mirror of
https://github.com/odin-lang/Odin.git
synced 2025-12-29 17:34:34 +00:00
1028 lines
23 KiB
Odin
1028 lines
23 KiB
Odin
package math
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import "intrinsics"
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_ :: intrinsics;
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Float_Class :: enum {
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Normal, // an ordinary nonzero floating point value
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Subnormal, // a subnormal floating point value
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Zero, // zero
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Neg_Zero, // the negative zero
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NaN, // Not-A-Number (NaN)
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Inf, // positive infinity
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Neg_Inf, // negative infinity
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};
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TAU :: 6.28318530717958647692528676655900576;
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PI :: 3.14159265358979323846264338327950288;
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E :: 2.71828182845904523536;
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τ :: TAU;
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π :: PI;
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e :: E;
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SQRT_TWO :: 1.41421356237309504880168872420969808;
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SQRT_THREE :: 1.73205080756887729352744634150587236;
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SQRT_FIVE :: 2.23606797749978969640917366873127623;
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LN2 :: 0.693147180559945309417232121458176568;
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LN10 :: 2.30258509299404568401799145468436421;
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MAX_F64_PRECISION :: 16; // Maximum number of meaningful digits after the decimal point for 'f64'
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MAX_F32_PRECISION :: 8; // Maximum number of meaningful digits after the decimal point for 'f32'
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MAX_F16_PRECISION :: 4; // Maximum number of meaningful digits after the decimal point for 'f16'
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RAD_PER_DEG :: TAU/360.0;
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DEG_PER_RAD :: 360.0/TAU;
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@(default_calling_convention="none")
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foreign _ {
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@(link_name="llvm.sqrt.f16")
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sqrt_f16 :: proc(x: f16) -> f16 ---;
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@(link_name="llvm.sqrt.f32")
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sqrt_f32 :: proc(x: f32) -> f32 ---;
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@(link_name="llvm.sqrt.f64")
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sqrt_f64 :: proc(x: f64) -> f64 ---;
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@(link_name="llvm.sin.f16")
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sin_f16 :: proc(θ: f16) -> f16 ---;
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@(link_name="llvm.sin.f32")
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sin_f32 :: proc(θ: f32) -> f32 ---;
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@(link_name="llvm.sin.f64")
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sin_f64 :: proc(θ: f64) -> f64 ---;
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@(link_name="llvm.cos.f16")
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cos_f16 :: proc(θ: f16) -> f16 ---;
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@(link_name="llvm.cos.f32")
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cos_f32 :: proc(θ: f32) -> f32 ---;
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@(link_name="llvm.cos.f64")
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cos_f64 :: proc(θ: f64) -> f64 ---;
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@(link_name="llvm.pow.f16")
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pow_f16 :: proc(x, power: f16) -> f16 ---;
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@(link_name="llvm.pow.f32")
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pow_f32 :: proc(x, power: f32) -> f32 ---;
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@(link_name="llvm.pow.f64")
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pow_f64 :: proc(x, power: f64) -> f64 ---;
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@(link_name="llvm.fmuladd.f16")
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fmuladd_f16 :: proc(a, b, c: f16) -> f16 ---;
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@(link_name="llvm.fmuladd.f32")
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fmuladd_f32 :: proc(a, b, c: f32) -> f32 ---;
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@(link_name="llvm.fmuladd.f64")
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fmuladd_f64 :: proc(a, b, c: f64) -> f64 ---;
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@(link_name="llvm.log.f16")
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ln_f16 :: proc(x: f16) -> f16 ---;
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@(link_name="llvm.log.f32")
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ln_f32 :: proc(x: f32) -> f32 ---;
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@(link_name="llvm.log.f64")
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ln_f64 :: proc(x: f64) -> f64 ---;
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@(link_name="llvm.exp.f16")
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exp_f16 :: proc(x: f16) -> f16 ---;
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@(link_name="llvm.exp.f32")
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exp_f32 :: proc(x: f32) -> f32 ---;
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@(link_name="llvm.exp.f64")
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exp_f64 :: proc(x: f64) -> f64 ---;
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@(link_name="llvm.ldexp.f16")
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ldexp_f16 :: proc(val: f16, exp: i32) -> f16 ---;
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@(link_name="llvm.ldexp.f32")
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ldexp_f32 :: proc(val: f32, exp: i32) -> f32 ---;
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@(link_name="llvm.ldexp.f64")
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ldexp_f64 :: proc(val: f64, exp: i32) -> f64 ---;
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}
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sqrt :: proc{sqrt_f16, sqrt_f32, sqrt_f64};
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sin :: proc{sin_f16, sin_f32, sin_f64};
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cos :: proc{cos_f16, cos_f32, cos_f64};
