diff options
Diffstat (limited to 'library/compiler-builtins/libm/src/math/rem_pio2.rs')
| -rw-r--r-- | library/compiler-builtins/libm/src/math/rem_pio2.rs | 223 |
1 files changed, 223 insertions, 0 deletions
diff --git a/library/compiler-builtins/libm/src/math/rem_pio2.rs b/library/compiler-builtins/libm/src/math/rem_pio2.rs new file mode 100644 index 00000000000..917e90819a5 --- /dev/null +++ b/library/compiler-builtins/libm/src/math/rem_pio2.rs @@ -0,0 +1,223 @@ +// 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); + } +} |