Jorge Aparicio
190 lines
6.0 KiB
Rust
190 lines
6.0 KiB
Rust
// origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c
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//
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// ====================================================
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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//
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// Developed at SunPro, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this
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// software is freely granted, provided that this notice
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// is preserved.
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// ====================================================
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//
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// Optimized by Bruce D. Evans. */
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use super::rem_pio2_large;
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// #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
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// #define EPS DBL_EPSILON
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const EPS: f64 = 2.2204460492503131e-16;
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// #elif FLT_EVAL_METHOD==2
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// #define EPS LDBL_EPSILON
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// #endif
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// TODO: Support FLT_EVAL_METHOD?
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const TO_INT: f64 = 1.5 / EPS;
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/// 53 bits of 2/pi
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const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
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/// first 33 bits of pi/2
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const PIO2_1: f64 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
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/// pi/2 - PIO2_1
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const PIO2_1T: f64 = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
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/// second 33 bits of pi/2
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const PIO2_2: f64 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
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/// pi/2 - (PIO2_1+PIO2_2)
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const PIO2_2T: f64 = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
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/// third 33 bits of pi/2
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const PIO2_3: f64 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
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/// pi/2 - (PIO2_1+PIO2_2+PIO2_3)
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const PIO2_3T: f64 = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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// return the remainder of x rem pi/2 in y[0]+y[1]
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// use rem_pio2_large() for large x
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//
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// caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
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#[inline]
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pub fn rem_pio2(x: f64) -> (i32, f64, f64) {
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let x1p24 = f64::from_bits(0x4170000000000000);
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let sign = (f64::to_bits(x) >> 63) as i32;
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let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
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#[inline]
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fn medium(x: f64, ix: u32) -> (i32, f64, f64) {
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/* rint(x/(pi/2)), Assume round-to-nearest. */
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let f_n = x as f64 * INV_PIO2 + TO_INT - TO_INT;
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let n = f_n as i32;
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let mut r = x - f_n * PIO2_1;
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let mut w = f_n * PIO2_1T; /* 1st round, good to 85 bits */
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let mut y0 = r - w;
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let ui = f64::to_bits(y0);
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let ey = (ui >> 52) as i32 & 0x7ff;
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let ex = (ix >> 20) as i32;
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if ex - ey > 16 {
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/* 2nd round, good to 118 bits */
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let t = r;
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w = f_n * PIO2_2;
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r = t - w;
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w = f_n * PIO2_2T - ((t - r) - w);
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y0 = r - w;
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let ey = (f64::to_bits(y0) >> 52) as i32 & 0x7ff;
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if ex - ey > 49 {
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/* 3rd round, good to 151 bits, covers all cases */
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let t = r;
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w = f_n * PIO2_3;
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r = t - w;
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w = f_n * PIO2_3T - ((t - r) - w);
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y0 = r - w;
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}
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}
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let y1 = (r - y0) - w;
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return (n, y0, y1);
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}
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if ix <= 0x400f6a7a {
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/* |x| ~<= 5pi/4 */
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if (ix & 0xfffff) == 0x921fb {
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/* |x| ~= pi/2 or 2pi/2 */
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medium(x, ix); /* cancellation -- use medium case */
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}
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if ix <= 0x4002d97c {
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/* |x| ~<= 3pi/4 */
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if sign == 0 {
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let z = x - PIO2_1; /* one round good to 85 bits */
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let y0 = z - PIO2_1T;
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let y1 = (z - y0) - PIO2_1T;
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return (1, y0, y1);
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} else {
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let z = x + PIO2_1;
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let y0 = z + PIO2_1T;
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let y1 = (z - y0) + PIO2_1T;
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return (-1, y0, y1);
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}
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} else {
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if sign == 0 {
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let z = x - 2.0 * PIO2_1;
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let y0 = z - 2.0 * PIO2_1T;
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let y1 = (z - y0) - 2.0 * PIO2_1T;
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return (2, y0, y1);
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} else {
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let z = x + 2.0 * PIO2_1;
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let y0 = z + 2.0 * PIO2_1T;
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let y1 = (z - y0) + 2.0 * PIO2_1T;
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return (-2, y0, y1);
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}
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}
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}
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if ix <= 0x401c463b {
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/* |x| ~<= 9pi/4 */
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if ix <= 0x4015fdbc {
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/* |x| ~<= 7pi/4 */
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if ix == 0x4012d97c {
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/* |x| ~= 3pi/2 */
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return medium(x, ix);
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}
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if sign == 0 {
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let z = x - 3.0 * PIO2_1;
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let y0 = z - 3.0 * PIO2_1T;
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let y1 = (z - y0) - 3.0 * PIO2_1T;
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return (3, y0, y1);
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} else {
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let z = x + 3.0 * PIO2_1;
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let y0 = z + 3.0 * PIO2_1T;
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let y1 = (z - y0) + 3.0 * PIO2_1T;
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return (-3, y0, y1);
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}
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} else {
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if ix == 0x401921fb {
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/* |x| ~= 4pi/2 */
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return medium(x, ix);
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}
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if sign == 0 {
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let z = x - 4.0 * PIO2_1;
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let y0 = z - 4.0 * PIO2_1T;
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let y1 = (z - y0) - 4.0 * PIO2_1T;
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return (4, y0, y1);
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} else {
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let z = x + 4.0 * PIO2_1;
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let y0 = z + 4.0 * PIO2_1T;
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let y1 = (z - y0) + 4.0 * PIO2_1T;
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return (-4, y0, y1);
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}
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}
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}
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if ix < 0x413921fb {
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/* |x| ~< 2^20*(pi/2), medium size */
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return medium(x, ix);
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}
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/*
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* all other (large) arguments
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*/
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if ix >= 0x7ff00000 {
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/* x is inf or NaN */
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let y0 = x - x;
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let y1 = y0;
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return (0, y0, y1);
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}
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/* set z = scalbn(|x|,-ilogb(x)+23) */
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let mut ui = f64::to_bits(x);
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ui &= (!1) >> 12;
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ui |= (0x3ff + 23) << 52;
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let mut z = f64::from_bits(ui);
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let mut tx = [0.0; 3];
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for i in 0..2 {
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tx[i] = z as i32 as f64;
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z = (z - tx[i]) * x1p24;
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}
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tx[2] = z;
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/* skip zero terms, first term is non-zero */
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let mut i = 2;
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while tx[i] == 0.0 {
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i -= 1;
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}
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let mut ty = [0.0; 3];
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let n = rem_pio2_large(&tx[..=i], &mut ty, ((ix >> 20) - (0x3ff + 23)) as i32, 1);
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if sign != 0 {
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return (-n, -ty[0], -ty[1]);
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}
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return (n, ty[0], ty[1]);
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}
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