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pow :: proc{pow_f16, pow_f32, pow_f64};
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fmuladd :: proc{fmuladd_f16, fmuladd_f32, fmuladd_f64};
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ln :: proc{ln_f16, ln_f32, ln_f64};
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exp :: proc{exp_f16, exp_f32, exp_f64};
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ldexp :: proc{ldexp_f16, ldexp_f32, ldexp_f64};
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log_f16 :: proc(x, base: f16) -> f16 { return ln(x) / ln(base); }
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log_f32 :: proc(x, base: f32) -> f32 { return ln(x) / ln(base); }
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log_f64 :: proc(x, base: f64) -> f64 { return ln(x) / ln(base); }
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log :: proc{log_f16, log_f32, log_f64};
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log2_f16 :: proc(x: f16) -> f16 { return ln(x)/LN2; }
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log2_f32 :: proc(x: f32) -> f32 { return ln(x)/LN2; }
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log2_f64 :: proc(x: f64) -> f64 { return ln(x)/LN2; }
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log2 :: proc{log2_f16, log2_f32, log2_f64};
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log10_f16 :: proc(x: f16) -> f16 { return ln(x)/LN10; }
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log10_f32 :: proc(x: f32) -> f32 { return ln(x)/LN10; }
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log10_f64 :: proc(x: f64) -> f64 { return ln(x)/LN10; }
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log10 :: proc{log10_f16, log10_f32, log10_f64};
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tan_f16 :: proc(θ: f16) -> f16 { return sin(θ)/cos(θ); }
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tan_f32 :: proc(θ: f32) -> f32 { return sin(θ)/cos(θ); }
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tan_f64 :: proc(θ: f64) -> f64 { return sin(θ)/cos(θ); }
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tan :: proc{tan_f16, tan_f32, tan_f64};
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lerp :: proc(a, b: $T, t: $E) -> (x: T) { return a*(1-t) + b*t; }
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saturate :: proc(a: $T) -> (x: T) { return clamp(a, 0, 1); };
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unlerp_f16 :: proc(a, b, x: f16) -> (t: f16) { return (x-a)/(b-a); }
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unlerp_f32 :: proc(a, b, x: f32) -> (t: f32) { return (x-a)/(b-a); }
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unlerp_f64 :: proc(a, b, x: f64) -> (t: f64) { return (x-a)/(b-a); }
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unlerp :: proc{unlerp_f16, unlerp_f32, unlerp_f64};
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wrap :: proc(x, y: $T) -> T where intrinsics.type_is_numeric(T), !intrinsics.type_is_array(T) {
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tmp := mod(x, y);
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return y + tmp if tmp < 0 else tmp;
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}
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angle_diff :: proc(a, b: $T) -> T where intrinsics.type_is_numeric(T), !intrinsics.type_is_array(T) {
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dist := wrap(b - a, TAU);
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return wrap(dist*2, TAU) - dist;
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}
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angle_lerp :: proc(a, b, t: $T) -> T where intrinsics.type_is_numeric(T), !intrinsics.type_is_array(T) {
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return a + angle_diff(a, b) * t;
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}
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step :: proc(edge, x: $T) -> T where intrinsics.type_is_numeric(T), !intrinsics.type_is_array(T) {
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return 0 if x < edge else 1;
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}
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smoothstep :: proc(edge0, edge1, x: $T) -> T where intrinsics.type_is_numeric(T), !intrinsics.type_is_array(T) {
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t := clamp((x - edge0) / (edge1 - edge0), 0, 1);
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return t * t * (3 - 2*t);
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}
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bias :: proc(t, b: $T) -> T where intrinsics.type_is_numeric(T) {
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return t / (((1/b) - 2) * (1 - t) + 1);
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}
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gain :: proc(t, g: $T) -> T where intrinsics.type_is_numeric(T) {
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if t < 0.5 {
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return bias(t*2, g)*0.5;
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}
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return bias(t*2 - 1, 1 - g)*0.5 + 0.5;
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}
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sign_f16 :: proc(x: f16) -> f16 { return f16(int(0 < x) - int(x < 0)); }
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sign_f32 :: proc(x: f32) -> f32 { return f32(int(0 < x) - int(x < 0)); }
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sign_f64 :: proc(x: f64) -> f64 { return f64(int(0 < x) - int(x < 0)); }
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sign :: proc{sign_f16, sign_f32, sign_f64};
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sign_bit_f16 :: proc(x: f16) -> bool {
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return (transmute(u16)x) & (1<<15) != 0;
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}
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sign_bit_f32 :: proc(x: f32) -> bool {
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return (transmute(u32)x) & (1<<31) != 0;
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}
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sign_bit_f64 :: proc(x: f64) -> bool {
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return (transmute(u64)x) & (1<<63) != 0;
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}
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sign_bit :: proc{sign_bit_f16, sign_bit_f32, sign_bit_f64};
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copy_sign_f16 :: proc(x, y: f16) -> f16 {
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ix := transmute(u16)x;
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iy := transmute(u16)y;
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ix &= 0x7fff;
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ix |= iy & 0x8000;
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return transmute(f16)ix;
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}
