ce02130e55
this eliminates panicking branches in the optimized version of the functions. We keep the bounds checks when running the test suite to check that we never do an out of bounds access. This commit also adds a "must link" test that ensures that future changes in our implementation won't add panicking branches. closes #129
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 i != 0 && 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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