
let y1 = (z - y0) - PIO2_1T;
return (1, y0, y1);
} else {
let z = x + PIO2_1;
let y0 = z + PIO2_1T;
let y1 = (z - y0) + PIO2_1T;
return (-1, y0, y1);
}
} else if sign == 0 {
let z = x - 2.0 * PIO2_1;
let y0 = z - 2.0 * PIO2_1T;
let y1 = (z - y0) - 2.0 * PIO2_1T;
return (2, y0, y1);
} else {
let z = x + 2.0 * PIO2_1;
let y0 = z + 2.0 * PIO2_1T;
let y1 = (z - y0) + 2.0 * PIO2_1T;
return (-2, y0, y1);
}
}
if ix <= 0x401c463b {
/* |x| ~<= 9pi/4 */
if ix <= 0x4015fdbc {
/* |x| ~<= 7pi/4 */
if ix == 0x4012d97c {
/* |x| ~= 3pi/2 */
return medium(x, ix);
}
if sign == 0 {
let z = x - 3.0 * PIO2_1;
let y0 = z - 3.0 * PIO2_1T;
let y1 = (z - y0) - 3.0 * PIO2_1T;
return (3, y0, y1);
} else {
let z = x + 3.0 * PIO2_1;
let y0 = z + 3.0 * PIO2_1T;
let y1 = (z - y0) + 3.0 * PIO2_1T;
return (-3, y0, y1);
}
} else {
if ix == 0x401921fb {
/* |x| ~= 4pi/2 */
return medium(x, ix);
}
if sign == 0 {
let z = x - 4.0 * PIO2_1;
let y0 = z - 4.0 * PIO2_1T;
let y1 = (z - y0) - 4.0 * PIO2_1T;
return (4, y0, y1);
} else {
let z = x + 4.0 * PIO2_1;
let y0 = z + 4.0 * PIO2_1T;
let y1 = (z - y0) + 4.0 * PIO2_1T;
return (-4, y0, y1);
}
}
}
if ix < 0x413921fb {
/* |x| ~< 2^20*(pi/2), medium size */
return medium(x, ix);
}
/*
* all other (large) arguments
*/
if ix >= 0x7ff00000 {
/* x is inf or NaN */
let y0 = x - x;
let y1 = y0;
return (0, y0, y1);
}
/* set z = scalbn(|x|,-ilogb(x)+23) */
let mut ui = f64::to_bits(x);
ui &= (!1) >> 12;
ui |= (0x3ff + 23) << 52;
let mut z = f64::from_bits(ui);
let mut tx = [0.0; 3];
for i in 0..2 {
i!(tx,i, =, z as i32 as f64);
z = (z - i!(tx, i)) * x1p24;
}
i!(tx,2, =, z);
/* skip zero terms, first term is non-zero */
let mut i = 2;
while i != 0 && i!(tx, i) == 0.0 {
i -= 1;
}
let mut ty = [0.0; 3];
let n = rem_pio2_large(&tx[..=i], &mut ty, ((ix as i32) >> 20) - (0x3ff + 23), 1);
if sign != 0 {
return (-n, -i!(ty, 0), -i!(ty, 1));
}
(n, i!(ty, 0), i!(ty, 1))
}
#[cfg(test)]
mod tests {
use super::rem_pio2;
#[test]
// FIXME(correctness): inaccurate results on i586
#[cfg_attr(all(target_arch = "x86", not(target_feature = "sse")), ignore)]
fn test_near_pi() {
let arg = 3.141592025756836;
let arg = force_eval!(arg);
assert_eq!(
rem_pio2(arg),
(2, -6.278329573009626e-7, -2.1125998133974653e-23)
);
let arg = 3.141592033207416;
let arg = force_eval!(arg);
assert_eq!(
rem_pio2(arg),
(2, -6.20382377148128e-7, -2.1125998133974653e-23)
);
let arg = 3.141592144966125;
let arg = force_eval!(arg);
assert_eq!(
rem_pio2(arg),
(2, -5.086236681942706e-7, -2.1125998133974653e-23)
);
let arg = 3.141592979431152;
let arg = force_eval!(arg);
assert_eq!(
rem_pio2(arg),
(2, 3.2584135866119817e-7, -2.1125998133974653e-23)
);
}
#[test]
fn test_overflow_b9b847() {
let _ = rem_pio2(-3054214.5490637687);
}
#[test]
fn test_overflow_4747b9() {
let _ = rem_pio2(917340800458.2274);
}
}