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copy_sign_f32 :: proc(x, y: f32) -> f32 {
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ix := transmute(u32)x;
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iy := transmute(u32)y;
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ix &= 0x7fff_ffff;
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ix |= iy & 0x8000_0000;
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return transmute(f32)ix;
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}
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copy_sign_f64 :: proc(x, y: f64) -> f64 {
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ix := transmute(u64)x;
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iy := transmute(u64)y;
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ix &= 0x7fff_ffff_ffff_ffff;
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ix |= iy & 0x8000_0000_0000_0000;
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return transmute(f64)ix;
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}
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copy_sign :: proc{copy_sign_f16, copy_sign_f32, copy_sign_f64};
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to_radians_f16 :: proc(degrees: f16) -> f16 { return degrees * RAD_PER_DEG; }
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to_radians_f32 :: proc(degrees: f32) -> f32 { return degrees * RAD_PER_DEG; }
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to_radians_f64 :: proc(degrees: f64) -> f64 { return degrees * RAD_PER_DEG; }
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to_degrees_f16 :: proc(radians: f16) -> f16 { return radians * DEG_PER_RAD; }
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to_degrees_f32 :: proc(radians: f32) -> f32 { return radians * DEG_PER_RAD; }
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to_degrees_f64 :: proc(radians: f64) -> f64 { return radians * DEG_PER_RAD; }
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to_radians :: proc{to_radians_f16, to_radians_f32, to_radians_f64};
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to_degrees :: proc{to_degrees_f16, to_degrees_f32, to_degrees_f64};
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trunc_f16 :: proc(x: f16) -> f16 {
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trunc_internal :: proc(f: f16) -> f16 {
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mask :: 0x1f;
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shift :: 16 - 6;
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bias :: 0xf;
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if f < 1 {
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switch {
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case f < 0: return -trunc_internal(-f);
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case f == 0: return f;
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case: return 0;
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}
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}
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x := transmute(u16)f;
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e := (x >> shift) & mask - bias;
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if e < shift {
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x &= ~(1 << (shift-e)) - 1;
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}
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return transmute(f16)x;
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}
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switch classify(x) {
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case .Zero, .Neg_Zero, .NaN, .Inf, .Neg_Inf:
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return x;
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case .Normal, .Subnormal: // carry on
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}
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return trunc_internal(x);
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}
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trunc_f32 :: proc(x: f32) -> f32 {
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trunc_internal :: proc(f: f32) -> f32 {
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mask :: 0xff;
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shift :: 32 - 9;
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bias :: 0x7f;
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if f < 1 {
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switch {
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case f < 0: return -trunc_internal(-f);
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case f == 0: return f;
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case: return 0;
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}
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}
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x := transmute(u32)f;
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e := (x >> shift) & mask - bias;
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if e < shift {
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x &= ~(1 << (shift-e)) - 1;
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}
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return transmute(f32)x;
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}
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switch classify(x) {
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case .Zero, .Neg_Zero, .NaN, .Inf, .Neg_Inf:
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return x;
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case .Normal, .Subnormal: // carry on
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}
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return trunc_internal(x);
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}
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trunc_f64 :: proc(x: f64) -> f64 {
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trunc_internal :: proc(f: f64) -> f64 {
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mask :: 0x7ff;
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shift :: 64 - 12;
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bias :: 0x3ff;
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if f < 1 {
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switch {
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case f < 0: return -trunc_internal(-f);
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case f == 0: return f;
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case: return 0;
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}
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}
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x := transmute(u64)f;
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e := (x >> shift) & mask - bias;
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if e < shift {
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x &= ~(1 << (shift-e)) - 1;
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}
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return transmute(f64)x;
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}
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switch classify(x) {
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case .Zero, .Neg_Zero, .NaN, .Inf, .Neg_Inf:
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return x;
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case .Normal, .Subnormal: // carry on
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}
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return trunc_internal(x);
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}
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trunc :: proc{trunc_f16, trunc_f32, trunc_f64};
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round_f16 :: proc(x: f16) -> f16 {
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return ceil(x - 0.5) if x < 0 else floor(x + 0.5);
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}
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round_f32 :: proc(x: f32) -> f32 {
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return ceil(x - 0.5) if x < 0 else floor(x + 0.5);
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}
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round_f64 :: proc(x: f64) -> f64 {
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return ceil(x - 0.5) if x < 0 else floor(x + 0.5);
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}
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round :: proc{round_f16, round_f32, round_f64};
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ceil_f16 :: proc(x: f16) -> f16 { return -floor(-x); }
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ceil_f32 :: proc(x: f32) -> f32 { return -floor(-x); }
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ceil_f64 :: proc(x: f64) -> f64 { return -floor(-x); }
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ceil :: proc{ceil_f16, ceil_f32, ceil_f64};
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floor_f16 :: proc(x: f16) -> f16 {
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if x == 0 || is_nan(x) || is_inf(x) {
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return x;
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}
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if x < 0 {
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d, fract := modf(-x);
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if fract != 0.0 {
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d = d + 1;
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}
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return -d;
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}
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d, _ := modf(x);
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return d;
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}
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floor_f32 :: proc(x: f32) -> f32 {
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if x == 0 || is_nan(x) || is_inf(x) {
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return x;
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}
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if x < 0 {
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d, fract := modf(-x);
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if fract != 0.0 {
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d = d + 1;
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}
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return -d;
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}
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d, _ := modf(x);
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return d;
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}
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floor_f64 :: proc(x: f64) -> f64 {
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if x == 0 || is_nan(x) || is_inf(x) {
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return x;
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}
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if x < 0 {
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d, fract := modf(-x);
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if fract != 0.0 {
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d = d + 1;
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}
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return -d;
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}
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d, _ := modf(x);
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return d;
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}
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floor :: proc{floor_f16, floor_f32, floor_f64};
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floor_div :: proc(x, y: $T) -> T
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where intrinsics.type_is_integer(T) {
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a := x / y;
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r := x % y;
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if (r > 0 && y < 0) || (r < 0 && y > 0) {
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a -= 1;
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}
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return a;
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}
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floor_mod :: proc(x, y: $T) -> T
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where intrinsics.type_is_integer(T) {
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r := x % y;
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if (r > 0 && y < 0) || (r < 0 && y > 0) {
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r += y;
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}
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return r;
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}
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modf_f16 :: proc(x: f16) -> (int: f16, frac: f16) {
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shift :: 16 - 5 - 1;
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mask :: 0x1f;
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bias :: 15;
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if x < 1 {
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switch {
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case x < 0:
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int, frac = modf(-x);
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return -int, -frac;
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case x == 0:
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return x, x;
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}
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return 0, x;
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}
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i := transmute(u16)x;
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e := uint(i>>shift)&mask - bias;
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if e < shift {
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i &~= 1<<(shift-e) - 1;
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}
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int = transmute(f16)i;
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frac = x - int;
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return;
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}
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modf_f32 :: proc(x: f32) -> (int: f32, frac: f32) {
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shift :: 32 - 8 - 1;
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mask :: 0xff;
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bias :: 127;
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if x < 1 {
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switch {
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case x < 0:
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int, frac = modf(-x);
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return -int, -frac;
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case x == 0:
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return x, x;
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}
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return 0, x;
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}
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i := transmute(u32)x;
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e := uint(i>>shift)&mask - bias;
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if e < shift {
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i &~= 1<<(shift-e) - 1;
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}
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int = transmute(f32)i;
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frac = x - int;
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return;
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}
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modf_f64 :: proc(x: f64) -> (int: f64, frac: f64) {
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|
shift :: 64 - 11 - 1;
|
|
mask :: 0x7ff;
|
|
bias :: 1023;
|
|
|
|
if x < 1 {
|
|
switch {
|
|
case x < 0:
|
|
int, frac = modf(-x);
|
|
return -int, -frac;
|
|
case x == 0:
|
|
return x, x;
|
|
}
|
|
return 0, x;
|
|
}
|
|
|
|
i := transmute(u64)x;
|
|
e := uint(i>>shift)&mask - bias;
|
|
|
|
if e < shift {
|
|
i &~= 1<<(shift-e) - 1;
|
|
}
|
|
int = transmute(f64)i;
|
|
frac = x - int;
|
|
return;
|
|
}
|
|
modf :: proc{modf_f16, modf_f32, modf_f64};
|
|
split_decimal :: modf;
|
|
|
|
mod_f16 :: proc(x, y: f16) -> (n: f16) {
|
|
z := abs(y);
|
|
n = remainder(abs(x), z);
|
|
if sign(n) < 0 {
|
|
n += z;
|
|
}
|
|
return copy_sign(n, x);
|
|
}
|
|
mod_f32 :: proc(x, y: f32) -> (n: f32) {
|
|
z := abs(y);
|
|
n = remainder(abs(x), z);
|
|
if sign(n) < 0 {
|
|
n += z;
|
|
}
|
|
return copy_sign(n, x);
|
|
}
|
|
mod_f64 :: proc(x, y: f64) -> (n: f64) {
|
|
z := abs(y);
|
|
n = remainder(abs(x), z);
|
|
if sign(n) < 0 {
|
|
n += z;
|
|
}
|
|
return copy_sign(n, x);
|
|
}
|
|
mod :: proc{mod_f16, mod_f32, mod_f64};
|
|
|
|
remainder_f16 :: proc(x, y: f16) -> f16 { return x - round(x/y) * y; }
|
|
remainder_f32 :: proc(x, y: f32) -> f32 { return x - round(x/y) * y; }
|
|
remainder_f64 :: proc(x, y: f64) -> f64 { return x - round(x/y) * y; }
|
|
remainder :: proc{remainder_f16, remainder_f32, remainder_f64};
|
|
|
|
|
|
|
|
gcd :: proc(x, y: $T) -> T
|
|
where intrinsics.type_is_ordered_numeric(T) {
|
|
x, y := x, y;
|
|
for y != 0 {
|
|
x %= y;
|
|
x, y = y, x;
|
|
}
|
|
return abs(x);
|
|
}
|
|
|
|
lcm :: proc(x, y: $T) -> T
|
|
where intrinsics.type_is_ordered_numeric(T) {
|
|
return x / gcd(x, y) * y;
|
|
}
|
|
|
|
frexp_f16 :: proc(x: f16) -> (significand: f16, exponent: int) {
|
|
f, e := frexp_f64(f64(x));
|
|
return f16(f), e;
|
|
}
|
|
frexp_f32 :: proc(x: f32) -> (significand: f32, exponent: int) {
|
|
f, e := frexp_f64(f64(x));
|
|
return f32(f), e;
|
|
}
|
|
frexp_f64 :: proc(x: f64) -> (significand: f64, exponent: int) {
|
|
switch {
|
|
case x == 0:
|
|
return 0, 0;
|
|
case x < 0:
|
|
significand, exponent = frexp(-x);
|
|
return -significand, exponent;
|
|
}
|
|
ex := trunc(log2(x));
|
|
exponent = int(ex);
|
|
significand = x / pow(2.0, ex);
|
|
if abs(significand) >= 1 {
|
|
exponent += 1;
|
|
significand /= 2;
|
|
}
|
|
if exponent == 1024 && significand == 0 {
|
|
significand = 0.99999999999999988898;
|
|
}
|
|
return;
|
|
}
|
|
frexp :: proc{frexp_f16, frexp_f32, frexp_f64};
|
|
|
|
|
|
|
|
|
|
binomial :: proc(n, k: int) -> int {
|
|
switch {
|
|
case k <= 0: return 1;
|
|
case 2*k > n: return binomial(n, n-k);
|
|
}
|
|
|
|
b := n;
|
|
for i in 2..<k {
|
|
b = (b * (n+1-i))/i;
|
|
}
|
|
return b;
|
|
}
|
|
|
|
factorial :: proc(n: int) -> int {
|
|
when size_of(int) == size_of(i64) {
|
|
@static table := [21]int{
|
|
1,
|
|
1,
|
|
2,
|
|
6,
|
|
24,
|
|
120,
|
|
720,
|
|
5_040,
|
|
40_320,
|
|
362_880,
|
|
3_628_800,
|
|
39_916_800,
|
|
479_001_600,
|
|
6_227_020_800,
|
|
87_178_291_200,
|
|
1_307_674_368_000,
|
|
20_922_789_888_000,
|
|
355_687_428_096_000,
|
|
6_402_373_705_728_000,
|
|
121_645_100_408_832_000,
|
|
2_432_902_008_176_640_000,
|
|
};
|
|
} else {
|
|
@static table := [13]int{
|
|
1,
|
|
1,
|
|
2,
|
|
6,
|
|
24,
|
|
120,
|
|
720,
|
|
5_040,
|
|
40_320,
|
|
362_880,
|
|
3_628_800,
|
|
39_916_800,
|
|
479_001_600,
|
|
};
|
|
}
|
|
|
|
assert(n >= 0, "parameter must not be negative");
|
|
assert(n < len(table), "parameter is too large to lookup in the table");
|
|
return table[n];
|
|
}
|
|
|
|
classify_f16 :: proc(x: f16) -> Float_Class {
|
|
switch {
|
|
case x == 0:
|
|
i := transmute(i16)x;
|
|
if i < 0 {
|
|
return .Neg_Zero;
|
|
}
|
|
return .Zero;
|
|
case x*0.5 == x:
|
|
if x < 0 {
|
|
return .Neg_Inf;
|
|
}
|
|
return .Inf;
|
|
case !(x == x):
|
|
return .NaN;
|
|
}
|
|
|
|
u := transmute(u16)x;
|
|
exp := int(u>>10) & (1<<5 - 1);
|
|
if exp == 0 {
|
|
return .Subnormal;
|
|
}
|
|
return .Normal;
|
|
}
|
|
classify_f32 :: proc(x: f32) -> Float_Class {
|
|
switch {
|
|
case x == 0:
|
|
i := transmute(i32)x;
|
|
if i < 0 {
|
|
return .Neg_Zero;
|
|
}
|
|
return .Zero;
|
|
case x*0.5 == x:
|
|
if x < 0 {
|
|
return .Neg_Inf;
|
|
}
|
|
return .Inf;
|
|
case !(x == x):
|
|
return .NaN;
|
|
}
|
|
|
|
u := transmute(u32)x;
|
|
exp := int(u>>23) & (1<<8 - 1);
|
|
if exp == 0 {
|
|
return .Subnormal;
|
|
}
|
|
return .Normal;
|
|
}
|
|
classify_f64 :: proc(x: f64) -> Float_Class {
|
|
switch {
|
|
case x == 0:
|
|
i := transmute(i64)x;
|
|
if i < 0 {
|
|
return .Neg_Zero;
|
|
}
|
|
return .Zero;
|
|
case x*0.5 == x:
|
|
if x < 0 {
|
|
return .Neg_Inf;
|
|
}
|
|
return .Inf;
|
|
case !(x == x):
|
|
return .NaN;
|
|
}
|
|
u := transmute(u64)x;
|
|
exp := int(u>>52) & (1<<11 - 1);
|
|
if exp == 0 {
|
|
return .Subnormal;
|
|
}
|
|
return .Normal;
|
|
}
|
|
classify :: proc{classify_f16, classify_f32, classify_f64};
|
|
|
|
is_nan_f16 :: proc(x: f16) -> bool { return classify(x) == .NaN; }
|
|
is_nan_f32 :: proc(x: f32) -> bool { return classify(x) == .NaN; }
|
|
is_nan_f64 :: proc(x: f64) -> bool { return classify(x) == .NaN; }
|
|
is_nan :: proc{is_nan_f16, is_nan_f32, is_nan_f64};
|
|
|
|
|
|
// is_inf reports whether f is an infinity, according to sign.
|
|
// If sign > 0, is_inf reports whether f is positive infinity.
|
|
// If sign < 0, is_inf reports whether f is negative infinity.
|
|
// If sign == 0, is_inf reports whether f is either infinity.
|
|
is_inf_f16 :: proc(x: f16, sign: int = 0) -> bool {
|
|
class := classify(abs(x));
|
|
switch {
|
|
case sign > 0:
|
|
return class == .Inf;
|
|
case sign < 0:
|
|
return class == .Neg_Inf;
|
|
}
|
|
return class == .Inf || class == .Neg_Inf;
|
|
}
|
|
is_inf_f32 :: proc(x: f32, sign: int = 0) -> bool {
|
|
class := classify(abs(x));
|
|
switch {
|
|
case sign > 0:
|
|
return class == .Inf;
|
|
case sign < 0:
|
|
return class == .Neg_Inf;
|
|
}
|
|
return class == .Inf || class == .Neg_Inf;
|
|
}
|
|
is_inf_f64 :: proc(x: f64, sign: int = 0) -> bool {
|
|
class := classify(abs(x));
|
|
switch {
|
|
case sign > 0:
|
|
return class == .Inf;
|
|
case sign < 0:
|
|
return class == .Neg_Inf;
|
|
}
|
|
return class == .Inf || class == .Neg_Inf;
|
|
}
|
|
is_inf :: proc{is_inf_f16, is_inf_f32, is_inf_f64};
|
|
|
|
|
|
inf_f16 :: proc(sign: int) -> f16 {
|
|
return f16(inf_f16(sign));
|
|
}
|
|
inf_f32 :: proc(sign: int) -> f32 {
|
|
return f32(inf_f64(sign));
|
|
}
|
|
inf_f64 :: proc(sign: int) -> f64 {
|
|
v: u64;
|
|
if sign >= 0 {
|
|
v = 0x7ff00000_00000000;
|
|
} else {
|
|
v = 0xfff00000_00000000;
|
|
}
|
|
return transmute(f64)v;
|
|
}
|
|
|
|
nan_f16 :: proc() -> f16 {
|
|
return f16(nan_f64());
|
|
}
|
|
nan_f32 :: proc() -> f32 {
|
|
return f32(nan_f64());
|
|
}
|
|
nan_f64 :: proc() -> f64 {
|
|
v: u64 = 0x7ff80000_00000001;
|
|
return transmute(f64)v;
|
|
}
|
|
|
|
|
|
|
|
is_power_of_two :: proc(x: int) -> bool {
|
|
return x > 0 && (x & (x-1)) == 0;
|
|
}
|
|
|
|
next_power_of_two :: proc(x: int) -> int {
|
|
k := x -1;
|
|
when size_of(int) == 8 {
|
|
k = k | (k >> 32);
|
|
}
|
|
k = k | (k >> 16);
|
|
k = k | (k >> 8);
|
|
k = k | (k >> 4);
|
|
k = k | (k >> 2);
|
|
k = k | (k >> 1);
|
|
k += 1 + int(x <= 0);
|
|
return k;
|
|
}
|
|
|
|
sum :: proc(x: $T/[]$E) -> (res: E)
|
|
where intrinsics.type_is_numeric(E) {
|
|
for i in x {
|
|
res += i;
|
|
}
|
|
return;
|
|
}
|
|
|
|
prod :: proc(x: $T/[]$E) -> (res: E)
|
|
where intrinsics.type_is_numeric(E) {
|
|
for i in x {
|
|
res *= i;
|
|
}
|
|
return;
|
|
}
|
|
|
|
cumsum_inplace :: proc(x: $T/[]$E) -> T
|
|
where intrinsics.type_is_numeric(E) {
|
|
for i in 1..<len(x) {
|
|
x[i] = x[i-1] + x[i];
|
|
}
|
|
}
|
|
|
|
|
|
cumsum :: proc(dst, src: $T/[]$E) -> T
|
|
where intrinsics.type_is_numeric(E) {
|
|
N := min(len(dst), len(src));
|
|
if N > 0 {
|
|
dst[0] = src[0];
|
|
for i in 1..<N {
|
|
dst[i] = dst[i-1] + src[i];
|
|
}
|
|
}
|
|
return dst[:N];
|
|
}
|
|
|
|
|
|
atan2_f16 :: proc(y, x: f16) -> f16 {
|
|
// TODO(bill): Better atan2_f16
|
|
return f16(atan2_f64(f64(y), f64(x)));
|
|
}
|
|
atan2_f32 :: proc(y, x: f32) -> f32 {
|
|
// TODO(bill): Better atan2_f32
|
|
return f32(atan2_f64(f64(y), f64(x)));
|
|
}
|
|
|
|
atan2_f64 :: proc(y, x: f64) -> f64 {
|
|
// TODO(bill): Faster atan2_f64 if possible
|
|
|
|
// The original C code:
|
|
// Stephen L. Moshier
|
|
// moshier@na-net.ornl.gov
|
|
|
|
NAN :: 0h7fff_ffff_ffff_ffff;
|
|
INF :: 0h7FF0_0000_0000_0000;
|
|
PI :: 0h4009_21fb_5444_2d18;
|
|
|
|
atan :: proc(x: f64) -> f64 {
|
|
if x == 0 {
|
|
return x;
|
|
}
|
|
if x > 0 {
|
|
return s_atan(x);
|
|
}
|
|
return -s_atan(-x);
|
|
}
|
|
// s_atan reduces its argument (known to be positive) to the range [0, 0.66] and calls x_atan.
|
|
s_atan :: proc(x: f64) -> f64 {
|
|
MORE_BITS :: 6.123233995736765886130e-17; // pi/2 = PIO2 + MORE_BITS
|
|
TAN3PI08 :: 2.41421356237309504880; // tan(3*pi/8)
|
|
if x <= 0.66 {
|
|
return x_atan(x);
|
|
}
|
|
if x > TAN3PI08 {
|
|
return PI/2 - x_atan(1/x) + MORE_BITS;
|
|
}
|
|
return PI/4 + x_atan((x-1)/(x+1)) + 0.5*MORE_BITS;
|
|
}
|
|
// x_atan evaluates a series valid in the range [0, 0.66].
|
|
x_atan :: proc(x: f64) -> f64 {
|
|
P0 :: -8.750608600031904122785e-01;
|
|
P1 :: -1.615753718733365076637e+01;
|
|
P2 :: -7.500855792314704667340e+01;
|
|
P3 :: -1.228866684490136173410e+02;
|
|
P4 :: -6.485021904942025371773e+01;
|
|
Q0 :: +2.485846490142306297962e+01;
|
|
Q1 :: +1.650270098316988542046e+02;
|
|
Q2 :: +4.328810604912902668951e+02;
|
|
Q3 :: +4.853903996359136964868e+02;
|
|
Q4 :: +1.945506571482613964425e+02;
|
|
|
|
z := x * x;
|
|
z = z * ((((P0*z+P1)*z+P2)*z+P3)*z + P4) / (((((z+Q0)*z+Q1)*z+Q2)*z+Q3)*z + Q4);
|
|
z = x*z + x;
|
|
return z;
|
|
}
|
|
|
|
switch {
|
|
case is_nan(y) || is_nan(x):
|
|
return NAN;
|
|
case y == 0:
|
|
if x >= 0 && !sign_bit(x) {
|
|
return copy_sign(0.0, y);
|
|
}
|
|
return copy_sign(PI, y);
|
|
case x == 0:
|
|
return copy_sign(PI*0.5, y);
|
|
case is_inf(x, 0):
|
|
if is_inf(x, 1) {
|
|
if is_inf(y, 0) {
|
|
return copy_sign(PI*0.25, y);
|
|
}
|
|
return copy_sign(0, y);
|
|
}
|
|
if is_inf(y, 0) {
|
|
return copy_sign(PI*0.75, y);
|
|
}
|
|
return copy_sign(PI, y);
|
|
case is_inf(y, 0):
|
|
return copy_sign(PI*0.5, y);
|
|
}
|
|
|
|
q := atan(y / x);
|
|
if x < 0 {
|
|
if q <= 0 {
|
|
return q + PI;
|
|
}
|
|
return q - PI;
|
|
}
|
|
return q;
|
|
}
|
|
|
|
|
|
atan2 :: proc{atan2_f16, atan2_f32, atan2_f64};
|
|
|
|
atan_f16 :: proc(x: f16) -> f16 {
|
|
return atan2_f16(x, 1);
|
|
}
|
|
atan_f32 :: proc(x: f32) -> f32 {
|
|
return atan2_f32(x, 1);
|
|
}
|
|
atan_f64 :: proc(x: f64) -> f64 {
|
|
return atan2_f64(x, 1);
|
|
}
|
|
atan :: proc{atan_f16, atan_f32, atan_f64};
|
|
|
|
asin_f16 :: proc(x: f16) -> f16 {
|
|
return atan2_f16(x, 1 + sqrt_f16(1 - x*x));
|
|
}
|
|
asin_f32 :: proc(x: f32) -> f32 {
|
|
return atan2_f32(x, 1 + sqrt_f32(1 - x*x));
|
|
}
|
|
asin_f64 :: proc(x: f64) -> f64 {
|
|
return atan2_f64(x, 1 + sqrt_f64(1 - x*x));
|
|
}
|
|
asin :: proc{asin_f16, asin_f32, asin_f64};
|
|
|
|
acos_f16 :: proc(x: f16) -> f16 {
|
|
return 2 * atan2_f16(sqrt_f16(1 - x), sqrt_f16(1 + x));
|
|
}
|
|
acos_f32 :: proc(x: f32) -> f32 {
|
|
return 2 * atan2_f32(sqrt_f32(1 - x), sqrt_f32(1 + x));
|
|
}
|
|
acos_f64 :: proc(x: f64) -> f64 {
|
|
return 2 * atan2_f64(sqrt_f64(1 - x), sqrt_f64(1 + x));
|
|
}
|
|
acos :: proc{acos_f16, acos_f32, acos_f64};
|
|
|
|
|
|
sinh_f16 :: proc(x: f16) -> f16 {
|
|
return (exp(x) - exp(-x))*0.5;
|
|
}
|
|
sinh_f32 :: proc(x: f32) -> f32 {
|
|
return (exp(x) - exp(-x))*0.5;
|
|
}
|
|
sinh_f64 :: proc(x: f64) -> f64 {
|
|
return (exp(x) - exp(-x))*0.5;
|
|
}
|
|
sinh :: proc{sinh_f16, sinh_f32, sinh_f64};
|
|
|
|
cosh_f16 :: proc(x: f16) -> f16 {
|
|
return (exp(x) + exp(-x))*0.5;
|
|
}
|
|
cosh_f32 :: proc(x: f32) -> f32 {
|
|
return (exp(x) + exp(-x))*0.5;
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}
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|
cosh_f64 :: proc(x: f64) -> f64 {
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|
return (exp(x) + exp(-x))*0.5;
|
|
}
|
|
cosh :: proc{cosh_f16, cosh_f32, cosh_f64};
|
|
|
|
tanh_f16 :: proc(x: f16) -> f16 {
|
|
t := exp(2*x);
|
|
return (t - 1) / (t + 1);
|
|
}
|
|
tanh_f32 :: proc(x: f32) -> f32 {
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|
t := exp(2*x);
|
|
return (t - 1) / (t + 1);
|
|
}
|
|
tanh_f64 :: proc(x: f64) -> f64 {
|
|
t := exp(2*x);
|
|
return (t - 1) / (t + 1);
|
|
}
|
|
tanh :: proc{tanh_f16, tanh_f32, tanh_f64};
|
|
|
|
|
|
F16_DIG :: 3;
|
|
F16_EPSILON :: 0.00097656;
|
|
F16_GUARD :: 0;
|
|
F16_MANT_DIG :: 11;
|
|
F16_MAX :: 65504.0;
|
|
F16_MAX_10_EXP :: 4;
|
|
F16_MAX_EXP :: 15;
|
|
F16_MIN :: 6.10351562e-5;
|
|
F16_MIN_10_EXP :: -4;
|
|
F16_MIN_EXP :: -14;
|
|
F16_NORMALIZE :: 0;
|
|
F16_RADIX :: 2;
|
|
F16_ROUNDS :: 1;
|
|
|
|
|
|
F32_DIG :: 6;
|
|
F32_EPSILON :: 1.192092896e-07;
|
|
F32_GUARD :: 0;
|
|
F32_MANT_DIG :: 24;
|
|
F32_MAX :: 3.402823466e+38;
|
|
F32_MAX_10_EXP :: 38;
|
|
F32_MAX_EXP :: 128;
|
|
F32_MIN :: 1.175494351e-38;
|
|
F32_MIN_10_EXP :: -37;
|
|
F32_MIN_EXP :: -125;
|
|
F32_NORMALIZE :: 0;
|
|
F32_RADIX :: 2;
|
|
F32_ROUNDS :: 1;
|
|
|
|
F64_DIG :: 15; // # of decimal digits of precision
|
|
F64_EPSILON :: 2.2204460492503131e-016; // smallest such that 1.0+F64_EPSILON != 1.0
|
|
F64_MANT_DIG :: 53; // # of bits in mantissa
|
|
F64_MAX :: 1.7976931348623158e+308; // max value
|
|
F64_MAX_10_EXP :: 308; // max decimal exponent
|
|
F64_MAX_EXP :: 1024; // max binary exponent
|
|
F64_MIN :: 2.2250738585072014e-308; // min positive value
|
|
F64_MIN_10_EXP :: -307; // min decimal exponent
|
|
F64_MIN_EXP :: -1021; // min binary exponent
|
|
F64_RADIX :: 2; // exponent radix
|
|
F64_ROUNDS :: 1; // addition rounding: near
|